LMFDB - Embedded newform 1849.2.a.m.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,2,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1849.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:	$14.7643393337$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{44})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 11x^{8} + 44x^{6} - 77x^{4} + 55x^{2} - 11 $ x^10 - 11x^8 + 44x^6 - 77x^4 + 55x^2 - 11
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			1.9
Root			$1.81926$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.81926 q^{2} +1.25580 q^{3} +1.30972 q^{4} +0.160379 q^{5} +2.28463 q^{6} -4.31672 q^{7} -1.25580 q^{8} -1.42297 q^{9} +O(q^{10})$	\(q+1.81926 q^{2} +1.25580 q^{3} +1.30972 q^{4} +0.160379 q^{5} +2.28463 q^{6} -4.31672 q^{7} -1.25580 q^{8} -1.42297 q^{9} +0.291772 q^{10} -0.148323 q^{11} +1.64475 q^{12} +1.68675 q^{13} -7.85326 q^{14} +0.201404 q^{15} -4.90407 q^{16} -5.73187 q^{17} -2.58876 q^{18} -4.22912 q^{19} +0.210052 q^{20} -5.42094 q^{21} -0.269839 q^{22} -3.75285 q^{23} -1.57703 q^{24} -4.97428 q^{25} +3.06865 q^{26} -5.55436 q^{27} -5.65371 q^{28} +8.83708 q^{29} +0.366406 q^{30} +8.64308 q^{31} -6.41020 q^{32} -0.186264 q^{33} -10.4278 q^{34} -0.692311 q^{35} -1.86369 q^{36} +7.19452 q^{37} -7.69389 q^{38} +2.11822 q^{39} -0.201404 q^{40} -3.67049 q^{41} -9.86211 q^{42} -0.194262 q^{44} -0.228214 q^{45} -6.82743 q^{46} -2.13120 q^{47} -6.15853 q^{48} +11.6341 q^{49} -9.04953 q^{50} -7.19807 q^{51} +2.20918 q^{52} +1.98798 q^{53} -10.1048 q^{54} -0.0237879 q^{55} +5.42094 q^{56} -5.31093 q^{57} +16.0770 q^{58} +11.3627 q^{59} +0.263783 q^{60} +5.65302 q^{61} +15.7240 q^{62} +6.14256 q^{63} -1.85371 q^{64} +0.270519 q^{65} -0.338863 q^{66} -1.42587 q^{67} -7.50715 q^{68} -4.71283 q^{69} -1.25950 q^{70} -7.56187 q^{71} +1.78696 q^{72} -4.99089 q^{73} +13.0887 q^{74} -6.24669 q^{75} -5.53898 q^{76} +0.640269 q^{77} +3.85360 q^{78} -14.8660 q^{79} -0.786510 q^{80} -2.70625 q^{81} -6.67759 q^{82} -6.11970 q^{83} -7.09992 q^{84} -0.919270 q^{85} +11.0976 q^{87} +0.186264 q^{88} -8.33340 q^{89} -0.415182 q^{90} -7.28124 q^{91} -4.91519 q^{92} +10.8540 q^{93} -3.87721 q^{94} -0.678262 q^{95} -8.04993 q^{96} +2.10967 q^{97} +21.1655 q^{98} +0.211059 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{4} + 22 q^{6} + 14 q^{9}+O(q^{10}) $ 10 * q + 2 * q^4 + 22 * q^6 + 14 * q^9	$ 10 q + 2 q^{4} + 22 q^{6} + 14 q^{9} - 22 q^{10} - 10 q^{11} - 14 q^{13} - 22 q^{14} - 22 q^{15} - 26 q^{16} - 16 q^{17} - 44 q^{21} - 18 q^{23} - 44 q^{24} - 6 q^{25} - 2 q^{31} - 28 q^{36} - 22 q^{38} + 22 q^{40} - 2 q^{44} - 18 q^{47} + 18 q^{49} + 28 q^{52} + 2 q^{53} + 44 q^{56} - 22 q^{57} - 22 q^{58} + 14 q^{59} + 8 q^{64} - 22 q^{66} + 26 q^{67} + 32 q^{68} + 44 q^{74} - 44 q^{78} - 56 q^{79} + 2 q^{81} - 38 q^{83} - 22 q^{87} - 22 q^{90} - 74 q^{92} + 22 q^{96} + 34 q^{97} - 36 q^{99}+O(q^{100}) $ 10 * q + 2 * q^4 + 22 * q^6 + 14 * q^9 - 22 * q^10 - 10 * q^11 - 14 * q^13 - 22 * q^14 - 22 * q^15 - 26 * q^16 - 16 * q^17 - 44 * q^21 - 18 * q^23 - 44 * q^24 - 6 * q^25 - 2 * q^31 - 28 * q^36 - 22 * q^38 + 22 * q^40 - 2 * q^44 - 18 * q^47 + 18 * q^49 + 28 * q^52 + 2 * q^53 + 44 * q^56 - 22 * q^57 - 22 * q^58 + 14 * q^59 + 8 * q^64 - 22 * q^66 + 26 * q^67 + 32 * q^68 + 44 * q^74 - 44 * q^78 - 56 * q^79 + 2 * q^81 - 38 * q^83 - 22 * q^87 - 22 * q^90 - 74 * q^92 + 22 * q^96 + 34 * q^97 - 36 * 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 $

$2$	1.81926	1.28641	0.643207	−	0.765692i	$-0.277603\pi$
$2$	1.81926	1.28641	0.643207	+	0.765692i	$0.277603\pi$
$3$	1.25580	0.725036	0.362518	−	0.931977i	$-0.381917\pi$
$3$	1.25580	0.725036	0.362518	+	0.931977i	$0.381917\pi$
$4$	1.30972	0.654861
$5$	0.160379	0.0717236	0.0358618	−	0.999357i	$-0.488582\pi$
$5$	0.160379	0.0717236	0.0358618	+	0.999357i	$0.488582\pi$
$6$	2.28463	0.932696
$7$	−4.31672	−1.63157	−0.815784	−	0.578357i	$-0.803694\pi$
$7$	−4.31672	−1.63157	−0.815784	+	0.578357i	$0.803694\pi$
$8$	−1.25580	−0.443992
$9$	−1.42297	−0.474323
$10$	0.291772	0.0922663
$11$	−0.148323	−0.0447211	−0.0223605	−	0.999750i	$-0.507118\pi$
$11$	−0.148323	−0.0447211	−0.0223605	+	0.999750i	$0.507118\pi$
$12$	1.64475	0.474797
$13$	1.68675	0.467821	0.233910	−	0.972258i	$-0.424848\pi$
$13$	1.68675	0.467821	0.233910	+	0.972258i	$0.424848\pi$
$14$	−7.85326	−2.09887
$15$	0.201404	0.0520022
$16$	−4.90407	−1.22602
$17$	−5.73187	−1.39018	−0.695091	−	0.718922i	$-0.744636\pi$
$17$	−5.73187	−1.39018	−0.695091	+	0.718922i	$0.744636\pi$
$18$	−2.58876	−0.610176
$19$	−4.22912	−0.970228	−0.485114	−	0.874451i	$-0.661222\pi$
$19$	−4.22912	−0.970228	−0.485114	+	0.874451i	$0.661222\pi$
$20$	0.210052	0.0469690
$21$	−5.42094	−1.18295
$22$	−0.269839	−0.0575298
$23$	−3.75285	−0.782524	−0.391262	−	0.920279i	$-0.627961\pi$
$23$	−3.75285	−0.782524	−0.391262	+	0.920279i	$0.627961\pi$
$24$	−1.57703	−0.321910
$25$	−4.97428	−0.994856
$26$	3.06865	0.601811
$27$	−5.55436	−1.06894
$28$	−5.65371	−1.06845
$29$	8.83708	1.64101	0.820503	−	0.571643i	$-0.193694\pi$
$29$	8.83708	1.64101	0.820503	+	0.571643i	$0.193694\pi$
$30$	0.366406	0.0668963
$31$	8.64308	1.55234	0.776172	−	0.630522i	$-0.217159\pi$
