LMFDB - Embedded newform 300.10.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,10,Mod(1,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("300.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	300.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:	$154.510750849$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 60)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	300.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+81.0000 q^{3} -3836.00 q^{7} +6561.00 q^{9} +O(q^{10})$

$q+81.0000 q^{3} -3836.00 q^{7} +6561.00 q^{9} -76344.0 q^{11} +54670.0 q^{13} +101034. q^{17} +669500. q^{19} -310716. q^{21} +276504. q^{23} +531441. q^{27} +4.81535e6 q^{29} +2.34802e6 q^{31} -6.18386e6 q^{33} -8.07250e6 q^{37} +4.42827e6 q^{39} +1.49353e7 q^{41} -2.96296e7 q^{43} -1.00678e7 q^{47} -2.56387e7 q^{49} +8.18375e6 q^{51} -4.07513e7 q^{53} +5.42295e7 q^{57} +1.21174e8 q^{59} +3.38810e7 q^{61} -2.51680e7 q^{63} -2.90012e8 q^{67} +2.23968e7 q^{69} -3.33712e8 q^{71} +5.80199e7 q^{73} +2.92856e8 q^{77} -3.25929e8 q^{79} +4.30467e7 q^{81} -3.07126e8 q^{83} +3.90044e8 q^{87} -7.70780e8 q^{89} -2.09714e8 q^{91} +1.90190e8 q^{93} +8.75080e8 q^{97} -5.00893e8 q^{99} +O(q^{100})$

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
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−3836.00	−0.603862	−0.301931	−	0.953330i	$-0.597631\pi$
$7$	−3836.00	−0.603862	−0.301931	+	0.953330i	$0.597631\pi$
$8$	0	0
$9$	6561.00	0.333333
$10$	0	0
$11$	−76344.0	−1.57220	−0.786100	−	0.618099i	$-0.787903\pi$
$11$	−76344.0	−1.57220	−0.786100	+	0.618099i	$0.787903\pi$
$12$	0	0
$13$	54670.0	0.530889	0.265445	−	0.964126i	$-0.414481\pi$
$13$	54670.0	0.530889	0.265445	+	0.964126i	$0.414481\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	101034.	0.293391	0.146696	−	0.989182i	$-0.453136\pi$
$17$	101034.	0.293391	0.146696	+	0.989182i	$0.453136\pi$
$18$	0	0
$19$	669500.	1.17858	0.589290	−	0.807921i	$-0.299407\pi$
$19$	669500.	1.17858	0.589290	+	0.807921i	$0.299407\pi$
$20$	0	0
$21$	−310716.	−0.348640
$22$	0	0
$23$	276504.	0.206028	0.103014	−	0.994680i	$-0.467151\pi$
$23$	276504.	0.206028	0.103014	+	0.994680i	$0.467151\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	531441.	0.192450
$28$	0	0
$29$	4.81535e6	1.26426	0.632131	−	0.774861i	$-0.282180\pi$
$29$	4.81535e6	1.26426	0.632131	+	0.774861i	$0.282180\pi$
$30$	0	0
$31$	2.34802e6	0.456641	0.228321	−	0.973586i	$-0.426677\pi$
$31$	2.34802e6	0.456641	0.228321	+	0.973586i	$0.426677\pi$
$32$	0	0
$33$	−6.18386e6	−0.907710
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−8.07250e6	−0.708109	−0.354055	−	0.935225i	$-0.615197\pi$
$37$	−8.07250e6	−0.708109	−0.354055	+	0.935225i	$0.615197\pi$
$38$	0	0
$39$	4.42827e6	0.306509
$40$	0	0
$41$	1.49353e7	0.825442	0.412721	−	0.910858i	$-0.364579\pi$
$41$	1.49353e7	0.825442	0.412721	+	0.910858i	$0.364579\pi$
$42$	0	0
$43$	−2.96296e7	−1.32165	−0.660826	−	0.750539i	$-0.729794\pi$
$43$	−2.96296e7	−1.32165	−0.660826	+	0.750539i	$0.729794\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−1.00678e7	−0.300949	−0.150475	−	0.988614i	$-0.548080\pi$
$47$	−1.00678e7	−0.300949	−0.150475	+	0.988614i	$0.548080\pi$
$48$	0	0
$49$	−2.56387e7	−0.635351
$50$	0	0
$51$	8.18375e6	0.169390
$52$	0	0
$53$	−4.07513e7	−0.709415	−0.354707	−	0.934977i	$-0.615420\pi$
$53$	−4.07513e7	−0.709415	−0.354707	+	0.934977i	$0.615420\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	5.42295e7	0.680454
$58$	0	0
$59$	1.21174e8	1.30189	0.650945	−	0.759125i	$-0.274373\pi$
$59$	1.21174e8	1.30189	0.650945	+	0.759125i	$0.274373\pi$
$60$	0	0
$61$	3.38810e7	0.313308	0.156654	−	0.987654i	$-0.449929\pi$
$61$	3.38810e7	0.313308	0.156654	+	0.987654i	$0.449929\pi$
$62$	0	0
$63$	−2.51680e7	−0.201287
$64$	0	0
$65$	0	0
$66$	0	0
$67$	−2.90012e8	−1.75825	−0.879123	−	0.476596i	$-0.841871\pi$
$67$	−2.90012e8	−1.75825	−0.879123	+	0.476596i	$0.841871\pi$
$68$	0	0
$69$	2.23968e7	0.118950
$70$	0	0
$71$	−3.33712e8	−1.55851	−0.779254	−	0.626708i	$-0.784402\pi$
$71$	−3.33712e8	−1.55851	−0.779254	+	0.626708i	$0.784402\pi$
$72$	0	0
$73$	5.80199e7	0.239125	0.119562	−	0.992827i	$-0.461851\pi$
$73$	5.80199e7	0.239125	0.119562	+	0.992827i	$0.461851\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	2.92856e8	0.949391
$78$	0	0
$79$	−3.25929e8	−0.941459	−0.470729	−	0.882278i	$-0.656009\pi$
$79$	−3.25929e8	−0.941459	−0.470729	+	0.882278i	$0.656009\pi$
$80$	0	0
$81$	4.30467e7	0.111111
$82$	0	0
$83$	−3.07126e8	−0.710338	−0.355169	−	0.934802i	$-0.615577\pi$
