LMFDB - Embedded newform 4664.2.a.k.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4664,2,Mod(1,4664)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4664, 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("4664.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4664 = 2^{3} \cdot 11 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4664.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:	$37.2422275027$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5x^{10} - 7x^{9} + 53x^{8} + 13x^{7} - 189x^{6} - 16x^{5} + 260x^{4} + 32x^{3} - 118x^{2} - 8x + 16 $ x^11 - 5x^10 - 7x^9 + 53x^8 + 13x^7 - 189x^6 - 16x^5 + 260x^4 + 32x^3 - 118x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.581022$ of defining polynomial
Character	$\chi$	$=$	4664.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.418978 q^{3} -0.101827 q^{5} -3.67256 q^{7} -2.82446 q^{9} +O(q^{10})$	$q-0.418978 q^{3} -0.101827 q^{5} -3.67256 q^{7} -2.82446 q^{9} +1.00000 q^{11} +3.53049 q^{13} +0.0426632 q^{15} +2.80513 q^{17} -1.58139 q^{19} +1.53872 q^{21} +6.11687 q^{23} -4.98963 q^{25} +2.44032 q^{27} +1.29144 q^{29} +1.36916 q^{31} -0.418978 q^{33} +0.373965 q^{35} -2.78728 q^{37} -1.47920 q^{39} +8.17202 q^{41} +4.21626 q^{43} +0.287606 q^{45} -11.4415 q^{47} +6.48773 q^{49} -1.17529 q^{51} +1.00000 q^{53} -0.101827 q^{55} +0.662566 q^{57} -7.70191 q^{59} +5.55970 q^{61} +10.3730 q^{63} -0.359498 q^{65} -3.90562 q^{67} -2.56283 q^{69} -10.8343 q^{71} +4.23131 q^{73} +2.09054 q^{75} -3.67256 q^{77} +12.9604 q^{79} +7.45094 q^{81} -9.91837 q^{83} -0.285638 q^{85} -0.541084 q^{87} -8.52289 q^{89} -12.9659 q^{91} -0.573649 q^{93} +0.161028 q^{95} +6.95768 q^{97} -2.82446 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 6 q^{3} + 3 q^{5} - 5 q^{7} + 7 q^{9}+O(q^{10}) $ 11 * q - 6 * q^3 + 3 * q^5 - 5 * q^7 + 7 * q^9	$ 11 q - 6 q^{3} + 3 q^{5} - 5 q^{7} + 7 q^{9} + 11 q^{11} - 13 q^{13} - 8 q^{15} - 7 q^{17} - 21 q^{19} + 6 q^{21} + 11 q^{23} + 4 q^{25} - 6 q^{27} - 5 q^{31} - 6 q^{33} - 25 q^{35} - 4 q^{37} - 19 q^{39} - 11 q^{41} + 16 q^{45} - 17 q^{47} - 2 q^{49} - 18 q^{51} + 11 q^{53} + 3 q^{55} - 5 q^{57} - 19 q^{59} - 2 q^{61} - 36 q^{63} - 13 q^{65} + 25 q^{67} + 3 q^{69} - 30 q^{71} + 5 q^{73} - 5 q^{75} - 5 q^{77} - 23 q^{79} - 9 q^{81} - 19 q^{83} + 2 q^{85} - 7 q^{87} + 6 q^{89} - 20 q^{91} + 43 q^{93} - 50 q^{95} - 35 q^{97} + 7 q^{99}+O(q^{100}) $ 11 * q - 6 * q^3 + 3 * q^5 - 5 * q^7 + 7 * q^9 + 11 * q^11 - 13 * q^13 - 8 * q^15 - 7 * q^17 - 21 * q^19 + 6 * q^21 + 11 * q^23 + 4 * q^25 - 6 * q^27 - 5 * q^31 - 6 * q^33 - 25 * q^35 - 4 * q^37 - 19 * q^39 - 11 * q^41 + 16 * q^45 - 17 * q^47 - 2 * q^49 - 18 * q^51 + 11 * q^53 + 3 * q^55 - 5 * q^57 - 19 * q^59 - 2 * q^61 - 36 * q^63 - 13 * q^65 + 25 * q^67 + 3 * q^69 - 30 * q^71 + 5 * q^73 - 5 * q^75 - 5 * q^77 - 23 * q^79 - 9 * q^81 - 19 * q^83 + 2 * q^85 - 7 * q^87 + 6 * q^89 - 20 * q^91 + 43 * q^93 - 50 * q^95 - 35 * q^97 + 7 * 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
$3$	−0.418978	−0.241897	−0.120948	−	0.992659i	$-0.538594\pi$
$3$	−0.418978	−0.241897	−0.120948	+	0.992659i	$0.538594\pi$
$4$	0	0
$5$	−0.101827	−0.0455383	−0.0227692	−	0.999741i	$-0.507248\pi$
$5$	−0.101827	−0.0455383	−0.0227692	+	0.999741i	$0.507248\pi$
$6$	0	0
$7$	−3.67256	−1.38810	−0.694049	−	0.719927i	$-0.744175\pi$
$7$	−3.67256	−1.38810	−0.694049	+	0.719927i	$0.744175\pi$
$8$	0	0
$9$	−2.82446	−0.941486
$10$	0	0
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0	0
$13$	3.53049	0.979181	0.489591	−	0.871952i	$-0.337146\pi$
$13$	3.53049	0.979181	0.489591	+	0.871952i	$0.337146\pi$
$14$	0	0
$15$	0.0426632	0.0110156
$16$	0	0
$17$	2.80513	0.680345	0.340172	−	0.940363i	$-0.389515\pi$
$17$	2.80513	0.680345	0.340172	+	0.940363i	$0.389515\pi$
$18$	0	0
$19$	−1.58139	−0.362795	−0.181398	−	0.983410i	$-0.558062\pi$
$19$	−1.58139	−0.362795	−0.181398	+	0.983410i	$0.558062\pi$
$20$	0	0
$21$	1.53872	0.335777
$22$	0	0
$23$	6.11687	1.27546	0.637728	−	0.770262i	$-0.279874\pi$
$23$	6.11687	1.27546	0.637728	+	0.770262i	$0.279874\pi$
$24$	0	0
$25$	−4.98963	−0.997926
$26$	0	0
$27$	2.44032	0.469639
$28$	0	0
$29$	1.29144	0.239814	0.119907	−	0.992785i	$-0.461740\pi$
$29$	1.29144	0.239814	0.119907	+	0.992785i	$0.461740\pi$
$30$	0	0
$31$	1.36916	0.245909	0.122954	−	0.992412i	$-0.460763\pi$
$31$	1.36916	0.245909	0.122954	+	0.992412i	$0.460763\pi$
$32$	0	0
$33$	−0.418978	−0.0729346
$34$	0	0
$35$	0.373965	0.0632117
$36$	0	0
$37$	−2.78728	−0.458226	−0.229113	−	0.973400i	$-0.573583\pi$
$37$	−2.78728	−0.458226	−0.229113	+	0.973400i	$0.573583\pi$
$38$	0	0
$39$	−1.47920	−0.236861
$40$	0	0
$41$	8.17202	1.27625	0.638127	−	0.769931i	$-0.279709\pi$
$41$	8.17202	1.27625	0.638127	+	0.769931i	$0.279709\pi$
$42$	0	0
$43$	4.21626	0.642974	0.321487	−	0.946914i	$-0.395817\pi$
$43$	4.21626	0.642974	0.321487	+	0.946914i	$0.395817\pi$