$31$	8.64308	1.55234	0.776172	+	0.630522i	$0.217159\pi$
$32$	−6.41020	−1.13317
$33$	−0.186264	−0.0324244
$34$	−10.4278	−1.78835
$35$	−0.692311	−0.117022
$36$	−1.86369	−0.310616
$37$	7.19452	1.18277	0.591386	−	0.806389i	$-0.298581\pi$
$37$	7.19452	1.18277	0.591386	+	0.806389i	$0.298581\pi$
$38$	−7.69389	−1.24811
$39$	2.11822	0.339187
$40$	−0.201404	−0.0318447
$41$	−3.67049	−0.573234	−0.286617	−	0.958045i	$-0.592531\pi$
$41$	−3.67049	−0.573234	−0.286617	+	0.958045i	$0.592531\pi$
$42$	−9.86211	−1.52176
$43$	0	0
$43$	0	0
$44$	−0.194262	−0.0292861
$45$	−0.228214	−0.0340202
$46$	−6.82743	−1.00665
$47$	−2.13120	−0.310867	−0.155434	−	0.987846i	$-0.549677\pi$
$47$	−2.13120	−0.310867	−0.155434	+	0.987846i	$0.549677\pi$
$48$	−6.15853	−0.888907
$49$	11.6341	1.66201
$50$	−9.04953	−1.27980
$51$	−7.19807	−1.00793
$52$	2.20918	0.306357
$53$	1.98798	0.273071	0.136535	−	0.990635i	$-0.456403\pi$
$53$	1.98798	0.273071	0.136535	+	0.990635i	$0.456403\pi$
$54$	−10.1048	−1.37510
$55$	−0.0237879	−0.00320756
$56$	5.42094	0.724403
$57$	−5.31093	−0.703450
$58$	16.0770	2.11101
$59$	11.3627	1.47930	0.739648	−	0.672993i	$-0.234992\pi$
$59$	11.3627	1.47930	0.739648	+	0.672993i	$0.234992\pi$
$60$	0.263783	0.0340542
$61$	5.65302	0.723796	0.361898	−	0.932218i	$-0.382129\pi$
$61$	5.65302	0.723796	0.361898	+	0.932218i	$0.382129\pi$
$62$	15.7240	1.99696
$63$	6.14256	0.773890
$64$	−1.85371	−0.231714
$65$	0.270519	0.0335538
$66$	−0.338863	−0.0417112
$67$	−1.42587	−0.174197	−0.0870986	−	0.996200i	$-0.527760\pi$
$67$	−1.42587	−0.174197	−0.0870986	+	0.996200i	$0.527760\pi$
$68$	−7.50715	−0.910375
$69$	−4.71283	−0.567358
$70$	−1.25950	−0.150539
$71$	−7.56187	−0.897429	−0.448715	−	0.893675i	$-0.648118\pi$
$71$	−7.56187	−0.897429	−0.448715	+	0.893675i	$0.648118\pi$
$72$	1.78696	0.210596
$73$	−4.99089	−0.584140	−0.292070	−	0.956397i	$-0.594344\pi$
$73$	−4.99089	−0.584140	−0.292070	+	0.956397i	$0.594344\pi$
$74$	13.0887	1.52153
$75$	−6.24669	−0.721306
$76$	−5.53898	−0.635364
$77$	0.640269	0.0729654
$78$	3.85360	0.436335
$79$	−14.8660	−1.67255	−0.836277	−	0.548306i	$-0.815273\pi$
$79$	−14.8660	−1.67255	−0.836277	+	0.548306i	$0.815273\pi$
$80$	−0.786510	−0.0879345
$81$	−2.70625	−0.300695
$82$	−6.67759	−0.737417
$83$	−6.11970	−0.671725	−0.335862	−	0.941911i	$-0.609028\pi$
$83$	−6.11970	−0.671725	−0.335862	+	0.941911i	$0.609028\pi$
$84$	−7.09992	−0.774664
$85$	−0.919270	−0.0997089
$86$	0	0
$87$	11.0976	1.18979
$88$	0.186264	0.0198558
$89$	−8.33340	−0.883339	−0.441670	−	0.897178i	$-0.645614\pi$
$89$	−8.33340	−0.883339	−0.441670	+	0.897178i	$0.645614\pi$
$90$	−0.415182	−0.0437640
$91$	−7.28124	−0.763281
$92$	−4.91519	−0.512444
$93$	10.8540	1.12550
$94$	−3.87721	−0.399904
$95$	−0.678262	−0.0695882
$96$	−8.04993	−0.821592
$97$	2.10967	0.214204	0.107102	−	0.994248i	$-0.465843\pi$
$97$	2.10967	0.214204	0.107102	+	0.994248i	$0.465843\pi$
$98$	21.1655	2.13804
$99$	0.211059	0.0212122
$100$	−6.51492	−0.651492
$101$	−9.16261	−0.911713	−0.455857	−	0.890053i	$-0.650667\pi$
$101$	−9.16261	−0.911713	−0.455857	+	0.890053i	$0.650667\pi$
$102$	−13.0952	−1.29662
$103$	4.29602	0.423299	0.211650	−	0.977346i	$-0.432116\pi$
$103$	4.29602	0.423299	0.211650	+	0.977346i	$0.432116\pi$
$104$	−2.11822	−0.207709
$105$	−0.869404	−0.0848451
$106$	3.61667	0.351282
$107$	−10.2188	−0.987888	−0.493944	−	0.869494i	$-0.664445\pi$
$107$	−10.2188	−0.987888	−0.493944	+	0.869494i	$0.664445\pi$
$108$	−7.27466	−0.700005
$109$	−13.8777	−1.32924	−0.664622	−	0.747179i	$-0.731408\pi$
$109$	−13.8777	−1.32924	−0.664622	+	0.747179i	$0.731408\pi$
$110$	−0.0432764	−0.00412624
$111$	9.03487	0.857552
$112$	21.1695	2.00033
$113$	9.56571	0.899866	0.449933	−	0.893062i	$-0.351448\pi$
$113$	9.56571	0.899866	0.449933	+	0.893062i	$0.351448\pi$
$114$	−9.66198	−0.904928
$115$	−0.601878	−0.0561254
$116$	11.5741	1.07463
$117$	−2.40020	−0.221898
$118$	20.6717	1.90299
$119$	24.7429	2.26818
$120$	−0.252922	−0.0230886
$121$	−10.9780	−0.998000
$122$	10.2843	0.931101
$123$	−4.60940	−0.415615
$124$	11.3200	1.01657
$125$	−1.59966	−0.143078
$126$	11.1749	0.995543
$127$	6.98124	0.619485	0.309742	−	0.950820i	$-0.399757\pi$
$127$	6.98124	0.619485	0.309742	+	0.950820i	$0.399757\pi$
$128$	9.44802	0.835095
$129$	0	0
$130$	0.492146	0.0431641
$131$	−7.19432	−0.628571	−0.314285	−	0.949329i	$-0.601765\pi$
$131$	−7.19432	−0.628571	−0.314285	+	0.949329i	$0.601765\pi$
$132$	−0.243954	−0.0212334
$133$	18.2560	1.58299
$134$	−2.59403	−0.224090
$135$	−0.890802	−0.0766680
$136$	7.19807	0.617229
$137$	4.78323	0.408659	0.204330	−	0.978902i	$-0.434499\pi$
$137$	4.78323	0.408659	0.204330	+	0.978902i	$0.434499\pi$
$138$	−8.57388	−0.729857
$139$	−2.42056	−0.205309	−0.102655	−	0.994717i	$-0.532734\pi$
$139$	−2.42056	−0.205309	−0.102655	+	0.994717i	$0.532734\pi$
$140$	−0.906735	−0.0766331
$141$	−2.67636	−0.225390
$142$	−13.7570	−1.15447
$143$	−0.250184	−0.0209214
$144$	6.97834	0.581529
$145$	1.41728	0.117699
$146$	−9.07975	−0.751446
$147$	14.6101	1.20502
$148$	9.42281	0.774550
$149$	3.68350	0.301764	0.150882	−	0.988552i	$-0.451789\pi$
$149$	3.68350	0.301764	0.150882	+	0.988552i	$0.451789\pi$
$150$	−11.3644	−0.927898
$151$	−8.15480	−0.663628	−0.331814	−	0.943345i	$-0.607661\pi$
