LMFDB - Embedded newform 5929.2.a.bv.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5929,2,Mod(1,5929)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5929, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("5929.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5929 = 7^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5929.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:	$47.3433033584$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 26x^{8} + 245x^{6} - 1038x^{4} + 1884x^{2} - 968 $ x^10 - 26x^8 + 245x^6 - 1038x^4 + 1884x^2 - 968
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 539)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$3.27614$ of defining polynomial
Character	$\chi$	$=$	5929.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.70296 q^{2} -3.27614 q^{3} +0.900071 q^{4} +0.246676 q^{5} +5.57913 q^{6} +1.87313 q^{8} +7.73309 q^{9} +O(q^{10})$	\(q-1.70296 q^{2} -3.27614 q^{3} +0.900071 q^{4} +0.246676 q^{5} +5.57913 q^{6} +1.87313 q^{8} +7.73309 q^{9} -0.420079 q^{10} -2.94876 q^{12} -3.17078 q^{13} -0.808144 q^{15} -4.99001 q^{16} -6.49256 q^{17} -13.1691 q^{18} -4.32335 q^{19} +0.222026 q^{20} +3.15700 q^{23} -6.13665 q^{24} -4.93915 q^{25} +5.39972 q^{26} -15.5063 q^{27} -6.48417 q^{29} +1.37624 q^{30} -1.78122 q^{31} +4.75152 q^{32} +11.0566 q^{34} +6.96033 q^{36} +8.38424 q^{37} +7.36248 q^{38} +10.3879 q^{39} +0.462057 q^{40} -0.553067 q^{41} -5.69023 q^{43} +1.90756 q^{45} -5.37624 q^{46} -10.2971 q^{47} +16.3480 q^{48} +8.41117 q^{50} +21.2705 q^{51} -2.85393 q^{52} -10.1744 q^{53} +26.4065 q^{54} +14.1639 q^{57} +11.0423 q^{58} +6.45660 q^{59} -0.727387 q^{60} -3.38149 q^{61} +3.03335 q^{62} +1.88838 q^{64} -0.782155 q^{65} -3.65484 q^{67} -5.84377 q^{68} -10.3428 q^{69} +0.345158 q^{71} +14.4851 q^{72} +2.97942 q^{73} -14.2780 q^{74} +16.1813 q^{75} -3.89132 q^{76} -17.6902 q^{78} +3.77595 q^{79} -1.23091 q^{80} +27.6014 q^{81} +0.941851 q^{82} -6.34157 q^{83} -1.60156 q^{85} +9.69023 q^{86} +21.2430 q^{87} +0.246676 q^{89} -3.24851 q^{90} +2.84152 q^{92} +5.83553 q^{93} +17.5356 q^{94} -1.06646 q^{95} -15.5667 q^{96} +4.81068 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} + 18 q^{4} + 6 q^{8} + 22 q^{9}+O(q^{10}) $ 10 * q - 2 * q^2 + 18 * q^4 + 6 * q^8 + 22 * q^9	$ 10 q - 2 q^{2} + 18 q^{4} + 6 q^{8} + 22 q^{9} + 8 q^{15} + 42 q^{16} - 6 q^{18} + 4 q^{23} + 18 q^{25} - 12 q^{29} + 4 q^{30} + 30 q^{32} - 2 q^{36} + 40 q^{37} + 16 q^{39} + 8 q^{43} - 44 q^{46} + 62 q^{50} + 16 q^{53} + 8 q^{57} - 28 q^{58} + 36 q^{60} + 106 q^{64} + 32 q^{65} - 4 q^{67} + 36 q^{71} + 90 q^{72} + 28 q^{74} - 112 q^{78} - 8 q^{79} - 6 q^{81} - 88 q^{85} + 32 q^{86} - 52 q^{92} + 44 q^{93} + 64 q^{95}+O(q^{100}) $ 10 * q - 2 * q^2 + 18 * q^4 + 6 * q^8 + 22 * q^9 + 8 * q^15 + 42 * q^16 - 6 * q^18 + 4 * q^23 + 18 * q^25 - 12 * q^29 + 4 * q^30 + 30 * q^32 - 2 * q^36 + 40 * q^37 + 16 * q^39 + 8 * q^43 - 44 * q^46 + 62 * q^50 + 16 * q^53 + 8 * q^57 - 28 * q^58 + 36 * q^60 + 106 * q^64 + 32 * q^65 - 4 * q^67 + 36 * q^71 + 90 * q^72 + 28 * q^74 - 112 * q^78 - 8 * q^79 - 6 * q^81 - 88 * q^85 + 32 * q^86 - 52 * q^92 + 44 * q^93 + 64 * q^95

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 $

$2$	−1.70296	−1.20417	−0.602087	−	0.798430i	$-0.705664\pi$
$2$	−1.70296	−1.20417	−0.602087	+	0.798430i	$0.705664\pi$
$3$	−3.27614	−1.89148	−0.945740	−	0.324924i	$-0.894661\pi$
$3$	−3.27614	−1.89148	−0.945740	+	0.324924i	$0.894661\pi$
$4$	0.900071	0.450036
$5$	0.246676	0.110317	0.0551584	−	0.998478i	$-0.482434\pi$
$5$	0.246676	0.110317	0.0551584	+	0.998478i	$0.482434\pi$
$6$	5.57913	2.27767
$7$	0	0
$7$	0	0
$8$	1.87313	0.662253
$9$	7.73309	2.57770
$10$	−0.420079	−0.132841
$11$	0	0
$11$	0	0
$12$	−2.94876	−0.851233
$13$	−3.17078	−0.879417	−0.439709	−	0.898140i	$-0.644918\pi$
$13$	−3.17078	−0.879417	−0.439709	+	0.898140i	$0.644918\pi$
$14$	0	0
$15$	−0.808144	−0.208662
$16$	−4.99001	−1.24750
$17$	−6.49256	−1.57468	−0.787339	−	0.616520i	$-0.788542\pi$
$17$	−6.49256	−1.57468	−0.787339	+	0.616520i	$0.788542\pi$
$18$	−13.1691	−3.10400
$19$	−4.32335	−0.991844	−0.495922	−	0.868367i	$-0.665170\pi$
$19$	−4.32335	−0.991844	−0.495922	+	0.868367i	$0.665170\pi$
$20$	0.222026	0.0496464
$21$	0	0
$22$	0	0
$23$	3.15700	0.658279	0.329140	−	0.944281i	$-0.393241\pi$
$23$	3.15700	0.658279	0.329140	+	0.944281i	$0.393241\pi$
$24$	−6.13665	−1.25264
$25$	−4.93915	−0.987830
$26$	5.39972	1.05897
$27$	−15.5063	−2.98418
$28$	0	0
$29$	−6.48417	−1.20408	−0.602040	−	0.798466i	$-0.705645\pi$
$29$	−6.48417	−1.20408	−0.602040	+	0.798466i	$0.705645\pi$
$30$	1.37624	0.251265
$31$	−1.78122	−0.319917	−0.159958	−	0.987124i	$-0.551136\pi$
$31$	−1.78122	−0.319917	−0.159958	+	0.987124i	$0.551136\pi$
$32$	4.75152	0.839959
$33$	0	0
$34$	11.0566	1.89619
$35$	0	0
$36$	6.96033	1.16006
$37$	8.38424	1.37836	0.689180	−	0.724590i	$-0.257971\pi$
$37$	8.38424	1.37836	0.689180	+	0.724590i	$0.257971\pi$
$38$	7.36248	1.19435
$39$	10.3879	1.66340
$40$	0.462057	0.0730576
$41$	−0.553067	−0.0863746	−0.0431873	−	0.999067i	$-0.513751\pi$
$41$	−0.553067	−0.0863746	−0.0431873	+	0.999067i	$0.513751\pi$
$42$	0	0
$43$	−5.69023	−0.867752	−0.433876	−	0.900973i	$-0.642854\pi$
$43$	−5.69023	−0.867752	−0.433876	+	0.900973i	$0.642854\pi$
$44$	0	0
$45$	1.90756	0.284363
$46$	−5.37624	−0.792683
$47$	−10.2971	−1.50199	−0.750995	−	0.660308i	$-0.770426\pi$
$47$	−10.2971	−1.50199	−0.750995	+	0.660308i	$0.770426\pi$
$48$	16.3480	2.35963
$49$	0	0
$50$	8.41117	1.18952