$44$	0	0
$45$	0.287606	0.0428737
$46$	0	0
$47$	−11.4415	−1.66891	−0.834454	−	0.551077i	$-0.814217\pi$
$47$	−11.4415	−1.66891	−0.834454	+	0.551077i	$0.814217\pi$
$48$	0	0
$49$	6.48773	0.926818
$50$	0	0
$51$	−1.17529	−0.164573
$52$	0	0
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	0	0
$55$	−0.101827	−0.0137303
$56$	0	0
$57$	0.662566	0.0877590
$58$	0	0
$59$	−7.70191	−1.00270	−0.501352	−	0.865244i	$-0.667164\pi$
$59$	−7.70191	−1.00270	−0.501352	+	0.865244i	$0.667164\pi$
$60$	0	0
$61$	5.55970	0.711847	0.355923	−	0.934515i	$-0.384166\pi$
$61$	5.55970	0.711847	0.355923	+	0.934515i	$0.384166\pi$
$62$	0	0
$63$	10.3730	1.30688
$64$	0	0
$65$	−0.359498	−0.0445903
$66$	0	0
$67$	−3.90562	−0.477148	−0.238574	−	0.971124i	$-0.576680\pi$
$67$	−3.90562	−0.477148	−0.238574	+	0.971124i	$0.576680\pi$
$68$	0	0
$69$	−2.56283	−0.308529
$70$	0	0
$71$	−10.8343	−1.28579	−0.642897	−	0.765953i	$-0.722268\pi$
$71$	−10.8343	−1.28579	−0.642897	+	0.765953i	$0.722268\pi$
$72$	0	0
$73$	4.23131	0.495237	0.247619	−	0.968858i	$-0.420352\pi$
$73$	4.23131	0.495237	0.247619	+	0.968858i	$0.420352\pi$
$74$	0	0
$75$	2.09054	0.241395
$76$	0	0
$77$	−3.67256	−0.418528
$78$	0	0
$79$	12.9604	1.45816	0.729079	−	0.684429i	$-0.239949\pi$
$79$	12.9604	1.45816	0.729079	+	0.684429i	$0.239949\pi$
$80$	0	0
$81$	7.45094	0.827882
$82$	0	0
$83$	−9.91837	−1.08868	−0.544341	−	0.838864i	$-0.683220\pi$
$83$	−9.91837	−1.08868	−0.544341	+	0.838864i	$0.683220\pi$
$84$	0	0
$85$	−0.285638	−0.0309818
$86$	0	0
$87$	−0.541084	−0.0580103
$88$	0	0
$89$	−8.52289	−0.903425	−0.451712	−	0.892164i	$-0.649187\pi$
$89$	−8.52289	−0.903425	−0.451712	+	0.892164i	$0.649187\pi$
$90$	0	0
$91$	−12.9659	−1.35920
$92$	0	0
$93$	−0.573649	−0.0594846
$94$	0	0
$95$	0.161028	0.0165211
$96$	0	0
$97$	6.95768	0.706445	0.353222	−	0.935539i	$-0.385086\pi$
$97$	6.95768	0.706445	0.353222	+	0.935539i	$0.385086\pi$
$98$	0	0
$99$	−2.82446	−0.283869
$100$	0	0
$101$	−12.1021	−1.20420	−0.602101	−	0.798420i	$-0.705670\pi$
$101$	−12.1021	−1.20420	−0.602101	+	0.798420i	$0.705670\pi$
$102$	0	0
$103$	−10.2619	−1.01113	−0.505566	−	0.862788i	$-0.668716\pi$
$103$	−10.2619	−1.01113	−0.505566	+	0.862788i	$0.668716\pi$
$104$	0	0
$105$	−0.156683	−0.0152907
$106$	0	0
$107$	−15.0194	−1.45198	−0.725989	−	0.687706i	$-0.758618\pi$
$107$	−15.0194	−1.45198	−0.725989	+	0.687706i	$0.758618\pi$
$108$	0	0
$109$	2.08087	0.199311	0.0996554	−	0.995022i	$-0.468226\pi$
$109$	2.08087	0.199311	0.0996554	+	0.995022i	$0.468226\pi$
$110$	0	0
$111$	1.16781	0.110843
$112$	0	0
$113$	1.30823	0.123068	0.0615339	−	0.998105i	$-0.480401\pi$
$113$	1.30823	0.123068	0.0615339	+	0.998105i	$0.480401\pi$
$114$	0	0
$115$	−0.622862	−0.0580822
$116$	0	0
$117$	−9.97172	−0.921886
$118$	0	0
$119$	−10.3020	−0.944386
$120$	0	0
$121$	1.00000	0.0909091
$122$	0	0
$123$	−3.42389	−0.308722
$124$	0	0
$125$	1.01721	0.0909822
$126$	0	0
$127$	−13.1065	−1.16302	−0.581508	−	0.813541i	$-0.697537\pi$
$127$	−13.1065	−1.16302	−0.581508	+	0.813541i	$0.697537\pi$
$128$	0	0
$129$	−1.76652	−0.155533
$130$	0	0
$131$	15.7453	1.37567	0.687835	−	0.725867i	$-0.258561\pi$
$131$	15.7453	1.37567	0.687835	+	0.725867i	$0.258561\pi$
$132$	0	0
$133$	5.80774	0.503595
$134$	0	0
$135$	−0.248490	−0.0213866
$136$	0	0
$137$	7.88191	0.673397	0.336698	−	0.941613i	$-0.390690\pi$
$137$	7.88191	0.673397	0.336698	+	0.941613i	$0.390690\pi$
$138$	0	0
$139$	−13.5980	−1.15337	−0.576683	−	0.816968i	$-0.695653\pi$
$139$	−13.5980	−1.15337	−0.576683	+	0.816968i	$0.695653\pi$
$140$	0	0
$141$	4.79371	0.403704
$142$	0	0
$143$	3.53049	0.295234
$144$	0	0
$145$	−0.131503	−0.0109207
$146$	0	0
$147$	−2.71821	−0.224194
$148$	0	0
$149$	−21.3966	−1.75288	−0.876439	−	0.481513i	$-0.840087\pi$
$149$	−21.3966	−1.75288	−0.876439	+	0.481513i	$0.840087\pi$
$150$	0	0
$151$	−3.85282	−0.313538	−0.156769	−	0.987635i	$-0.550108\pi$
$151$	−3.85282	−0.313538	−0.156769	+	0.987635i	$0.550108\pi$
$152$	0	0
$153$	−7.92298	−0.640535
$154$	0	0
$155$	−0.139418	−0.0111983
$156$	0	0
$157$	−6.56735	−0.524131	−0.262066	−	0.965050i	$-0.584404\pi$
$157$	−6.56735	−0.524131	−0.262066	+	0.965050i	$0.584404\pi$
$158$	0	0
$159$	−0.418978	−0.0332271
$160$	0	0
$161$	−22.4646	−1.77046
$162$	0	0
$163$	8.07020	0.632107	0.316053	−	0.948741i	$-0.397642\pi$
$163$	8.07020	0.632107	0.316053	+	0.948741i	$0.397642\pi$
$164$	0	0
$165$	0.0426632	0.00332132
$166$	0	0
$167$	−11.4235	−0.883977	−0.441989	−	0.897021i	$-0.645727\pi$
$167$	−11.4235	−0.883977	−0.441989	+	0.897021i	$0.645727\pi$
$168$	0	0
$169$	−0.535649	−0.0412037
$170$	0	0
$171$	4.46656	0.341566
$172$	0	0
$173$	−25.3958	−1.93081	−0.965404	−	0.260758i	$-0.916028\pi$
$173$	−25.3958	−1.93081	−0.965404	+	0.260758i	$0.916028\pi$
$174$	0	0
$175$	18.3247	1.38522
$176$	0	0
$177$	3.22693	0.242551
$178$	0	0
$179$	−26.0080	−1.94393	−0.971963	−	0.235135i	$-0.924447\pi$
$179$	−26.0080	−1.94393	−0.971963	+	0.235135i	$0.924447\pi$