$151$	−8.15480	−0.663628	−0.331814	+	0.943345i	$0.607661\pi$
$152$	5.31093	0.430773
$153$	8.15627	0.659395
$154$	1.16482	0.0938638
$155$	1.38617	0.111340
$156$	2.77428	0.222120
$157$	4.84998	0.387071	0.193535	−	0.981093i	$-0.438005\pi$
$157$	4.84998	0.387071	0.193535	+	0.981093i	$0.438005\pi$
$158$	−27.0452	−2.15160
$159$	2.49651	0.197986
$160$	−1.02806	−0.0812754
$161$	16.2000	1.27674
$162$	−4.92339	−0.386818
$163$	12.4423	0.974554	0.487277	−	0.873247i	$-0.337990\pi$
$163$	12.4423	0.974554	0.487277	+	0.873247i	$0.337990\pi$
$164$	−4.80732	−0.375389
$165$	−0.0298728	−0.00232559
$166$	−11.1334	−0.864116
$167$	−15.6217	−1.20884	−0.604420	−	0.796666i	$-0.706595\pi$
$167$	−15.6217	−1.20884	−0.604420	+	0.796666i	$0.706595\pi$
$168$	6.80761	0.525218
$169$	−10.1549	−0.781144
$170$	−1.67240	−0.128267
$171$	6.01791	0.460201
$172$	0	0
$173$	10.5555	0.802518	0.401259	−	0.915965i	$-0.368573\pi$
$173$	10.5555	0.802518	0.401259	+	0.915965i	$0.368573\pi$
$174$	20.1895	1.53056
$175$	21.4726	1.62317
$176$	0.727387	0.0548288
$177$	14.2693	1.07254
$178$	−15.1607	−1.13634
$179$	−6.10540	−0.456339	−0.228169	−	0.973621i	$-0.573274\pi$
$179$	−6.10540	−0.456339	−0.228169	+	0.973621i	$0.573274\pi$
$180$	−0.298897	−0.0222785
$181$	−23.6663	−1.75910	−0.879552	−	0.475802i	$-0.842158\pi$
$181$	−23.6663	−1.75910	−0.879552	+	0.475802i	$0.842158\pi$
$182$	−13.2465	−0.981896
$183$	7.09906	0.524778
$184$	4.71283	0.347434
$185$	1.15385	0.0848326
$186$	19.7462	1.44786
$187$	0.850167	0.0621704
$188$	−2.79128	−0.203575
$189$	23.9766	1.74404
$190$	−1.23394	−0.0895193
$191$	15.7807	1.14185	0.570925	−	0.821002i	$-0.306585\pi$
$191$	15.7807	1.14185	0.570925	+	0.821002i	$0.306585\pi$
$192$	−2.32789	−0.168001
$193$	21.4398	1.54327	0.771637	−	0.636064i	$-0.219438\pi$
$193$	21.4398	1.54327	0.771637	+	0.636064i	$0.219438\pi$
$194$	3.83804	0.275555
$195$	0.339718	0.0243277
$196$	15.2374	1.08839
$197$	−15.5242	−1.10606	−0.553028	−	0.833163i	$-0.686528\pi$
$197$	−15.5242	−1.10606	−0.553028	+	0.833163i	$0.686528\pi$
$198$	0.383972	0.0272877
$199$	8.14166	0.577147	0.288573	−	0.957458i	$-0.406819\pi$
$199$	8.14166	0.577147	0.288573	+	0.957458i	$0.406819\pi$
$200$	6.24669	0.441708
$201$	−1.79060	−0.126299
$202$	−16.6692	−1.17284
$203$	−38.1472	−2.67741
$204$	−9.42747	−0.660055
$205$	−0.588669	−0.0411144
$206$	7.81559	0.544538
$207$	5.34019	0.371169
$208$	−8.27195	−0.573557
$209$	0.627276	0.0433896
$210$	−1.58167	−0.109146
$211$	−6.35814	−0.437712	−0.218856	−	0.975757i	$-0.570233\pi$
$211$	−6.35814	−0.437712	−0.218856	+	0.975757i	$0.570233\pi$
$212$	2.60371	0.178823
$213$	−9.49619	−0.650668
$214$	−18.5907	−1.27083
$215$	0	0
$216$	6.97516	0.474599
$217$	−37.3098	−2.53275
$218$	−25.2472	−1.70996
$219$	−6.26756	−0.423522
$220$	−0.0311555	−0.00210050
$221$	−9.66824	−0.650356
$222$	16.4368	1.10317
$223$	−11.8266	−0.791969	−0.395984	−	0.918257i	$-0.629597\pi$
$223$	−11.8266	−0.791969	−0.395984	+	0.918257i	$0.629597\pi$
$224$	27.6711	1.84885
$225$	7.07825	0.471883
$226$	17.4026	1.15760
$227$	−23.9172	−1.58744	−0.793720	−	0.608283i	$-0.791859\pi$
$227$	−23.9172	−1.58744	−0.793720	+	0.608283i	$0.791859\pi$
$228$	−6.95584	−0.460662
$229$	6.12429	0.404705	0.202352	−	0.979313i	$-0.435141\pi$
$229$	6.12429	0.404705	0.202352	+	0.979313i	$0.435141\pi$
$230$	−1.09498	−0.0722006
$231$	0.804049	0.0529026
$232$	−11.0976	−0.728593
$233$	11.7698	0.771066	0.385533	−	0.922694i	$-0.374018\pi$
$233$	11.7698	0.771066	0.385533	+	0.922694i	$0.374018\pi$
$234$	−4.36659	−0.285453
$235$	−0.341799	−0.0222965
$236$	14.8820	0.968733
$237$	−18.6687	−1.21266
$238$	45.0138	2.91781
$239$	−16.6746	−1.07859	−0.539294	−	0.842118i	$-0.681309\pi$
$239$	−16.6746	−1.07859	−0.539294	+	0.842118i	$0.681309\pi$
$240$	−0.987698	−0.0637556
$241$	1.75804	0.113245	0.0566226	−	0.998396i	$-0.481967\pi$
$241$	1.75804	0.113245	0.0566226	+	0.998396i	$0.481967\pi$
$242$	−19.9719	−1.28384
$243$	13.2646	0.850923
$244$	7.40389	0.473985
$245$	1.86586	0.119206
$246$	−8.38571	−0.534653
$247$	−7.13348	−0.453893
$248$	−10.8540	−0.689228
$249$	−7.68512	−0.487025
$250$	−2.91021	−0.184058
$251$	1.53584	0.0969415	0.0484708	−	0.998825i	$-0.484565\pi$
$251$	1.53584	0.0969415	0.0484708	+	0.998825i	$0.484565\pi$
$252$	8.04505	0.506790
$253$	0.556634	0.0349953
$254$	12.7007	0.796914
$255$	−1.15442	−0.0722925
$256$	20.8959	1.30599
$257$	29.4257	1.83552	0.917761	−	0.397133i	$-0.129995\pi$
$257$	29.4257	1.83552	0.917761	+	0.397133i	$0.129995\pi$
$258$	0	0
$259$	−31.0567	−1.92977
$260$	0.354305	0.0219731
$261$	−12.5749	−0.778367
$262$	−13.0884	−0.808602
$263$	7.93106	0.489050	0.244525	−	0.969643i	$-0.421368\pi$
$263$	7.93106	0.489050	0.244525	+	0.969643i	$0.421368\pi$
$264$	0.233910	0.0143962
$265$	0.318831	0.0195856
$266$	33.2124	2.03638
$267$	−10.4651	−0.640452
$268$	−1.86749	−0.114075
$269$	1.25644	0.0766066	0.0383033	−	0.999266i	$-0.487805\pi$
$269$	1.25644	0.0766066	0.0383033	+	0.999266i	$0.487805\pi$
$270$	−1.62060	−0.0986268
$271$	−28.0838	−1.70597	−0.852983	−	0.521938i	$-0.825209\pi$
$271$	−28.0838	−1.70597	−0.852983	+	0.521938i	$0.825209\pi$
$272$	28.1095	1.70439
$273$	−9.14377	−0.553406
