LMFDB - Embedded newform 725.2.a.h.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [725,2,Mod(1,725)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(725, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("725.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.a (trivial)

Newform invariants

comment:select newform

sage:traces = [5,-2,-6,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$5.78915414654$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.240881.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 9x^{2} + 5x - 7 $ x^5 - 2x^4 - 5x^3 + 9x^2 + 5x - 7
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$0.838718$ of defining polynomial
Character	$\chi$	$=$	725.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.838718 q^{2} +1.90376 q^{3} -1.29655 q^{4} -1.59672 q^{6} -2.46832 q^{7} +2.76488 q^{8} +0.624302 q^{9} -1.49072 q^{11} -2.46832 q^{12} -0.929772 q^{13} +2.07023 q^{14} +0.274153 q^{16} -2.80583 q^{17} -0.523614 q^{18} -0.0373385 q^{19} -4.69910 q^{21} +1.25030 q^{22} -6.79703 q^{23} +5.26366 q^{24} +0.779816 q^{26} -4.52276 q^{27} +3.20031 q^{28} +1.00000 q^{29} +2.15767 q^{31} -5.75969 q^{32} -2.83798 q^{33} +2.35330 q^{34} -0.809441 q^{36} -7.43182 q^{37} +0.0313164 q^{38} -1.77006 q^{39} -1.97399 q^{41} +3.94122 q^{42} -9.61550 q^{43} +1.93280 q^{44} +5.70079 q^{46} +5.17430 q^{47} +0.521922 q^{48} -0.907373 q^{49} -5.34162 q^{51} +1.20550 q^{52} +1.33750 q^{53} +3.79332 q^{54} -6.82462 q^{56} -0.0710835 q^{57} -0.838718 q^{58} +4.57758 q^{59} +12.1506 q^{61} -1.80968 q^{62} -1.54098 q^{63} +4.28245 q^{64} +2.38027 q^{66} +0.291367 q^{67} +3.63790 q^{68} -12.9399 q^{69} -10.7486 q^{71} +1.72612 q^{72} -0.0141028 q^{73} +6.23320 q^{74} +0.0484113 q^{76} +3.67959 q^{77} +1.48458 q^{78} +5.37881 q^{79} -10.4832 q^{81} +1.65562 q^{82} -10.1503 q^{83} +6.09263 q^{84} +8.06469 q^{86} +1.90376 q^{87} -4.12167 q^{88} -6.88136 q^{89} +2.29498 q^{91} +8.81271 q^{92} +4.10769 q^{93} -4.33978 q^{94} -10.9651 q^{96} +9.42386 q^{97} +0.761030 q^{98} -0.930663 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 2 q^{2} - 6 q^{3} + 4 q^{4} - q^{6} - 6 q^{7} - 3 q^{8} + 11 q^{9} - 2 q^{11} - 6 q^{12} - 4 q^{13} + 11 q^{14} - 10 q^{16} - 9 q^{17} + 2 q^{19} - q^{21} - 4 q^{22} - q^{23} + 13 q^{24} - 16 q^{26}+ \cdots - 26 q^{99}+O(q^{100}) $ 5 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 - q^6 - 6 * q^7 - 3 * q^8 + 11 * q^9 - 2 * q^11 - 6 * q^12 - 4 * q^13 + 11 * q^14 - 10 * q^16 - 9 * q^17 + 2 * q^19 - q^21 - 4 * q^22 - q^23 + 13 * q^24 - 16 * q^26 - 27 * q^27 - 10 * q^28 + 5 * q^29 - q^31 + 2 * q^32 + 7 * q^33 + 3 * q^34 - 13 * q^36 - 14 * q^37 + 3 * q^38 - 6 * q^39 + 5 * q^41 - 24 * q^42 - 28 * q^43 + 7 * q^44 - 20 * q^46 - 15 * q^47 + 26 * q^48 - 3 * q^49 + 5 * q^51 - 6 * q^52 + 8 * q^53 + 10 * q^54 - 16 * q^56 + 6 * q^57 - 2 * q^58 - 11 * q^59 - 5 * q^61 + 6 * q^62 + 5 * q^63 - 5 * q^64 - 27 * q^66 - 23 * q^67 - q^68 - 26 * q^69 - 5 * q^71 - 3 * q^72 - 16 * q^73 + 8 * q^74 + 16 * q^76 + 30 * q^77 + 33 * q^78 - 10 * q^79 + 49 * q^81 + 19 * q^82 - 9 * q^83 + 32 * q^84 - 13 * q^86 - 6 * q^87 - 35 * q^88 - 18 * q^89 + q^91 + 27 * q^92 - 7 * q^93 - 13 * q^94 - 38 * q^96 - 23 * q^97 - 3 * q^98 - 26 * q^99

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 $

$2$	−0.838718	−0.593063	−0.296532	−	0.955023i	$-0.595830\pi$
$2$	−0.838718	−0.593063	−0.296532	+	0.955023i	$0.595830\pi$
$3$	1.90376	1.09914	0.549568	−	0.835449i	$-0.314792\pi$
$3$	1.90376	1.09914	0.549568	+	0.835449i	$0.314792\pi$
$4$	−1.29655	−0.648276
$5$	0	0
$5$	0	0
$6$	−1.59672	−0.651857
$7$	−2.46832	−0.932939	−0.466470	−	0.884537i	$-0.654474\pi$
$7$	−2.46832	−0.932939	−0.466470	+	0.884537i	$0.654474\pi$
$8$	2.76488	0.977532
$9$	0.624302	0.208101
$10$	0	0
$11$	−1.49072	−0.449470	−0.224735	−	0.974420i	$-0.572152\pi$
$11$	−1.49072	−0.449470	−0.224735	+	0.974420i	$0.572152\pi$
$12$	−2.46832	−0.712544
$13$	−0.929772	−0.257872	−0.128936	−	0.991653i	$-0.541156\pi$
$13$	−0.929772	−0.257872	−0.128936	+	0.991653i	$0.541156\pi$
$14$	2.07023	0.553292
$15$	0	0
$16$	0.274153	0.0685383
$17$	−2.80583	−0.680513	−0.340257	−	0.940333i	$-0.610514\pi$
$17$	−2.80583	−0.680513	−0.340257	+	0.940333i	$0.610514\pi$
$18$	−0.523614	−0.123417
$19$	−0.0373385	−0.00856603	−0.00428302	−	0.999991i	$-0.501363\pi$
$19$	−0.0373385	−0.00856603	−0.00428302	+	0.999991i	$0.501363\pi$
$20$	0	0
$21$	−4.69910	−1.02543
$22$	1.25030	0.266564
$23$	−6.79703	−1.41728	−0.708639	−	0.705571i	$-0.750691\pi$
$23$	−6.79703	−1.41728	−0.708639	+	0.705571i	$0.750691\pi$
$24$	5.26366	1.07444
$25$	0	0
$26$	0.779816	0.152935
$27$	−4.52276	−0.870405
$28$	3.20031	0.604802
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0	0
$31$	2.15767	0.387529	0.193764	−	0.981048i	$-0.437930\pi$
$31$	2.15767	0.387529	0.193764	+	0.981048i	$0.437930\pi$
$32$	−5.75969	−1.01818
$33$	−2.83798	−0.494029
$34$	2.35330	0.403587
$35$	0	0
$36$	−0.809441	−0.134907
$37$	−7.43182	−1.22178	−0.610892	−	0.791714i	$-0.709189\pi$
$37$	−7.43182	−1.22178	−0.610892	+	0.791714i	$0.709189\pi$
$38$	0.0313164	0.00508020
$39$	−1.77006	−0.283437
$40$	0	0
$41$	−1.97399	−0.308285	−0.154143	−	0.988049i	$-0.549262\pi$
$41$	−1.97399	−0.308285	−0.154143	+	0.988049i	$0.549262\pi$
$42$	3.94122	0.608143
$43$	−9.61550	−1.46635	−0.733175	−	0.680040i	$-0.761963\pi$
$43$	−9.61550	−1.46635	−0.733175	+	0.680040i	$0.761963\pi$
$44$	1.93280	0.291381
$45$	0	0
$46$	5.70079	0.840536
$47$	5.17430	0.754749	0.377375	−	0.926061i	$-0.376827\pi$
$47$	5.17430	0.754749	0.377375	+	0.926061i	$0.376827\pi$