$180$	0	0
$181$	3.86281	0.287121	0.143560	−	0.989642i	$-0.454145\pi$
$181$	3.86281	0.287121	0.143560	+	0.989642i	$0.454145\pi$
$182$	0	0
$183$	−2.32939	−0.172193
$184$	0	0
$185$	0.283820	0.0208669
$186$	0	0
$187$	2.80513	0.205132
$188$	0	0
$189$	−8.96222	−0.651906
$190$	0	0
$191$	19.4491	1.40729	0.703645	−	0.710552i	$-0.251555\pi$
$191$	19.4491	1.40729	0.703645	+	0.710552i	$0.251555\pi$
$192$	0	0
$193$	−18.4424	−1.32751	−0.663757	−	0.747948i	$-0.731039\pi$
$193$	−18.4424	−1.32751	−0.663757	+	0.747948i	$0.731039\pi$
$194$	0	0
$195$	0.150622	0.0107862
$196$	0	0
$197$	16.6472	1.18606	0.593031	−	0.805180i	$-0.297931\pi$
$197$	16.6472	1.18606	0.593031	+	0.805180i	$0.297931\pi$
$198$	0	0
$199$	−14.7071	−1.04256	−0.521278	−	0.853387i	$-0.674545\pi$
$199$	−14.7071	−1.04256	−0.521278	+	0.853387i	$0.674545\pi$
$200$	0	0
$201$	1.63637	0.115421
$202$	0	0
$203$	−4.74289	−0.332886
$204$	0	0
$205$	−0.832130	−0.0581185
$206$	0	0
$207$	−17.2769	−1.20082
$208$	0	0
$209$	−1.58139	−0.109387
$210$	0	0
$211$	−4.89567	−0.337032	−0.168516	−	0.985699i	$-0.553897\pi$
$211$	−4.89567	−0.337032	−0.168516	+	0.985699i	$0.553897\pi$
$212$	0	0
$213$	4.53932	0.311029
$214$	0	0
$215$	−0.429329	−0.0292800
$216$	0	0
$217$	−5.02834	−0.341346
$218$	0	0
$219$	−1.77282	−0.119796
$220$	0	0
$221$	9.90349	0.666181
$222$	0	0
$223$	17.7167	1.18640	0.593200	−	0.805055i	$-0.297864\pi$
$223$	17.7167	1.18640	0.593200	+	0.805055i	$0.297864\pi$
$224$	0	0
$225$	14.0930	0.939534
$226$	0	0
$227$	−2.03921	−0.135347	−0.0676735	−	0.997708i	$-0.521558\pi$
$227$	−2.03921	−0.135347	−0.0676735	+	0.997708i	$0.521558\pi$
$228$	0	0
$229$	10.4109	0.687969	0.343984	−	0.938975i	$-0.388223\pi$
$229$	10.4109	0.687969	0.343984	+	0.938975i	$0.388223\pi$
$230$	0	0
$231$	1.53872	0.101240
$232$	0	0
$233$	14.6170	0.957591	0.478796	−	0.877926i	$-0.341074\pi$
$233$	14.6170	0.957591	0.478796	+	0.877926i	$0.341074\pi$
$234$	0	0
$235$	1.16505	0.0759993
$236$	0	0
$237$	−5.43011	−0.352724
$238$	0	0
$239$	−13.1763	−0.852307	−0.426153	−	0.904651i	$-0.640132\pi$
$239$	−13.1763	−0.852307	−0.426153	+	0.904651i	$0.640132\pi$
$240$	0	0
$241$	−11.2922	−0.727392	−0.363696	−	0.931518i	$-0.618485\pi$
$241$	−11.2922	−0.727392	−0.363696	+	0.931518i	$0.618485\pi$
$242$	0	0
$243$	−10.4427	−0.669901
$244$	0	0
$245$	−0.660624	−0.0422058
$246$	0	0
$247$	−5.58307	−0.355242
$248$	0	0
$249$	4.15557	0.263349
$250$	0	0
$251$	−1.91962	−0.121165	−0.0605827	−	0.998163i	$-0.519296\pi$
$251$	−1.91962	−0.121165	−0.0605827	+	0.998163i	$0.519296\pi$
$252$	0	0
$253$	6.11687	0.384565
$254$	0	0
$255$	0.119676	0.00749439
$256$	0	0
$257$	−3.50789	−0.218816	−0.109408	−	0.993997i	$-0.534896\pi$
$257$	−3.50789	−0.218816	−0.109408	+	0.993997i	$0.534896\pi$
$258$	0	0
$259$	10.2365	0.636063
$260$	0	0
$261$	−3.64762	−0.225782
$262$	0	0
$263$	0.0231472	0.00142732	0.000713660	−	1.00000i	$-0.499773\pi$
$263$	0.0231472	0.00142732	0.000713660		1.00000i	$0.499773\pi$
$264$	0	0
$265$	−0.101827	−0.00625517
$266$	0	0
$267$	3.57090	0.218536
$268$	0	0
$269$	15.2414	0.929284	0.464642	−	0.885499i	$-0.346183\pi$
$269$	15.2414	0.929284	0.464642	+	0.885499i	$0.346183\pi$
$270$	0	0
$271$	−13.8936	−0.843979	−0.421989	−	0.906601i	$-0.638668\pi$
$271$	−13.8936	−0.843979	−0.421989	+	0.906601i	$0.638668\pi$
$272$	0	0
$273$	5.43244	0.328786
$274$	0	0
$275$	−4.98963	−0.300886
$276$	0	0
$277$	−28.2117	−1.69508	−0.847538	−	0.530735i	$-0.821916\pi$
$277$	−28.2117	−1.69508	−0.847538	+	0.530735i	$0.821916\pi$
$278$	0	0
$279$	−3.86714	−0.231520
$280$	0	0
$281$	22.2140	1.32517	0.662587	−	0.748985i	$-0.269458\pi$
$281$	22.2140	1.32517	0.662587	+	0.748985i	$0.269458\pi$
$282$	0	0
$283$	9.03654	0.537167	0.268583	−	0.963256i	$-0.413445\pi$
$283$	9.03654	0.537167	0.268583	+	0.963256i	$0.413445\pi$
$284$	0	0
$285$	−0.0674670	−0.00399640
$286$	0	0
$287$	−30.0122	−1.77157
$288$	0	0
$289$	−9.13122	−0.537131
$290$	0	0
$291$	−2.91511	−0.170887
$292$	0	0
$293$	32.3614	1.89057	0.945285	−	0.326245i	$-0.105784\pi$
$293$	32.3614	1.89057	0.945285	+	0.326245i	$0.105784\pi$
$294$	0	0
$295$	0.784261	0.0456614
$296$	0	0
$297$	2.44032	0.141602
$298$	0	0
$299$	21.5956	1.24890
$300$	0	0
$301$	−15.4845	−0.892511
$302$	0	0
$303$	5.07050	0.291293
$304$	0	0
$305$	−0.566127	−0.0324163
$306$	0	0
$307$	−1.61929	−0.0924178	−0.0462089	−	0.998932i	$-0.514714\pi$
$307$	−1.61929	−0.0924178	−0.0462089	+	0.998932i	$0.514714\pi$
$308$	0	0
$309$	4.29949	0.244589
$310$	0	0
$311$	−5.30183	−0.300639	−0.150320	−	0.988637i	$-0.548030\pi$
$311$	−5.30183	−0.300639	−0.150320	+	0.988637i	$0.548030\pi$
$312$	0	0
$313$	14.7559	0.834051	0.417026	−	0.908895i	$-0.363073\pi$
$313$	14.7559	0.834051	0.417026	+	0.908895i	$0.363073\pi$
$314$	0	0
$315$	−1.05625	−0.0595129
$316$	0	0
$317$	30.5257	1.71449	0.857246	−	0.514907i	$-0.172173\pi$
$317$	30.5257	1.71449	0.857246	+	0.514907i	$0.172173\pi$
$318$	0	0