$83$	−3.07126e8	−0.710338	−0.355169	+	0.934802i	$0.615577\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	3.90044e8	0.729922
$88$	0	0
$89$	−7.70780e8	−1.30219	−0.651097	−	0.758995i	$-0.725691\pi$
$89$	−7.70780e8	−1.30219	−0.651097	+	0.758995i	$0.725691\pi$
$90$	0	0
$91$	−2.09714e8	−0.320584
$92$	0	0
$93$	1.90190e8	0.263642
$94$	0	0
$95$	0	0
$96$	0	0
$97$	8.75080e8	1.00363	0.501816	−	0.864974i	$-0.332665\pi$
$97$	8.75080e8	1.00363	0.501816	+	0.864974i	$0.332665\pi$
$98$	0	0
$99$	−5.00893e8	−0.524067
$100$	0	0
$101$	−8.51086e8	−0.813818	−0.406909	−	0.913469i	$-0.633393\pi$
$101$	−8.51086e8	−0.813818	−0.406909	+	0.913469i	$0.633393\pi$
$102$	0	0
$103$	−1.64853e9	−1.44321	−0.721604	−	0.692306i	$-0.756595\pi$
$103$	−1.64853e9	−1.44321	−0.721604	+	0.692306i	$0.756595\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	−3.15004e8	−0.232322	−0.116161	−	0.993230i	$-0.537059\pi$
$107$	−3.15004e8	−0.232322	−0.116161	+	0.993230i	$0.537059\pi$
$108$	0	0
$109$	1.54717e9	1.04983	0.524914	−	0.851156i	$-0.324098\pi$
$109$	1.54717e9	1.04983	0.524914	+	0.851156i	$0.324098\pi$
$110$	0	0
$111$	−6.53872e8	−0.408827
$112$	0	0
$113$	1.44963e9	0.836383	0.418192	−	0.908359i	$-0.362664\pi$
$113$	1.44963e9	0.836383	0.418192	+	0.908359i	$0.362664\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	3.58690e8	0.176963
$118$	0	0
$119$	−3.87566e8	−0.177168
$120$	0	0
$121$	3.47046e9	1.47181
$122$	0	0
$123$	1.20976e9	0.476569
$124$	0	0
$125$	0	0
$126$	0	0
$127$	−1.06697e9	−0.363945	−0.181972	−	0.983304i	$-0.558248\pi$
$127$	−1.06697e9	−0.363945	−0.181972	+	0.983304i	$0.558248\pi$
$128$	0	0
$129$	−2.39999e9	−0.763056
$130$	0	0
$131$	1.04843e9	0.311042	0.155521	−	0.987833i	$-0.450294\pi$
$131$	1.04843e9	0.311042	0.155521	+	0.987833i	$0.450294\pi$
$132$	0	0
$133$	−2.56820e9	−0.711700
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−3.91172e9	−0.948692	−0.474346	−	0.880338i	$-0.657315\pi$
$137$	−3.91172e9	−0.948692	−0.474346	+	0.880338i	$0.657315\pi$
$138$	0	0
$139$	3.25147e9	0.738776	0.369388	−	0.929275i	$-0.379567\pi$
$139$	3.25147e9	0.738776	0.369388	+	0.929275i	$0.379567\pi$
$140$	0	0
$141$	−8.15491e8	−0.173753
$142$	0	0
$143$	−4.17373e9	−0.834664
$144$	0	0
$145$	0	0
$146$	0	0
$147$	−2.07674e9	−0.366820
$148$	0	0
$149$	−8.79647e9	−1.46208	−0.731038	−	0.682336i	$-0.760964\pi$
$149$	−8.79647e9	−1.46208	−0.731038	+	0.682336i	$0.760964\pi$
$150$	0	0
$151$	1.14598e10	1.79383	0.896916	−	0.442201i	$-0.145802\pi$
$151$	1.14598e10	1.79383	0.896916	+	0.442201i	$0.145802\pi$
$152$	0	0
$153$	6.62884e8	0.0977971
$154$	0	0
$155$	0	0
$156$	0	0
$157$	−1.14603e10	−1.50538	−0.752692	−	0.658373i	$-0.771245\pi$
$157$	−1.14603e10	−1.50538	−0.752692	+	0.658373i	$0.771245\pi$
$158$	0	0
$159$	−3.30086e9	−0.409581
$160$	0	0
$161$	−1.06067e9	−0.124412
$162$	0	0
$163$	−1.52488e10	−1.69196	−0.845981	−	0.533213i	$-0.820985\pi$
$163$	−1.52488e10	−1.69196	−0.845981	+	0.533213i	$0.820985\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	7.45661e9	0.741852	0.370926	−	0.928662i	$-0.379040\pi$
$167$	7.45661e9	0.741852	0.370926	+	0.928662i	$0.379040\pi$
$168$	0	0
$169$	−7.61569e9	−0.718157
$170$	0	0
$171$	4.39259e9	0.392860
$172$	0	0
$173$	5.53566e9	0.469853	0.234927	−	0.972013i	$-0.424515\pi$
$173$	5.53566e9	0.469853	0.234927	+	0.972013i	$0.424515\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	9.81506e9	0.751646
$178$	0	0
$179$	6.32607e8	0.0460570	0.0230285	−	0.999735i	$-0.492669\pi$
$179$	6.32607e8	0.0460570	0.0230285	+	0.999735i	$0.492669\pi$
$180$	0	0
$181$	−2.12125e9	−0.146906	−0.0734528	−	0.997299i	$-0.523402\pi$
$181$	−2.12125e9	−0.146906	−0.0734528	+	0.997299i	$0.523402\pi$
$182$	0	0
$183$	2.74436e9	0.180889
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−7.71334e9	−0.461270
$188$	0	0
$189$	−2.03861e9	−0.116213
$190$	0	0
$191$	1.94558e10	1.05779	0.528894	−	0.848688i	$-0.322607\pi$
$191$	1.94558e10	1.05779	0.528894	+	0.848688i	$0.322607\pi$
$192$	0	0
$193$	1.41920e10	0.736269	0.368134	−	0.929773i	$-0.379997\pi$
$193$	1.41920e10	0.736269	0.368134	+	0.929773i	$0.379997\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	3.22634e10	1.52620	0.763101	−	0.646280i	$-0.223676\pi$
$197$	3.22634e10	1.52620	0.763101	+	0.646280i	$0.223676\pi$
$198$	0	0
$199$	−3.17772e10	−1.43641	−0.718203	−	0.695833i	$-0.755035\pi$
$199$	−3.17772e10	−1.43641	−0.718203	+	0.695833i	$0.755035\pi$
$200$	0	0
$201$	−2.34910e10	−1.01512
$202$	0	0
$203$	−1.84717e10	−0.763440
$204$	0	0