$274$	8.70197	0.525705
$275$	0.737800	0.0444910
$276$	−6.17249	−0.371540
$277$	−13.0713	−0.785379	−0.392690	−	0.919671i	$-0.628455\pi$
$277$	−13.0713	−0.785379	−0.392690	+	0.919671i	$0.628455\pi$
$278$	−4.40364	−0.264113
$279$	−12.2988	−0.736312
$280$	0.869404	0.0519568
$281$	−13.2238	−0.788868	−0.394434	−	0.918924i	$-0.629059\pi$
$281$	−13.2238	−0.788868	−0.394434	+	0.918924i	$0.629059\pi$
$282$	−4.86900	−0.289945
$283$	17.0833	1.01550	0.507748	−	0.861506i	$-0.330478\pi$
$283$	17.0833	1.01550	0.507748	+	0.861506i	$0.330478\pi$
$284$	−9.90395	−0.587691
$285$	−0.851761	−0.0504540
$286$	−0.455151	−0.0269136
$287$	15.8445	0.935271
$288$	9.12152	0.537491
$289$	15.8543	0.932605
$290$	2.57841	0.151409
$291$	2.64932	0.155306
$292$	−6.53668	−0.382530
$293$	25.8110	1.50790	0.753949	−	0.656933i	$-0.228147\pi$
$293$	25.8110	1.50790	0.753949	+	0.656933i	$0.228147\pi$
$294$	26.5796	1.55015
$295$	1.82234	0.106101
$296$	−9.03487	−0.525141
$297$	0.823839	0.0478040
$298$	6.70125	0.388193
$299$	−6.33013	−0.366081
$300$	−8.18143	−0.472355
$301$	0	0
$302$	−14.8357	−0.853701
$303$	−11.5064	−0.661025
$304$	20.7399	1.18952
$305$	0.906626	0.0519132
$306$	14.8384	0.848255
$307$	−8.06495	−0.460291	−0.230145	−	0.973156i	$-0.573920\pi$
$307$	−8.06495	−0.460291	−0.230145	+	0.973156i	$0.573920\pi$
$308$	0.838574	0.0477822
$309$	5.39493	0.306907
$310$	2.52180	0.143229
$311$	−2.25085	−0.127634	−0.0638171	−	0.997962i	$-0.520327\pi$
$311$	−2.25085	−0.127634	−0.0638171	+	0.997962i	$0.520327\pi$
$312$	−2.66006	−0.150596
$313$	−21.6275	−1.22246	−0.611229	−	0.791454i	$-0.709325\pi$
$313$	−21.6275	−1.22246	−0.611229	+	0.791454i	$0.709325\pi$
$314$	8.82340	0.497933
$315$	0.985138	0.0555062
$316$	−19.4703	−1.09529
$317$	−4.66235	−0.261864	−0.130932	−	0.991391i	$-0.541797\pi$
$317$	−4.66235	−0.261864	−0.130932	+	0.991391i	$0.541797\pi$
$318$	4.54181	0.254692
$319$	−1.31074	−0.0733875
$320$	−0.297296	−0.0166193
$321$	−12.8328	−0.716254
$322$	29.4721	1.64242
$323$	24.2408	1.34879
$324$	−3.54444	−0.196913
$325$	−8.39037	−0.465414
$326$	22.6358	1.25368
$327$	−17.4276	−0.963750
$328$	4.60940	0.254511
$329$	9.19979	0.507201
$330$	−0.0543465	−0.00299168
$331$	6.77060	0.372146	0.186073	−	0.982536i	$-0.440424\pi$
$331$	6.77060	0.372146	0.186073	+	0.982536i	$0.440424\pi$
$332$	−8.01511	−0.439886
$333$	−10.2376	−0.561016
$334$	−28.4199	−1.55507
$335$	−0.228679	−0.0124941
$336$	26.5847	1.45031
$337$	−14.1869	−0.772808	−0.386404	−	0.922330i	$-0.626283\pi$
$337$	−14.1869	−0.772808	−0.386404	+	0.922330i	$0.626283\pi$
$338$	−18.4744	−1.00487
$339$	12.0126	0.652435
$340$	−1.20399	−0.0652954
$341$	−1.28197	−0.0694224
$342$	10.9482	0.592009
$343$	−20.0041	−1.08012
$344$	0	0
$345$	−0.755838	−0.0406930
$346$	19.2032	1.03237
$347$	24.8725	1.33523	0.667614	−	0.744508i	$-0.267316\pi$
$347$	24.8725	1.33523	0.667614	+	0.744508i	$0.267316\pi$
$348$	14.5348	0.779145
$349$	11.2707	0.603307	0.301654	−	0.953418i	$-0.402461\pi$
$349$	11.2707	0.603307	0.301654	+	0.953418i	$0.402461\pi$
$350$	39.0643	2.08807
$351$	−9.36883	−0.500071
$352$	0.950781	0.0506768
$353$	19.5266	1.03930	0.519648	−	0.854380i	$-0.326063\pi$
$353$	19.5266	1.03930	0.519648	+	0.854380i	$0.326063\pi$
$354$	25.9596	1.37973
$355$	−1.21277	−0.0643669
$356$	−10.9144	−0.578464
$357$	31.0721	1.64451
$358$	−11.1073	−0.587041
$359$	−8.98116	−0.474008	−0.237004	−	0.971509i	$-0.576165\pi$
$359$	−8.98116	−0.474008	−0.237004	+	0.971509i	$0.576165\pi$
$360$	0.286591	0.0151047
$361$	−1.11451	−0.0586583
$362$	−43.0553	−2.26294
$363$	−13.7862	−0.723586
$364$	−9.53640	−0.499843
$365$	−0.800434	−0.0418966
$366$	12.9151	0.675081
$367$	8.93222	0.466258	0.233129	−	0.972446i	$-0.425104\pi$
$367$	8.93222	0.466258	0.233129	+	0.972446i	$0.425104\pi$
$368$	18.4043	0.959388
$369$	5.22300	0.271898
$370$	2.09916	0.109130
$371$	−8.58158	−0.445533
$372$	14.2157	0.737049
$373$	−15.3197	−0.793224	−0.396612	−	0.917986i	$-0.629814\pi$
$373$	−15.3197	−0.793224	−0.396612	+	0.917986i	$0.629814\pi$
$374$	1.54668	0.0799769
$375$	−2.00886	−0.103737
$376$	2.67636	0.138023
$377$	14.9060	0.767696
$378$	43.6198	2.24356
$379$	−30.2720	−1.55497	−0.777484	−	0.628903i	$-0.783504\pi$
$379$	−30.2720	−1.55497	−0.777484	+	0.628903i	$0.783504\pi$
$380$	−0.888335	−0.0455706
$381$	8.76703	0.449149
$382$	28.7092	1.46889
$383$	1.02239	0.0522415	0.0261208	−	0.999659i	$-0.491685\pi$
$383$	1.02239	0.0522415	0.0261208	+	0.999659i	$0.491685\pi$
$384$	11.8648	0.605474
$385$	0.102686	0.00523335
$386$	39.0047	1.98529
$387$	0	0
$388$	2.76307	0.140274
$389$	32.6968	1.65780	0.828898	−	0.559400i	$-0.188969\pi$
$389$	32.6968	1.65780	0.828898	+	0.559400i	$0.188969\pi$
$390$	0.618037	0.0312955
$391$	21.5108	1.08785
$392$	−14.6101	−0.737921
$393$	−9.03462	−0.455736
$394$	−28.2427	−1.42285
$395$	−2.38419	−0.119962
$396$	0.276429	0.0138911
$397$	17.6659	0.886625	0.443312	−	0.896367i	$-0.353803\pi$
$397$	17.6659	0.886625	0.443312	+	0.896367i	$0.353803\pi$
$398$	14.8118	0.742450
$399$	22.9258	1.14773
$400$	24.3942	1.21971
$401$	−35.2016	−1.75788	−0.878942	−	0.476929i	$-0.841750\pi$
$401$	−35.2016	−1.75788	−0.878942	+	0.476929i	$0.841750\pi$
$402$	−3.25758	−0.162473
$403$	14.5787	0.726218