$319$	1.29144	0.0723067
$320$	0	0
$321$	6.29278	0.351229
$322$	0	0
$323$	−4.43600	−0.246826
$324$	0	0
$325$	−17.6158	−0.977151
$326$	0	0
$327$	−0.871836	−0.0482127
$328$	0	0
$329$	42.0195	2.31661
$330$	0	0
$331$	−29.5762	−1.62565	−0.812827	−	0.582505i	$-0.802073\pi$
$331$	−29.5762	−1.62565	−0.812827	+	0.582505i	$0.802073\pi$
$332$	0	0
$333$	7.87256	0.431413
$334$	0	0
$335$	0.397697	0.0217285
$336$	0	0
$337$	−33.1763	−1.80723	−0.903614	−	0.428348i	$-0.859096\pi$
$337$	−33.1763	−1.80723	−0.903614	+	0.428348i	$0.859096\pi$
$338$	0	0
$339$	−0.548118	−0.0297697
$340$	0	0
$341$	1.36916	0.0741443
$342$	0	0
$343$	1.88136	0.101584
$344$	0	0
$345$	0.260965	0.0140499
$346$	0	0
$347$	−34.5213	−1.85320	−0.926600	−	0.376049i	$-0.877282\pi$
$347$	−34.5213	−1.85320	−0.926600	+	0.376049i	$0.877282\pi$
$348$	0	0
$349$	35.5607	1.90352	0.951760	−	0.306845i	$-0.0992732\pi$
$349$	35.5607	1.90352	0.951760	+	0.306845i	$0.0992732\pi$
$350$	0	0
$351$	8.61551	0.459862
$352$	0	0
$353$	−6.24914	−0.332608	−0.166304	−	0.986075i	$-0.553183\pi$
$353$	−6.24914	−0.332608	−0.166304	+	0.986075i	$0.553183\pi$
$354$	0	0
$355$	1.10322	0.0585529
$356$	0	0
$357$	4.31632	0.228444
$358$	0	0
$359$	26.3262	1.38944	0.694721	−	0.719280i	$-0.255528\pi$
$359$	26.3262	1.38944	0.694721	+	0.719280i	$0.255528\pi$
$360$	0	0
$361$	−16.4992	−0.868380
$362$	0	0
$363$	−0.418978	−0.0219906
$364$	0	0
$365$	−0.430861	−0.0225523
$366$	0	0
$367$	26.2439	1.36992	0.684960	−	0.728580i	$-0.259820\pi$
$367$	26.2439	1.36992	0.684960	+	0.728580i	$0.259820\pi$
$368$	0	0
$369$	−23.0815	−1.20158
$370$	0	0
$371$	−3.67256	−0.190670
$372$	0	0
$373$	−17.7542	−0.919277	−0.459638	−	0.888106i	$-0.652021\pi$
$373$	−17.7542	−0.919277	−0.459638	+	0.888106i	$0.652021\pi$
$374$	0	0
$375$	−0.426189	−0.0220083
$376$	0	0
$377$	4.55941	0.234822
$378$	0	0
$379$	−17.3991	−0.893734	−0.446867	−	0.894601i	$-0.647460\pi$
$379$	−17.3991	−0.893734	−0.446867	+	0.894601i	$0.647460\pi$
$380$	0	0
$381$	5.49134	0.281330
$382$	0	0
$383$	−12.8912	−0.658712	−0.329356	−	0.944206i	$-0.606832\pi$
$383$	−12.8912	−0.658712	−0.329356	+	0.944206i	$0.606832\pi$
$384$	0	0
$385$	0.373965	0.0190590
$386$	0	0
$387$	−11.9087	−0.605351
$388$	0	0
$389$	15.6028	0.791096	0.395548	−	0.918445i	$-0.370555\pi$
$389$	15.6028	0.791096	0.395548	+	0.918445i	$0.370555\pi$
$390$	0	0
$391$	17.1586	0.867750
$392$	0	0
$393$	−6.59691	−0.332770
$394$	0	0
$395$	−1.31972	−0.0664021
$396$	0	0
$397$	5.15195	0.258569	0.129284	−	0.991608i	$-0.458732\pi$
$397$	5.15195	0.258569	0.129284	+	0.991608i	$0.458732\pi$
$398$	0	0
$399$	−2.43331	−0.121818
$400$	0	0
$401$	11.3123	0.564910	0.282455	−	0.959281i	$-0.408851\pi$
$401$	11.3123	0.564910	0.282455	+	0.959281i	$0.408851\pi$
$402$	0	0
$403$	4.83382	0.240789
$404$	0	0
$405$	−0.758705	−0.0377004
$406$	0	0
$407$	−2.78728	−0.138160
$408$	0	0
$409$	−14.7488	−0.729280	−0.364640	−	0.931148i	$-0.618808\pi$
$409$	−14.7488	−0.729280	−0.364640	+	0.931148i	$0.618808\pi$
$410$	0	0
$411$	−3.30234	−0.162893
$412$	0	0
$413$	28.2858	1.39185
$414$	0	0
$415$	1.00996	0.0495768
$416$	0	0
$417$	5.69725	0.278996
$418$	0	0
$419$	17.4380	0.851901	0.425950	−	0.904747i	$-0.359940\pi$
$419$	17.4380	0.851901	0.425950	+	0.904747i	$0.359940\pi$
$420$	0	0
$421$	4.23193	0.206252	0.103126	−	0.994668i	$-0.467116\pi$
$421$	4.23193	0.206252	0.103126	+	0.994668i	$0.467116\pi$
$422$	0	0
$423$	32.3159	1.57125
$424$	0	0
$425$	−13.9966	−0.678934
$426$	0	0
$427$	−20.4184	−0.988114
$428$	0	0
$429$	−1.47920	−0.0714162
$430$	0	0
$431$	17.7013	0.852640	0.426320	−	0.904572i	$-0.359810\pi$
$431$	17.7013	0.852640	0.426320	+	0.904572i	$0.359810\pi$
$432$	0	0
$433$	12.5034	0.600874	0.300437	−	0.953802i	$-0.402868\pi$
$433$	12.5034	0.600874	0.300437	+	0.953802i	$0.402868\pi$
$434$	0	0
$435$	0.0550969	0.00264169
$436$	0	0
$437$	−9.67314	−0.462729
$438$	0	0
$439$	−20.9236	−0.998630	−0.499315	−	0.866421i	$-0.666415\pi$
$439$	−20.9236	−0.998630	−0.499315	+	0.866421i	$0.666415\pi$
$440$	0	0
$441$	−18.3243	−0.872586
$442$	0	0
$443$	−40.4467	−1.92168	−0.960841	−	0.277100i	$-0.910627\pi$
$443$	−40.4467	−1.92168	−0.960841	+	0.277100i	$0.910627\pi$
$444$	0	0
$445$	0.867859	0.0411405
$446$	0	0
$447$	8.96470	0.424016
$448$	0	0
$449$	−22.7290	−1.07265	−0.536324	−	0.844012i	$-0.680188\pi$
$449$	−22.7290	−1.07265	−0.536324	+	0.844012i	$0.680188\pi$
$450$	0	0
$451$	8.17202	0.384805
$452$	0	0
$453$	1.61425	0.0758439
$454$	0	0
$455$	1.32028	0.0618957
$456$	0	0
$457$	−22.3101	−1.04362	−0.521812	−	0.853061i	$-0.674744\pi$
$457$	−22.3101	−1.04362	−0.521812	+	0.853061i	$0.674744\pi$
$458$	0	0
$459$	6.84542	0.319517
$460$	0	0
$461$	−20.5280	−0.956083	−0.478042	−	0.878337i	$-0.658653\pi$
$461$	−20.5280	−0.956083	−0.478042	+	0.878337i	$0.658653\pi$
$462$	0	0
$463$	23.7350	1.10306	0.551530	−	0.834155i	$-0.314044\pi$
$463$	23.7350	1.10306	0.551530	+	0.834155i	$0.314044\pi$
$464$	0	0