$48$	0.521922	0.0753329
$49$	−0.907373	−0.129625
$50$	0	0
$51$	−5.34162	−0.747977
$52$	1.20550	0.167173
$53$	1.33750	0.183720	0.0918601	−	0.995772i	$-0.470719\pi$
$53$	1.33750	0.183720	0.0918601	+	0.995772i	$0.470719\pi$
$54$	3.79332	0.516205
$55$	0	0
$56$	−6.82462	−0.911978
$57$	−0.0710835	−0.00941524
$58$	−0.838718	−0.110129
$59$	4.57758	0.595951	0.297975	−	0.954574i	$-0.403689\pi$
$59$	4.57758	0.595951	0.297975	+	0.954574i	$0.403689\pi$
$60$	0	0
$61$	12.1506	1.55572	0.777860	−	0.628437i	$-0.216305\pi$
$61$	12.1506	1.55572	0.777860	+	0.628437i	$0.216305\pi$
$62$	−1.80968	−0.229829
$63$	−1.54098	−0.194145
$64$	4.28245	0.535306
$65$	0	0
$66$	2.38027	0.292990
$67$	0.291367	0.0355961	0.0177981	−	0.999842i	$-0.494334\pi$
$67$	0.291367	0.0355961	0.0177981	+	0.999842i	$0.494334\pi$
$68$	3.63790	0.441161
$69$	−12.9399	−1.55778
$70$	0	0
$71$	−10.7486	−1.27563	−0.637813	−	0.770191i	$-0.720161\pi$
$71$	−10.7486	−1.27563	−0.637813	+	0.770191i	$0.720161\pi$
$72$	1.72612	0.203425
$73$	−0.0141028	−0.00165061	−0.000825303	−	1.00000i	$-0.500263\pi$
$73$	−0.0141028	−0.00165061	−0.000825303		1.00000i	$0.500263\pi$
$74$	6.23320	0.724595
$75$	0	0
$76$	0.0484113	0.00555315
$77$	3.67959	0.419328
$78$	1.48458	0.168096
$79$	5.37881	0.605163	0.302582	−	0.953123i	$-0.402152\pi$
$79$	5.37881	0.605163	0.302582	+	0.953123i	$0.402152\pi$
$80$	0	0
$81$	−10.4832	−1.16479
$82$	1.65562	0.182833
$83$	−10.1503	−1.11414	−0.557072	−	0.830464i	$-0.688075\pi$
$83$	−10.1503	−1.11414	−0.557072	+	0.830464i	$0.688075\pi$
$84$	6.09263	0.664760
$85$	0	0
$86$	8.06469	0.869638
$87$	1.90376	0.204105
$88$	−4.12167	−0.439371
$89$	−6.88136	−0.729423	−0.364711	−	0.931121i	$-0.618832\pi$
$89$	−6.88136	−0.729423	−0.364711	+	0.931121i	$0.618832\pi$
$90$	0	0
$91$	2.29498	0.240579
$92$	8.81271	0.918788
$93$	4.10769	0.425947
$94$	−4.33978	−0.447614
$95$	0	0
$96$	−10.9651	−1.11912
$97$	9.42386	0.956848	0.478424	−	0.878129i	$-0.341208\pi$
$97$	9.42386	0.956848	0.478424	+	0.878129i	$0.341208\pi$
$98$	0.761030	0.0768756
$99$	−0.930663	−0.0935351
$100$	0	0
$101$	11.0204	1.09657	0.548284	−	0.836293i	$-0.315281\pi$
$101$	11.0204	1.09657	0.548284	+	0.836293i	$0.315281\pi$
$102$	4.48012	0.443598
$103$	4.51423	0.444801	0.222400	−	0.974955i	$-0.428611\pi$
$103$	4.51423	0.444801	0.222400	+	0.974955i	$0.428611\pi$
$104$	−2.57071	−0.252078
$105$	0	0
$106$	−1.12179	−0.108958
$107$	0.277920	0.0268675	0.0134338	−	0.999910i	$-0.495724\pi$
$107$	0.277920	0.0268675	0.0134338	+	0.999910i	$0.495724\pi$
$108$	5.86399	0.564263
$109$	−16.6659	−1.59630	−0.798150	−	0.602459i	$-0.794188\pi$
$109$	−16.6659	−1.59630	−0.798150	+	0.602459i	$0.794188\pi$
$110$	0	0
$111$	−14.1484	−1.34291
$112$	−0.676699	−0.0639420
$113$	14.9017	1.40183	0.700916	−	0.713244i	$-0.252775\pi$
$113$	14.9017	1.40183	0.700916	+	0.713244i	$0.252775\pi$
$114$	0.0596190	0.00558383
$115$	0	0
$116$	−1.29655	−0.120382
$117$	−0.580459	−0.0536635
$118$	−3.83930	−0.353436
$119$	6.92570	0.634877
$120$	0	0
$121$	−8.77774	−0.797977
$122$	−10.1909	−0.922640
$123$	−3.75800	−0.338847
$124$	−2.79753	−0.251226
$125$	0	0
$126$	1.29245	0.115140
$127$	−14.2274	−1.26248	−0.631240	−	0.775587i	$-0.717454\pi$
$127$	−14.2274	−1.26248	−0.631240	+	0.775587i	$0.717454\pi$
$128$	7.92762	0.700709
$129$	−18.3056	−1.61172
$130$	0	0
$131$	19.7992	1.72987	0.864933	−	0.501888i	$-0.167361\pi$
$131$	19.7992	1.72987	0.864933	+	0.501888i	$0.167361\pi$
$132$	3.67959	0.320267
$133$	0.0921635	0.00799159
$134$	−0.244374	−0.0211107
$135$	0	0
$136$	−7.75777	−0.665223
$137$	0.954829	0.0815765	0.0407883	−	0.999168i	$-0.487013\pi$
$137$	0.954829	0.0815765	0.0407883	+	0.999168i	$0.487013\pi$
$138$	10.8529	0.923863
$139$	−22.5382	−1.91166	−0.955831	−	0.293916i	$-0.905041\pi$
$139$	−22.5382	−1.91166	−0.955831	+	0.293916i	$0.905041\pi$
$140$	0	0
$141$	9.85063	0.829572
$142$	9.01506	0.756527
$143$	1.38603	0.115906
$144$	0.171154	0.0142629
$145$	0	0
$146$	0.0118282	0.000978913 0
$147$	−1.72742	−0.142475
$148$	9.63575	0.792054
$149$	8.56867	0.701972	0.350986	−	0.936381i	$-0.385846\pi$
$149$	8.56867	0.701972	0.350986	+	0.936381i	$0.385846\pi$
$150$	0	0
$151$	13.2588	1.07898	0.539491	−	0.841991i	$-0.318617\pi$
$151$	13.2588	1.07898	0.539491	+	0.841991i	$0.318617\pi$
$152$	−0.103236	−0.00837357
$153$	−1.75169	−0.141615
$154$	−3.08614	−0.248688
$155$	0	0
$156$	2.29498	0.183745
$157$	−14.1001	−1.12531	−0.562656	−	0.826691i	$-0.690220\pi$
$157$	−14.1001	−1.12531	−0.562656	+	0.826691i	$0.690220\pi$
$158$	−4.51130	−0.358900
$159$	2.54629	0.201934
$160$	0	0
$161$	16.7773	1.32223
$162$	8.79241	0.690797
$163$	−17.2267	−1.34930	−0.674650	−	0.738138i	$-0.735705\pi$
$163$	−17.2267	−1.34930	−0.674650	+	0.738138i	$0.735705\pi$
$164$	2.55938	0.199854
$165$	0	0
$166$	8.51326	0.660757
$167$	14.4358	1.11707	0.558537	−	0.829480i	$-0.311363\pi$
$167$	14.4358	1.11707	0.558537	+	0.829480i	$0.311363\pi$
$168$	−12.9924	−1.00239
$169$	−12.1355	−0.933502
$170$	0	0
$171$	−0.0233105	−0.00178260
$172$	12.4670	0.950600
$173$	15.5680	1.18362	0.591808	−	0.806079i	$-0.298414\pi$
$173$	15.5680	1.18362	0.591808	+	0.806079i	$0.298414\pi$
$174$	−1.59672	−0.121047
$175$	0	0
$176$	−0.408687	−0.0308059
$177$	8.71462	0.655031
$178$	5.77152	0.432594
$179$	20.5247	1.53409	0.767044	−	0.641594i	$-0.221727\pi$
$179$	20.5247	1.53409	0.767044	+	0.641594i	$0.221727\pi$
$180$	0	0
$181$	17.5111	1.30159	0.650794	−	0.759255i	$-0.274436\pi$
$181$	17.5111	1.30159	0.650794	+	0.759255i	$0.274436\pi$
$182$	−1.92484	−0.142679
$183$	23.1318	1.70995