$404$	−12.0005	−0.597045
$405$	−0.434026	−0.0215669
$406$	−69.3999	−3.44426
$407$	−1.06711	−0.0528948
$408$	9.03933	0.447513
$409$	23.8017	1.17692	0.588459	−	0.808527i	$-0.299735\pi$
$409$	23.8017	1.17692	0.588459	+	0.808527i	$0.299735\pi$
$410$	−1.07094	−0.0528902
$411$	6.00678	0.296293
$412$	5.62658	0.277202
$413$	−49.0496	−2.41357
$414$	9.71522	0.477477
$415$	−0.981471	−0.0481785
$416$	−10.8124	−0.530123
$417$	−3.03974	−0.148857
$418$	1.14118	0.0558170
$419$	−21.1878	−1.03509	−0.517546	−	0.855656i	$-0.673154\pi$
$419$	−21.1878	−1.03509	−0.517546	+	0.855656i	$0.673154\pi$
$420$	−1.13868	−0.0555617
$421$	−1.36811	−0.0666774	−0.0333387	−	0.999444i	$-0.510614\pi$
$421$	−1.36811	−0.0666774	−0.0333387	+	0.999444i	$0.510614\pi$
$422$	−11.5671	−0.563079
$423$	3.03263	0.147451
$424$	−2.49651	−0.121241
$425$	28.5119	1.38303
$426$	−17.2761	−0.837029
$427$	−24.4025	−1.18092
$428$	−13.3838	−0.646929
$429$	−0.314181	−0.0151688
$430$	0	0
$431$	−3.95981	−0.190737	−0.0953687	−	0.995442i	$-0.530403\pi$
$431$	−3.95981	−0.190737	−0.0953687	+	0.995442i	$0.530403\pi$
$432$	27.2390	1.31054
$433$	−0.859593	−0.0413094	−0.0206547	−	0.999787i	$-0.506575\pi$
$433$	−0.859593	−0.0413094	−0.0206547	+	0.999787i	$0.506575\pi$
$434$	−67.8764	−3.25817
$435$	1.77982	0.0853359
$436$	−18.1759	−0.870470
$437$	15.8713	0.759226
$438$	−11.4023	−0.544825
$439$	16.0673	0.766850	0.383425	−	0.923572i	$-0.374745\pi$
$439$	16.0673	0.766850	0.383425	+	0.923572i	$0.374745\pi$
$440$	0.0298728	0.00142413
$441$	−16.5550	−0.788332
$442$	−17.5891	−0.836627
$443$	−7.12994	−0.338754	−0.169377	−	0.985551i	$-0.554175\pi$
$443$	−7.12994	−0.338754	−0.169377	+	0.985551i	$0.554175\pi$
$444$	11.8332	0.561577
$445$	−1.33650	−0.0633563
$446$	−21.5157	−1.01880
$447$	4.62573	0.218790
$448$	8.00195	0.378057
$449$	−22.0200	−1.03919	−0.519594	−	0.854413i	$-0.673917\pi$
$449$	−22.0200	−1.03919	−0.519594	+	0.854413i	$0.673917\pi$
$450$	12.8772	0.607037
$451$	0.544418	0.0256356
$452$	12.5284	0.589287
$453$	−10.2408	−0.481154
$454$	−43.5117	−2.04211
$455$	−1.16776	−0.0547453
$456$	6.66946	0.312326
$457$	18.1341	0.848277	0.424138	−	0.905597i	$-0.360577\pi$
$457$	18.1341	0.848277	0.424138	+	0.905597i	$0.360577\pi$
$458$	11.1417	0.520618
$459$	31.8368	1.48602
$460$	−0.788293	−0.0367543
$461$	9.59608	0.446934	0.223467	−	0.974712i	$-0.428263\pi$
$461$	9.59608	0.446934	0.223467	+	0.974712i	$0.428263\pi$
$462$	1.46278	0.0680546
$463$	4.05803	0.188593	0.0942964	−	0.995544i	$-0.469940\pi$
$463$	4.05803	0.188593	0.0942964	+	0.995544i	$0.469940\pi$
$464$	−43.3377	−2.01190
$465$	1.74075	0.0807252
$466$	21.4124	0.991910
$467$	−10.5710	−0.489170	−0.244585	−	0.969628i	$-0.578652\pi$
$467$	−10.5710	−0.489170	−0.244585	+	0.969628i	$0.578652\pi$
$468$	−3.14359	−0.145312
$469$	6.15507	0.284215
$470$	−0.621823	−0.0286825
$471$	6.09061	0.280640
$472$	−14.2693	−0.656796
$473$	0	0
$474$	−33.9633	−1.55999
$475$	21.0368	0.965237
$476$	32.4063	1.48534
$477$	−2.82884	−0.129524
$478$	−30.3354	−1.38751
$479$	25.8866	1.18279	0.591395	−	0.806382i	$-0.298577\pi$
$479$	25.8866	1.18279	0.591395	+	0.806382i	$0.298577\pi$
$480$	−1.29104	−0.0589276
$481$	12.1354	0.553325
$482$	3.19833	0.145680
$483$	20.3440	0.925683
$484$	−14.3781	−0.653551
$485$	0.338346	0.0153635
$486$	24.1318	1.09464
$487$	3.65177	0.165477	0.0827387	−	0.996571i	$-0.473633\pi$
$487$	3.65177	0.165477	0.0827387	+	0.996571i	$0.473633\pi$
$488$	−7.09906	−0.321359
$489$	15.6250	0.706587
$490$	3.39450	0.153348
$491$	−32.0540	−1.44658	−0.723289	−	0.690545i	$-0.757371\pi$
$491$	−32.0540	−1.44658	−0.723289	+	0.690545i	$0.757371\pi$
$492$	−6.03703	−0.272170
$493$	−50.6530	−2.28130
$494$	−12.9777	−0.583894
$495$	0.0338494	0.00152142
$496$	−42.3863	−1.90320
$497$	32.6425	1.46422
$498$	−13.9813	−0.626515
$499$	16.0927	0.720407	0.360204	−	0.932874i	$-0.382707\pi$
$499$	16.0927	0.720407	0.360204	+	0.932874i	$0.382707\pi$
$500$	−2.09511	−0.0936963
$501$	−19.6177	−0.876452
$502$	2.79410	0.124707
$503$	−13.4838	−0.601212	−0.300606	−	0.953748i	$-0.597189\pi$
$503$	−13.4838	−0.601212	−0.300606	+	0.953748i	$0.597189\pi$
$504$	−7.71383	−0.343601
$505$	−1.46949	−0.0653914
$506$	1.01266	0.0450184
$507$	−12.7525	−0.566357
$508$	9.14348	0.405676
$509$	26.2654	1.16419	0.582097	−	0.813120i	$-0.302232\pi$
$509$	26.2654	1.16419	0.582097	+	0.813120i	$0.302232\pi$
$510$	−2.10019	−0.0929981
$511$	21.5443	0.953064
$512$	19.1191	0.844951
$513$	23.4901	1.03711
$514$	53.5330	2.36124
$515$	0.688990	0.0303605
$516$	0	0
$517$	0.316106	0.0139023
$518$	−56.5004	−2.48249
$519$	13.2556	0.581854
$520$	−0.339718	−0.0148976
$521$	11.0938	0.486027	0.243013	−	0.970023i	$-0.421864\pi$
$521$	11.0938	0.486027	0.243013	+	0.970023i	$0.421864\pi$
$522$	−22.8771	−1.00130
$523$	0.981100	0.0429005	0.0214502	−	0.999770i	$-0.493172\pi$
$523$	0.981100	0.0429005	0.0214502	+	0.999770i	$0.493172\pi$
$524$	−9.42256	−0.411626
$525$	26.9652	1.17686
$526$	14.4287	0.629121
$527$	−49.5410	−2.15804
$528$	0.913451	0.0397529
$529$	−8.91610	−0.387656
$530$	0.580037	0.0251952
$531$	−16.1688	−0.701665
$532$	23.9102	1.03664
$533$	−6.19121	−0.268171
$534$	−19.0387	−0.823887
$535$	−1.63888	−0.0708549
$536$	1.79060	0.0773422