$465$	0.0584128	0.00270883
$466$	0	0
$467$	2.62939	0.121674	0.0608368	−	0.998148i	$-0.480623\pi$
$467$	2.62939	0.121674	0.0608368	+	0.998148i	$0.480623\pi$
$468$	0	0
$469$	14.3437	0.662328
$470$	0	0
$471$	2.75157	0.126786
$472$	0	0
$473$	4.21626	0.193864
$474$	0	0
$475$	7.89054	0.362043
$476$	0	0
$477$	−2.82446	−0.129323
$478$	0	0
$479$	11.9115	0.544249	0.272124	−	0.962262i	$-0.412274\pi$
$479$	11.9115	0.544249	0.272124	+	0.962262i	$0.412274\pi$
$480$	0	0
$481$	−9.84046	−0.448686
$482$	0	0
$483$	9.41217	0.428268
$484$	0	0
$485$	−0.708478	−0.0321703
$486$	0	0
$487$	−29.3912	−1.33184	−0.665922	−	0.746022i	$-0.731962\pi$
$487$	−29.3912	−1.33184	−0.665922	+	0.746022i	$0.731962\pi$
$488$	0	0
$489$	−3.38123	−0.152905
$490$	0	0
$491$	−35.3662	−1.59605	−0.798027	−	0.602621i	$-0.794123\pi$
$491$	−35.3662	−1.59605	−0.798027	+	0.602621i	$0.794123\pi$
$492$	0	0
$493$	3.62266	0.163156
$494$	0	0
$495$	0.287606	0.0129269
$496$	0	0
$497$	39.7896	1.78481
$498$	0	0
$499$	−17.2624	−0.772773	−0.386387	−	0.922337i	$-0.626277\pi$
$499$	−17.2624	−0.772773	−0.386387	+	0.922337i	$0.626277\pi$
$500$	0	0
$501$	4.78619	0.213831
$502$	0	0
$503$	−16.5698	−0.738811	−0.369405	−	0.929268i	$-0.620439\pi$
$503$	−16.5698	−0.738811	−0.369405	+	0.929268i	$0.620439\pi$
$504$	0	0
$505$	1.23232	0.0548374
$506$	0	0
$507$	0.224425	0.00996705
$508$	0	0
$509$	−17.5714	−0.778839	−0.389420	−	0.921060i	$-0.627324\pi$
$509$	−17.5714	−0.778839	−0.389420	+	0.921060i	$0.627324\pi$
$510$	0	0
$511$	−15.5398	−0.687438
$512$	0	0
$513$	−3.85909	−0.170383
$514$	0	0
$515$	1.04493	0.0460452
$516$	0	0
$517$	−11.4415	−0.503195
$518$	0	0
$519$	10.6403	0.467056
$520$	0	0
$521$	−12.7446	−0.558352	−0.279176	−	0.960240i	$-0.590061\pi$
$521$	−12.7446	−0.558352	−0.279176	+	0.960240i	$0.590061\pi$
$522$	0	0
$523$	1.84322	0.0805985	0.0402993	−	0.999188i	$-0.487169\pi$
$523$	1.84322	0.0805985	0.0402993	+	0.999188i	$0.487169\pi$
$524$	0	0
$525$	−7.67766	−0.335080
$526$	0	0
$527$	3.84069	0.167303
$528$	0	0
$529$	14.4161	0.626789
$530$	0	0
$531$	21.7537	0.944031
$532$	0	0
$533$	28.8512	1.24968
$534$	0	0
$535$	1.52938	0.0661207
$536$	0	0
$537$	10.8967	0.470229
$538$	0	0
$539$	6.48773	0.279446
$540$	0	0
$541$	10.8903	0.468211	0.234106	−	0.972211i	$-0.424784\pi$
$541$	10.8903	0.468211	0.234106	+	0.972211i	$0.424784\pi$
$542$	0	0
$543$	−1.61843	−0.0694535
$544$	0	0
$545$	−0.211888	−0.00907628
$546$	0	0
$547$	21.9694	0.939346	0.469673	−	0.882841i	$-0.344372\pi$
$547$	21.9694	0.939346	0.469673	+	0.882841i	$0.344372\pi$
$548$	0	0
$549$	−15.7031	−0.670194
$550$	0	0
$551$	−2.04227	−0.0870034
$552$	0	0
$553$	−47.5979	−2.02407
$554$	0	0
$555$	−0.118914	−0.00504763
$556$	0	0
$557$	5.38343	0.228103	0.114052	−	0.993475i	$-0.463617\pi$
$557$	5.38343	0.228103	0.114052	+	0.993475i	$0.463617\pi$
$558$	0	0
$559$	14.8855	0.629588
$560$	0	0
$561$	−1.17529	−0.0496207
$562$	0	0
$563$	−37.1174	−1.56431	−0.782156	−	0.623083i	$-0.785880\pi$
$563$	−37.1174	−1.56431	−0.782156	+	0.623083i	$0.785880\pi$
$564$	0	0
$565$	−0.133213	−0.00560430
$566$	0	0
$567$	−27.3640	−1.14918
$568$	0	0
$569$	−33.8309	−1.41827	−0.709133	−	0.705075i	$-0.750913\pi$
$569$	−33.8309	−1.41827	−0.709133	+	0.705075i	$0.750913\pi$
$570$	0	0
$571$	12.9647	0.542555	0.271278	−	0.962501i	$-0.412554\pi$
$571$	12.9647	0.542555	0.271278	+	0.962501i	$0.412554\pi$
$572$	0	0
$573$	−8.14875	−0.340419
$574$	0	0
$575$	−30.5209	−1.27281
$576$	0	0
$577$	−25.4732	−1.06046	−0.530232	−	0.847853i	$-0.677895\pi$
$577$	−25.4732	−1.06046	−0.530232	+	0.847853i	$0.677895\pi$
$578$	0	0
$579$	7.72696	0.321122
$580$	0	0
$581$	36.4258	1.51120
$582$	0	0
$583$	1.00000	0.0414158
$584$	0	0
$585$	1.01539	0.0419811
$586$	0	0
$587$	42.2973	1.74580	0.872899	−	0.487901i	$-0.162237\pi$
$587$	42.2973	1.74580	0.872899	+	0.487901i	$0.162237\pi$
$588$	0	0
$589$	−2.16518	−0.0892146
$590$	0	0
$591$	−6.97479	−0.286905
$592$	0	0
$593$	−44.7867	−1.83917	−0.919585	−	0.392891i	$-0.871475\pi$
$593$	−44.7867	−1.83917	−0.919585	+	0.392891i	$0.871475\pi$
$594$	0	0
$595$	1.04902	0.0430058
$596$	0	0
$597$	6.16193	0.252191
$598$	0	0
$599$	−41.5780	−1.69883	−0.849415	−	0.527726i	$-0.823045\pi$
$599$	−41.5780	−1.69883	−0.849415	+	0.527726i	$0.823045\pi$
$600$	0	0
$601$	−13.2603	−0.540897	−0.270449	−	0.962734i	$-0.587172\pi$
$601$	−13.2603	−0.540897	−0.270449	+	0.962734i	$0.587172\pi$
$602$	0	0
$603$	11.0313	0.449228
$604$	0	0
$605$	−0.101827	−0.00413985
$606$	0	0
$607$	−21.1689	−0.859221	−0.429610	−	0.903014i	$-0.641349\pi$
$607$	−21.1689	−0.859221	−0.429610	+	0.903014i	$0.641349\pi$
$608$	0	0
$609$	1.98717	0.0805240
$610$	0	0
$611$	−40.3939	−1.63416
$612$	0	0
$613$	7.64552	0.308800	0.154400	−	0.988008i	$-0.450656\pi$
$613$	7.64552	0.308800	0.154400	+	0.988008i	$0.450656\pi$
$614$	0	0
$615$	0.348644	0.0140587
$616$	0	0
$617$	19.9246	0.802134	0.401067	−	0.916049i	$-0.368639\pi$