$51$	21.2705	2.97847
$52$	−2.85393	−0.395769
$53$	−10.1744	−1.39756	−0.698780	−	0.715336i	$-0.746273\pi$
$53$	−10.1744	−1.39756	−0.698780	+	0.715336i	$0.746273\pi$
$54$	26.4065	3.59347
$55$	0	0
$56$	0	0
$57$	14.1639	1.87605
$58$	11.0423	1.44992
$59$	6.45660	0.840577	0.420289	−	0.907390i	$-0.361929\pi$
$59$	6.45660	0.840577	0.420289	+	0.907390i	$0.361929\pi$
$60$	−0.727387	−0.0939053
$61$	−3.38149	−0.432956	−0.216478	−	0.976287i	$-0.569457\pi$
$61$	−3.38149	−0.432956	−0.216478	+	0.976287i	$0.569457\pi$
$62$	3.03335	0.385235
$63$	0	0
$64$	1.88838	0.236047
$65$	−0.782155	−0.0970144
$66$	0	0
$67$	−3.65484	−0.446510	−0.223255	−	0.974760i	$-0.571668\pi$
$67$	−3.65484	−0.446510	−0.223255	+	0.974760i	$0.571668\pi$
$68$	−5.84377	−0.708661
$69$	−10.3428	−1.24512
$70$	0	0
$71$	0.345158	0.0409627	0.0204813	−	0.999790i	$-0.493480\pi$
$71$	0.345158	0.0409627	0.0204813	+	0.999790i	$0.493480\pi$
$72$	14.4851	1.70709
$73$	2.97942	0.348715	0.174357	−	0.984682i	$-0.444215\pi$
$73$	2.97942	0.348715	0.174357	+	0.984682i	$0.444215\pi$
$74$	−14.2780	−1.65979
$75$	16.1813	1.86846
$76$	−3.89132	−0.446365
$77$	0	0
$78$	−17.6902	−2.00302
$79$	3.77595	0.424828	0.212414	−	0.977180i	$-0.431868\pi$
$79$	3.77595	0.424828	0.212414	+	0.977180i	$0.431868\pi$
$80$	−1.23091	−0.137620
$81$	27.6014	3.06682
$82$	0.941851	0.104010
$83$	−6.34157	−0.696078	−0.348039	−	0.937480i	$-0.613152\pi$
$83$	−6.34157	−0.696078	−0.348039	+	0.937480i	$0.613152\pi$
$84$	0	0
$85$	−1.60156	−0.173713
$86$	9.69023	1.04492
$87$	21.2430	2.27749
$88$	0	0
$89$	0.246676	0.0261476	0.0130738	−	0.999915i	$-0.495838\pi$
$89$	0.246676	0.0261476	0.0130738	+	0.999915i	$0.495838\pi$
$90$	−3.24851	−0.342423
$91$	0	0
$92$	2.84152	0.296249
$93$	5.83553	0.605116
$94$	17.5356	1.80866
$95$	−1.06646	−0.109417
$96$	−15.5667	−1.58877
$97$	4.81068	0.488451	0.244226	−	0.969718i	$-0.421466\pi$
$97$	4.81068	0.488451	0.244226	+	0.969718i	$0.421466\pi$
$98$	0	0
$99$	0	0
$100$	−4.44559	−0.444559
$101$	−6.86468	−0.683061	−0.341531	−	0.939871i	$-0.610945\pi$
$101$	−6.86468	−0.683061	−0.341531	+	0.939871i	$0.610945\pi$
$102$	−36.2229	−3.58660
$103$	−5.07835	−0.500385	−0.250192	−	0.968196i	$-0.580494\pi$
$103$	−5.07835	−0.500385	−0.250192	+	0.968196i	$0.580494\pi$
$104$	−5.93930	−0.582397
$105$	0	0
$106$	17.3266	1.68291
$107$	−0.897562	−0.0867706	−0.0433853	−	0.999058i	$-0.513814\pi$
$107$	−0.897562	−0.0867706	−0.0433853	+	0.999058i	$0.513814\pi$
$108$	−13.9567	−1.34299
$109$	−5.71569	−0.547464	−0.273732	−	0.961806i	$-0.588258\pi$
$109$	−5.71569	−0.547464	−0.273732	+	0.961806i	$0.588258\pi$
$110$	0	0
$111$	−27.4679	−2.60714
$112$	0	0
$113$	−5.99001	−0.563493	−0.281747	−	0.959489i	$-0.590914\pi$
$113$	−5.99001	−0.563493	−0.281747	+	0.959489i	$0.590914\pi$
$114$	−24.1205	−2.25909
$115$	0.778754	0.0726192
$116$	−5.83621	−0.541879
$117$	−24.5200	−2.26687
$118$	−10.9953	−1.01220
$119$	0	0
$120$	−1.51376	−0.138187
$121$	0	0
$122$	5.75855	0.521354
$123$	1.81193	0.163376
$124$	−1.60323	−0.143974
$125$	−2.45175	−0.219291
$126$	0	0
$127$	−2.31399	−0.205334	−0.102667	−	0.994716i	$-0.532738\pi$
$127$	−2.31399	−0.205334	−0.102667	+	0.994716i	$0.532738\pi$
$128$	−12.7189	−1.12420
$129$	18.6420	1.64133
$130$	1.33198	0.116822
$131$	14.4800	1.26513	0.632564	−	0.774508i	$-0.282003\pi$
$131$	14.4800	1.26513	0.632564	+	0.774508i	$0.282003\pi$
$132$	0	0
$133$	0	0
$134$	6.22405	0.537676
$135$	−3.82502	−0.329205
$136$	−12.1614	−1.04284
$137$	−10.9962	−0.939470	−0.469735	−	0.882807i	$-0.655651\pi$
$137$	−10.9962	−0.939470	−0.469735	+	0.882807i	$0.655651\pi$
$138$	17.6133	1.49934
$139$	1.05087	0.0891334	0.0445667	−	0.999006i	$-0.485809\pi$
$139$	1.05087	0.0891334	0.0445667	+	0.999006i	$0.485809\pi$
$140$	0	0
$141$	33.7348	2.84098
$142$	−0.587790	−0.0493262
$143$	0	0
$144$	−38.5882	−3.21569
$145$	−1.59949	−0.132830
$146$	−5.07383	−0.419913
$147$	0	0
$148$	7.54641	0.620311
$149$	−18.4185	−1.50890	−0.754452	−	0.656356i	$-0.772097\pi$
$149$	−18.4185	−1.50890	−0.754452	+	0.656356i	$0.772097\pi$
$150$	−27.5562	−2.24995
$151$	−19.1564	−1.55893	−0.779463	−	0.626448i	$-0.784508\pi$
$151$	−19.1564	−1.55893	−0.779463	+	0.626448i	$0.784508\pi$
$152$	−8.09821	−0.656851
$153$	−50.2076	−4.05904
$154$	0	0
$155$	−0.439384	−0.0352922
$156$	9.34988	0.748589
$157$	−23.0214	−1.83731	−0.918653	−	0.395065i	$-0.870722\pi$
$157$	−23.0214	−1.83731	−0.918653	+	0.395065i	$0.870722\pi$
$158$	−6.43029	−0.511567
$159$	33.3327	2.64346
$160$	1.17209	0.0926615
$161$	0	0
$162$	−47.0041	−3.69299
$163$	−4.93865	−0.386825	−0.193412	−	0.981118i	$-0.561956\pi$
$163$	−4.93865	−0.386825	−0.193412	+	0.981118i	$0.561956\pi$
$164$	−0.497800	−0.0388716
$165$	0	0
$166$	10.7994	0.838199
$167$	7.39244	0.572044	0.286022	−	0.958223i	$-0.407667\pi$
$167$	7.39244	0.572044	0.286022	+	0.958223i	$0.407667\pi$
$168$	0	0
$169$	−2.94613	−0.226625
$170$	2.72739	0.209181
$171$	−33.4328	−2.55667
$172$	−5.12161	−0.390519
$173$	−18.2383	−1.38663	−0.693316	−	0.720634i	$-0.743851\pi$
$173$	−18.2383	−1.38663	−0.693316	+	0.720634i	$0.743851\pi$
$174$	−36.1760	−2.74250
$175$	0	0
$176$	0	0
$177$	−21.1527	−1.58994
$178$	−0.420079	−0.0314862
$179$	−2.37373	−0.177421	−0.0887103	−	0.996057i	$-0.528275\pi$
$179$	−2.37373	−0.177421	−0.0887103	+	0.996057i	$0.528275\pi$
$180$	1.71694	0.127973
$181$	21.6459	1.60893	0.804463	−	0.594002i	$-0.202453\pi$
$181$	21.6459	1.60893	0.804463	+	0.594002i	$0.202453\pi$
$182$	0	0
$183$	11.0782	0.818928
$184$	5.91348	0.435947
$185$	2.06819	0.152056
$186$	−9.93767	−0.728665