$205$	0	0
$206$	0	0
$207$	1.81414e9	0.0686760
$208$	0	0
$209$	−5.11123e10	−1.85296
$210$	0	0
$211$	−1.50370e10	−0.522265	−0.261132	−	0.965303i	$-0.584096\pi$
$211$	−1.50370e10	−0.522265	−0.261132	+	0.965303i	$0.584096\pi$
$212$	0	0
$213$	−2.70307e10	−0.899805
$214$	0	0
$215$	0	0
$216$	0	0
$217$	−9.00702e9	−0.275748
$218$	0	0
$219$	4.69961e9	0.138059
$220$	0	0
$221$	5.52353e9	0.155758
$222$	0	0
$223$	−6.63040e10	−1.79543	−0.897713	−	0.440580i	$-0.854773\pi$
$223$	−6.63040e10	−1.79543	−0.897713	+	0.440580i	$0.854773\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	−4.01644e10	−1.00398	−0.501990	−	0.864874i	$-0.667398\pi$
$227$	−4.01644e10	−1.00398	−0.501990	+	0.864874i	$0.667398\pi$
$228$	0	0
$229$	−8.13596e10	−1.95501	−0.977505	−	0.210913i	$-0.932356\pi$
$229$	−8.13596e10	−1.95501	−0.977505	+	0.210913i	$0.932356\pi$
$230$	0	0
$231$	2.37213e10	0.548131
$232$	0	0
$233$	−8.28749e10	−1.84213	−0.921067	−	0.389404i	$-0.872681\pi$
$233$	−8.28749e10	−1.84213	−0.921067	+	0.389404i	$0.872681\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−2.64003e10	−0.543551
$238$	0	0
$239$	−4.09988e10	−0.812794	−0.406397	−	0.913697i	$-0.633215\pi$
$239$	−4.09988e10	−0.812794	−0.406397	+	0.913697i	$0.633215\pi$
$240$	0	0
$241$	2.81420e10	0.537375	0.268688	−	0.963227i	$-0.413410\pi$
$241$	2.81420e10	0.537375	0.268688	+	0.963227i	$0.413410\pi$
$242$	0	0
$243$	3.48678e9	0.0641500
$244$	0	0
$245$	0	0
$246$	0	0
$247$	3.66016e10	0.625696
$248$	0	0
$249$	−2.48772e10	−0.410114
$250$	0	0
$251$	2.81718e10	0.448005	0.224003	−	0.974589i	$-0.428088\pi$
$251$	2.81718e10	0.448005	0.224003	+	0.974589i	$0.428088\pi$
$252$	0	0
$253$	−2.11094e10	−0.323917
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−2.59587e10	−0.371179	−0.185590	−	0.982627i	$-0.559419\pi$
$257$	−2.59587e10	−0.371179	−0.185590	+	0.982627i	$0.559419\pi$
$258$	0	0
$259$	3.09661e10	0.427600
$260$	0	0
$261$	3.15935e10	0.421421
$262$	0	0
$263$	−7.71181e10	−0.993929	−0.496964	−	0.867771i	$-0.665552\pi$
$263$	−7.71181e10	−0.993929	−0.496964	+	0.867771i	$0.665552\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	−6.24332e10	−0.751822
$268$	0	0
$269$	−2.40528e9	−0.0280079	−0.0140040	−	0.999902i	$-0.504458\pi$
$269$	−2.40528e9	−0.0280079	−0.0140040	+	0.999902i	$0.504458\pi$
$270$	0	0
$271$	−4.01325e10	−0.451996	−0.225998	−	0.974128i	$-0.572564\pi$
$271$	−4.01325e10	−0.451996	−0.225998	+	0.974128i	$0.572564\pi$
$272$	0	0
$273$	−1.69868e10	−0.185089
$274$	0	0
$275$	0	0
$276$	0	0
$277$	6.57653e10	0.671178	0.335589	−	0.942008i	$-0.391065\pi$
$277$	6.57653e10	0.671178	0.335589	+	0.942008i	$0.391065\pi$
$278$	0	0
$279$	1.54054e10	0.152214
$280$	0	0
$281$	3.32780e10	0.318404	0.159202	−	0.987246i	$-0.449108\pi$
$281$	3.32780e10	0.318404	0.159202	+	0.987246i	$0.449108\pi$
$282$	0	0
$283$	−3.10703e10	−0.287943	−0.143972	−	0.989582i	$-0.545987\pi$
$283$	−3.10703e10	−0.287943	−0.143972	+	0.989582i	$0.545987\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	−5.72918e10	−0.498452
$288$	0	0
$289$	−1.08380e11	−0.913921
$290$	0	0
$291$	7.08815e10	0.579448
$292$	0	0
$293$	−1.03041e11	−0.816782	−0.408391	−	0.912807i	$-0.633910\pi$
$293$	−1.03041e11	−0.816782	−0.408391	+	0.912807i	$0.633910\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	−4.05723e10	−0.302570
$298$	0	0
$299$	1.51165e10	0.109378
$300$	0	0
$301$	1.13659e11	0.798095
$302$	0	0
$303$	−6.89380e10	−0.469858
$304$	0	0
$305$	0	0
$306$	0	0
$307$	1.86335e11	1.19721	0.598606	−	0.801043i	$-0.295721\pi$
$307$	1.86335e11	1.19721	0.598606	+	0.801043i	$0.295721\pi$
$308$	0	0
$309$	−1.33531e11	−0.833236
$310$	0	0
$311$	7.91317e10	0.479654	0.239827	−	0.970816i	$-0.422909\pi$
$311$	7.91317e10	0.479654	0.239827	+	0.970816i	$0.422909\pi$
$312$	0	0
$313$	4.93563e10	0.290665	0.145332	−	0.989383i	$-0.453575\pi$
$313$	4.93563e10	0.290665	0.145332	+	0.989383i	$0.453575\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	−2.21916e10	−0.123430	−0.0617151	−	0.998094i	$-0.519657\pi$
$317$	−2.21916e10	−0.123430	−0.0617151	+	0.998094i	$0.519657\pi$
$318$	0	0
$319$	−3.67623e11	−1.98767
$320$	0	0
$321$	−2.55154e10	−0.134131
$322$	0	0
$323$	6.76423e10	0.345786
$324$	0	0
$325$	0	0
$326$	0	0
$327$	1.25320e11	0.606118
$328$	0	0
$329$	3.86200e10	0.181732
$330$	0	0
$331$	−2.02833e11	−0.928781	−0.464390	−	0.885631i	$-0.653726\pi$
$331$	−2.02833e11	−0.928781	−0.464390	+	0.885631i	$0.653726\pi$
$332$	0	0
$333$	−5.29637e10	−0.236036