$184$	−18.7930	−1.38543
$185$	0	0
$186$	−3.44519	−0.252613
$187$	4.18272	0.305870
$188$	−6.70875	−0.489286
$189$	11.1636	0.812035
$190$	0	0
$191$	15.5726	1.12680	0.563398	−	0.826186i	$-0.309494\pi$
$191$	15.5726	1.12680	0.563398	+	0.826186i	$0.309494\pi$
$192$	8.15276	0.588375
$193$	8.44449	0.607847	0.303924	−	0.952696i	$-0.401703\pi$
$193$	8.44449	0.607847	0.303924	+	0.952696i	$0.401703\pi$
$194$	−7.90396	−0.567471
$195$	0	0
$196$	1.17646	0.0840326
$197$	10.1937	0.726272	0.363136	−	0.931736i	$-0.381706\pi$
$197$	10.1937	0.726272	0.363136	+	0.931736i	$0.381706\pi$
$198$	0.780563	0.0554722
$199$	6.54034	0.463633	0.231816	−	0.972760i	$-0.425533\pi$
$199$	6.54034	0.463633	0.231816	+	0.972760i	$0.425533\pi$
$200$	0	0
$201$	0.554692	0.0391250
$202$	−9.24297	−0.650333
$203$	−2.46832	−0.173242
$204$	6.92570	0.484896
$205$	0	0
$206$	−3.78617	−0.263795
$207$	−4.24340	−0.294937
$208$	−0.254900	−0.0176741
$209$	0.0556614	0.00385018
$210$	0	0
$211$	15.5988	1.07386	0.536932	−	0.843625i	$-0.319583\pi$
$211$	15.5988	1.07386	0.536932	+	0.843625i	$0.319583\pi$
$212$	−1.73414	−0.119101
$213$	−20.4628	−1.40209
$214$	−0.233096	−0.0159341
$215$	0	0
$216$	−12.5049	−0.850849
$217$	−5.32583	−0.361541
$218$	13.9780	0.946707
$219$	−0.0268483	−0.00181424
$220$	0	0
$221$	2.60878	0.175486
$222$	11.8665	0.796429
$223$	−23.7662	−1.59150	−0.795751	−	0.605623i	$-0.792924\pi$
$223$	−23.7662	−1.59150	−0.795751	+	0.605623i	$0.792924\pi$
$224$	14.2168	0.949899
$225$	0	0
$226$	−12.4983	−0.831375
$227$	9.10250	0.604154	0.302077	−	0.953284i	$-0.402320\pi$
$227$	9.10250	0.604154	0.302077	+	0.953284i	$0.402320\pi$
$228$	0.0921635	0.00610367
$229$	24.3822	1.61122	0.805611	−	0.592445i	$-0.201837\pi$
$229$	24.3822	1.61122	0.805611	+	0.592445i	$0.201837\pi$
$230$	0	0
$231$	7.00506	0.460899
$232$	2.76488	0.181523
$233$	−18.6324	−1.22065	−0.610325	−	0.792151i	$-0.708961\pi$
$233$	−18.6324	−1.22065	−0.610325	+	0.792151i	$0.708961\pi$
$234$	0.486841	0.0318258
$235$	0	0
$236$	−5.93508	−0.386341
$237$	10.2400	0.665157
$238$	−5.80870	−0.376522
$239$	1.69469	0.109620	0.0548101	−	0.998497i	$-0.482545\pi$
$239$	1.69469	0.109620	0.0548101	+	0.998497i	$0.482545\pi$
$240$	0	0
$241$	8.57531	0.552384	0.276192	−	0.961102i	$-0.410927\pi$
$241$	8.57531	0.552384	0.276192	+	0.961102i	$0.410927\pi$
$242$	7.36205	0.473250
$243$	−6.38914	−0.409863
$244$	−15.7538	−1.00854
$245$	0	0
$246$	3.15190	0.200958
$247$	0.0347163	0.00220894
$248$	5.96569	0.378822
$249$	−19.3238	−1.22460
$250$	0	0
$251$	−27.6230	−1.74355	−0.871774	−	0.489909i	$-0.837030\pi$
$251$	−27.6230	−1.74355	−0.871774	+	0.489909i	$0.837030\pi$
$252$	1.99796	0.125860
$253$	10.1325	0.637025
$254$	11.9328	0.748731
$255$	0	0
$256$	−15.2139	−0.950871
$257$	−6.02021	−0.375530	−0.187765	−	0.982214i	$-0.560124\pi$
$257$	−6.02021	−0.375530	−0.187765	+	0.982214i	$0.560124\pi$
$258$	15.3532	0.955851
$259$	18.3442	1.13985
$260$	0	0
$261$	0.624302	0.0386434
$262$	−16.6060	−1.02592
$263$	−8.13397	−0.501562	−0.250781	−	0.968044i	$-0.580687\pi$
$263$	−8.13397	−0.501562	−0.250781	+	0.968044i	$0.580687\pi$
$264$	−7.84667	−0.482929
$265$	0	0
$266$	−0.0772991	−0.00473951
$267$	−13.1005	−0.801735
$268$	−0.377772	−0.0230761
$269$	−3.43905	−0.209682	−0.104841	−	0.994489i	$-0.533433\pi$
$269$	−3.43905	−0.209682	−0.104841	+	0.994489i	$0.533433\pi$
$270$	0	0
$271$	−10.4822	−0.636748	−0.318374	−	0.947965i	$-0.603137\pi$
$271$	−10.4822	−0.636748	−0.318374	+	0.947965i	$0.603137\pi$
$272$	−0.769227	−0.0466412
$273$	4.36909	0.264429
$274$	−0.800832	−0.0483800
$275$	0	0
$276$	16.7773	1.00987
$277$	−18.9262	−1.13716	−0.568582	−	0.822627i	$-0.692508\pi$
$277$	−18.9262	−1.13716	−0.568582	+	0.822627i	$0.692508\pi$
$278$	18.9032	1.13374
$279$	1.34704	0.0806451
$280$	0	0
$281$	−24.6790	−1.47223	−0.736113	−	0.676859i	$-0.763341\pi$
$281$	−24.6790	−1.47223	−0.736113	+	0.676859i	$0.763341\pi$
$282$	−8.26190	−0.491989
$283$	−3.12685	−0.185872	−0.0929361	−	0.995672i	$-0.529625\pi$
$283$	−3.12685	−0.185872	−0.0929361	+	0.995672i	$0.529625\pi$
$284$	13.9361	0.826958
$285$	0	0
$286$	−1.16249	−0.0687395
$287$	4.87244	0.287611
$288$	−3.59579	−0.211884
$289$	−9.12733	−0.536902
$290$	0	0
$291$	17.9408	1.05171
$292$	0.0182850	0.00107005
$293$	6.95025	0.406038	0.203019	−	0.979175i	$-0.434925\pi$
$293$	6.95025	0.406038	0.203019	+	0.979175i	$0.434925\pi$
$294$	1.44882	0.0844968
$295$	0	0
$296$	−20.5481	−1.19433
$297$	6.74218	0.391221
$298$	−7.18669	−0.416314
$299$	6.31969	0.365477
$300$	0	0
$301$	23.7342	1.36802
$302$	−11.1203	−0.639904
$303$	20.9801	1.20528
$304$	−0.0102365	−0.000587101 0
$305$	0	0
$306$	1.46917	0.0839869
$307$	−15.4392	−0.881160	−0.440580	−	0.897713i	$-0.645227\pi$
$307$	−15.4392	−0.881160	−0.440580	+	0.897713i	$0.645227\pi$
$308$	−4.77078	−0.271841
$309$	8.59402	0.488896
$310$	0	0
$311$	−12.9889	−0.736534	−0.368267	−	0.929720i	$-0.620049\pi$
$311$	−12.9889	−0.736534	−0.368267	+	0.929720i	$0.620049\pi$
$312$	−4.89401	−0.277069
$313$	−24.8765	−1.40611	−0.703053	−	0.711138i	$-0.748180\pi$
$313$	−24.8765	−1.40611	−0.703053	+	0.711138i	$0.748180\pi$
$314$	11.8260	0.667381
$315$	0	0
$316$	−6.97391	−0.392313
$317$	17.1132	0.961176	0.480588	−	0.876947i	$-0.340423\pi$
$317$	17.1132	0.961176	0.480588	+	0.876947i	$0.340423\pi$
$318$	−2.13562	−0.119759
$319$	−1.49072	−0.0834645
$320$	0	0
$321$	0.529093	0.0295311
$322$	−14.0714	−0.784169
$323$	0.104765	0.00582930
$324$	13.5920	0.755109
$325$	0	0
$326$	14.4483	0.800219
$327$	−31.7278	−1.75455
$328$	−5.45783	−0.301359
$329$	−12.7719	−0.704135
$330$	0	0