$187$	0	0
$188$	−9.26814	−0.675949
$189$	0	0
$190$	1.81615	0.131757
$191$	7.22154	0.522532	0.261266	−	0.965267i	$-0.415860\pi$
$191$	7.22154	0.522532	0.261266	+	0.965267i	$0.415860\pi$
$192$	−6.18658	−0.446478
$193$	3.66604	0.263887	0.131944	−	0.991257i	$-0.457878\pi$
$193$	3.66604	0.263887	0.131944	+	0.991257i	$0.457878\pi$
$194$	−8.19240	−0.588180
$195$	2.56245	0.183501
$196$	0	0
$197$	3.81615	0.271889	0.135945	−	0.990716i	$-0.456593\pi$
$197$	3.81615	0.271889	0.135945	+	0.990716i	$0.456593\pi$
$198$	0	0
$199$	19.3819	1.37395	0.686973	−	0.726683i	$-0.258939\pi$
$199$	19.3819	1.37395	0.686973	+	0.726683i	$0.258939\pi$
$200$	−9.25169	−0.654193
$201$	11.9738	0.844565
$202$	11.6903	0.822525
$203$	0	0
$204$	19.1450	1.34042
$205$	−0.136428	−0.00952856
$206$	8.64822	0.602550
$207$	24.4133	1.69684
$208$	15.8223	1.09708
$209$	0	0
$210$	0	0
$211$	−24.1279	−1.66103	−0.830517	−	0.556993i	$-0.811955\pi$
$211$	−24.1279	−1.66103	−0.830517	+	0.556993i	$0.811955\pi$
$212$	−9.15768	−0.628952
$213$	−1.13078	−0.0774801
$214$	1.52851	0.104487
$215$	−1.40364	−0.0957275
$216$	−29.0453	−1.97628
$217$	0	0
$218$	9.73359	0.659242
$219$	−9.76100	−0.659587
$220$	0	0
$221$	20.5865	1.38480
$222$	46.7768	3.13945
$223$	−14.6952	−0.984061	−0.492030	−	0.870578i	$-0.663745\pi$
$223$	−14.6952	−0.984061	−0.492030	+	0.870578i	$0.663745\pi$
$224$	0	0
$225$	−38.1949	−2.54633
$226$	10.2008	0.678544
$227$	9.19531	0.610314	0.305157	−	0.952302i	$-0.401291\pi$
$227$	9.19531	0.610314	0.305157	+	0.952302i	$0.401291\pi$
$228$	12.7485	0.844290
$229$	−17.4339	−1.15207	−0.576033	−	0.817427i	$-0.695400\pi$
$229$	−17.4339	−1.15207	−0.576033	+	0.817427i	$0.695400\pi$
$230$	−1.32619	−0.0874461
$231$	0	0
$232$	−12.1457	−0.797405
$233$	27.7505	1.81799	0.908997	−	0.416802i	$-0.136849\pi$
$233$	27.7505	1.81799	0.908997	+	0.416802i	$0.136849\pi$
$234$	41.7565	2.72971
$235$	−2.54005	−0.165695
$236$	5.81140	0.378290
$237$	−12.3705	−0.803553
$238$	0	0
$239$	22.5326	1.45752	0.728758	−	0.684772i	$-0.240098\pi$
$239$	22.5326	1.45752	0.728758	+	0.684772i	$0.240098\pi$
$240$	4.03265	0.260306
$241$	−7.22658	−0.465505	−0.232752	−	0.972536i	$-0.574773\pi$
$241$	−7.22658	−0.465505	−0.232752	+	0.972536i	$0.574773\pi$
$242$	0	0
$243$	−43.9073	−2.81665
$244$	−3.04359	−0.194846
$245$	0	0
$246$	−3.08564	−0.196733
$247$	13.7084	0.872244
$248$	−3.33647	−0.211866
$249$	20.7759	1.31662
$250$	4.17523	0.264064
$251$	−12.8842	−0.813245	−0.406622	−	0.913596i	$-0.633294\pi$
$251$	−12.8842	−0.813245	−0.406622	+	0.913596i	$0.633294\pi$
$252$	0	0
$253$	0	0
$254$	3.94063	0.247257
$255$	5.24692	0.328575
$256$	17.8830	1.11769
$257$	−31.0932	−1.93954	−0.969771	−	0.244016i	$-0.921535\pi$
$257$	−31.0932	−1.93954	−0.969771	+	0.244016i	$0.921535\pi$
$258$	−31.7465	−1.97645
$259$	0	0
$260$	−0.703995	−0.0436599
$261$	−50.1426	−3.10375
$262$	−24.6589	−1.52343
$263$	7.50215	0.462603	0.231301	−	0.972882i	$-0.425702\pi$
$263$	7.50215	0.462603	0.231301	+	0.972882i	$0.425702\pi$
$264$	0	0
$265$	−2.50978	−0.154174
$266$	0	0
$267$	−0.808144	−0.0494576
$268$	−3.28962	−0.200945
$269$	1.93752	0.118133	0.0590663	−	0.998254i	$-0.481188\pi$
$269$	1.93752	0.118133	0.0590663	+	0.998254i	$0.481188\pi$
$270$	6.51385	0.396420
$271$	22.9786	1.39585	0.697926	−	0.716170i	$-0.254107\pi$
$271$	22.9786	1.39585	0.697926	+	0.716170i	$0.254107\pi$
$272$	32.3980	1.96442
$273$	0	0
$274$	18.7261	1.13129
$275$	0	0
$276$	−9.30922	−0.560349
$277$	5.52095	0.331722	0.165861	−	0.986149i	$-0.446960\pi$
$277$	5.52095	0.331722	0.165861	+	0.986149i	$0.446960\pi$
$278$	−1.78958	−0.107332
$279$	−13.7743	−0.824648
$280$	0	0
$281$	7.28000	0.434288	0.217144	−	0.976140i	$-0.430326\pi$
$281$	7.28000	0.434288	0.217144	+	0.976140i	$0.430326\pi$
$282$	−57.4490	−3.42104
$283$	−13.2600	−0.788225	−0.394113	−	0.919062i	$-0.628948\pi$
$283$	−13.2600	−0.788225	−0.394113	+	0.919062i	$0.628948\pi$
$284$	0.310666	0.0184347
$285$	3.49389	0.206960
$286$	0	0
$287$	0	0
$288$	36.7440	2.16516
$289$	25.1534	1.47961
$290$	2.72386	0.159951
$291$	−15.7605	−0.923895
$292$	2.68169	0.156934
$293$	−5.56718	−0.325238	−0.162619	−	0.986689i	$-0.551994\pi$
$293$	−5.56718	−0.325238	−0.162619	+	0.986689i	$0.551994\pi$
$294$	0	0
$295$	1.59269	0.0927297
$296$	15.7048	0.912823
$297$	0	0
$298$	31.3660	1.81698
$299$	−10.0102	−0.578902
$300$	14.5644	0.840874
$301$	0	0
$302$	32.6226	1.87722
$303$	22.4897	1.29200
$304$	21.5736	1.23733
$305$	−0.834132	−0.0477623
$306$	85.5015	4.88779
$307$	−14.2467	−0.813102	−0.406551	−	0.913628i	$-0.633269\pi$
$307$	−14.2467	−0.813102	−0.406551	+	0.913628i	$0.633269\pi$
$308$	0	0
$309$	16.6374	0.946468
$310$	0.748253	0.0424979
$311$	3.56834	0.202342	0.101171	−	0.994869i	$-0.467741\pi$
$311$	3.56834	0.202342	0.101171	+	0.994869i	$0.467741\pi$
$312$	19.4580	1.10159
$313$	−9.11394	−0.515150	−0.257575	−	0.966258i	$-0.582924\pi$
$313$	−9.11394	−0.515150	−0.257575	+	0.966258i	$0.582924\pi$
$314$	39.2045	2.21244
$315$	0	0
$316$	3.39863	0.191188
$317$	−11.7542	−0.660181	−0.330090	−	0.943949i	$-0.607079\pi$
$317$	−11.7542	−0.660181	−0.330090	+	0.943949i	$0.607079\pi$
$318$	−56.7643	−3.18318
$319$	0	0
$320$	0.465816	0.0260399
$321$	2.94054	0.164125
$322$	0	0
$323$	28.0696	1.56183
$324$	24.8432	1.38018
$325$	15.6610	0.868715
$326$	8.41032	0.465805
$327$	18.7254	1.03552
$328$	−1.03597	−0.0572018
$329$	0	0
$330$	0	0
$331$	−25.6748	−1.41122	−0.705609	−	0.708602i	$-0.749326\pi$
$331$	−25.6748	−1.41122	−0.705609	+	0.708602i	$0.749326\pi$
$332$	−5.70786	−0.313260