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−4.34548e11	−1.83529	−0.917643	−	0.397406i	$-0.869910\pi$
$337$	−4.34548e11	−1.83529	−0.917643	+	0.397406i	$0.869910\pi$
$338$	0	0
$339$	1.17420e11	0.482886
$340$	0	0
$341$	−1.79258e11	−0.717931
$342$	0	0
$343$	2.53147e11	0.987526
$344$	0	0
$345$	0	0
$346$	0	0
$347$	2.13138e11	0.789184	0.394592	−	0.918856i	$-0.370886\pi$
$347$	2.13138e11	0.789184	0.394592	+	0.918856i	$0.370886\pi$
$348$	0	0
$349$	1.09625e10	0.0395543	0.0197772	−	0.999804i	$-0.493704\pi$
$349$	1.09625e10	0.0395543	0.0197772	+	0.999804i	$0.493704\pi$
$350$	0	0
$351$	2.90539e10	0.102170
$352$	0	0
$353$	4.51508e11	1.54767	0.773836	−	0.633386i	$-0.218335\pi$
$353$	4.51508e11	1.54767	0.773836	+	0.633386i	$0.218335\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	−3.13929e10	−0.102288
$358$	0	0
$359$	−2.31886e10	−0.0736800	−0.0368400	−	0.999321i	$-0.511729\pi$
$359$	−2.31886e10	−0.0736800	−0.0368400	+	0.999321i	$0.511729\pi$
$360$	0	0
$361$	1.25543e11	0.389053
$362$	0	0
$363$	2.81107e11	0.849752
$364$	0	0
$365$	0	0
$366$	0	0
$367$	7.68476e10	0.221123	0.110561	−	0.993869i	$-0.464735\pi$
$367$	7.68476e10	0.221123	0.110561	+	0.993869i	$0.464735\pi$
$368$	0	0
$369$	9.79904e10	0.275147
$370$	0	0
$371$	1.56322e11	0.428388
$372$	0	0
$373$	4.01740e10	0.107462	0.0537310	−	0.998555i	$-0.482889\pi$
$373$	4.01740e10	0.107462	0.0537310	+	0.998555i	$0.482889\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	2.63255e11	0.671183
$378$	0	0
$379$	2.69313e11	0.670474	0.335237	−	0.942134i	$-0.391184\pi$
$379$	2.69313e11	0.670474	0.335237	+	0.942134i	$0.391184\pi$
$380$	0	0
$381$	−8.64246e10	−0.210124
$382$	0	0
$383$	−5.80519e11	−1.37855	−0.689275	−	0.724500i	$-0.742071\pi$
$383$	−5.80519e11	−1.37855	−0.689275	+	0.724500i	$0.742071\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−1.94400e11	−0.440551
$388$	0	0
$389$	5.69626e11	1.26129	0.630647	−	0.776069i	$-0.282789\pi$
$389$	5.69626e11	1.26129	0.630647	+	0.776069i	$0.282789\pi$
$390$	0	0
$391$	2.79363e10	0.0604468
$392$	0	0
$393$	8.49230e10	0.179580
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−7.91150e11	−1.59846	−0.799230	−	0.601026i	$-0.794759\pi$
$397$	−7.91150e11	−1.59846	−0.799230	+	0.601026i	$0.794759\pi$
$398$	0	0
$399$	−2.08024e11	−0.410900
$400$	0	0
$401$	4.09809e10	0.0791466	0.0395733	−	0.999217i	$-0.487400\pi$
$401$	4.09809e10	0.0791466	0.0395733	+	0.999217i	$0.487400\pi$
$402$	0	0
$403$	1.28366e11	0.242426
$404$	0	0
$405$	0	0
$406$	0	0
$407$	6.16287e11	1.11329
$408$	0	0
$409$	6.01968e11	1.06370	0.531849	−	0.846839i	$-0.321497\pi$
$409$	6.01968e11	1.06370	0.531849	+	0.846839i	$0.321497\pi$
$410$	0	0
$411$	−3.16849e11	−0.547728
$412$	0	0
$413$	−4.64822e11	−0.786161
$414$	0	0
$415$	0	0
$416$	0	0
$417$	2.63369e11	0.426533
$418$	0	0
$419$	4.03285e11	0.639218	0.319609	−	0.947550i	$-0.396449\pi$
$419$	4.03285e11	0.639218	0.319609	+	0.947550i	$0.396449\pi$
$420$	0	0
$421$	5.73760e11	0.890146	0.445073	−	0.895494i	$-0.353178\pi$
$421$	5.73760e11	0.890146	0.445073	+	0.895494i	$0.353178\pi$
$422$	0	0
$423$	−6.60547e10	−0.100316
$424$	0	0
$425$	0	0
$426$	0	0
$427$	−1.29967e11	−0.189195
$428$	0	0
$429$	−3.38072e11	−0.481894
$430$	0	0
$431$	−7.34689e11	−1.02555	−0.512774	−	0.858524i	$-0.671382\pi$
$431$	−7.34689e11	−1.02555	−0.512774	+	0.858524i	$0.671382\pi$
$432$	0	0
$433$	−1.08337e12	−1.48109	−0.740547	−	0.672005i	$-0.765433\pi$
$433$	−1.08337e12	−1.48109	−0.740547	+	0.672005i	$0.765433\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	1.85119e11	0.242821
$438$	0	0
$439$	1.33041e12	1.70961	0.854804	−	0.518951i	$-0.173677\pi$
$439$	1.33041e12	1.70961	0.854804	+	0.518951i	$0.173677\pi$
$440$	0	0
$441$	−1.68216e11	−0.211784
$442$	0	0
$443$	1.19977e12	1.48007	0.740035	−	0.672568i	$-0.234809\pi$
$443$	1.19977e12	1.48007	0.740035	+	0.672568i	$0.234809\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	−7.12514e11	−0.844130
$448$	0	0
$449$	3.42831e11	0.398081	0.199041	−	0.979991i	$-0.436217\pi$
$449$	3.42831e11	0.398081	0.199041	+	0.979991i	$0.436217\pi$
$450$	0	0
$451$	−1.14022e12	−1.29776
$452$	0	0
$453$	9.28246e11	1.03567
$454$	0	0
$455$	0	0
$456$	0	0
$457$	7.86728e11	0.843727	0.421863	−	0.906659i	$-0.361376\pi$
$457$	7.86728e11	0.843727	0.421863	+	0.906659i	$0.361376\pi$
$458$	0	0
$459$	5.36936e10	0.0564632
$460$	0	0
$461$	6.13770e11	0.632924	0.316462	−	0.948605i	$-0.397505\pi$
$461$	6.13770e11	0.632924	0.316462	+	0.948605i	$0.397505\pi$
$462$	0	0
$463$	7.78503e11	0.787310	0.393655	−	0.919258i	$-0.371210\pi$