$331$	−25.9203	−1.42471	−0.712353	−	0.701821i	$-0.752371\pi$
$331$	−25.9203	−1.42471	−0.712353	+	0.701821i	$0.752371\pi$
$332$	13.1604	0.722273
$333$	−4.63971	−0.254254
$334$	−12.1075	−0.662495
$335$	0	0
$336$	−1.28827	−0.0702810
$337$	18.9557	1.03258	0.516290	−	0.856414i	$-0.327313\pi$
$337$	18.9557	1.03258	0.516290	+	0.856414i	$0.327313\pi$
$338$	10.1783	0.553625
$339$	28.3692	1.54081
$340$	0	0
$341$	−3.21649	−0.174183
$342$	0.0195509	0.00105719
$343$	19.5180	1.05387
$344$	−26.5857	−1.43340
$345$	0	0
$346$	−13.0572	−0.701959
$347$	−7.70815	−0.413795	−0.206898	−	0.978363i	$-0.566337\pi$
$347$	−7.70815	−0.413795	−0.206898	+	0.978363i	$0.566337\pi$
$348$	−2.46832	−0.132316
$349$	−15.0015	−0.803014	−0.401507	−	0.915856i	$-0.631513\pi$
$349$	−15.0015	−0.803014	−0.401507	+	0.915856i	$0.631513\pi$
$350$	0	0
$351$	4.20513	0.224453
$352$	8.58611	0.457641
$353$	16.9486	0.902085	0.451043	−	0.892502i	$-0.351052\pi$
$353$	16.9486	0.902085	0.451043	+	0.892502i	$0.351052\pi$
$354$	−7.30911	−0.388475
$355$	0	0
$356$	8.92205	0.472867
$357$	13.1849	0.697817
$358$	−17.2144	−0.909811
$359$	−5.23876	−0.276491	−0.138246	−	0.990398i	$-0.544146\pi$
$359$	−5.23876	−0.276491	−0.138246	+	0.990398i	$0.544146\pi$
$360$	0	0
$361$	−18.9986	−0.999927
$362$	−14.6868	−0.771923
$363$	−16.7107	−0.877085
$364$	−2.97556	−0.155962
$365$	0	0
$366$	−19.4010	−1.01411
$367$	−15.2817	−0.797701	−0.398850	−	0.917016i	$-0.630591\pi$
$367$	−15.2817	−0.797701	−0.398850	+	0.917016i	$0.630591\pi$
$368$	−1.86343	−0.0971378
$369$	−1.23237	−0.0641544
$370$	0	0
$371$	−3.30139	−0.171400
$372$	−5.32583	−0.276131
$373$	−24.3674	−1.26169	−0.630847	−	0.775907i	$-0.717292\pi$
$373$	−24.3674	−1.26169	−0.630847	+	0.775907i	$0.717292\pi$
$374$	−3.50812	−0.181400
$375$	0	0
$376$	14.3063	0.737791
$377$	−0.929772	−0.0478857
$378$	−9.36314	−0.481588
$379$	−12.1058	−0.621832	−0.310916	−	0.950437i	$-0.600636\pi$
$379$	−12.1058	−0.621832	−0.310916	+	0.950437i	$0.600636\pi$
$380$	0	0
$381$	−27.0856	−1.38764
$382$	−13.0610	−0.668261
$383$	−21.0250	−1.07432	−0.537162	−	0.843479i	$-0.680504\pi$
$383$	−21.0250	−1.07432	−0.537162	+	0.843479i	$0.680504\pi$
$384$	15.0923	0.770175
$385$	0	0
$386$	−7.08254	−0.360492
$387$	−6.00298	−0.305149
$388$	−12.2185	−0.620302
$389$	−10.3647	−0.525509	−0.262755	−	0.964863i	$-0.584631\pi$
$389$	−10.3647	−0.525509	−0.262755	+	0.964863i	$0.584631\pi$
$390$	0	0
$391$	19.0713	0.964477
$392$	−2.50877	−0.126712
$393$	37.6929	1.90136
$394$	−8.54964	−0.430725
$395$	0	0
$396$	1.20665	0.0606366
$397$	17.7864	0.892673	0.446337	−	0.894865i	$-0.352728\pi$
$397$	17.7864	0.892673	0.446337	+	0.894865i	$0.352728\pi$
$398$	−5.48550	−0.274963
$399$	0.175457	0.00878384
$400$	0	0
$401$	−29.9868	−1.49747	−0.748734	−	0.662870i	$-0.769338\pi$
$401$	−29.9868	−1.49747	−0.748734	+	0.662870i	$0.769338\pi$
$402$	−0.465230	−0.0232036
$403$	−2.00614	−0.0999330
$404$	−14.2885	−0.710878
$405$	0	0
$406$	2.07023	0.102744
$407$	11.0788	0.549156
$408$	−14.7689	−0.731171
$409$	30.6717	1.51662	0.758309	−	0.651896i	$-0.226026\pi$
$409$	30.6717	1.51662	0.758309	+	0.651896i	$0.226026\pi$
$410$	0	0
$411$	1.81776	0.0896637
$412$	−5.85294	−0.288354
$413$	−11.2990	−0.555986
$414$	3.55902	0.174916
$415$	0	0
$416$	5.35520	0.262560
$417$	−42.9073	−2.10118
$418$	−0.0466842	−0.00228340
$419$	−15.0395	−0.734729	−0.367364	−	0.930077i	$-0.619740\pi$
$419$	−15.0395	−0.734729	−0.367364	+	0.930077i	$0.619740\pi$
$420$	0	0
$421$	−31.3625	−1.52852	−0.764258	−	0.644911i	$-0.776894\pi$
$421$	−31.3625	−1.52852	−0.764258	+	0.644911i	$0.776894\pi$
$422$	−13.0830	−0.636869
$423$	3.23033	0.157064
$424$	3.69803	0.179592
$425$	0	0
$426$	17.1625	0.831526
$427$	−29.9915	−1.45139
$428$	−0.360338	−0.0174176
$429$	2.63868	0.127396
$430$	0	0
$431$	−28.7116	−1.38299	−0.691495	−	0.722381i	$-0.743048\pi$
$431$	−28.7116	−1.38299	−0.691495	+	0.722381i	$0.743048\pi$
$432$	−1.23993	−0.0596561
$433$	−30.9086	−1.48537	−0.742686	−	0.669640i	$-0.766448\pi$
$433$	−30.9086	−1.48537	−0.742686	+	0.669640i	$0.766448\pi$
$434$	4.46687	0.214417
$435$	0	0
$436$	21.6082	1.03484
$437$	0.253791	0.0121405
$438$	0.0225181	0.00107596
$439$	18.5828	0.886907	0.443454	−	0.896297i	$-0.353753\pi$
$439$	18.5828	0.886907	0.443454	+	0.896297i	$0.353753\pi$
$440$	0	0
$441$	−0.566475	−0.0269750
$442$	−2.18803	−0.104074
$443$	32.4127	1.53997	0.769986	−	0.638061i	$-0.220263\pi$
$443$	32.4127	1.53997	0.769986	+	0.638061i	$0.220263\pi$
$444$	18.3442	0.870575
$445$	0	0
$446$	19.9331	0.943862
$447$	16.3127	0.771563
$448$	−10.5705	−0.499408
$449$	−12.7486	−0.601645	−0.300822	−	0.953680i	$-0.597261\pi$
$449$	−12.7486	−0.601645	−0.300822	+	0.953680i	$0.597261\pi$
$450$	0	0
$451$	2.94267	0.138565
$452$	−19.3208	−0.908775
$453$	25.2415	1.18595
$454$	−7.63443	−0.358301
$455$	0	0
$456$	−0.196537	−0.00920369
$457$	20.5383	0.960742	0.480371	−	0.877065i	$-0.340502\pi$
$457$	20.5383	0.960742	0.480371	+	0.877065i	$0.340502\pi$
$458$	−20.4498	−0.955556
$459$	12.6901	0.592322
$460$	0	0
$461$	15.0965	0.703114	0.351557	−	0.936167i	$-0.385652\pi$
$461$	15.0965	0.703114	0.351557	+	0.936167i	$0.385652\pi$
$462$	−5.87527	−0.273342
$463$	1.19501	0.0555367	0.0277684	−	0.999614i	$-0.491160\pi$
$463$	1.19501	0.0555367	0.0277684	+	0.999614i	$0.491160\pi$
$464$	0.274153	0.0127272
$465$	0	0
$466$	15.6273	0.723922
$467$	7.08659	0.327929	0.163964	−	0.986466i	$-0.447572\pi$
$467$	7.08659	0.327929	0.163964	+	0.986466i	$0.447572\pi$
$468$	0.752596	0.0347887
$469$	−0.719188	−0.0332090
$470$	0	0
$471$	−26.8432	−1.23687
$472$	12.6565	0.582561