$333$	64.8361	3.55299
$334$	−12.5890	−0.688841
$335$	−0.901561	−0.0492575
$336$	0	0
$337$	−33.5644	−1.82837	−0.914185	−	0.405298i	$-0.867168\pi$
$337$	−33.5644	−1.82837	−0.914185	+	0.405298i	$0.867168\pi$
$338$	5.01713	0.272896
$339$	19.6241	1.06584
$340$	−1.44152	−0.0781772
$341$	0	0
$342$	56.9347	3.07868
$343$	0	0
$344$	−10.6586	−0.574671
$345$	−2.55131	−0.137358
$346$	31.0591	1.66975
$347$	26.7567	1.43637	0.718187	−	0.695850i	$-0.244972\pi$
$347$	26.7567	1.43637	0.718187	+	0.695850i	$0.244972\pi$
$348$	19.1202	1.02495
$349$	19.9411	1.06742	0.533711	−	0.845667i	$-0.320797\pi$
$349$	19.9411	1.06742	0.533711	+	0.845667i	$0.320797\pi$
$350$	0	0
$351$	49.1670	2.62434
$352$	0	0
$353$	−10.0436	−0.534566	−0.267283	−	0.963618i	$-0.586126\pi$
$353$	−10.0436	−0.534566	−0.267283	+	0.963618i	$0.586126\pi$
$354$	36.0222	1.91456
$355$	0.0851420	0.00451887
$356$	0.222026	0.0117673
$357$	0	0
$358$	4.04236	0.213645
$359$	17.0519	0.899964	0.449982	−	0.893038i	$-0.351430\pi$
$359$	17.0519	0.899964	0.449982	+	0.893038i	$0.351430\pi$
$360$	3.57313	0.188320
$361$	−0.308682	−0.0162464
$362$	−36.8621	−1.93743
$363$	0	0
$364$	0	0
$365$	0.734951	0.0384691
$366$	−18.8658	−0.986132
$367$	0.115028	0.00600443	0.00300221	−	0.999995i	$-0.499044\pi$
$367$	0.115028	0.00600443	0.00300221	+	0.999995i	$0.499044\pi$
$368$	−15.7535	−0.821206
$369$	−4.27692	−0.222648
$370$	−3.52204	−0.183102
$371$	0	0
$372$	5.25239	0.272324
$373$	17.5106	0.906664	0.453332	−	0.891342i	$-0.350235\pi$
$373$	17.5106	0.906664	0.453332	+	0.891342i	$0.350235\pi$
$374$	0	0
$375$	8.03226	0.414784
$376$	−19.2879	−0.994697
$377$	20.5599	1.05889
$378$	0	0
$379$	7.72561	0.396838	0.198419	−	0.980117i	$-0.436419\pi$
$379$	7.72561	0.396838	0.198419	+	0.980117i	$0.436419\pi$
$380$	−0.959894	−0.0492415
$381$	7.58096	0.388384
$382$	−12.2980	−0.629220
$383$	10.6044	0.541860	0.270930	−	0.962599i	$-0.412669\pi$
$383$	10.6044	0.541860	0.270930	+	0.962599i	$0.412669\pi$
$384$	41.6688	2.12640
$385$	0	0
$386$	−6.24311	−0.317766
$387$	−44.0030	−2.23680
$388$	4.32996	0.219820
$389$	−22.2172	−1.12646	−0.563228	−	0.826302i	$-0.690441\pi$
$389$	−22.2172	−1.12646	−0.563228	+	0.826302i	$0.690441\pi$
$390$	−4.36375	−0.220967
$391$	−20.4970	−1.03658
$392$	0	0
$393$	−47.4386	−2.39296
$394$	−6.49874	−0.327402
$395$	0.931435	0.0468656
$396$	0	0
$397$	−19.8781	−0.997654	−0.498827	−	0.866702i	$-0.666236\pi$
$397$	−19.8781	−0.997654	−0.498827	+	0.866702i	$0.666236\pi$
$398$	−33.0066	−1.65447
$399$	0	0
$400$	24.6464	1.23232
$401$	−24.7759	−1.23725	−0.618624	−	0.785687i	$-0.712309\pi$
$401$	−24.7759	−1.23725	−0.618624	+	0.785687i	$0.712309\pi$
$402$	−20.3909	−1.01700
$403$	5.64787	0.281340
$404$	−6.17870	−0.307402
$405$	6.80859	0.338322
$406$	0	0
$407$	0	0
$408$	39.8426	1.97250
$409$	−21.7215	−1.07406	−0.537029	−	0.843564i	$-0.680454\pi$
$409$	−21.7215	−1.07406	−0.537029	+	0.843564i	$0.680454\pi$
$410$	0.232332	0.0114740
$411$	36.0251	1.77699
$412$	−4.57088	−0.225191
$413$	0	0
$414$	−41.5749	−2.04330
$415$	−1.56431	−0.0767890
$416$	−15.0661	−0.738674
$417$	−3.44279	−0.168594
$418$	0	0
$419$	25.6815	1.25462	0.627311	−	0.778769i	$-0.284155\pi$
$419$	25.6815	1.25462	0.627311	+	0.778769i	$0.284155\pi$
$420$	0	0
$421$	28.7580	1.40158	0.700789	−	0.713369i	$-0.252832\pi$
$421$	28.7580	1.40158	0.700789	+	0.713369i	$0.252832\pi$
$422$	41.0889	2.00017
$423$	−79.6285	−3.87167
$424$	−19.0580	−0.925539
$425$	32.0677	1.55551
$426$	1.92568	0.0932995
$427$	0	0
$428$	−0.807869	−0.0390498
$429$	0	0
$430$	2.39034	0.115273
$431$	9.84034	0.473992	0.236996	−	0.971511i	$-0.423837\pi$
$431$	9.84034	0.473992	0.236996	+	0.971511i	$0.423837\pi$
$432$	77.3765	3.72278
$433$	0.424750	0.0204122	0.0102061	−	0.999948i	$-0.496751\pi$
$433$	0.424750	0.0204122	0.0102061	+	0.999948i	$0.496751\pi$
$434$	0	0
$435$	5.24014	0.251245
$436$	−5.14453	−0.246378
$437$	−13.6488	−0.652910
$438$	16.6226	0.794258
$439$	−3.98983	−0.190424	−0.0952121	−	0.995457i	$-0.530353\pi$
$439$	−3.98983	−0.190424	−0.0952121	+	0.995457i	$0.530353\pi$
$440$	0	0
$441$	0	0
$442$	−35.0580	−1.66754
$443$	−19.9380	−0.947285	−0.473642	−	0.880717i	$-0.657061\pi$
$443$	−19.9380	−0.947285	−0.473642	+	0.880717i	$0.657061\pi$
$444$	−24.7231	−1.17331
$445$	0.0608489	0.00288451
$446$	25.0253	1.18498
$447$	60.3416	2.85406
$448$	0	0
$449$	9.97100	0.470561	0.235280	−	0.971928i	$-0.424399\pi$
$449$	9.97100	0.470561	0.235280	+	0.971928i	$0.424399\pi$
$450$	65.0444	3.06622
$451$	0	0
$452$	−5.39144	−0.253592
$453$	62.7591	2.94868
$454$	−15.6592	−0.734925
$455$	0	0
$456$	26.5309	1.24242
$457$	−34.9248	−1.63371	−0.816856	−	0.576841i	$-0.804285\pi$
$457$	−34.9248	−1.63371	−0.816856	+	0.576841i	$0.804285\pi$
$458$	29.6893	1.38729
$459$	100.675	4.69912
$460$	0.700934	0.0326812
$461$	26.8042	1.24839	0.624197	−	0.781267i	$-0.285426\pi$
$461$	26.8042	1.24839	0.624197	+	0.781267i	$0.285426\pi$
$462$	0	0
$463$	−28.1253	−1.30709	−0.653547	−	0.756886i	$-0.726720\pi$
$463$	−28.1253	−1.30709	−0.653547	+	0.756886i	$0.726720\pi$
$464$	32.3561	1.50209
$465$	1.43948	0.0667544
$466$	−47.2580	−2.18918
$467$	27.7857	1.28577	0.642884	−	0.765964i	$-0.277738\pi$
$467$	27.7857	1.28577	0.642884	+	0.765964i	$0.277738\pi$
$468$	−22.0697	−1.02017
$469$	0	0
$470$	4.32560	0.199525
$471$	75.4213	3.47523
$472$	12.0941	0.556675
$473$	0	0
$474$	21.0665	0.967618
$475$	21.3537	0.979773
$476$	0	0
$477$	−78.6795	−3.60249
$478$	−38.3722	−1.75510
$479$	−9.27456	−0.423766	−0.211883	−	0.977295i	$-0.567960\pi$