$537$	−7.66715	−0.330862
$538$	2.28580	0.0985477
$539$	−1.72560	−0.0743270
$540$	−1.16670	−0.0502069
$541$	−9.12256	−0.392209	−0.196105	−	0.980583i	$-0.562829\pi$
$541$	−9.12256	−0.392209	−0.196105	+	0.980583i	$0.562829\pi$
$542$	−51.0918	−2.19458
$543$	−29.7202	−1.27541
$544$	36.7424	1.57532
$545$	−2.22569	−0.0953382
$546$	−16.6349	−0.711910
$547$	43.4839	1.85924	0.929618	−	0.368524i	$-0.120137\pi$
$547$	43.4839	1.85924	0.929618	+	0.368524i	$0.120137\pi$
$548$	6.26471	0.267615
$549$	−8.04408	−0.343313
$550$	1.34225	0.0572338
$551$	−37.3731	−1.59215
$552$	5.91836	0.251902
$553$	64.1724	2.72889
$554$	−23.7802	−1.01032
$555$	1.44900	0.0615067
$556$	−3.17026	−0.134449
$557$	−19.6219	−0.831406	−0.415703	−	0.909500i	$-0.636464\pi$
$557$	−19.6219	−0.831406	−0.415703	+	0.909500i	$0.636464\pi$
$558$	−22.3748	−0.947202
$559$	0	0
$560$	3.39514	0.143471
$561$	1.06764	0.0450758
$562$	−24.0576	−1.01481
$563$	−14.5633	−0.613769	−0.306885	−	0.951747i	$-0.599287\pi$
$563$	−14.5633	−0.613769	−0.306885	+	0.951747i	$0.599287\pi$
$564$	−3.50528	−0.147599
$565$	1.53414	0.0645417
$566$	31.0790	1.30635
$567$	11.6821	0.490604
$568$	9.49619	0.398451
$569$	−40.0828	−1.68036	−0.840179	−	0.542310i	$-0.817550\pi$
$569$	−40.0828	−1.68036	−0.840179	+	0.542310i	$0.817550\pi$
$570$	−1.54958	−0.0649047
$571$	−4.38952	−0.183696	−0.0918479	−	0.995773i	$-0.529277\pi$
$571$	−4.38952	−0.183696	−0.0918479	+	0.995773i	$0.529277\pi$
$572$	−0.327671	−0.0137006
$573$	19.8174	0.827882
$574$	28.8253	1.20315
$575$	18.6677	0.778498
$576$	2.63777	0.109907
$577$	21.1471	0.880367	0.440184	−	0.897908i	$-0.354913\pi$
$577$	21.1471	0.880367	0.440184	+	0.897908i	$0.354913\pi$
$578$	28.8431	1.19972
$579$	26.9241	1.11893
$580$	1.85624	0.0770763
$581$	26.4171	1.09596
$582$	4.81980	0.199787
$583$	−0.294864	−0.0122120
$584$	6.26756	0.259353
$585$	−0.384941	−0.0159153
$586$	46.9571	1.93978
$587$	−16.7484	−0.691280	−0.345640	−	0.938367i	$-0.612338\pi$
$587$	−16.7484	−0.691280	−0.345640	+	0.938367i	$0.612338\pi$
$588$	19.1351	0.789120
$589$	−36.5527	−1.50613
$590$	3.31531	0.136489
$591$	−19.4953	−0.801930
$592$	−35.2824	−1.45010
$593$	28.2891	1.16170	0.580848	−	0.814012i	$-0.302721\pi$
$593$	28.2891	1.16170	0.580848	+	0.814012i	$0.302721\pi$
$594$	1.49878	0.0614957
$595$	3.96824	0.162682
$596$	4.82435	0.197613
$597$	10.2243	0.418452
$598$	−11.5162	−0.470932
$599$	12.1871	0.497951	0.248975	−	0.968510i	$-0.419906\pi$
$599$	12.1871	0.497951	0.248975	+	0.968510i	$0.419906\pi$
$600$	7.84459	0.320254
$601$	−13.5029	−0.550793	−0.275397	−	0.961331i	$-0.588809\pi$
$601$	−13.5029	−0.550793	−0.275397	+	0.961331i	$0.588809\pi$
$602$	0	0
$603$	2.02896	0.0826258
$604$	−10.6805	−0.434584
$605$	−1.76064	−0.0715802
$606$	−20.9332	−0.850352
$607$	−3.28555	−0.133356	−0.0666781	−	0.997775i	$-0.521240\pi$
$607$	−3.28555	−0.133356	−0.0666781	+	0.997775i	$0.521240\pi$
$608$	27.1096	1.09944
$609$	−47.9053	−1.94122
$610$	1.64939	0.0667819
$611$	−3.59480	−0.145430
$612$	10.6824	0.431812
$613$	41.4735	1.67510	0.837549	−	0.546362i	$-0.183988\pi$
$613$	41.4735	1.67510	0.837549	+	0.546362i	$0.183988\pi$
$614$	−14.6723	−0.592125
$615$	−0.739250	−0.0298094
$616$	−0.804049	−0.0323961
$617$	34.7109	1.39741	0.698704	−	0.715411i	$-0.253760\pi$
$617$	34.7109	1.39741	0.698704	+	0.715411i	$0.253760\pi$
$618$	9.81481	0.394809
$619$	8.57623	0.344708	0.172354	−	0.985035i	$-0.444863\pi$
$619$	8.57623	0.344708	0.172354	+	0.985035i	$0.444863\pi$
$620$	1.81549	0.0729120
$621$	20.8447	0.836469
$622$	−4.09490	−0.164190
$623$	35.9730	1.44123
$624$	−10.3879	−0.415849
$625$	24.6148	0.984594
$626$	−39.3461	−1.57259
$627$	0.787733	0.0314590
$628$	6.35213	0.253478
$629$	−41.2380	−1.64427
$630$	1.79223	0.0714040
$631$	0.378009	0.0150483	0.00752415	−	0.999972i	$-0.497605\pi$
$631$	0.378009	0.0150483	0.00752415	+	0.999972i	$0.497605\pi$
$632$	18.6687	0.742601
$633$	−7.98455	−0.317357
$634$	−8.48205	−0.336865
$635$	1.11964	0.0444317
$636$	3.26973	0.129653
$637$	19.6238	0.777525
$638$	−2.38459	−0.0944067
$639$	10.7603	0.425671
$640$	1.51526	0.0598960
$641$	−23.7922	−0.939734	−0.469867	−	0.882737i	$-0.655698\pi$
$641$	−23.7922	−0.939734	−0.469867	+	0.882737i	$0.655698\pi$
$642$	−23.3462	−0.921400
$643$	−47.4615	−1.87170	−0.935849	−	0.352403i	$-0.885365\pi$
$643$	−47.4615	−1.87170	−0.935849	+	0.352403i	$0.885365\pi$
$644$	21.2175	0.836088
$645$	0	0
$646$	44.1004	1.73511
$647$	1.66417	0.0654254	0.0327127	−	0.999465i	$-0.489585\pi$
$647$	1.66417	0.0654254	0.0327127	+	0.999465i	$0.489585\pi$
$648$	3.39851	0.133506
$649$	−1.68535	−0.0661557
$650$	−15.2643	−0.598715
$651$	−46.8536	−1.83634
$652$	16.2959	0.638197
$653$	−16.6432	−0.651299	−0.325650	−	0.945491i	$-0.605583\pi$
$653$	−16.6432	−0.651299	−0.325650	+	0.945491i	$0.605583\pi$
$654$	−31.7055	−1.23978
$655$	−1.15382	−0.0450834
$656$	18.0004	0.702796
$657$	7.10189	0.277071
$658$	16.7368	0.652470
$659$	4.15199	0.161739	0.0808693	−	0.996725i	$-0.474230\pi$
$659$	4.15199	0.161739	0.0808693	+	0.996725i	$0.474230\pi$
$660$	−0.0391250	−0.00152294
$661$	−48.7851	−1.89752	−0.948761	−	0.315995i	$-0.897662\pi$
$661$	−48.7851	−1.89752	−0.948761	+	0.315995i	$0.897662\pi$