$473$	14.3341	0.659081
$474$	−8.58844	−0.394480
$475$	0	0
$476$	−8.97953	−0.411576
$477$	0.835007	0.0382323
$478$	−1.42136	−0.0650117
$479$	38.8768	1.77633	0.888163	−	0.459528i	$-0.151981\pi$
$479$	38.8768	1.77633	0.888163	+	0.459528i	$0.151981\pi$
$480$	0	0
$481$	6.90990	0.315064
$482$	−7.19226	−0.327599
$483$	31.9399	1.45332
$484$	11.3808	0.517309
$485$	0	0
$486$	5.35868	0.243075
$487$	−30.3083	−1.37340	−0.686701	−	0.726940i	$-0.740942\pi$
$487$	−30.3083	−1.37340	−0.686701	+	0.726940i	$0.740942\pi$
$488$	33.5948	1.52077
$489$	−32.7955	−1.48306
$490$	0	0
$491$	−9.84537	−0.444315	−0.222158	−	0.975011i	$-0.571310\pi$
$491$	−9.84537	−0.444315	−0.222158	+	0.975011i	$0.571310\pi$
$492$	4.87244	0.219667
$493$	−2.80583	−0.126368
$494$	−0.0291171	−0.00131004
$495$	0	0
$496$	0.591532	0.0265606
$497$	26.5311	1.19008
$498$	16.2072	0.726262
$499$	20.9719	0.938829	0.469415	−	0.882978i	$-0.344465\pi$
$499$	20.9719	0.938829	0.469415	+	0.882978i	$0.344465\pi$
$500$	0	0
$501$	27.4822	1.22782
$502$	23.1679	1.03403
$503$	−42.2017	−1.88168	−0.940841	−	0.338849i	$-0.889963\pi$
$503$	−42.2017	−1.88168	−0.940841	+	0.338849i	$0.889963\pi$
$504$	−4.26062	−0.189783
$505$	0	0
$506$	−8.49831	−0.377796
$507$	−23.1031	−1.02605
$508$	18.4466	0.818436
$509$	7.00080	0.310305	0.155153	−	0.987891i	$-0.450413\pi$
$509$	7.00080	0.310305	0.155153	+	0.987891i	$0.450413\pi$
$510$	0	0
$511$	0.0348102	0.00153991
$512$	−3.09504	−0.136783
$513$	0.168873	0.00745592
$514$	5.04925	0.222713
$515$	0	0
$516$	23.7342	1.04484
$517$	−7.71345	−0.339237
$518$	−15.3856	−0.676003
$519$	29.6378	1.30096
$520$	0	0
$521$	12.0767	0.529091	0.264545	−	0.964373i	$-0.414778\pi$
$521$	12.0767	0.529091	0.264545	+	0.964373i	$0.414778\pi$
$522$	−0.523614	−0.0229179
$523$	−30.9879	−1.35500	−0.677502	−	0.735521i	$-0.736938\pi$
$523$	−30.9879	−1.35500	−0.677502	+	0.735521i	$0.736938\pi$
$524$	−25.6707	−1.12143
$525$	0	0
$526$	6.82211	0.297458
$527$	−6.05405	−0.263719
$528$	−0.778041	−0.0338599
$529$	23.1996	1.00868
$530$	0	0
$531$	2.85780	0.124018
$532$	−0.119495	−0.00518075
$533$	1.83536	0.0794982
$534$	10.9876	0.475479
$535$	0	0
$536$	0.805593	0.0347963
$537$	39.0741	1.68617
$538$	2.88439	0.124355
$539$	1.35264	0.0582624
$540$	0	0
$541$	−5.40732	−0.232479	−0.116240	−	0.993221i	$-0.537084\pi$
$541$	−5.40732	−0.232479	−0.116240	+	0.993221i	$0.537084\pi$
$542$	8.79161	0.377632
$543$	33.3369	1.43062
$544$	16.1607	0.692885
$545$	0	0
$546$	−3.66443	−0.156823
$547$	0.766804	0.0327862	0.0163931	−	0.999866i	$-0.494782\pi$
$547$	0.766804	0.0327862	0.0163931	+	0.999866i	$0.494782\pi$
$548$	−1.23799	−0.0528841
$549$	7.58563	0.323747
$550$	0	0
$551$	−0.0373385	−0.00159067
$552$	−35.7773	−1.52278
$553$	−13.2766	−0.564580
$554$	15.8737	0.674410
$555$	0	0
$556$	29.2219	1.23929
$557$	38.2414	1.62034	0.810170	−	0.586195i	$-0.199375\pi$
$557$	38.2414	1.62034	0.810170	+	0.586195i	$0.199375\pi$
$558$	−1.12979	−0.0478276
$559$	8.94023	0.378131
$560$	0	0
$561$	7.96289	0.336193
$562$	20.6987	0.873123
$563$	−36.0317	−1.51855	−0.759277	−	0.650768i	$-0.774447\pi$
$563$	−36.0317	−1.51855	−0.759277	+	0.650768i	$0.774447\pi$
$564$	−12.7719	−0.537792
$565$	0	0
$566$	2.62255	0.110234
$567$	25.8758	1.08668
$568$	−29.7186	−1.24697
$569$	−17.6536	−0.740077	−0.370038	−	0.929016i	$-0.620655\pi$
$569$	−17.6536	−0.740077	−0.370038	+	0.929016i	$0.620655\pi$
$570$	0	0
$571$	−3.66464	−0.153360	−0.0766801	−	0.997056i	$-0.524432\pi$
$571$	−3.66464	−0.153360	−0.0766801	+	0.997056i	$0.524432\pi$
$572$	−1.79707	−0.0751391
$573$	29.6466	1.23850
$574$	−4.08661	−0.170572
$575$	0	0
$576$	2.67354	0.111398
$577$	25.9865	1.08183	0.540917	−	0.841076i	$-0.318077\pi$
$577$	25.9865	1.08183	0.540917	+	0.841076i	$0.318077\pi$
$578$	7.65525	0.318417
$579$	16.0763	0.668107
$580$	0	0
$581$	25.0543	1.03943
$582$	−15.0472	−0.623728
$583$	−1.99385	−0.0825768
$584$	−0.0389924	−0.00161352
$585$	0	0
$586$	−5.82930	−0.240806
$587$	26.3857	1.08905	0.544527	−	0.838744i	$-0.316709\pi$
$587$	26.3857	1.08905	0.544527	+	0.838744i	$0.316709\pi$
$588$	2.23969	0.0923633
$589$	−0.0805641	−0.00331958
$590$	0	0
$591$	19.4064	0.798272
$592$	−2.03746	−0.0837390
$593$	37.1560	1.52581	0.762907	−	0.646508i	$-0.223771\pi$
$593$	37.1560	1.52581	0.762907	+	0.646508i	$0.223771\pi$
$594$	−5.65479	−0.232019
$595$	0	0
$596$	−11.1097	−0.455072
$597$	12.4512	0.509596
$598$	−5.30044	−0.216751
$599$	−5.96103	−0.243561	−0.121781	−	0.992557i	$-0.538860\pi$
$599$	−5.96103	−0.243561	−0.121781	+	0.992557i	$0.538860\pi$
$600$	0	0
$601$	9.40636	0.383693	0.191847	−	0.981425i	$-0.438552\pi$
$601$	9.40636	0.383693	0.191847	+	0.981425i	$0.438552\pi$
$602$	−19.9063	−0.811320
$603$	0.181901	0.00740758
$604$	−17.1907	−0.699478
$605$	0	0
$606$	−17.5964	−0.714805
$607$	11.5121	0.467263	0.233632	−	0.972325i	$-0.424939\pi$
$607$	11.5121	0.467263	0.233632	+	0.972325i	$0.424939\pi$
$608$	0.215058	0.00872176
$609$	−4.69910	−0.190417
$610$	0	0
$611$	−4.81092	−0.194629
$612$	2.27115	0.0918059
$613$	33.9655	1.37185	0.685927	−	0.727670i	$-0.259397\pi$
$613$	33.9655	1.37185	0.685927	+	0.727670i	$0.259397\pi$
$614$	12.9491	0.522583
$615$	0	0
$616$	10.1736	0.409907
$617$	−18.1241	−0.729650	−0.364825	−	0.931076i	$-0.618871\pi$
$617$	−18.1241	−0.729650	−0.364825	+	0.931076i	$0.618871\pi$
$618$	−7.20795	−0.289946
$619$	−43.7822	−1.75976	−0.879878	−	0.475200i	$-0.842376\pi$
$619$	−43.7822	−1.75976	−0.879878	+	0.475200i	$0.842376\pi$
$620$	0	0
$621$	30.7413	1.23361
$622$	10.8940	0.436811
$623$	16.9854	0.680507
$624$	−0.485268	−0.0194263
$625$	0	0