$463$	7.78503e11	0.787310	0.393655	+	0.919258i	$0.371210\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	1.01905e12	0.991445	0.495722	−	0.868481i	$-0.334903\pi$
$467$	1.01905e12	0.991445	0.495722	+	0.868481i	$0.334903\pi$
$468$	0	0
$469$	1.11249e12	1.06174
$470$	0	0
$471$	−9.28283e11	−0.869133
$472$	0	0
$473$	2.26204e12	2.07790
$474$	0	0
$475$	0	0
$476$	0	0
$477$	−2.67369e11	−0.236472
$478$	0	0
$479$	1.76394e12	1.53099	0.765496	−	0.643440i	$-0.222494\pi$
$479$	1.76394e12	1.53099	0.765496	+	0.643440i	$0.222494\pi$
$480$	0	0
$481$	−4.41323e11	−0.375928
$482$	0	0
$483$	−8.59142e10	−0.0718295
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−9.02219e11	−0.726828	−0.363414	−	0.931628i	$-0.618389\pi$
$487$	−9.02219e11	−0.726828	−0.363414	+	0.931628i	$0.618389\pi$
$488$	0	0
$489$	−1.23515e12	−0.976855
$490$	0	0
$491$	−9.41120e11	−0.730766	−0.365383	−	0.930857i	$-0.619062\pi$
$491$	−9.41120e11	−0.730766	−0.365383	+	0.930857i	$0.619062\pi$
$492$	0	0
$493$	4.86514e11	0.370924
$494$	0	0
$495$	0	0
$496$	0	0
$497$	1.28012e12	0.941123
$498$	0	0
$499$	−1.14802e12	−0.828892	−0.414446	−	0.910074i	$-0.636025\pi$
$499$	−1.14802e12	−0.828892	−0.414446	+	0.910074i	$0.636025\pi$
$500$	0	0
$501$	6.03986e11	0.428309
$502$	0	0
$503$	−1.46210e12	−1.01841	−0.509205	−	0.860645i	$-0.670060\pi$
$503$	−1.46210e12	−1.01841	−0.509205	+	0.860645i	$0.670060\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−6.16871e11	−0.414628
$508$	0	0
$509$	7.94065e11	0.524356	0.262178	−	0.965020i	$-0.415559\pi$
$509$	7.94065e11	0.524356	0.262178	+	0.965020i	$0.415559\pi$
$510$	0	0
$511$	−2.22564e11	−0.144398
$512$	0	0
$513$	3.55800e11	0.226818
$514$	0	0
$515$	0	0
$516$	0	0
$517$	7.68615e11	0.473153
$518$	0	0
$519$	4.48389e11	0.271270
$520$	0	0
$521$	−2.12155e12	−1.26149	−0.630746	−	0.775989i	$-0.717251\pi$
$521$	−2.12155e12	−1.26149	−0.630746	+	0.775989i	$0.717251\pi$
$522$	0	0
$523$	3.33938e12	1.95168	0.975839	−	0.218493i	$-0.0701140\pi$
$523$	3.33938e12	1.95168	0.975839	+	0.218493i	$0.0701140\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	2.37230e11	0.133975
$528$	0	0
$529$	−1.72470e12	−0.957552
$530$	0	0
$531$	7.95020e11	0.433963
$532$	0	0
$533$	8.16512e11	0.438218
$534$	0	0
$535$	0	0
$536$	0	0
$537$	5.12412e10	0.0265910
$538$	0	0
$539$	1.95736e12	0.998899
$540$	0	0
$541$	8.57796e11	0.430523	0.215261	−	0.976556i	$-0.430940\pi$
$541$	8.57796e11	0.430523	0.215261	+	0.976556i	$0.430940\pi$
$542$	0	0
$543$	−1.71821e11	−0.0848160
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−2.74542e12	−1.31119	−0.655595	−	0.755113i	$-0.727582\pi$
$547$	−2.74542e12	−1.31119	−0.655595	+	0.755113i	$0.727582\pi$
$548$	0	0
$549$	2.22293e11	0.104436
$550$	0	0
$551$	3.22388e12	1.49004
$552$	0	0
$553$	1.25026e12	0.568511
$554$	0	0
$555$	0	0
$556$	0	0
$557$	4.09158e12	1.80112	0.900560	−	0.434731i	$-0.143157\pi$
$557$	4.09158e12	1.80112	0.900560	+	0.434731i	$0.143157\pi$
$558$	0	0
$559$	−1.61985e12	−0.701651
$560$	0	0
$561$	−6.24781e11	−0.266314
$562$	0	0
$563$	−4.55516e12	−1.91080	−0.955401	−	0.295312i	$-0.904576\pi$
$563$	−4.55516e12	−1.91080	−0.955401	+	0.295312i	$0.904576\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	−1.65127e11	−0.0670957
$568$	0	0
$569$	3.49454e12	1.39761	0.698804	−	0.715313i	$-0.253716\pi$
$569$	3.49454e12	1.39761	0.698804	+	0.715313i	$0.253716\pi$
$570$	0	0
$571$	7.38657e11	0.290791	0.145395	−	0.989374i	$-0.453555\pi$
$571$	7.38657e11	0.290791	0.145395	+	0.989374i	$0.453555\pi$
$572$	0	0
$573$	1.57592e12	0.610714
$574$	0	0
$575$	0	0
$576$	0	0
$577$	−1.72036e12	−0.646141	−0.323070	−	0.946375i	$-0.604715\pi$
$577$	−1.72036e12	−0.646141	−0.323070	+	0.946375i	$0.604715\pi$
$578$	0	0
$579$	1.14955e12	0.425085
$580$	0	0
$581$	1.17813e12	0.428946
$582$	0	0
$583$	3.11112e12	1.11534
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−4.51413e12	−1.56929	−0.784643	−	0.619948i	$-0.787154\pi$
$587$	−4.51413e12	−1.56929	−0.784643	+	0.619948i	$0.787154\pi$
$588$	0	0
$589$	1.57200e12	0.538188
$590$	0	0
$591$	2.61333e12	0.881153
$592$	0	0
$593$	−1.98140e12	−0.658000	−0.329000	−	0.944330i	$-0.606712\pi$
$593$	−1.98140e12	−0.658000	−0.329000	+	0.944330i	$0.606712\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−2.57396e12	−0.829310
$598$	0	0
$599$	5.44033e12	1.72665	0.863326	−	0.504646i	$-0.168377\pi$
$599$	5.44033e12	1.72665	0.863326	+	0.504646i	$0.168377\pi$
$600$	0	0
$601$	−3.20789e12	−1.00296	−0.501482	−	0.865168i	$-0.667212\pi$
$601$	−3.20789e12	−1.00296	−0.501482	+	0.865168i	$0.667212\pi$