$662$	12.3175	0.478734
$663$	−12.1414	−0.471531
$664$	7.68512	0.298240
$665$	2.92787	0.113538
$666$	−18.6249	−0.721698
$667$	−33.1643	−1.28413
$668$	−20.4600	−0.791622
$669$	−14.8518	−0.574206
$670$	−0.416027	−0.0160725
$671$	−0.838473	−0.0323689
$672$	34.7493	1.34048
$673$	27.6667	1.06647	0.533236	−	0.845967i	$-0.320976\pi$
$673$	27.6667	1.06647	0.533236	+	0.845967i	$0.320976\pi$
$674$	−25.8097	−0.994151
$675$	27.6289	1.06344
$676$	−13.3000	−0.511540
$677$	−12.8622	−0.494336	−0.247168	−	0.968973i	$-0.579500\pi$
$677$	−12.8622	−0.494336	−0.247168	+	0.968973i	$0.579500\pi$
$678$	21.8541	0.839302
$679$	−9.10684	−0.349489
$680$	1.15442	0.0442699
$681$	−30.0352	−1.15095
$682$	−2.33224	−0.0893060
$683$	23.5818	0.902333	0.451167	−	0.892440i	$-0.351008\pi$
$683$	23.5818	0.902333	0.451167	+	0.892440i	$0.351008\pi$
$684$	7.88179	0.301368
$685$	0.767130	0.0293105
$686$	−36.3928	−1.38948
$687$	7.69088	0.293425
$688$	0	0
$689$	3.35324	0.127748
$690$	−1.37507	−0.0523480
$691$	−1.26897	−0.0482738	−0.0241369	−	0.999709i	$-0.507684\pi$
$691$	−1.26897	−0.0482738	−0.0241369	+	0.999709i	$0.507684\pi$
$692$	13.8247	0.525538
$693$	−0.911083	−0.0346092
$694$	45.2497	1.71766
$695$	−0.388207	−0.0147255
$696$	−13.9364	−0.528256
$697$	21.0388	0.796900
$698$	20.5044	0.776103
$699$	14.7805	0.559051
$700$	28.1231	1.06295
$701$	−40.4042	−1.52604	−0.763022	−	0.646372i	$-0.776285\pi$
$701$	−40.4042	−1.52604	−0.763022	+	0.646372i	$0.776285\pi$
$702$	−17.0444	−0.643298
$703$	−30.4265	−1.14756
$704$	0.274948	0.0103625
$705$	−0.429231	−0.0161658
$706$	35.5240	1.33697
$707$	39.5524	1.48752
$708$	18.6888	0.702366
$709$	−41.6968	−1.56596	−0.782978	−	0.622050i	$-0.786300\pi$
$709$	−41.6968	−1.56596	−0.782978	+	0.622050i	$0.786300\pi$
$710$	−2.20634	−0.0828025
$711$	21.1539	0.793331
$712$	10.4651	0.392195
$713$	−32.4362	−1.21475
$714$	56.5283	2.11552
$715$	−0.0401242	−0.00150056
$716$	−7.99637	−0.298838
$717$	−20.9399	−0.782014
$718$	−16.3391	−0.609770
$719$	−32.8441	−1.22488	−0.612439	−	0.790518i	$-0.709812\pi$
$719$	−32.8441	−1.22488	−0.612439	+	0.790518i	$0.709812\pi$
$720$	1.11918	0.0417093
$721$	−18.5447	−0.690641
$722$	−2.02758	−0.0754588
$723$	2.20774	0.0821068
$724$	−30.9963	−1.15197
$725$	−43.9581	−1.63256
$726$	−25.0807	−0.930831
$727$	−9.89017	−0.366806	−0.183403	−	0.983038i	$-0.558711\pi$
$727$	−9.89017	−0.366806	−0.183403	+	0.983038i	$0.558711\pi$
$728$	9.14377	0.338891
$729$	24.7764	0.917644
$730$	−1.45620	−0.0538964
$731$	0	0
$732$	9.29779	0.343656
$733$	−8.65503	−0.319681	−0.159840	−	0.987143i	$-0.551098\pi$
$733$	−8.65503	−0.319681	−0.159840	+	0.987143i	$0.551098\pi$
$734$	16.2501	0.599801
$735$	2.34315	0.0864284
$736$	24.0566	0.886736
$737$	0.211489	0.00779029
$738$	9.50201	0.349774
$739$	11.4741	0.422082	0.211041	−	0.977477i	$-0.432315\pi$
$739$	11.4741	0.422082	0.211041	+	0.977477i	$0.432315\pi$
$740$	1.51122	0.0555536
$741$	−8.95822	−0.329088
$742$	−15.6122	−0.573140
$743$	32.4692	1.19118	0.595590	−	0.803288i	$-0.296918\pi$
$743$	32.4692	1.19118	0.595590	+	0.803288i	$0.296918\pi$
$744$	−13.6304	−0.499715
$745$	0.590755	0.0216436
$746$	−27.8706	−1.02041
$747$	8.70815	0.318615
$748$	1.11348	0.0407129
$749$	44.1117	1.61181
$750$	−3.65464	−0.133449
$751$	17.8947	0.652988	0.326494	−	0.945199i	$-0.394133\pi$
$751$	17.8947	0.652988	0.326494	+	0.945199i	$0.394133\pi$
$752$	10.4515	0.381129
$753$	1.92871	0.0702861
$754$	27.1179	0.987575
$755$	−1.30786	−0.0475978
$756$	31.4027	1.14211
$757$	40.5848	1.47508	0.737539	−	0.675304i	$-0.235988\pi$
$757$	40.5848	1.47508	0.737539	+	0.675304i	$0.235988\pi$
$758$	−55.0727	−2.00033
$759$	0.699021	0.0253728
$760$	0.851761	0.0308966
$761$	31.1825	1.13036	0.565182	−	0.824967i	$-0.308806\pi$
$761$	31.1825	1.13036	0.565182	+	0.824967i	$0.308806\pi$
$762$	15.9496	0.577791
$763$	59.9063	2.16875
$764$	20.6683	0.747753
$765$	1.30809	0.0472942
$766$	1.85999	0.0672042
$767$	19.1660	0.692046
$768$	26.2410	0.946891
$769$	−16.8244	−0.606704	−0.303352	−	0.952879i	$-0.598106\pi$
$769$	−16.8244	−0.606704	−0.303352	+	0.952879i	$0.598106\pi$
$770$	0.186812	0.00673225
$771$	36.9527	1.33082
$772$	28.0802	1.01063
$773$	1.36295	0.0490219	0.0245110	−	0.999700i	$-0.492197\pi$
$773$	1.36295	0.0490219	0.0245110	+	0.999700i	$0.492197\pi$
$774$	0	0
$775$	−42.9931	−1.54436
$776$	−2.64932	−0.0951049
$777$	−39.0010	−1.39915
$778$	59.4842	2.13261
$779$	15.5230	0.556168
$780$	0.444936	0.0159313
$781$	1.12160	0.0401340
$782$	39.1339	1.39943
$783$	−49.0843	−1.75413
$784$	−57.0545	−2.03766
$785$	0.777835	0.0277621
$786$	−16.4364	−0.586266
$787$	−10.8870	−0.388081	−0.194040	−	0.980994i	$-0.562159\pi$
$787$	−10.8870	−0.388081	−0.194040	+	0.980994i	$0.562159\pi$
$788$	−20.3324	−0.724313
$789$	9.95981	0.354579
$790$	−4.33747	−0.154320
$791$	−41.2925	−1.46819
$792$	−0.265048	−0.00941806
$793$	9.53525	0.338607
$794$	32.1389	1.14057
$795$	0.400387	0.0142003
$796$	10.6633	0.377951
$797$	−40.5891	−1.43774	−0.718870	−	0.695145i	$-0.755340\pi$
$797$	−40.5891	−1.43774	−0.718870	+	0.695145i	$0.755340\pi$
$798$	41.7081	1.47645
$799$	12.2157	0.432162
$800$	31.8861	1.12735
$801$	11.8582	0.418988
$802$	−64.0410	−2.26137
$803$	0.740264	0.0261234