$617$	19.9246	0.802134	0.401067	+	0.916049i	$0.368639\pi$
$618$	0	0
$619$	−20.3356	−0.817355	−0.408678	−	0.912679i	$-0.634010\pi$
$619$	−20.3356	−0.817355	−0.408678	+	0.912679i	$0.634010\pi$
$620$	0	0
$621$	14.9271	0.599004
$622$	0	0
$623$	31.3009	1.25404
$624$	0	0
$625$	24.8446	0.993783
$626$	0	0
$627$	0.662566	0.0264603
$628$	0	0
$629$	−7.81869	−0.311752
$630$	0	0
$631$	22.8487	0.909594	0.454797	−	0.890595i	$-0.349712\pi$
$631$	22.8487	0.909594	0.454797	+	0.890595i	$0.349712\pi$
$632$	0	0
$633$	2.05117	0.0815268
$634$	0	0
$635$	1.33459	0.0529618
$636$	0	0
$637$	22.9048	0.907523
$638$	0	0
$639$	30.6010	1.21056
$640$	0	0
$641$	41.4186	1.63594	0.817969	−	0.575262i	$-0.195100\pi$
$641$	41.4186	1.63594	0.817969	+	0.575262i	$0.195100\pi$
$642$	0	0
$643$	20.7010	0.816366	0.408183	−	0.912900i	$-0.366163\pi$
$643$	20.7010	0.816366	0.408183	+	0.912900i	$0.366163\pi$
$644$	0	0
$645$	0.179879	0.00708273
$646$	0	0
$647$	−30.8737	−1.21377	−0.606885	−	0.794790i	$-0.707581\pi$
$647$	−30.8737	−1.21377	−0.606885	+	0.794790i	$0.707581\pi$
$648$	0	0
$649$	−7.70191	−0.302326
$650$	0	0
$651$	2.10676	0.0825705
$652$	0	0
$653$	−24.8462	−0.972306	−0.486153	−	0.873874i	$-0.661600\pi$
$653$	−24.8462	−0.972306	−0.486153	+	0.873874i	$0.661600\pi$
$654$	0	0
$655$	−1.60329	−0.0626457
$656$	0	0
$657$	−11.9512	−0.466259
$658$	0	0
$659$	−3.81368	−0.148560	−0.0742800	−	0.997237i	$-0.523666\pi$
$659$	−3.81368	−0.148560	−0.0742800	+	0.997237i	$0.523666\pi$
$660$	0	0
$661$	−4.11390	−0.160012	−0.0800061	−	0.996794i	$-0.525494\pi$
$661$	−4.11390	−0.160012	−0.0800061	+	0.996794i	$0.525494\pi$
$662$	0	0
$663$	−4.14934	−0.161147
$664$	0	0
$665$	−0.591384	−0.0229329
$666$	0	0
$667$	7.89957	0.305873
$668$	0	0
$669$	−7.42291	−0.286986
$670$	0	0
$671$	5.55970	0.214630
$672$	0	0
$673$	−7.54632	−0.290889	−0.145445	−	0.989366i	$-0.546461\pi$
$673$	−7.54632	−0.290889	−0.145445	+	0.989366i	$0.546461\pi$
$674$	0	0
$675$	−12.1763	−0.468665
$676$	0	0
$677$	7.71239	0.296411	0.148206	−	0.988957i	$-0.452650\pi$
$677$	7.71239	0.296411	0.148206	+	0.988957i	$0.452650\pi$
$678$	0	0
$679$	−25.5525	−0.980615
$680$	0	0
$681$	0.854383	0.0327400
$682$	0	0
$683$	37.3225	1.42811	0.714053	−	0.700092i	$-0.246858\pi$
$683$	37.3225	1.42811	0.714053	+	0.700092i	$0.246858\pi$
$684$	0	0
$685$	−0.802590	−0.0306654
$686$	0	0
$687$	−4.36192	−0.166417
$688$	0	0
$689$	3.53049	0.134501
$690$	0	0
$691$	−7.53267	−0.286556	−0.143278	−	0.989682i	$-0.545764\pi$
$691$	−7.53267	−0.286556	−0.143278	+	0.989682i	$0.545764\pi$
$692$	0	0
$693$	10.3730	0.394038
$694$	0	0
$695$	1.38464	0.0525224
$696$	0	0
$697$	22.9236	0.868293
$698$	0	0
$699$	−6.12419	−0.231638
$700$	0	0
$701$	47.4164	1.79089	0.895445	−	0.445171i	$-0.146857\pi$
$701$	47.4164	1.79089	0.895445	+	0.445171i	$0.146857\pi$
$702$	0	0
$703$	4.40777	0.166242
$704$	0	0
$705$	−0.488129	−0.0183840
$706$	0	0
$707$	44.4457	1.67155
$708$	0	0
$709$	14.7425	0.553666	0.276833	−	0.960918i	$-0.410715\pi$
$709$	14.7425	0.553666	0.276833	+	0.960918i	$0.410715\pi$
$710$	0	0
$711$	−36.6061	−1.37284
$712$	0	0
$713$	8.37500	0.313646
$714$	0	0
$715$	−0.359498	−0.0134445
$716$	0	0
$717$	5.52059	0.206170
$718$	0	0
$719$	53.0227	1.97741	0.988706	−	0.149869i	$-0.0478851\pi$
$719$	53.0227	1.97741	0.988706	+	0.149869i	$0.0478851\pi$
$720$	0	0
$721$	37.6873	1.40355
$722$	0	0
$723$	4.73116	0.175954
$724$	0	0
$725$	−6.44381	−0.239317
$726$	0	0
$727$	2.29321	0.0850506	0.0425253	−	0.999095i	$-0.486460\pi$
$727$	2.29321	0.0850506	0.0425253	+	0.999095i	$0.486460\pi$
$728$	0	0
$729$	−17.9775	−0.665835
$730$	0	0
$731$	11.8272	0.437444
$732$	0	0
$733$	35.4410	1.30904	0.654521	−	0.756044i	$-0.272870\pi$
$733$	35.4410	1.30904	0.654521	+	0.756044i	$0.272870\pi$
$734$	0	0
$735$	0.276787	0.0102094
$736$	0	0
$737$	−3.90562	−0.143865
$738$	0	0
$739$	−12.4123	−0.456595	−0.228297	−	0.973591i	$-0.573316\pi$
$739$	−12.4123	−0.456595	−0.228297	+	0.973591i	$0.573316\pi$
$740$	0	0
$741$	2.33918	0.0859319
$742$	0	0
$743$	−13.7902	−0.505914	−0.252957	−	0.967477i	$-0.581403\pi$
$743$	−13.7902	−0.505914	−0.252957	+	0.967477i	$0.581403\pi$
$744$	0	0
$745$	2.17875	0.0798231
$746$	0	0
$747$	28.0140	1.02498
$748$	0	0
$749$	55.1596	2.01549
$750$	0	0
$751$	−30.9051	−1.12774	−0.563872	−	0.825862i	$-0.690689\pi$
$751$	−30.9051	−1.12774	−0.563872	+	0.825862i	$0.690689\pi$
$752$	0	0
$753$	0.804278	0.0293095
$754$	0	0
$755$	0.392321	0.0142780
$756$	0	0
$757$	−17.6993	−0.643293	−0.321647	−	0.946860i	$-0.604236\pi$
$757$	−17.6993	−0.643293	−0.321647	+	0.946860i	$0.604236\pi$
$758$	0	0
$759$	−2.56283	−0.0930249
$760$	0	0
$761$	−4.46859	−0.161986	−0.0809931	−	0.996715i	$-0.525809\pi$
$761$	−4.46859	−0.161986	−0.0809931	+	0.996715i	$0.525809\pi$
$762$	0	0
$763$	−7.64211	−0.276663
$764$	0	0
$765$	0.806772	0.0291689
$766$	0	0
$767$	−27.1915	−0.981829
$768$	0	0
$769$	−1.55268	−0.0559912	−0.0279956	−	0.999608i	$-0.508912\pi$