$479$	−9.27456	−0.423766	−0.211883	+	0.977295i	$0.567960\pi$
$480$	−3.83991	−0.175267
$481$	−26.5846	−1.21215
$482$	12.3066	0.560549
$483$	0	0
$484$	0	0
$485$	1.18668	0.0538843
$486$	74.7723	3.39174
$487$	10.6356	0.481944	0.240972	−	0.970532i	$-0.422534\pi$
$487$	10.6356	0.481944	0.240972	+	0.970532i	$0.422534\pi$
$488$	−6.33399	−0.286726
$489$	16.1797	0.731672
$490$	0	0
$491$	19.9832	0.901829	0.450915	−	0.892567i	$-0.351098\pi$
$491$	19.9832	0.901829	0.450915	+	0.892567i	$0.351098\pi$
$492$	1.63086	0.0735249
$493$	42.0989	1.89604
$494$	−23.3448	−1.05033
$495$	0	0
$496$	8.88832	0.399097
$497$	0	0
$498$	−35.3805	−1.58544
$499$	−10.9536	−0.490351	−0.245175	−	0.969479i	$-0.578846\pi$
$499$	−10.9536	−0.490351	−0.245175	+	0.969479i	$0.578846\pi$
$500$	−2.20675	−0.0986887
$501$	−24.2187	−1.08201
$502$	21.9413	0.979288
$503$	−25.5069	−1.13729	−0.568647	−	0.822582i	$-0.692533\pi$
$503$	−25.5069	−1.13729	−0.568647	+	0.822582i	$0.692533\pi$
$504$	0	0
$505$	−1.69335	−0.0753531
$506$	0	0
$507$	9.65192	0.428657
$508$	−2.08276	−0.0924074
$509$	−5.16877	−0.229102	−0.114551	−	0.993417i	$-0.536543\pi$
$509$	−5.16877	−0.229102	−0.114551	+	0.993417i	$0.536543\pi$
$510$	−8.93530	−0.395662
$511$	0	0
$512$	−5.01624	−0.221689
$513$	67.0389	2.95984
$514$	52.9505	2.33555
$515$	−1.25271	−0.0552008
$516$	16.7791	0.738659
$517$	0	0
$518$	0	0
$519$	59.7512	2.62279
$520$	−1.46508	−0.0642481
$521$	−15.4837	−0.678352	−0.339176	−	0.940723i	$-0.610148\pi$
$521$	−15.4837	−0.678352	−0.339176	+	0.940723i	$0.610148\pi$
$522$	85.3909	3.73746
$523$	−10.2761	−0.449344	−0.224672	−	0.974434i	$-0.572131\pi$
$523$	−10.2761	−0.449344	−0.224672	+	0.974434i	$0.572131\pi$
$524$	13.0331	0.569352
$525$	0	0
$526$	−12.7759	−0.557054
$527$	11.5647	0.503766
$528$	0	0
$529$	−13.0334	−0.566669
$530$	4.27405	0.185653
$531$	49.9294	2.16675
$532$	0	0
$533$	1.75366	0.0759593
$534$	1.37624	0.0595556
$535$	−0.221407	−0.00957224
$536$	−6.84601	−0.295703
$537$	7.77666	0.335588
$538$	−3.29952	−0.142252
$539$	0	0
$540$	−3.44279	−0.148154
$541$	−32.5212	−1.39820	−0.699099	−	0.715025i	$-0.746415\pi$
$541$	−32.5212	−1.39820	−0.699099	+	0.715025i	$0.746415\pi$
$542$	−39.1317	−1.68085
$543$	−70.9150	−3.04325
$544$	−30.8496	−1.32266
$545$	−1.40992	−0.0603944
$546$	0	0
$547$	32.7759	1.40139	0.700697	−	0.713459i	$-0.252872\pi$
$547$	32.7759	1.40139	0.700697	+	0.713459i	$0.252872\pi$
$548$	−9.89738	−0.422795
$549$	−26.1494	−1.11603
$550$	0	0
$551$	28.0333	1.19426
$552$	−19.3734	−0.824586
$553$	0	0
$554$	−9.40195	−0.399451
$555$	−6.77567	−0.287611
$556$	0.945855	0.0401132
$557$	14.3574	0.608341	0.304170	−	0.952618i	$-0.401621\pi$
$557$	14.3574	0.608341	0.304170	+	0.952618i	$0.401621\pi$
$558$	23.4571	0.993020
$559$	18.0425	0.763116
$560$	0	0
$561$	0	0
$562$	−12.3975	−0.522959
$563$	−13.3422	−0.562305	−0.281152	−	0.959663i	$-0.590717\pi$
$563$	−13.3422	−0.562305	−0.281152	+	0.959663i	$0.590717\pi$
$564$	30.3637	1.27854
$565$	−1.47759	−0.0621627
$566$	22.5812	0.949160
$567$	0	0
$568$	0.646527	0.0271277
$569$	18.6491	0.781809	0.390904	−	0.920431i	$-0.372162\pi$
$569$	18.6491	0.781809	0.390904	+	0.920431i	$0.372162\pi$
$570$	−5.94994	−0.249216
$571$	−32.0508	−1.34128	−0.670642	−	0.741781i	$-0.733981\pi$
$571$	−32.0508	−1.34128	−0.670642	+	0.741781i	$0.733981\pi$
$572$	0	0
$573$	−23.6588	−0.988359
$574$	0	0
$575$	−15.5929	−0.650268
$576$	14.6030	0.608457
$577$	16.4352	0.684206	0.342103	−	0.939662i	$-0.388861\pi$
$577$	16.4352	0.684206	0.342103	+	0.939662i	$0.388861\pi$
$578$	−42.8352	−1.78171
$579$	−12.0104	−0.499137
$580$	−1.43965	−0.0597783
$581$	0	0
$582$	26.8394	1.11253
$583$	0	0
$584$	5.58086	0.230937
$585$	−6.04848	−0.250074
$586$	9.48069	0.391644
$587$	−11.8148	−0.487647	−0.243824	−	0.969820i	$-0.578402\pi$
$587$	−11.8148	−0.487647	−0.243824	+	0.969820i	$0.578402\pi$
$588$	0	0
$589$	7.70083	0.317307
$590$	−2.71228	−0.111663
$591$	−12.5022	−0.514273
$592$	−41.8375	−1.71951
$593$	−20.7452	−0.851905	−0.425952	−	0.904746i	$-0.640061\pi$
$593$	−20.7452	−0.851905	−0.425952	+	0.904746i	$0.640061\pi$
$594$	0	0
$595$	0	0
$596$	−16.5780	−0.679060
$597$	−63.4978	−2.59879
$598$	17.0469	0.697099
$599$	8.71038	0.355897	0.177948	−	0.984040i	$-0.443054\pi$
$599$	8.71038	0.355897	0.177948	+	0.984040i	$0.443054\pi$
$600$	30.3098	1.23739
$601$	46.2310	1.88580	0.942902	−	0.333072i	$-0.108085\pi$
$601$	46.2310	1.88580	0.942902	+	0.333072i	$0.108085\pi$
$602$	0	0
$603$	−28.2632	−1.15097
$604$	−17.2421	−0.701572
$605$	0	0
$606$	−38.2990	−1.55579
$607$	−30.1304	−1.22295	−0.611477	−	0.791262i	$-0.709424\pi$
$607$	−30.1304	−1.22295	−0.611477	+	0.791262i	$0.709424\pi$
$608$	−20.5425	−0.833108
$609$	0	0
$610$	1.42049	0.0575141
$611$	32.6499	1.32088
$612$	−45.1904	−1.82671
$613$	−41.7643	−1.68684	−0.843421	−	0.537253i	$-0.819462\pi$
$613$	−41.7643	−1.68684	−0.843421	+	0.537253i	$0.819462\pi$
$614$	24.2616	0.979117
$615$	0.446958	0.0180231
$616$	0	0
$617$	8.94182	0.359984	0.179992	−	0.983668i	$-0.442393\pi$
$617$	8.94182	0.359984	0.179992	+	0.983668i	$0.442393\pi$
$618$	−28.3328	−1.13971
$619$	30.9126	1.24248	0.621241	−	0.783620i	$-0.286629\pi$
$619$	30.9126	1.24248	0.621241	+	0.783620i	$0.286629\pi$
$620$	−0.395477	−0.0158827
$621$	−48.9532	−1.96442
$622$	−6.07674	−0.243655
$623$	0	0
$624$	−51.8359	−2.07510
$625$	24.0910	0.963639
$626$	15.5207	0.620331
$627$	0	0
$628$	−20.7209	−0.826853
$629$	−54.4352	−2.17047
$630$	0	0
$631$	30.5300	1.21538	0.607691	−	0.794174i	$-0.292096\pi$
$631$	30.5300	1.21538	0.607691	+	0.794174i	$0.292096\pi$