$602$	0	0
$603$	−1.90277e12	−0.586082
$604$	0	0
$605$	0	0
$606$	0	0
$607$	1.15060e12	0.344014	0.172007	−	0.985096i	$-0.444975\pi$
$607$	1.15060e12	0.344014	0.172007	+	0.985096i	$0.444975\pi$
$608$	0	0
$609$	−1.49621e12	−0.440772
$610$	0	0
$611$	−5.50406e11	−0.159771
$612$	0	0
$613$	−4.20438e12	−1.20262	−0.601312	−	0.799014i	$-0.705355\pi$
$613$	−4.20438e12	−1.20262	−0.601312	+	0.799014i	$0.705355\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	6.42782e12	1.78558	0.892792	−	0.450470i	$-0.148743\pi$
$617$	6.42782e12	1.78558	0.892792	+	0.450470i	$0.148743\pi$
$618$	0	0
$619$	−5.05810e12	−1.38477	−0.692387	−	0.721526i	$-0.743441\pi$
$619$	−5.05810e12	−1.38477	−0.692387	+	0.721526i	$0.743441\pi$
$620$	0	0
$621$	1.46946e11	0.0396501
$622$	0	0
$623$	2.95671e12	0.786344
$624$	0	0
$625$	0	0
$626$	0	0
$627$	−4.14010e12	−1.06981
$628$	0	0
$629$	−8.15597e11	−0.207753
$630$	0	0
$631$	−3.32669e12	−0.835374	−0.417687	−	0.908591i	$-0.637159\pi$
$631$	−3.32669e12	−0.835374	−0.417687	+	0.908591i	$0.637159\pi$
$632$	0	0
$633$	−1.21800e12	−0.301530
$634$	0	0
$635$	0	0
$636$	0	0
$637$	−1.40167e12	−0.337301
$638$	0	0
$639$	−2.18948e12	−0.519503
$640$	0	0
$641$	6.36214e12	1.48848	0.744238	−	0.667914i	$-0.232813\pi$
$641$	6.36214e12	1.48848	0.744238	+	0.667914i	$0.232813\pi$
$642$	0	0
$643$	−2.45562e12	−0.566515	−0.283257	−	0.959044i	$-0.591415\pi$
$643$	−2.45562e12	−0.566515	−0.283257	+	0.959044i	$0.591415\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	2.20480e12	0.494652	0.247326	−	0.968932i	$-0.420448\pi$
$647$	2.20480e12	0.494652	0.247326	+	0.968932i	$0.420448\pi$
$648$	0	0
$649$	−9.25088e12	−2.04683
$650$	0	0
$651$	−7.29569e11	−0.159203
$652$	0	0
$653$	−6.73520e12	−1.44958	−0.724788	−	0.688972i	$-0.758062\pi$
$653$	−6.73520e12	−1.44958	−0.724788	+	0.688972i	$0.758062\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	3.80669e11	0.0797082
$658$	0	0
$659$	−5.36916e12	−1.10898	−0.554488	−	0.832192i	$-0.687086\pi$
$659$	−5.36916e12	−1.10898	−0.554488	+	0.832192i	$0.687086\pi$
$660$	0	0
$661$	6.87767e12	1.40131	0.700656	−	0.713500i	$-0.252891\pi$
$661$	6.87767e12	1.40131	0.700656	+	0.713500i	$0.252891\pi$
$662$	0	0
$663$	4.47406e11	0.0899271
$664$	0	0
$665$	0	0
$666$	0	0
$667$	1.33146e12	0.260473
$668$	0	0
$669$	−5.37062e12	−1.03659
$670$	0	0
$671$	−2.58661e12	−0.492583
$672$	0	0
$673$	2.99021e12	0.561867	0.280933	−	0.959727i	$-0.409356\pi$
$673$	2.99021e12	0.561867	0.280933	+	0.959727i	$0.409356\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	4.34213e12	0.794427	0.397213	−	0.917726i	$-0.369977\pi$
$677$	4.34213e12	0.794427	0.397213	+	0.917726i	$0.369977\pi$
$678$	0	0
$679$	−3.35681e12	−0.606055
$680$	0	0
$681$	−3.25332e12	−0.579648
$682$	0	0
$683$	−8.54214e12	−1.50201	−0.751006	−	0.660295i	$-0.770431\pi$
$683$	−8.54214e12	−1.50201	−0.751006	+	0.660295i	$0.770431\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	−6.59012e12	−1.12873
$688$	0	0
$689$	−2.22787e12	−0.376621
$690$	0	0
$691$	−6.00326e12	−1.00170	−0.500848	−	0.865535i	$-0.666978\pi$
$691$	−6.00326e12	−1.00170	−0.500848	+	0.865535i	$0.666978\pi$
$692$	0	0
$693$	1.92143e12	0.316464
$694$	0	0
$695$	0	0
$696$	0	0
$697$	1.50897e12	0.242177
$698$	0	0
$699$	−6.71287e12	−1.06356
$700$	0	0
$701$	−2.58040e12	−0.403605	−0.201802	−	0.979426i	$-0.564680\pi$
$701$	−2.58040e12	−0.403605	−0.201802	+	0.979426i	$0.564680\pi$
$702$	0	0
$703$	−5.40454e12	−0.834564
$704$	0	0
$705$	0	0
$706$	0	0
$707$	3.26477e12	0.491433
$708$	0	0
$709$	4.68641e12	0.696517	0.348259	−	0.937398i	$-0.386773\pi$
$709$	4.68641e12	0.696517	0.348259	+	0.937398i	$0.386773\pi$
$710$	0	0
$711$	−2.13842e12	−0.313820
$712$	0	0
$713$	6.49238e11	0.0940808
$714$	0	0
$715$	0	0
$716$	0	0
$717$	−3.32090e12	−0.469267
$718$	0	0
$719$	4.22715e12	0.589885	0.294943	−	0.955515i	$-0.404699\pi$
$719$	4.22715e12	0.589885	0.294943	+	0.955515i	$0.404699\pi$
$720$	0	0
$721$	6.32375e12	0.871498
$722$	0	0
$723$	2.27950e12	0.310254
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−6.35794e12	−0.844135	−0.422067	−	0.906564i	$-0.638695\pi$
$727$	−6.35794e12	−0.844135	−0.422067	+	0.906564i	$0.638695\pi$
$728$	0	0
$729$	2.82430e11	0.0370370
$730$	0	0
$731$	−2.99359e12	−0.387761
$732$	0	0
$733$	−6.86030e12	−0.877759	−0.438880	−	0.898546i	$-0.644625\pi$
$733$	−6.86030e12	−0.877759	−0.438880	+	0.898546i	$0.644625\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	2.21407e13	2.76431
$738$	0	0
$739$	−7.20072e12	−0.888129	−0.444064	−	0.895995i	$-0.646464\pi$