$769$	−1.55268	−0.0559912	−0.0279956	+	0.999608i	$0.508912\pi$
$770$	0	0
$771$	1.46973	0.0529309
$772$	0	0
$773$	3.44776	0.124007	0.0620037	−	0.998076i	$-0.480251\pi$
$773$	3.44776	0.124007	0.0620037	+	0.998076i	$0.480251\pi$
$774$	0	0
$775$	−6.83162	−0.245399
$776$	0	0
$777$	−4.28885	−0.153862
$778$	0	0
$779$	−12.9231	−0.463019
$780$	0	0
$781$	−10.8343	−0.387681
$782$	0	0
$783$	3.15152	0.112626
$784$	0	0
$785$	0.668732	0.0238681
$786$	0	0
$787$	40.9003	1.45794	0.728970	−	0.684546i	$-0.239999\pi$
$787$	40.9003	1.45794	0.728970	+	0.684546i	$0.239999\pi$
$788$	0	0
$789$	−0.00969817	−0.000345264 0
$790$	0	0
$791$	−4.80455	−0.170830
$792$	0	0
$793$	19.6285	0.697027
$794$	0	0
$795$	0.0426632	0.00151311
$796$	0	0
$797$	−26.6607	−0.944370	−0.472185	−	0.881499i	$-0.656535\pi$
$797$	−26.6607	−0.944370	−0.472185	+	0.881499i	$0.656535\pi$
$798$	0	0
$799$	−32.0948	−1.13543
$800$	0	0
$801$	24.0726	0.850562
$802$	0	0
$803$	4.23131	0.149320
$804$	0	0
$805$	2.28750	0.0806238
$806$	0	0
$807$	−6.38580	−0.224791
$808$	0	0
$809$	−3.40712	−0.119788	−0.0598940	−	0.998205i	$-0.519076\pi$
$809$	−3.40712	−0.119788	−0.0598940	+	0.998205i	$0.519076\pi$
$810$	0	0
$811$	8.42919	0.295989	0.147994	−	0.988988i	$-0.452718\pi$
$811$	8.42919	0.295989	0.147994	+	0.988988i	$0.452718\pi$
$812$	0	0
$813$	5.82112	0.204156
$814$	0	0
$815$	−0.821763	−0.0287851
$816$	0	0
$817$	−6.66754	−0.233268
$818$	0	0
$819$	36.6218	1.27967
$820$	0	0
$821$	34.5582	1.20609	0.603045	−	0.797707i	$-0.293954\pi$
$821$	34.5582	1.20609	0.603045	+	0.797707i	$0.293954\pi$
$822$	0	0
$823$	−18.4008	−0.641413	−0.320706	−	0.947179i	$-0.603920\pi$
$823$	−18.4008	−0.641413	−0.320706	+	0.947179i	$0.603920\pi$
$824$	0	0
$825$	2.09054	0.0727834
$826$	0	0
$827$	−9.36298	−0.325583	−0.162791	−	0.986661i	$-0.552050\pi$
$827$	−9.36298	−0.325583	−0.162791	+	0.986661i	$0.552050\pi$
$828$	0	0
$829$	−23.3172	−0.809839	−0.404919	−	0.914352i	$-0.632700\pi$
$829$	−23.3172	−0.809839	−0.404919	+	0.914352i	$0.632700\pi$
$830$	0	0
$831$	11.8201	0.410033
$832$	0	0
$833$	18.1989	0.630556
$834$	0	0
$835$	1.16322	0.0402548
$836$	0	0
$837$	3.34119	0.115489
$838$	0	0
$839$	20.7373	0.715932	0.357966	−	0.933735i	$-0.383470\pi$
$839$	20.7373	0.715932	0.357966	+	0.933735i	$0.383470\pi$
$840$	0	0
$841$	−27.3322	−0.942489
$842$	0	0
$843$	−9.30716	−0.320556
$844$	0	0
$845$	0.0545434	0.00187635
$846$	0	0
$847$	−3.67256	−0.126191
$848$	0	0
$849$	−3.78611	−0.129939
$850$	0	0
$851$	−17.0494	−0.584447
$852$	0	0
$853$	9.53234	0.326381	0.163190	−	0.986595i	$-0.447821\pi$
$853$	9.53234	0.326381	0.163190	+	0.986595i	$0.447821\pi$
$854$	0	0
$855$	−0.454816	−0.0155544
$856$	0	0
$857$	24.1173	0.823833	0.411916	−	0.911222i	$-0.364860\pi$
$857$	24.1173	0.823833	0.411916	+	0.911222i	$0.364860\pi$
$858$	0	0
$859$	52.7473	1.79971	0.899857	−	0.436184i	$-0.143670\pi$
$859$	52.7473	1.79971	0.899857	+	0.436184i	$0.143670\pi$
$860$	0	0
$861$	12.5745	0.428536
$862$	0	0
$863$	38.1006	1.29696	0.648480	−	0.761231i	$-0.275405\pi$
$863$	38.1006	1.29696	0.648480	+	0.761231i	$0.275405\pi$
$864$	0	0
$865$	2.58598	0.0879258
$866$	0	0
$867$	3.82578	0.129930
$868$	0	0
$869$	12.9604	0.439651
$870$	0	0
$871$	−13.7888	−0.467214
$872$	0	0
$873$	−19.6517	−0.665108
$874$	0	0
$875$	−3.73578	−0.126292
$876$	0	0
$877$	48.5975	1.64102	0.820511	−	0.571631i	$-0.193689\pi$
$877$	48.5975	1.64102	0.820511	+	0.571631i	$0.193689\pi$
$878$	0	0
$879$	−13.5587	−0.457323
$880$	0	0
$881$	45.7985	1.54299	0.771496	−	0.636234i	$-0.219509\pi$
$881$	45.7985	1.54299	0.771496	+	0.636234i	$0.219509\pi$
$882$	0	0
$883$	37.5909	1.26503	0.632517	−	0.774547i	$-0.282022\pi$
$883$	37.5909	1.26503	0.632517	+	0.774547i	$0.282022\pi$
$884$	0	0
$885$	−0.328588	−0.0110454
$886$	0	0
$887$	−7.19942	−0.241733	−0.120866	−	0.992669i	$-0.538567\pi$
$887$	−7.19942	−0.241733	−0.120866	+	0.992669i	$0.538567\pi$
$888$	0	0
$889$	48.1345	1.61438
$890$	0	0
$891$	7.45094	0.249616
$892$	0	0
$893$	18.0934	0.605472
$894$	0	0
$895$	2.64831	0.0885231
$896$	0	0
$897$	−9.04805	−0.302106
$898$	0	0
$899$	1.76819	0.0589725
$900$	0	0
$901$	2.80513	0.0934526
$902$	0	0
$903$	6.48766	0.215896
$904$	0	0
$905$	−0.393338	−0.0130750
$906$	0	0
$907$	−4.98568	−0.165547	−0.0827734	−	0.996568i	$-0.526378\pi$
$907$	−4.98568	−0.165547	−0.0827734	+	0.996568i	$0.526378\pi$
$908$	0	0
$909$	34.1818	1.13374
$910$	0	0
$911$	−19.0628	−0.631578	−0.315789	−	0.948829i	$-0.602269\pi$
$911$	−19.0628	−0.631578	−0.315789	+	0.948829i	$0.602269\pi$
$912$	0	0
$913$	−9.91837	−0.328250
$914$	0	0
$915$	0.237194	0.00784140
$916$	0	0
$917$	−57.8254	−1.90956
$918$	0	0
$919$	−56.9424	−1.87836	−0.939179	−	0.343429i	$-0.888411\pi$
$919$	−56.9424	−1.87836	−0.939179	+	0.343429i	$0.888411\pi$
$920$	0	0
$921$	0.678447	0.0223556
$922$	0	0
$923$	−38.2503	−1.25902
$924$	0	0
$925$	13.9075	0.457276
$926$	0	0
$927$	28.9842	0.951966
$928$	0	0
$929$	55.4431	1.81903	0.909515	−	0.415672i	$-0.136454\pi$