$632$	7.07286	0.281343
$633$	79.0464	3.14181
$634$	20.0169	0.794973
$635$	−0.570805	−0.0226517
$636$	30.0018	1.18965
$637$	0	0
$638$	0	0
$639$	2.66914	0.105589
$640$	−3.13744	−0.124018
$641$	−10.4287	−0.411907	−0.205953	−	0.978562i	$-0.566030\pi$
$641$	−10.4287	−0.411907	−0.205953	+	0.978562i	$0.566030\pi$
$642$	−5.00762	−0.197635
$643$	16.4973	0.650590	0.325295	−	0.945613i	$-0.394536\pi$
$643$	16.4973	0.650590	0.325295	+	0.945613i	$0.394536\pi$
$644$	0	0
$645$	4.59852	0.181067
$646$	−47.8014	−1.88072
$647$	−41.0615	−1.61429	−0.807147	−	0.590350i	$-0.798990\pi$
$647$	−41.0615	−1.61429	−0.807147	+	0.590350i	$0.798990\pi$
$648$	51.7011	2.03101
$649$	0	0
$650$	−26.6700	−1.04608
$651$	0	0
$652$	−4.44514	−0.174085
$653$	−20.1454	−0.788350	−0.394175	−	0.919035i	$-0.628970\pi$
$653$	−20.1454	−0.788350	−0.394175	+	0.919035i	$0.628970\pi$
$654$	−31.8886	−1.24694
$655$	3.57187	0.139565
$656$	2.75981	0.107753
$657$	23.0401	0.898881
$658$	0	0
$659$	−6.46125	−0.251694	−0.125847	−	0.992050i	$-0.540165\pi$
$659$	−6.46125	−0.251694	−0.125847	+	0.992050i	$0.540165\pi$
$660$	0	0
$661$	−14.3775	−0.559221	−0.279611	−	0.960114i	$-0.590205\pi$
$661$	−14.3775	−0.559221	−0.279611	+	0.960114i	$0.590205\pi$
$662$	43.7232	1.69935
$663$	−67.4443	−2.61932
$664$	−11.8786	−0.460979
$665$	0	0
$666$	−110.413	−4.27842
$667$	−20.4705	−0.792620
$668$	6.65372	0.257440
$669$	48.1434	1.86133
$670$	1.53532	0.0593146
$671$	0	0
$672$	0	0
$673$	−27.0790	−1.04382	−0.521909	−	0.853001i	$-0.674780\pi$
$673$	−27.0790	−1.04382	−0.521909	+	0.853001i	$0.674780\pi$
$674$	57.1588	2.20168
$675$	76.5878	2.94786
$676$	−2.65172	−0.101989
$677$	15.8329	0.608506	0.304253	−	0.952591i	$-0.401593\pi$
$677$	15.8329	0.608506	0.304253	+	0.952591i	$0.401593\pi$
$678$	−33.4191	−1.28345
$679$	0	0
$680$	−2.99993	−0.115042
$681$	−30.1251	−1.15440
$682$	0	0
$683$	37.0041	1.41592	0.707962	−	0.706251i	$-0.249615\pi$
$683$	37.0041	1.41592	0.707962	+	0.706251i	$0.249615\pi$
$684$	−30.0919	−1.15059
$685$	−2.71250	−0.103639
$686$	0	0
$687$	57.1159	2.17911
$688$	28.3943	1.08252
$689$	32.2608	1.22904
$690$	4.34477	0.165403
$691$	−14.5966	−0.555283	−0.277641	−	0.960685i	$-0.589553\pi$
$691$	−14.5966	−0.555283	−0.277641	+	0.960685i	$0.589553\pi$
$692$	−16.4158	−0.624034
$693$	0	0
$694$	−45.5656	−1.72965
$695$	0.259223	0.00983290
$696$	39.7911	1.50828
$697$	3.59082	0.136012
$698$	−33.9589	−1.28536
$699$	−90.9145	−3.43870
$700$	0	0
$701$	40.3475	1.52390	0.761952	−	0.647633i	$-0.224241\pi$
$701$	40.3475	1.52390	0.761952	+	0.647633i	$0.224241\pi$
$702$	−83.7294	−3.16016
$703$	−36.2480	−1.36712
$704$	0	0
$705$	8.32155	0.313408
$706$	17.1038	0.643710
$707$	0	0
$708$	−19.0389	−0.715527
$709$	0.763572	0.0286766	0.0143383	−	0.999897i	$-0.495436\pi$
$709$	0.763572	0.0286766	0.0143383	+	0.999897i	$0.495436\pi$
$710$	−0.144993	−0.00544150
$711$	29.1998	1.09508
$712$	0.462057	0.0173163
$713$	−5.62331	−0.210594
$714$	0	0
$715$	0	0
$716$	−2.13652	−0.0798456
$717$	−73.8201	−2.75686
$718$	−29.0387	−1.08371
$719$	7.59172	0.283123	0.141562	−	0.989929i	$-0.454788\pi$
$719$	7.59172	0.283123	0.141562	+	0.989929i	$0.454788\pi$
$720$	−9.51878	−0.354744
$721$	0	0
$722$	0.525673	0.0195635
$723$	23.6753	0.880493
$724$	19.4828	0.724074
$725$	32.0263	1.18943
$726$	0	0
$727$	−2.08478	−0.0773204	−0.0386602	−	0.999252i	$-0.512309\pi$
$727$	−2.08478	−0.0773204	−0.0386602	+	0.999252i	$0.512309\pi$
$728$	0	0
$729$	61.0421	2.26082
$730$	−1.25159	−0.0463235
$731$	36.9442	1.36643
$732$	9.97121	0.368547
$733$	−37.7859	−1.39566	−0.697828	−	0.716266i	$-0.745850\pi$
$733$	−37.7859	−1.39566	−0.697828	+	0.716266i	$0.745850\pi$
$734$	−0.195889	−0.00723038
$735$	0	0
$736$	15.0005	0.552927
$737$	0	0
$738$	7.28342	0.268106
$739$	−36.8466	−1.35543	−0.677713	−	0.735327i	$-0.737029\pi$
$739$	−36.8466	−1.35543	−0.677713	+	0.735327i	$0.737029\pi$
$740$	1.86152	0.0684307
$741$	−44.9106	−1.64983
$742$	0	0
$743$	44.4863	1.63204	0.816022	−	0.578020i	$-0.196175\pi$
$743$	44.4863	1.63204	0.816022	+	0.578020i	$0.196175\pi$
$744$	10.9307	0.400740
$745$	−4.54340	−0.166457
$746$	−29.8198	−1.09178
$747$	−49.0399	−1.79428
$748$	0	0
$749$	0	0
$750$	−13.6786	−0.499473
$751$	26.6146	0.971179	0.485590	−	0.874187i	$-0.338605\pi$
$751$	26.6146	0.971179	0.485590	+	0.874187i	$0.338605\pi$
$752$	51.3828	1.87374
$753$	42.2105	1.53824
$754$	−35.0127	−1.27509
$755$	−4.72542	−0.171976
$756$	0	0
$757$	−6.38731	−0.232151	−0.116075	−	0.993240i	$-0.537031\pi$
$757$	−6.38731	−0.232151	−0.116075	+	0.993240i	$0.537031\pi$
$758$	−13.1564	−0.477862
$759$	0	0
$760$	−1.99763	−0.0724617
$761$	40.1614	1.45585	0.727925	−	0.685657i	$-0.240485\pi$
$761$	40.1614	1.45585	0.727925	+	0.685657i	$0.240485\pi$
$762$	−12.9101	−0.467682
$763$	0	0
$764$	6.49990	0.235158
$765$	−12.3850	−0.447780
$766$	−18.0589	−0.652494
$767$	−20.4725	−0.739218
$768$	−58.5871	−2.11408
$769$	−0.481136	−0.0173502	−0.00867510	−	0.999962i	$-0.502761\pi$
$769$	−0.481136	−0.0173502	−0.00867510	+	0.999962i	$0.502761\pi$
$770$	0	0
$771$	101.866	3.66861
$772$	3.29969	0.118759
$773$	−24.1864	−0.869924	−0.434962	−	0.900449i	$-0.643238\pi$
$773$	−24.1864	−0.869924	−0.434962	+	0.900449i	$0.643238\pi$
$774$	74.9354	2.69350
$775$	8.79772	0.316023
$776$	9.01106	0.323478
$777$	0	0
$778$	37.8349	1.35645
$779$	2.39110	0.0856701
$780$	2.30639	0.0825819
$781$	0	0
$782$	34.9056	1.24822
$783$	100.545	3.59319
$784$	0	0
$785$	−5.67881	−0.202686
$786$	80.7861	2.88154
$787$	37.8595	1.34954	0.674772	−	0.738026i	$-0.264242\pi$