$626$	20.8644	0.833909
$627$	0.105966	0.00423187
$628$	18.2815	0.729513
$629$	20.8524	0.831440
$630$	0	0
$631$	−31.8836	−1.26927	−0.634633	−	0.772814i	$-0.718849\pi$
$631$	−31.8836	−1.26927	−0.634633	+	0.772814i	$0.718849\pi$
$632$	14.8717	0.591566
$633$	29.6963	1.18032
$634$	−14.3532	−0.570038
$635$	0	0
$636$	−3.30139	−0.130909
$637$	0.843650	0.0334266
$638$	1.25030	0.0494997
$639$	−6.71039	−0.265459
$640$	0	0
$641$	−7.56055	−0.298624	−0.149312	−	0.988790i	$-0.547706\pi$
$641$	−7.56055	−0.298624	−0.149312	+	0.988790i	$0.547706\pi$
$642$	−0.443759	−0.0175138
$643$	6.78946	0.267750	0.133875	−	0.990998i	$-0.457258\pi$
$643$	6.78946	0.267750	0.133875	+	0.990998i	$0.457258\pi$
$644$	−21.7526	−0.857173
$645$	0	0
$646$	−0.0878685	−0.00345714
$647$	−32.4336	−1.27510	−0.637549	−	0.770410i	$-0.720051\pi$
$647$	−32.4336	−1.27510	−0.637549	+	0.770410i	$0.720051\pi$
$648$	−28.9846	−1.13862
$649$	−6.82391	−0.267862
$650$	0	0
$651$	−10.1391	−0.397383
$652$	22.3353	0.874718
$653$	−20.3067	−0.794661	−0.397331	−	0.917676i	$-0.630063\pi$
$653$	−20.3067	−0.794661	−0.397331	+	0.917676i	$0.630063\pi$
$654$	26.6107	1.04056
$655$	0	0
$656$	−0.541175	−0.0211293
$657$	−0.00880440	−0.000343492 0
$658$	10.7120	0.417597
$659$	−47.3789	−1.84562	−0.922809	−	0.385257i	$-0.874113\pi$
$659$	−47.3789	−1.84562	−0.922809	+	0.385257i	$0.874113\pi$
$660$	0	0
$661$	23.1097	0.898862	0.449431	−	0.893315i	$-0.351627\pi$
$661$	23.1097	0.898862	0.449431	+	0.893315i	$0.351627\pi$
$662$	21.7398	0.844941
$663$	4.96649	0.192883
$664$	−28.0644	−1.08911
$665$	0	0
$666$	3.89140	0.150789
$667$	−6.79703	−0.263182
$668$	−18.7167	−0.724172
$669$	−45.2452	−1.74928
$670$	0	0
$671$	−18.1131	−0.699250
$672$	27.0654	1.04407
$673$	−0.691021	−0.0266369	−0.0133184	−	0.999911i	$-0.504240\pi$
$673$	−0.691021	−0.0266369	−0.0133184	+	0.999911i	$0.504240\pi$
$674$	−15.8984	−0.612385
$675$	0	0
$676$	15.7343	0.605167
$677$	−10.2253	−0.392989	−0.196494	−	0.980505i	$-0.562956\pi$
$677$	−10.2253	−0.392989	−0.196494	+	0.980505i	$0.562956\pi$
$678$	−23.7938	−0.913795
$679$	−23.2611	−0.892681
$680$	0	0
$681$	17.3290	0.664048
$682$	2.69773	0.103301
$683$	9.74838	0.373012	0.186506	−	0.982454i	$-0.440284\pi$
$683$	9.74838	0.373012	0.186506	+	0.982454i	$0.440284\pi$
$684$	0.0302233	0.00115562
$685$	0	0
$686$	−16.3701	−0.625012
$687$	46.4179	1.77095
$688$	−2.63612	−0.100501
$689$	−1.24357	−0.0473764
$690$	0	0
$691$	−32.7638	−1.24639	−0.623197	−	0.782065i	$-0.714167\pi$
$691$	−32.7638	−1.24639	−0.623197	+	0.782065i	$0.714167\pi$
$692$	−20.1848	−0.767311
$693$	2.29718	0.0872626
$694$	6.46496	0.245407
$695$	0	0
$696$	5.26366	0.199519
$697$	5.53867	0.209792
$698$	12.5821	0.476238
$699$	−35.4716	−1.34166
$700$	0	0
$701$	−14.7894	−0.558588	−0.279294	−	0.960206i	$-0.590100\pi$
$701$	−14.7894	−0.558588	−0.279294	+	0.960206i	$0.590100\pi$
$702$	−3.52692	−0.133115
$703$	0.277493	0.0104658
$704$	−6.38395	−0.240604
$705$	0	0
$706$	−14.2151	−0.534993
$707$	−27.2018	−1.02303
$708$	−11.2990	−0.424641
$709$	42.1665	1.58360	0.791799	−	0.610782i	$-0.209145\pi$
$709$	42.1665	1.58360	0.791799	+	0.610782i	$0.209145\pi$
$710$	0	0
$711$	3.35800	0.125935
$712$	−19.0261	−0.713034
$713$	−14.6657	−0.549236
$714$	−11.0584	−0.413849
$715$	0	0
$716$	−26.6114	−0.994513
$717$	3.22628	0.120488
$718$	4.39384	0.163977
$719$	−16.2819	−0.607211	−0.303606	−	0.952798i	$-0.598191\pi$
$719$	−16.2819	−0.607211	−0.303606	+	0.952798i	$0.598191\pi$
$720$	0	0
$721$	−11.1426	−0.414972
$722$	15.9345	0.593020
$723$	16.3253	0.607146
$724$	−22.7040	−0.843788
$725$	0	0
$726$	14.0156	0.520167
$727$	−10.2431	−0.379894	−0.189947	−	0.981794i	$-0.560832\pi$
$727$	−10.2431	−0.379894	−0.189947	+	0.981794i	$0.560832\pi$
$728$	6.34534	0.235174
$729$	19.2861	0.714299
$730$	0	0
$731$	26.9795	0.997871
$732$	−29.9915	−1.10852
$733$	−1.34776	−0.0497807	−0.0248904	−	0.999690i	$-0.507924\pi$
$733$	−1.34776	−0.0497807	−0.0248904	+	0.999690i	$0.507924\pi$
$734$	12.8171	0.473087
$735$	0	0
$736$	39.1488	1.44304
$737$	−0.434347	−0.0159994
$738$	1.03361	0.0380476
$739$	−33.2111	−1.22169	−0.610844	−	0.791751i	$-0.709170\pi$
$739$	−33.2111	−1.22169	−0.610844	+	0.791751i	$0.709170\pi$
$740$	0	0
$741$	0.0660914	0.00242793
$742$	2.76894	0.101651
$743$	36.6826	1.34576	0.672878	−	0.739754i	$-0.265058\pi$
$743$	36.6826	1.34576	0.672878	+	0.739754i	$0.265058\pi$
$744$	11.3572	0.416377
$745$	0	0
$746$	20.4373	0.748264
$747$	−6.33688	−0.231854
$748$	−5.42311	−0.198289
$749$	−0.685996	−0.0250658
$750$	0	0
$751$	−16.0304	−0.584959	−0.292480	−	0.956272i	$-0.594480\pi$
$751$	−16.0304	−0.584959	−0.292480	+	0.956272i	$0.594480\pi$
$752$	1.41855	0.0517292
$753$	−52.5875	−1.91640
$754$	0.779816	0.0283992
$755$	0	0
$756$	−14.4742	−0.526423
$757$	42.4991	1.54466	0.772328	−	0.635224i	$-0.219092\pi$
$757$	42.4991	1.54466	0.772328	+	0.635224i	$0.219092\pi$
$758$	10.1533	0.368786
$759$	19.2898	0.700177
$760$	0	0
$761$	24.7756	0.898114	0.449057	−	0.893503i	$-0.351760\pi$
$761$	24.7756	0.898114	0.449057	+	0.893503i	$0.351760\pi$
$762$	22.7172	0.822957
$763$	41.1368	1.48925
$764$	−20.1907	−0.730475
$765$	0	0
$766$	17.6340	0.637142
$767$	−4.25611	−0.153679
$768$	−28.9637	−1.04514
$769$	22.9249	0.826694	0.413347	−	0.910573i	$-0.364360\pi$
$769$	22.9249	0.826694	0.413347	+	0.910573i	$0.364360\pi$
$770$	0	0
$771$	−11.4610	−0.412759
$772$	−10.9487	−0.394053
$773$	46.2921	1.66501	0.832506	−	0.554016i	$-0.186905\pi$
$773$	46.2921	1.66501	0.832506	+	0.554016i	$0.186905\pi$
$774$	5.03481	0.180972
$775$	0	0
$776$	26.0558	0.935349
$777$	34.9229	1.25285