$929$	55.4431	1.81903	0.909515	+	0.415672i	$0.136454\pi$
$930$	0	0
$931$	−10.2596	−0.336245
$932$	0	0
$933$	2.22135	0.0727237
$934$	0	0
$935$	−0.285638	−0.00934136
$936$	0	0
$937$	−3.48816	−0.113953	−0.0569766	−	0.998376i	$-0.518146\pi$
$937$	−3.48816	−0.113953	−0.0569766	+	0.998376i	$0.518146\pi$
$938$	0	0
$939$	−6.18238	−0.201754
$940$	0	0
$941$	−14.0562	−0.458219	−0.229110	−	0.973401i	$-0.573581\pi$
$941$	−14.0562	−0.458219	−0.229110	+	0.973401i	$0.573581\pi$
$942$	0	0
$943$	49.9872	1.62781
$944$	0	0
$945$	0.912594	0.0296867
$946$	0	0
$947$	24.7278	0.803546	0.401773	−	0.915739i	$-0.368394\pi$
$947$	24.7278	0.803546	0.401773	+	0.915739i	$0.368394\pi$
$948$	0	0
$949$	14.9386	0.484927
$950$	0	0
$951$	−12.7896	−0.414730
$952$	0	0
$953$	24.0749	0.779862	0.389931	−	0.920844i	$-0.372499\pi$
$953$	24.0749	0.779862	0.389931	+	0.920844i	$0.372499\pi$
$954$	0	0
$955$	−1.98044	−0.0640856
$956$	0	0
$957$	−0.541084	−0.0174908
$958$	0	0
$959$	−28.9468	−0.934741
$960$	0	0
$961$	−29.1254	−0.939529
$962$	0	0
$963$	42.4216	1.36702
$964$	0	0
$965$	1.87793	0.0604528
$966$	0	0
$967$	37.3532	1.20120	0.600600	−	0.799550i	$-0.294929\pi$
$967$	37.3532	1.20120	0.600600	+	0.799550i	$0.294929\pi$
$968$	0	0
$969$	1.85859	0.0597064
$970$	0	0
$971$	−35.9694	−1.15431	−0.577156	−	0.816634i	$-0.695838\pi$
$971$	−35.9694	−1.15431	−0.577156	+	0.816634i	$0.695838\pi$
$972$	0	0
$973$	49.9395	1.60099
$974$	0	0
$975$	7.38064	0.236370
$976$	0	0
$977$	10.4855	0.335461	0.167730	−	0.985833i	$-0.446356\pi$
$977$	10.4855	0.335461	0.167730	+	0.985833i	$0.446356\pi$
$978$	0	0
$979$	−8.52289	−0.272393
$980$	0	0
$981$	−5.87732	−0.187648
$982$	0	0
$983$	54.3276	1.73278	0.866391	−	0.499366i	$-0.166434\pi$
$983$	54.3276	1.73278	0.866391	+	0.499366i	$0.166434\pi$
$984$	0	0
$985$	−1.69513	−0.0540113
$986$	0	0
$987$	−17.6052	−0.560380
$988$	0	0
$989$	25.7903	0.820085
$990$	0	0
$991$	11.6139	0.368928	0.184464	−	0.982839i	$-0.440945\pi$
$991$	11.6139	0.368928	0.184464	+	0.982839i	$0.440945\pi$
$992$	0	0
$993$	12.3918	0.393241
$994$	0	0
$995$	1.49757	0.0474763
$996$	0	0
$997$	19.7923	0.626829	0.313414	−	0.949616i	$-0.398527\pi$
$997$	19.7923	0.626829	0.313414	+	0.949616i	$0.398527\pi$
$998$	0	0
$999$	−6.80185	−0.215201

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4664.2.a.k.1.7	✓	11
4.3	odd	2		9328.2.a.bm.1.5		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4664.2.a.k.1.7	✓	11	1.1	even	1	trivial
9328.2.a.bm.1.5		11	4.3	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:	\( N \)	\(=\)	\( 4664 = 2^{3} \cdot 11 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4664.a (trivial)

\(f(q)\)	\(=\)	\(q-0.418978 q^{3} -0.101827 q^{5} -3.67256 q^{7} -2.82446 q^{9} +O(q^{10})\)	\(q-0.418978 q^{3} -0.101827 q^{5} -3.67256 q^{7} -2.82446 q^{9} +1.00000 q^{11} +3.53049 q^{13} +0.0426632 q^{15} +2.80513 q^{17} -1.58139 q^{19} +1.53872 q^{21} +6.11687 q^{23} -4.98963 q^{25} +2.44032 q^{27} +1.29144 q^{29} +1.36916 q^{31} -0.418978 q^{33} +0.373965 q^{35} -2.78728 q^{37} -1.47920 q^{39} +8.17202 q^{41} +4.21626 q^{43} +0.287606 q^{45} -11.4415 q^{47} +6.48773 q^{49} -1.17529 q^{51} +1.00000 q^{53} -0.101827 q^{55} +0.662566 q^{57} -7.70191 q^{59} +5.55970 q^{61} +10.3730 q^{63} -0.359498 q^{65} -3.90562 q^{67} -2.56283 q^{69} -10.8343 q^{71} +4.23131 q^{73} +2.09054 q^{75} -3.67256 q^{77} +12.9604 q^{79} +7.45094 q^{81} -9.91837 q^{83} -0.285638 q^{85} -0.541084 q^{87} -8.52289 q^{89} -12.9659 q^{91} -0.573649 q^{93} +0.161028 q^{95} +6.95768 q^{97} -2.82446 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 6 q^{3} + 3 q^{5} - 5 q^{7} + 7 q^{9}+O(q^{10}) \) 11 * q - 6 * q^3 + 3 * q^5 - 5 * q^7 + 7 * q^9	\( 11 q - 6 q^{3} + 3 q^{5} - 5 q^{7} + 7 q^{9} + 11 q^{11} - 13 q^{13} - 8 q^{15} - 7 q^{17} - 21 q^{19} + 6 q^{21} + 11 q^{23} + 4 q^{25} - 6 q^{27} - 5 q^{31} - 6 q^{33} - 25 q^{35} - 4 q^{37} - 19 q^{39} - 11 q^{41} + 16 q^{45} - 17 q^{47} - 2 q^{49} - 18 q^{51} + 11 q^{53} + 3 q^{55} - 5 q^{57} - 19 q^{59} - 2 q^{61} - 36 q^{63} - 13 q^{65} + 25 q^{67} + 3 q^{69} - 30 q^{71} + 5 q^{73} - 5 q^{75} - 5 q^{77} - 23 q^{79} - 9 q^{81} - 19 q^{83} + 2 q^{85} - 7 q^{87} + 6 q^{89} - 20 q^{91} + 43 q^{93} - 50 q^{95} - 35 q^{97} + 7 q^{99}+O(q^{100}) \) 11 * q - 6 * q^3 + 3 * q^5 - 5 * q^7 + 7 * q^9 + 11 * q^11 - 13 * q^13 - 8 * q^15 - 7 * q^17 - 21 * q^19 + 6 * q^21 + 11 * q^23 + 4 * q^25 - 6 * q^27 - 5 * q^31 - 6 * q^33 - 25 * q^35 - 4 * q^37 - 19 * q^39 - 11 * q^41 + 16 * q^45 - 17 * q^47 - 2 * q^49 - 18 * q^51 + 11 * q^53 + 3 * q^55 - 5 * q^57 - 19 * q^59 - 2 * q^61 - 36 * q^63 - 13 * q^65 + 25 * q^67 + 3 * q^69 - 30 * q^71 + 5 * q^73 - 5 * q^75 - 5 * q^77 - 23 * q^79 - 9 * q^81 - 19 * q^83 + 2 * q^85 - 7 * q^87 + 6 * q^89 - 20 * q^91 + 43 * q^93 - 50 * q^95 - 35 * q^97 + 7 * q^99

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