$787$	37.8595	1.34954	0.674772	+	0.738026i	$0.264242\pi$
$788$	3.43480	0.122360
$789$	−24.5781	−0.875004
$790$	−1.58620	−0.0564343
$791$	0	0
$792$	0	0
$793$	10.7220	0.380749
$794$	33.8516	1.20135
$795$	8.22237	0.291618
$796$	17.4451	0.618325
$797$	27.0930	0.959683	0.479842	−	0.877355i	$-0.340694\pi$
$797$	27.0930	0.959683	0.479842	+	0.877355i	$0.340694\pi$
$798$	0	0
$799$	66.8547	2.36515
$800$	−23.4685	−0.829737
$801$	1.90756	0.0674005
$802$	42.1923	1.48986
$803$	0	0
$804$	10.7772	0.380084
$805$	0	0
$806$	−9.61809	−0.338783
$807$	−6.34758	−0.223445
$808$	−12.8585	−0.452359
$809$	−15.7254	−0.552876	−0.276438	−	0.961032i	$-0.589154\pi$
$809$	−15.7254	−0.552876	−0.276438	+	0.961032i	$0.589154\pi$
$810$	−11.5948	−0.407398
$811$	32.3327	1.13536	0.567678	−	0.823251i	$-0.307842\pi$
$811$	32.3327	1.13536	0.567678	+	0.823251i	$0.307842\pi$
$812$	0	0
$813$	−75.2811	−2.64023
$814$	0	0
$815$	−1.21824	−0.0426732
$816$	−106.140	−3.71565
$817$	24.6008	0.860674
$818$	36.9908	1.29335
$819$	0	0
$820$	−0.122795	−0.00428819
$821$	−9.55190	−0.333364	−0.166682	−	0.986011i	$-0.553305\pi$
$821$	−9.55190	−0.333364	−0.166682	+	0.986011i	$0.553305\pi$
$822$	−61.3494	−2.13980
$823$	28.6991	1.00039	0.500194	−	0.865913i	$-0.333262\pi$
$823$	28.6991	1.00039	0.500194	+	0.865913i	$0.333262\pi$
$824$	−9.51243	−0.331381
$825$	0	0
$826$	0	0
$827$	9.66064	0.335933	0.167967	−	0.985793i	$-0.446280\pi$
$827$	9.66064	0.335933	0.167967	+	0.985793i	$0.446280\pi$
$828$	21.9737	0.763640
$829$	−16.4010	−0.569629	−0.284815	−	0.958583i	$-0.591932\pi$
$829$	−16.4010	−0.569629	−0.284815	+	0.958583i	$0.591932\pi$
$830$	2.66396	0.0924673
$831$	−18.0874	−0.627445
$832$	−5.98763	−0.207584
$833$	0	0
$834$	5.86293	0.203017
$835$	1.82353	0.0631060
$836$	0	0
$837$	27.6201	0.954690
$838$	−43.7345	−1.51078
$839$	15.0128	0.518301	0.259150	−	0.965837i	$-0.416557\pi$
$839$	15.0128	0.518301	0.259150	+	0.965837i	$0.416557\pi$
$840$	0	0
$841$	13.0444	0.449807
$842$	−48.9736	−1.68774
$843$	−23.8503	−0.821448
$844$	−21.7168	−0.747524
$845$	−0.726738	−0.0250005
$846$	135.604	4.66217
$847$	0	0
$848$	50.7704	1.74346
$849$	43.4416	1.49091
$850$	−54.6101	−1.87311
$851$	26.4690	0.907346
$852$	−1.01779	−0.0348688
$853$	57.4026	1.96543	0.982714	−	0.185133i	$-0.0592715\pi$
$853$	57.4026	1.96543	0.982714	+	0.185133i	$0.0592715\pi$
$854$	0	0
$855$	−8.24706	−0.282044
$856$	−1.68125	−0.0574641
$857$	32.1817	1.09931	0.549654	−	0.835393i	$-0.314760\pi$
$857$	32.1817	1.09931	0.549654	+	0.835393i	$0.314760\pi$
$858$	0	0
$859$	−23.9856	−0.818380	−0.409190	−	0.912449i	$-0.634189\pi$
$859$	−23.9856	−0.818380	−0.409190	+	0.912449i	$0.634189\pi$
$860$	−1.26338	−0.0430808
$861$	0	0
$862$	−16.7577	−0.570769
$863$	36.7485	1.25093	0.625467	−	0.780251i	$-0.284909\pi$
$863$	36.7485	1.25093	0.625467	+	0.780251i	$0.284909\pi$
$864$	−73.6784	−2.50659
$865$	−4.49894	−0.152969
$866$	−0.723331	−0.0245798
$867$	−82.4060	−2.79865
$868$	0	0
$869$	0	0
$870$	−8.92374	−0.302543
$871$	11.5887	0.392669
$872$	−10.7063	−0.362560
$873$	37.2015	1.25908
$874$	23.2433	0.786217
$875$	0	0
$876$	−8.78559	−0.296838
$877$	25.3446	0.855826	0.427913	−	0.903820i	$-0.359249\pi$
$877$	25.3446	0.855826	0.427913	+	0.903820i	$0.359249\pi$
$878$	6.79452	0.229304
$879$	18.2389	0.615182
$880$	0	0
$881$	12.7302	0.428890	0.214445	−	0.976736i	$-0.431206\pi$
$881$	12.7302	0.428890	0.214445	+	0.976736i	$0.431206\pi$
$882$	0	0
$883$	10.0508	0.338235	0.169117	−	0.985596i	$-0.445908\pi$
$883$	10.0508	0.338235	0.169117	+	0.985596i	$0.445908\pi$
$884$	18.5293	0.623209
$885$	−5.21786	−0.175396
$886$	33.9537	1.14070
$887$	−18.9974	−0.637871	−0.318936	−	0.947776i	$-0.603325\pi$
$887$	−18.9974	−0.637871	−0.318936	+	0.947776i	$0.603325\pi$
$888$	−51.4511	−1.72659
$889$	0	0
$890$	−0.103623	−0.00347346
$891$	0	0
$892$	−13.2267	−0.442862
$893$	44.5180	1.48974
$894$	−102.759	−3.43679
$895$	−0.585541	−0.0195725
$896$	0	0
$897$	32.7947	1.09498
$898$	−16.9802	−0.566637
$899$	11.5497	0.385205
$900$	−34.3781	−1.14594
$901$	66.0579	2.20071
$902$	0	0
$903$	0	0
$904$	−11.2201	−0.373175
$905$	5.33951	0.177491
$906$	−106.876	−3.55072
$907$	−59.1419	−1.96378	−0.981888	−	0.189464i	$-0.939325\pi$
$907$	−59.1419	−1.96378	−0.981888	+	0.189464i	$0.939325\pi$
$908$	8.27643	0.274663
$909$	−53.0852	−1.76073
$910$	0	0
$911$	−11.5307	−0.382028	−0.191014	−	0.981587i	$-0.561178\pi$
$911$	−11.5307	−0.382028	−0.191014	+	0.981587i	$0.561178\pi$
$912$	−70.6780	−2.34038
$913$	0	0
$914$	59.4755	1.96728
$915$	2.73273	0.0903414
$916$	−15.6918	−0.518471
$917$	0	0
$918$	−171.446	−5.65856
$919$	−27.8583	−0.918962	−0.459481	−	0.888188i	$-0.651964\pi$
$919$	−27.8583	−0.918962	−0.459481	+	0.888188i	$0.651964\pi$
$920$	1.45871	0.0480923
$921$	46.6742	1.53797
$922$	−45.6464	−1.50328
$923$	−1.09442	−0.0360233
$924$	0	0
$925$	−41.4110	−1.36159
$926$	47.8963	1.57397
$927$	−39.2713	−1.28984
$928$	−30.8097	−1.01138
$929$	51.3944	1.68619	0.843097	−	0.537761i	$-0.180730\pi$
$929$	51.3944	1.68619	0.843097	+	0.537761i	$0.180730\pi$
$930$	−2.45138	−0.0803839
$931$	0	0
$932$	24.9774	0.818162
$933$	−11.6904	−0.382726
$934$	−47.3179	−1.54829
$935$	0	0
$936$	−45.9292	−1.50124
$937$	8.07437	0.263778	0.131889	−	0.991264i	$-0.457896\pi$
$937$	8.07437	0.263778	0.131889	+	0.991264i	$0.457896\pi$
$938$	0	0
$939$	29.8585	0.974397
$940$	−2.28622	−0.0745684
$941$	−24.3020	−0.792223	−0.396112	−	0.918202i	$-0.629641\pi$
$941$	−24.3020	−0.792223	−0.396112	+	0.918202i	$0.629641\pi$
$942$	−128.439	−4.18478
$943$	−1.74603	−0.0568586