$778$	8.69302	0.311660
$779$	0.0737057	0.00264078
$780$	0	0
$781$	16.0232	0.573356
$782$	−15.9954	−0.571996
$783$	−4.52276	−0.161630
$784$	−0.248759	−0.00888425
$785$	0	0
$786$	−31.6137	−1.12762
$787$	−3.89849	−0.138966	−0.0694832	−	0.997583i	$-0.522135\pi$
$787$	−3.89849	−0.138966	−0.0694832	+	0.997583i	$0.522135\pi$
$788$	−13.2167	−0.470825
$789$	−15.4851	−0.551285
$790$	0	0
$791$	−36.7822	−1.30782
$792$	−2.57317	−0.0914336
$793$	−11.2973	−0.401177
$794$	−14.9178	−0.529411
$795$	0	0
$796$	−8.47990	−0.300562
$797$	−21.1877	−0.750506	−0.375253	−	0.926922i	$-0.622444\pi$
$797$	−21.1877	−0.750506	−0.375253	+	0.926922i	$0.622444\pi$
$798$	−0.147159	−0.00520937
$799$	−14.5182	−0.513617
$800$	0	0
$801$	−4.29605	−0.151793
$802$	25.1504	0.888093
$803$	0.0210233	0.000741898 0
$804$	−0.719188	−0.0253638
$805$	0	0
$806$	1.68259	0.0592666
$807$	−6.54712	−0.230470
$808$	30.4699	1.07193
$809$	23.9959	0.843651	0.421826	−	0.906677i	$-0.361389\pi$
$809$	23.9959	0.843651	0.421826	+	0.906677i	$0.361389\pi$
$810$	0	0
$811$	−8.15390	−0.286322	−0.143161	−	0.989699i	$-0.545727\pi$
$811$	−8.15390	−0.286322	−0.143161	+	0.989699i	$0.545727\pi$
$812$	3.20031	0.112309
$813$	−19.9556	−0.699873
$814$	−9.29198	−0.325684
$815$	0	0
$816$	−1.46442	−0.0512651
$817$	0.359028	0.0125608
$818$	−25.7249	−0.899450
$819$	1.43276	0.0500647
$820$	0	0
$821$	−8.76657	−0.305955	−0.152978	−	0.988230i	$-0.548886\pi$
$821$	−8.76657	−0.305955	−0.152978	+	0.988230i	$0.548886\pi$
$822$	−1.52459	−0.0531762
$823$	−49.1112	−1.71191	−0.855955	−	0.517050i	$-0.827030\pi$
$823$	−49.1112	−1.71191	−0.855955	+	0.517050i	$0.827030\pi$
$824$	12.4813	0.434807
$825$	0	0
$826$	9.47664	0.329734
$827$	−34.1055	−1.18597	−0.592983	−	0.805215i	$-0.702050\pi$
$827$	−34.1055	−1.18597	−0.592983	+	0.805215i	$0.702050\pi$
$828$	5.50179	0.191201
$829$	1.20117	0.0417183	0.0208591	−	0.999782i	$-0.493360\pi$
$829$	1.20117	0.0417183	0.0208591	+	0.999782i	$0.493360\pi$
$830$	0	0
$831$	−36.0309	−1.24990
$832$	−3.98170	−0.138041
$833$	2.54593	0.0882113
$834$	35.9871	1.24613
$835$	0	0
$836$	−0.0721679	−0.00249598
$837$	−9.75862	−0.337307
$838$	12.6139	0.435740
$839$	−1.87849	−0.0648526	−0.0324263	−	0.999474i	$-0.510323\pi$
$839$	−1.87849	−0.0648526	−0.0324263	+	0.999474i	$0.510323\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	26.3043	0.906506
$843$	−46.9829	−1.61818
$844$	−20.2246	−0.696161
$845$	0	0
$846$	−2.70933	−0.0931488
$847$	21.6663	0.744463
$848$	0.366681	0.0125919
$849$	−5.95278	−0.204299
$850$	0	0
$851$	50.5143	1.73161
$852$	26.5311	0.908940
$853$	33.0917	1.13304	0.566519	−	0.824049i	$-0.308290\pi$
$853$	33.0917	1.13304	0.566519	+	0.824049i	$0.308290\pi$
$854$	25.1544	0.860767
$855$	0	0
$856$	0.768414	0.0262639
$857$	47.6859	1.62892	0.814460	−	0.580220i	$-0.197034\pi$
$857$	47.6859	1.62892	0.814460	+	0.580220i	$0.197034\pi$
$858$	−2.21310	−0.0755541
$859$	0.746091	0.0254563	0.0127281	−	0.999919i	$-0.495948\pi$
$859$	0.746091	0.0254563	0.0127281	+	0.999919i	$0.495948\pi$
$860$	0	0
$861$	9.27596	0.316124
$862$	24.0810	0.820201
$863$	46.8245	1.59392	0.796962	−	0.604030i	$-0.206439\pi$
$863$	46.8245	1.59392	0.796962	+	0.604030i	$0.206439\pi$
$864$	26.0497	0.886229
$865$	0	0
$866$	25.9236	0.880919
$867$	−17.3762	−0.590128
$868$	6.90522	0.234378
$869$	−8.01832	−0.272003
$870$	0	0
$871$	−0.270905	−0.00917925
$872$	−46.0791	−1.56043
$873$	5.88334	0.199121
$874$	−0.212859	−0.00720005
$875$	0	0
$876$	0.0348102	0.00117613
$877$	−0.970257	−0.0327632	−0.0163816	−	0.999866i	$-0.505215\pi$
$877$	−0.970257	−0.0327632	−0.0163816	+	0.999866i	$0.505215\pi$
$878$	−15.5857	−0.525992
$879$	13.2316	0.446291
$880$	0	0
$881$	0.755979	0.0254696	0.0127348	−	0.999919i	$-0.495946\pi$
$881$	0.755979	0.0254696	0.0127348	+	0.999919i	$0.495946\pi$
$882$	0.475113	0.0159979
$883$	−15.8839	−0.534536	−0.267268	−	0.963622i	$-0.586121\pi$
$883$	−15.8839	−0.534536	−0.267268	+	0.963622i	$0.586121\pi$
$884$	−3.38242	−0.113763
$885$	0	0
$886$	−27.1851	−0.913300
$887$	12.5061	0.419915	0.209958	−	0.977710i	$-0.432667\pi$
$887$	12.5061	0.419915	0.209958	+	0.977710i	$0.432667\pi$
$888$	−39.1186	−1.31273
$889$	35.1179	1.17782
$890$	0	0
$891$	15.6275	0.523541
$892$	30.8141	1.03173
$893$	−0.193200	−0.00646521
$894$	−13.6817	−0.457586
$895$	0	0
$896$	−19.5679	−0.653719
$897$	12.0312	0.401709
$898$	10.6925	0.356813
$899$	2.15767	0.0719623
$900$	0	0
$901$	−3.75281	−0.125024
$902$	−2.46807	−0.0821778
$903$	45.1842	1.50364
$904$	41.2013	1.37034
$905$	0	0
$906$	−21.1705	−0.703342
$907$	−0.966094	−0.0320786	−0.0160393	−	0.999871i	$-0.505106\pi$
$907$	−0.966094	−0.0320786	−0.0160393	+	0.999871i	$0.505106\pi$
$908$	−11.8019	−0.391659
$909$	6.88004	0.228197
$910$	0	0
$911$	−21.2288	−0.703340	−0.351670	−	0.936124i	$-0.614386\pi$
$911$	−21.2288	−0.703340	−0.351670	+	0.936124i	$0.614386\pi$
$912$	−0.0194878	−0.000645304 0
$913$	15.1313	0.500774
$914$	−17.2259	−0.569781
$915$	0	0
$916$	−31.6128	−1.04452
$917$	−48.8709	−1.61386
$918$	−10.6434	−0.351284
$919$	16.9547	0.559284	0.279642	−	0.960104i	$-0.409784\pi$
$919$	16.9547	0.559284	0.279642	+	0.960104i	$0.409784\pi$
$920$	0	0
$921$	−29.3925	−0.968515
$922$	−12.6617	−0.416991
$923$	9.99377	0.328949
$924$	−9.08243	−0.298790
$925$	0	0
$926$	−1.00227	−0.0329368
$927$	2.81825	0.0925634
$928$	−5.75969	−0.189071
$929$	−26.0792	−0.855632	−0.427816	−	0.903866i	$-0.640717\pi$
$929$	−26.0792	−0.855632	−0.427816	+	0.903866i	$0.640717\pi$
$930$	0	0
$931$	0.0338799	0.00111037
$932$	24.1579	0.791318
$933$	−24.7278	−0.809552
$934$	−5.94365	−0.194482