$739$	−7.20072e12	−0.888129	−0.444064	+	0.895995i	$0.646464\pi$
$740$	0	0
$741$	2.96473e12	0.361246
$742$	0	0
$743$	−2.71266e12	−0.326546	−0.163273	−	0.986581i	$-0.552205\pi$
$743$	−2.71266e12	−0.326546	−0.163273	+	0.986581i	$0.552205\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	−2.01505e12	−0.236779
$748$	0	0
$749$	1.20836e12	0.140290
$750$	0	0
$751$	−1.04772e13	−1.20189	−0.600944	−	0.799291i	$-0.705209\pi$
$751$	−1.04772e13	−1.20189	−0.600944	+	0.799291i	$0.705209\pi$
$752$	0	0
$753$	2.28192e12	0.258656
$754$	0	0
$755$	0	0
$756$	0	0
$757$	−9.53807e12	−1.05567	−0.527836	−	0.849346i	$-0.676996\pi$
$757$	−9.53807e12	−1.05567	−0.527836	+	0.849346i	$0.676996\pi$
$758$	0	0
$759$	−1.70986e12	−0.187014
$760$	0	0
$761$	1.63317e13	1.76523	0.882614	−	0.470098i	$-0.155782\pi$
$761$	1.63317e13	1.76523	0.882614	+	0.470098i	$0.155782\pi$
$762$	0	0
$763$	−5.93493e12	−0.633950
$764$	0	0
$765$	0	0
$766$	0	0
$767$	6.62456e12	0.691159
$768$	0	0
$769$	−1.06116e13	−1.09424	−0.547120	−	0.837054i	$-0.684276\pi$
$769$	−1.06116e13	−1.09424	−0.547120	+	0.837054i	$0.684276\pi$
$770$	0	0
$771$	−2.10265e12	−0.214300
$772$	0	0
$773$	−1.21558e13	−1.22455	−0.612274	−	0.790646i	$-0.709745\pi$
$773$	−1.21558e13	−1.22455	−0.612274	+	0.790646i	$0.709745\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	2.50825e12	0.246875
$778$	0	0
$779$	9.99918e12	0.972850
$780$	0	0
$781$	2.54769e13	2.45029
$782$	0	0
$783$	2.55908e12	0.243307
$784$	0	0
$785$	0	0
$786$	0	0
$787$	−1.93979e13	−1.80247	−0.901234	−	0.433332i	$-0.857338\pi$
$787$	−1.93979e13	−1.80247	−0.901234	+	0.433332i	$0.857338\pi$
$788$	0	0
$789$	−6.24656e12	−0.573845
$790$	0	0
$791$	−5.56080e12	−0.505060
$792$	0	0
$793$	1.85227e12	0.166332
$794$	0	0
$795$	0	0
$796$	0	0
$797$	−6.31604e12	−0.554475	−0.277238	−	0.960801i	$-0.589419\pi$
$797$	−6.31604e12	−0.554475	−0.277238	+	0.960801i	$0.589419\pi$
$798$	0	0
$799$	−1.01719e12	−0.0882960
$800$	0	0
$801$	−5.05709e12	−0.434064
$802$	0	0
$803$	−4.42947e12	−0.375952
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−1.94828e11	−0.0161704
$808$	0	0
$809$	−1.40057e13	−1.14957	−0.574786	−	0.818304i	$-0.694915\pi$
$809$	−1.40057e13	−1.14957	−0.574786	+	0.818304i	$0.694915\pi$
$810$	0	0
$811$	2.01224e12	0.163338	0.0816689	−	0.996660i	$-0.473975\pi$
$811$	2.01224e12	0.163338	0.0816689	+	0.996660i	$0.473975\pi$
$812$	0	0
$813$	−3.25073e12	−0.260960
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−1.98370e13	−1.55767
$818$	0	0
$819$	−1.37593e12	−0.106861
$820$	0	0
$821$	1.73316e13	1.33136	0.665680	−	0.746237i	$-0.268142\pi$
$821$	1.73316e13	1.33136	0.665680	+	0.746237i	$0.268142\pi$
$822$	0	0
$823$	−2.71327e12	−0.206155	−0.103078	−	0.994673i	$-0.532869\pi$
$823$	−2.71327e12	−0.206155	−0.103078	+	0.994673i	$0.532869\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	1.15092e13	0.855599	0.427799	−	0.903874i	$-0.359289\pi$
$827$	1.15092e13	0.855599	0.427799	+	0.903874i	$0.359289\pi$
$828$	0	0
$829$	3.58109e12	0.263342	0.131671	−	0.991293i	$-0.457966\pi$
$829$	3.58109e12	0.263342	0.131671	+	0.991293i	$0.457966\pi$
$830$	0	0
$831$	5.32699e12	0.387505
$832$	0	0
$833$	−2.59038e12	−0.186407
$834$	0	0
$835$	0	0
$836$	0	0
$837$	1.24784e12	0.0878806
$838$	0	0
$839$	1.71547e13	1.19524	0.597621	−	0.801779i	$-0.296113\pi$
$839$	1.71547e13	1.19524	0.597621	+	0.801779i	$0.296113\pi$
$840$	0	0
$841$	8.68049e12	0.598359
$842$	0	0
$843$	2.69552e12	0.183831
$844$	0	0
$845$	0	0
$846$	0	0
$847$	−1.33127e13	−0.888772
$848$	0	0
$849$	−2.51670e12	−0.166244
$850$	0	0
$851$	−2.23208e12	−0.145890
$852$	0	0
$853$	1.09299e13	0.706881	0.353441	−	0.935457i	$-0.385012\pi$
$853$	1.09299e13	0.706881	0.353441	+	0.935457i	$0.385012\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	1.16980e13	0.740794	0.370397	−	0.928874i	$-0.379222\pi$
$857$	1.16980e13	0.740794	0.370397	+	0.928874i	$0.379222\pi$
$858$	0	0
$859$	−2.25450e12	−0.141280	−0.0706399	−	0.997502i	$-0.522504\pi$
$859$	−2.25450e12	−0.141280	−0.0706399	+	0.997502i	$0.522504\pi$
$860$	0	0
$861$	−4.64063e12	−0.287782
$862$	0	0
$863$	2.96552e13	1.81992	0.909960	−	0.414696i	$-0.136112\pi$
$863$	2.96552e13	1.81992	0.909960	+	0.414696i	$0.136112\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−8.77878e12	−0.527653
$868$	0	0
$869$	2.48827e13	1.48016
$870$	0	0
$871$	−1.58550e13	−0.933434
$872$	0	0
$873$	5.74140e12	0.334544
$874$	0	0
$875$	0	0
$876$	0	0
$877$	1.82549e13	1.04203	0.521016	−	0.853547i	$-0.325553\pi$