$944$	−32.2185	−1.04862
$945$	0	0
$946$	0	0
$947$	40.5660	1.31822	0.659109	−	0.752047i	$-0.270933\pi$
$947$	40.5660	1.31822	0.659109	+	0.752047i	$0.270933\pi$
$948$	−11.1344	−0.361628
$949$	−9.44710	−0.306666
$950$	−36.3644	−1.17982
$951$	38.5083	1.24872
$952$	0	0
$953$	4.52347	0.146529	0.0732647	−	0.997313i	$-0.476658\pi$
$953$	4.52347	0.146529	0.0732647	+	0.997313i	$0.476658\pi$
$954$	133.988	4.33802
$955$	1.78138	0.0576440
$956$	20.2810	0.655934
$957$	0	0
$958$	15.7942	0.510288
$959$	0	0
$960$	−1.52608	−0.0492540
$961$	−27.8273	−0.897653
$962$	45.2725	1.45964
$963$	−6.94092	−0.223668
$964$	−6.50443	−0.209494
$965$	0.904322	0.0291112
$966$	0	0
$967$	48.3508	1.55486	0.777428	−	0.628972i	$-0.216524\pi$
$967$	48.3508	1.55486	0.777428	+	0.628972i	$0.216524\pi$
$968$	0	0
$969$	−91.9599	−2.95418
$970$	−2.02087	−0.0648861
$971$	−12.7515	−0.409217	−0.204608	−	0.978844i	$-0.565592\pi$
$971$	−12.7515	−0.409217	−0.204608	+	0.978844i	$0.565592\pi$
$972$	−39.5197	−1.26759
$973$	0	0
$974$	−18.1120	−0.580345
$975$	−51.3076	−1.64316
$976$	16.8737	0.540114
$977$	21.9973	0.703757	0.351879	−	0.936046i	$-0.385543\pi$
$977$	21.9973	0.703757	0.351879	+	0.936046i	$0.385543\pi$
$978$	−27.5534	−0.881060
$979$	0	0
$980$	0	0
$981$	−44.2000	−1.41120
$982$	−34.0306	−1.08596
$983$	51.4813	1.64200	0.820999	−	0.570930i	$-0.193417\pi$
$983$	51.4813	1.64200	0.820999	+	0.570930i	$0.193417\pi$
$984$	3.39398	0.108196
$985$	0.941350	0.0299939
$986$	−71.6927	−2.28316
$987$	0	0
$988$	12.3385	0.392541
$989$	−17.9640	−0.571223
$990$	0	0
$991$	−12.8667	−0.408724	−0.204362	−	0.978895i	$-0.565512\pi$
$991$	−12.8667	−0.408724	−0.204362	+	0.978895i	$0.565512\pi$
$992$	−8.46351	−0.268717
$993$	84.1144	2.66929
$994$	0	0
$995$	4.78104	0.151569
$996$	18.6998	0.592524
$997$	−30.0438	−0.951496	−0.475748	−	0.879582i	$-0.657823\pi$
$997$	−30.0438	−0.951496	−0.475748	+	0.879582i	$0.657823\pi$
$998$	18.6535	0.590468
$999$	−130.008	−4.11328

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5929.2.a.bv.1.3		10
7.6	odd	2	inner	5929.2.a.bv.1.4		10
11.10	odd	2		539.2.a.l.1.7	✓	10
33.32	even	2		4851.2.a.cg.1.3		10
44.43	even	2		8624.2.a.df.1.10		10
77.10	even	6		539.2.e.o.177.3		20
77.32	odd	6		539.2.e.o.177.4		20
77.54	even	6		539.2.e.o.67.3		20
77.65	odd	6		539.2.e.o.67.4		20
77.76	even	2		539.2.a.l.1.8	yes	10
231.230	odd	2		4851.2.a.cg.1.4		10
308.307	odd	2		8624.2.a.df.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
539.2.a.l.1.7	✓	10	11.10	odd	2
539.2.a.l.1.8	yes	10	77.76	even	2
539.2.e.o.67.3		20	77.54	even	6
539.2.e.o.67.4		20	77.65	odd	6
539.2.e.o.177.3		20	77.10	even	6
539.2.e.o.177.4		20	77.32	odd	6
4851.2.a.cg.1.3		10	33.32	even	2
4851.2.a.cg.1.4		10	231.230	odd	2
5929.2.a.bv.1.3		10	1.1	even	1	trivial
5929.2.a.bv.1.4		10	7.6	odd	2	inner
8624.2.a.df.1.1		10	308.307	odd	2
8624.2.a.df.1.10		10	44.43	even	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:	\( N \)	\(=\)	\( 5929 = 7^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5929.a (trivial)

\(f(q)\)	\(=\)	\(q-1.70296 q^{2} -3.27614 q^{3} +0.900071 q^{4} +0.246676 q^{5} +5.57913 q^{6} +1.87313 q^{8} +7.73309 q^{9} +O(q^{10})\)	\(q-1.70296 q^{2} -3.27614 q^{3} +0.900071 q^{4} +0.246676 q^{5} +5.57913 q^{6} +1.87313 q^{8} +7.73309 q^{9} -0.420079 q^{10} -2.94876 q^{12} -3.17078 q^{13} -0.808144 q^{15} -4.99001 q^{16} -6.49256 q^{17} -13.1691 q^{18} -4.32335 q^{19} +0.222026 q^{20} +3.15700 q^{23} -6.13665 q^{24} -4.93915 q^{25} +5.39972 q^{26} -15.5063 q^{27} -6.48417 q^{29} +1.37624 q^{30} -1.78122 q^{31} +4.75152 q^{32} +11.0566 q^{34} +6.96033 q^{36} +8.38424 q^{37} +7.36248 q^{38} +10.3879 q^{39} +0.462057 q^{40} -0.553067 q^{41} -5.69023 q^{43} +1.90756 q^{45} -5.37624 q^{46} -10.2971 q^{47} +16.3480 q^{48} +8.41117 q^{50} +21.2705 q^{51} -2.85393 q^{52} -10.1744 q^{53} +26.4065 q^{54} +14.1639 q^{57} +11.0423 q^{58} +6.45660 q^{59} -0.727387 q^{60} -3.38149 q^{61} +3.03335 q^{62} +1.88838 q^{64} -0.782155 q^{65} -3.65484 q^{67} -5.84377 q^{68} -10.3428 q^{69} +0.345158 q^{71} +14.4851 q^{72} +2.97942 q^{73} -14.2780 q^{74} +16.1813 q^{75} -3.89132 q^{76} -17.6902 q^{78} +3.77595 q^{79} -1.23091 q^{80} +27.6014 q^{81} +0.941851 q^{82} -6.34157 q^{83} -1.60156 q^{85} +9.69023 q^{86} +21.2430 q^{87} +0.246676 q^{89} -3.24851 q^{90} +2.84152 q^{92} +5.83553 q^{93} +17.5356 q^{94} -1.06646 q^{95} -15.5667 q^{96} +4.81068 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} + 18 q^{4} + 6 q^{8} + 22 q^{9}+O(q^{10}) \) 10 * q - 2 * q^2 + 18 * q^4 + 6 * q^8 + 22 * q^9	\( 10 q - 2 q^{2} + 18 q^{4} + 6 q^{8} + 22 q^{9} + 8 q^{15} + 42 q^{16} - 6 q^{18} + 4 q^{23} + 18 q^{25} - 12 q^{29} + 4 q^{30} + 30 q^{32} - 2 q^{36} + 40 q^{37} + 16 q^{39} + 8 q^{43} - 44 q^{46} + 62 q^{50} + 16 q^{53} + 8 q^{57} - 28 q^{58} + 36 q^{60} + 106 q^{64} + 32 q^{65} - 4 q^{67} + 36 q^{71} + 90 q^{72} + 28 q^{74} - 112 q^{78} - 8 q^{79} - 6 q^{81} - 88 q^{85} + 32 q^{86} - 52 q^{92} + 44 q^{93} + 64 q^{95}+O(q^{100}) \) 10 * q - 2 * q^2 + 18 * q^4 + 6 * q^8 + 22 * q^9 + 8 * q^15 + 42 * q^16 - 6 * q^18 + 4 * q^23 + 18 * q^25 - 12 * q^29 + 4 * q^30 + 30 * q^32 - 2 * q^36 + 40 * q^37 + 16 * q^39 + 8 * q^43 - 44 * q^46 + 62 * q^50 + 16 * q^53 + 8 * q^57 - 28 * q^58 + 36 * q^60 + 106 * q^64 + 32 * q^65 - 4 * q^67 + 36 * q^71 + 90 * q^72 + 28 * q^74 - 112 * q^78 - 8 * q^79 - 6 * q^81 - 88 * q^85 + 32 * q^86 - 52 * q^92 + 44 * q^93 + 64 * q^95

Introduction

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