$935$	0	0
$936$	−1.60490	−0.0524577
$937$	−6.07903	−0.198593	−0.0992967	−	0.995058i	$-0.531659\pi$
$937$	−6.07903	−0.198593	−0.0992967	+	0.995058i	$0.531659\pi$
$938$	0.603196	0.0196950
$939$	−47.3590	−1.54550
$940$	0	0
$941$	49.5166	1.61419	0.807097	−	0.590419i	$-0.201037\pi$
$941$	49.5166	1.61419	0.807097	+	0.590419i	$0.201037\pi$
$942$	22.5139	0.733542
$943$	13.4173	0.436926
$944$	1.25496	0.0408454
$945$	0	0
$946$	−12.0222	−0.390877
$947$	26.9125	0.874539	0.437269	−	0.899331i	$-0.355946\pi$
$947$	26.9125	0.874539	0.437269	+	0.899331i	$0.355946\pi$
$948$	−13.2766	−0.431205
$949$	0.0131124	0.000425645 0
$950$	0	0
$951$	32.5795	1.05646
$952$	19.1487	0.620613
$953$	−30.8022	−0.997781	−0.498891	−	0.866665i	$-0.666259\pi$
$953$	−30.8022	−0.997781	−0.498891	+	0.866665i	$0.666259\pi$
$954$	−0.700335	−0.0226742
$955$	0	0
$956$	−2.19725	−0.0710642
$957$	−2.83798	−0.0917389
$958$	−32.6067	−1.05347
$959$	−2.35683	−0.0761059
$960$	0	0
$961$	−26.3445	−0.849821
$962$	−5.79546	−0.186853
$963$	0.173506	0.00559115
$964$	−11.1183	−0.358098
$965$	0	0
$966$	−26.7886	−0.861908
$967$	−50.1110	−1.61146	−0.805730	−	0.592283i	$-0.798227\pi$
$967$	−50.1110	−1.61146	−0.805730	+	0.592283i	$0.798227\pi$
$968$	−24.2694	−0.780047
$969$	0.199448	0.00640719
$970$	0	0
$971$	−13.0301	−0.418156	−0.209078	−	0.977899i	$-0.567046\pi$
$971$	−13.0301	−0.418156	−0.209078	+	0.977899i	$0.567046\pi$
$972$	8.28385	0.265705
$973$	55.6315	1.78346
$974$	25.4201	0.814514
$975$	0	0
$976$	3.33111	0.106626
$977$	3.50116	0.112012	0.0560060	−	0.998430i	$-0.482163\pi$
$977$	3.50116	0.112012	0.0560060	+	0.998430i	$0.482163\pi$
$978$	27.5062	0.879550
$979$	10.2582	0.327854
$980$	0	0
$981$	−10.4045	−0.332191
$982$	8.25748	0.263507
$983$	41.2281	1.31497	0.657486	−	0.753467i	$-0.271620\pi$
$983$	41.2281	1.31497	0.657486	+	0.753467i	$0.271620\pi$
$984$	−10.3904	−0.331234
$985$	0	0
$986$	2.35330	0.0749443
$987$	−24.3145	−0.773941
$988$	−0.0450115	−0.00143201
$989$	65.3569	2.07823
$990$	0	0
$991$	3.17997	0.101015	0.0505076	−	0.998724i	$-0.483916\pi$
$991$	3.17997	0.101015	0.0505076	+	0.998724i	$0.483916\pi$
$992$	−12.4275	−0.394574
$993$	−49.3460	−1.56595
$994$	−22.2521	−0.705793
$995$	0	0
$996$	25.0543	0.793876
$997$	−33.8545	−1.07218	−0.536092	−	0.844160i	$-0.680100\pi$
$997$	−33.8545	−1.07218	−0.536092	+	0.844160i	$0.680100\pi$
$998$	−17.5895	−0.556785
$999$	33.6123	1.06345

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.a.h.1.3	✓	5
3.2	odd	2		6525.2.a.bq.1.3		5
5.2	odd	4		725.2.b.f.349.5		10
5.3	odd	4		725.2.b.f.349.6		10
5.4	even	2		725.2.a.k.1.3	yes	5
15.14	odd	2		6525.2.a.bm.1.3		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
725.2.a.h.1.3	✓	5	1.1	even	1	trivial
725.2.a.k.1.3	yes	5	5.4	even	2
725.2.b.f.349.5		10	5.2	odd	4
725.2.b.f.349.6		10	5.3	odd	4
6525.2.a.bm.1.3		5	15.14	odd	2
6525.2.a.bq.1.3		5	3.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.a (trivial)

\(f(q)\)	\(=\)	\(q-0.838718 q^{2} +1.90376 q^{3} -1.29655 q^{4} -1.59672 q^{6} -2.46832 q^{7} +2.76488 q^{8} +0.624302 q^{9} -1.49072 q^{11} -2.46832 q^{12} -0.929772 q^{13} +2.07023 q^{14} +0.274153 q^{16} -2.80583 q^{17} -0.523614 q^{18} -0.0373385 q^{19} -4.69910 q^{21} +1.25030 q^{22} -6.79703 q^{23} +5.26366 q^{24} +0.779816 q^{26} -4.52276 q^{27} +3.20031 q^{28} +1.00000 q^{29} +2.15767 q^{31} -5.75969 q^{32} -2.83798 q^{33} +2.35330 q^{34} -0.809441 q^{36} -7.43182 q^{37} +0.0313164 q^{38} -1.77006 q^{39} -1.97399 q^{41} +3.94122 q^{42} -9.61550 q^{43} +1.93280 q^{44} +5.70079 q^{46} +5.17430 q^{47} +0.521922 q^{48} -0.907373 q^{49} -5.34162 q^{51} +1.20550 q^{52} +1.33750 q^{53} +3.79332 q^{54} -6.82462 q^{56} -0.0710835 q^{57} -0.838718 q^{58} +4.57758 q^{59} +12.1506 q^{61} -1.80968 q^{62} -1.54098 q^{63} +4.28245 q^{64} +2.38027 q^{66} +0.291367 q^{67} +3.63790 q^{68} -12.9399 q^{69} -10.7486 q^{71} +1.72612 q^{72} -0.0141028 q^{73} +6.23320 q^{74} +0.0484113 q^{76} +3.67959 q^{77} +1.48458 q^{78} +5.37881 q^{79} -10.4832 q^{81} +1.65562 q^{82} -10.1503 q^{83} +6.09263 q^{84} +8.06469 q^{86} +1.90376 q^{87} -4.12167 q^{88} -6.88136 q^{89} +2.29498 q^{91} +8.81271 q^{92} +4.10769 q^{93} -4.33978 q^{94} -10.9651 q^{96} +9.42386 q^{97} +0.761030 q^{98} -0.930663 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 2 q^{2} - 6 q^{3} + 4 q^{4} - q^{6} - 6 q^{7} - 3 q^{8} + 11 q^{9} - 2 q^{11} - 6 q^{12} - 4 q^{13} + 11 q^{14} - 10 q^{16} - 9 q^{17} + 2 q^{19} - q^{21} - 4 q^{22} - q^{23} + 13 q^{24} - 16 q^{26}+ \cdots - 26 q^{99}+O(q^{100}) \) 5 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 - q^6 - 6 * q^7 - 3 * q^8 + 11 * q^9 - 2 * q^11 - 6 * q^12 - 4 * q^13 + 11 * q^14 - 10 * q^16 - 9 * q^17 + 2 * q^19 - q^21 - 4 * q^22 - q^23 + 13 * q^24 - 16 * q^26 - 27 * q^27 - 10 * q^28 + 5 * q^29 - q^31 + 2 * q^32 + 7 * q^33 + 3 * q^34 - 13 * q^36 - 14 * q^37 + 3 * q^38 - 6 * q^39 + 5 * q^41 - 24 * q^42 - 28 * q^43 + 7 * q^44 - 20 * q^46 - 15 * q^47 + 26 * q^48 - 3 * q^49 + 5 * q^51 - 6 * q^52 + 8 * q^53 + 10 * q^54 - 16 * q^56 + 6 * q^57 - 2 * q^58 - 11 * q^59 - 5 * q^61 + 6 * q^62 + 5 * q^63 - 5 * q^64 - 27 * q^66 - 23 * q^67 - q^68 - 26 * q^69 - 5 * q^71 - 3 * q^72 - 16 * q^73 + 8 * q^74 + 16 * q^76 + 30 * q^77 + 33 * q^78 - 10 * q^79 + 49 * q^81 + 19 * q^82 - 9 * q^83 + 32 * q^84 - 13 * q^86 - 6 * q^87 - 35 * q^88 - 18 * q^89 + q^91 + 27 * q^92 - 7 * q^93 - 13 * q^94 - 38 * q^96 - 23 * q^97 - 3 * q^98 - 26 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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