$877$	1.82549e13	1.04203	0.521016	+	0.853547i	$0.325553\pi$
$878$	0	0
$879$	−8.34633e12	−0.471569
$880$	0	0
$881$	−2.37511e13	−1.32829	−0.664143	−	0.747606i	$-0.731203\pi$
$881$	−2.37511e13	−1.32829	−0.664143	+	0.747606i	$0.731203\pi$
$882$	0	0
$883$	9.81054e12	0.543087	0.271544	−	0.962426i	$-0.412466\pi$
$883$	9.81054e12	0.543087	0.271544	+	0.962426i	$0.412466\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	4.28130e12	0.232230	0.116115	−	0.993236i	$-0.462956\pi$
$887$	4.28130e12	0.232230	0.116115	+	0.993236i	$0.462956\pi$
$888$	0	0
$889$	4.09290e12	0.219772
$890$	0	0
$891$	−3.28636e12	−0.174689
$892$	0	0
$893$	−6.74038e12	−0.354693
$894$	0	0
$895$	0	0
$896$	0	0
$897$	1.22443e12	0.0631494
$898$	0	0
$899$	1.13066e13	0.577314
$900$	0	0
$901$	−4.11727e12	−0.208136
$902$	0	0
$903$	9.20638e12	0.460780
$904$	0	0
$905$	0	0
$906$	0	0
$907$	2.62299e13	1.28696	0.643478	−	0.765465i	$-0.277491\pi$
$907$	2.62299e13	1.28696	0.643478	+	0.765465i	$0.277491\pi$
$908$	0	0
$909$	−5.58398e12	−0.271273
$910$	0	0
$911$	−2.25716e13	−1.08575	−0.542876	−	0.839813i	$-0.682664\pi$
$911$	−2.25716e13	−1.08575	−0.542876	+	0.839813i	$0.682664\pi$
$912$	0	0
$913$	2.34472e13	1.11679
$914$	0	0
$915$	0	0
$916$	0	0
$917$	−4.02179e12	−0.187827
$918$	0	0
$919$	−8.38232e12	−0.387654	−0.193827	−	0.981036i	$-0.562090\pi$
$919$	−8.38232e12	−0.387654	−0.193827	+	0.981036i	$0.562090\pi$
$920$	0	0
$921$	1.50931e13	0.691211
$922$	0	0
$923$	−1.82440e13	−0.827395
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−1.08160e13	−0.481069
$928$	0	0
$929$	1.20068e13	0.528881	0.264440	−	0.964402i	$-0.414813\pi$
$929$	1.20068e13	0.528881	0.264440	+	0.964402i	$0.414813\pi$
$930$	0	0
$931$	−1.71651e13	−0.748813
$932$	0	0
$933$	6.40966e12	0.276929
$934$	0	0
$935$	0	0
$936$	0	0
$937$	3.29524e13	1.39656	0.698278	−	0.715826i	$-0.253950\pi$
$937$	3.29524e13	1.39656	0.698278	+	0.715826i	$0.253950\pi$
$938$	0	0
$939$	3.99786e12	0.167815
$940$	0	0
$941$	4.29108e12	0.178408	0.0892038	−	0.996013i	$-0.471568\pi$
$941$	4.29108e12	0.178408	0.0892038	+	0.996013i	$0.471568\pi$
$942$	0	0
$943$	4.12967e12	0.170064
$944$	0	0
$945$	0	0
$946$	0	0
$947$	1.80921e13	0.730993	0.365497	−	0.930813i	$-0.380899\pi$
$947$	1.80921e13	0.730993	0.365497	+	0.930813i	$0.380899\pi$
$948$	0	0
$949$	3.17195e12	0.126949
$950$	0	0
$951$	−1.79752e12	−0.0712625
$952$	0	0
$953$	2.91788e13	1.14591	0.572954	−	0.819587i	$-0.305797\pi$
$953$	2.91788e13	1.14591	0.572954	+	0.819587i	$0.305797\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	−2.97775e13	−1.14758
$958$	0	0
$959$	1.50054e13	0.572879
$960$	0	0
$961$	−2.09264e13	−0.791479
$962$	0	0
$963$	−2.06674e12	−0.0774405
$964$	0	0
$965$	0	0
$966$	0	0
$967$	−3.08297e13	−1.13383	−0.566917	−	0.823775i	$-0.691864\pi$
$967$	−3.08297e13	−1.13383	−0.566917	+	0.823775i	$0.691864\pi$
$968$	0	0
$969$	5.47902e12	0.199639
$970$	0	0
$971$	−8.62158e12	−0.311244	−0.155622	−	0.987817i	$-0.549738\pi$
$971$	−8.62158e12	−0.311244	−0.155622	+	0.987817i	$0.549738\pi$
$972$	0	0
$973$	−1.24726e13	−0.446119
$974$	0	0
$975$	0	0
$976$	0	0
$977$	1.79155e13	0.629077	0.314539	−	0.949245i	$-0.398150\pi$
$977$	1.79155e13	0.629077	0.314539	+	0.949245i	$0.398150\pi$
$978$	0	0
$979$	5.88444e13	2.04731
$980$	0	0
$981$	1.01510e13	0.349942
$982$	0	0
$983$	−2.46012e13	−0.840360	−0.420180	−	0.907441i	$-0.638033\pi$
$983$	−2.46012e13	−0.840360	−0.420180	+	0.907441i	$0.638033\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	3.12822e12	0.104923
$988$	0	0
$989$	−8.19269e12	−0.272297
$990$	0	0
$991$	3.39956e13	1.11967	0.559837	−	0.828603i	$-0.310864\pi$
$991$	3.39956e13	1.11967	0.559837	+	0.828603i	$0.310864\pi$
$992$	0	0
$993$	−1.64295e13	−0.536232
$994$	0	0
$995$	0	0
$996$	0	0
$997$	4.92611e13	1.57898	0.789488	−	0.613766i	$-0.210346\pi$
$997$	4.92611e13	1.57898	0.789488	+	0.613766i	$0.210346\pi$
$998$	0	0
$999$	−4.29006e12	−0.136276

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.10.a.b.1.1		1
5.2	odd	4		300.10.d.a.49.1		2
5.3	odd	4		300.10.d.a.49.2		2
5.4	even	2		60.10.a.a.1.1	✓	1
15.14	odd	2		180.10.a.c.1.1		1
20.19	odd	2		240.10.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.10.a.a.1.1	✓	1	5.4	even	2
180.10.a.c.1.1		1	15.14	odd	2
240.10.a.e.1.1		1	20.19	odd	2
300.10.a.b.1.1		1	1.1	even	1	trivial
300.10.d.a.49.1		2	5.2	odd	4
300.10.d.a.49.2		2	5.3	odd	4

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	300.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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