$804$	−2.34519	−0.0827084
$805$	2.59814	0.0915725
$806$	26.5226	0.934217
$807$	1.57784	0.0555425
$808$	11.5064	0.404793
$809$	3.98406	0.140072	0.0700361	−	0.997544i	$-0.477689\pi$
$809$	3.98406	0.140072	0.0700361	+	0.997544i	$0.477689\pi$
$810$	−0.789607	−0.0277440
$811$	−35.9179	−1.26125	−0.630623	−	0.776089i	$-0.717201\pi$
$811$	−35.9179	−1.26125	−0.630623	+	0.776089i	$0.717201\pi$
$812$	−49.9623	−1.75333
$813$	−35.2675	−1.23689
$814$	−1.94136	−0.0680446
$815$	1.99548	0.0698986
$816$	35.2999	1.23574
$817$	0	0
$818$	43.3016	1.51400
$819$	10.3610	0.362042
$820$	−0.770993	−0.0269242
$821$	25.7670	0.899276	0.449638	−	0.893211i	$-0.351553\pi$
$821$	25.7670	0.899276	0.449638	+	0.893211i	$0.351553\pi$
$822$	10.9279	0.381155
$823$	−37.1671	−1.29556	−0.647782	−	0.761825i	$-0.724303\pi$
$823$	−37.1671	−1.29556	−0.647782	+	0.761825i	$0.724303\pi$
$824$	−5.39493	−0.187941
$825$	0.926528	0.0322576
$826$	−89.2342	−3.10485
$827$	−14.5102	−0.504568	−0.252284	−	0.967653i	$-0.581182\pi$
$827$	−14.5102	−0.504568	−0.252284	+	0.967653i	$0.581182\pi$
$828$	6.99417	0.243064
$829$	−22.2586	−0.773074	−0.386537	−	0.922274i	$-0.626329\pi$
$829$	−22.2586	−0.773074	−0.386537	+	0.922274i	$0.626329\pi$
$830$	−1.78556	−0.0619775
$831$	−16.4149	−0.569428
$832$	−3.12675	−0.108400
$833$	−66.6851	−2.31050
$834$	−5.53009	−0.191491
$835$	−2.50538	−0.0867024
$836$	0.821557	0.0284141
$837$	−48.0068	−1.65936
$838$	−38.5462	−1.33156
$839$	−51.0812	−1.76352	−0.881760	−	0.471699i	$-0.843641\pi$
$839$	−51.0812	−1.76352	−0.881760	+	0.471699i	$0.843641\pi$
$840$	1.09180	0.0376706
$841$	49.0940	1.69290
$842$	−2.48895	−0.0857748
$843$	−16.6065	−0.571957
$844$	−8.32739	−0.286641
$845$	−1.62863	−0.0560265
$846$	5.51715	0.189684
$847$	47.3890	1.62830
$848$	−9.74922	−0.334789
$849$	21.4532	0.736271
$850$	51.8707	1.77915
$851$	−27.0000	−0.925547
$852$	−12.4374	−0.426097
$853$	12.8355	0.439478	0.219739	−	0.975559i	$-0.429479\pi$
$853$	12.8355	0.439478	0.219739	+	0.975559i	$0.429479\pi$
$854$	−44.3947	−1.51915
$855$	0.965146	0.0330073
$856$	12.8328	0.438614
$857$	−38.8025	−1.32547	−0.662734	−	0.748855i	$-0.730604\pi$
$857$	−38.8025	−1.32547	−0.662734	+	0.748855i	$0.730604\pi$
$858$	−0.571578	−0.0195133
$859$	−32.0864	−1.09477	−0.547387	−	0.836879i	$-0.684378\pi$
$859$	−32.0864	−1.09477	−0.547387	+	0.836879i	$0.684378\pi$
$860$	0	0
$861$	19.8975	0.678105
$862$	−7.20394	−0.245367
$863$	−23.6312	−0.804416	−0.402208	−	0.915548i	$-0.631757\pi$
$863$	−23.6312	−0.804416	−0.402208	+	0.915548i	$0.631757\pi$
$864$	35.6046	1.21129
$865$	1.69288	0.0575595
$866$	−1.56383	−0.0531410
$867$	19.9098	0.676172
$868$	−48.8654	−1.65860
$869$	2.20497	0.0747984
$870$	3.23796	0.109777
$871$	−2.40508	−0.0814931
$872$	17.4276	0.590174
$873$	−3.00199	−0.101602
$874$	28.8740	0.976679
$875$	6.90531	0.233442
$876$	−8.20876	−0.277348
$877$	18.7974	0.634743	0.317372	−	0.948301i	$-0.397200\pi$
$877$	18.7974	0.634743	0.317372	+	0.948301i	$0.397200\pi$
$878$	29.2306	0.986486
$879$	32.4135	1.09328
$880$	0.116657	0.00393252
$881$	8.12108	0.273606	0.136803	−	0.990598i	$-0.456317\pi$
$881$	8.12108	0.273606	0.136803	+	0.990598i	$0.456317\pi$
$882$	−30.1179	−1.01412
$883$	28.9422	0.973982	0.486991	−	0.873407i	$-0.338094\pi$
$883$	28.9422	0.973982	0.486991	+	0.873407i	$0.338094\pi$
$884$	−12.6627	−0.425893
$885$	2.28849	0.0769267
$886$	−12.9712	−0.435777
$887$	32.4245	1.08871	0.544353	−	0.838856i	$-0.316775\pi$
$887$	32.4245	1.08871	0.544353	+	0.838856i	$0.316775\pi$
$888$	−11.3460	−0.380746
$889$	−30.1361	−1.01073
$890$	−2.43145	−0.0815024
$891$	0.401399	0.0134474
$892$	−15.4896	−0.518629
$893$	9.01310	0.301612
$894$	8.41542	0.281454
$895$	−0.979177	−0.0327303
$896$	−40.7845	−1.36251
$897$	−7.94937	−0.265422
$898$	−40.0602	−1.33683
$899$	76.3796	2.54740
$900$	9.27053	0.309018
$901$	−11.3949	−0.379618
$902$	0.990440	0.0329781
$903$	0	0
$904$	−12.0126	−0.399533
$905$	−3.79558	−0.126169
$906$	−18.6307	−0.618964
$907$	−8.15760	−0.270869	−0.135434	−	0.990786i	$-0.543243\pi$
$907$	−8.15760	−0.270869	−0.135434	+	0.990786i	$0.543243\pi$
$908$	−31.3249	−1.03955
$909$	13.0381	0.432447
$910$	−2.12446	−0.0704251
$911$	−11.3023	−0.374463	−0.187231	−	0.982316i	$-0.559951\pi$
$911$	−11.3023	−0.374463	−0.187231	+	0.982316i	$0.559951\pi$
$912$	26.0452	0.862442
$913$	0.907693	0.0300402
$914$	32.9907	1.09123
$915$	1.13854	0.0376390
$916$	8.02111	0.265025
$917$	31.0559	1.02556
$918$	57.9196	1.91163
$919$	17.7676	0.586098	0.293049	−	0.956097i	$-0.405330\pi$
$919$	17.7676	0.586098	0.293049	+	0.956097i	$0.405330\pi$
$920$	0.755838	0.0249192
$921$	−10.1280	−0.333727
$922$	17.4578	0.574942
$923$	−12.7550	−0.419836
$924$	1.05308	0.0346438
$925$	−35.7875	−1.17669
$926$	7.38264	0.242608
$927$	−6.11310	−0.200781
$928$	−56.6475	−1.85955
$929$	32.1876	1.05604	0.528020	−	0.849232i	$-0.322935\pi$
$929$	32.1876	1.05604	0.528020	+	0.849232i	$0.322935\pi$
$930$	3.16688	0.103846
$931$	−49.2021	−1.61253
$932$	15.4152	0.504941
$933$	−2.82662	−0.0925394
$934$	−19.2315	−0.629275
$935$	0.136349	0.00445909
$936$	3.01416	0.0985210
$937$	19.4270	0.634652	0.317326	−	0.948316i	$-0.397215\pi$
$937$	19.4270	0.634652	0.317326	+	0.948316i	$0.397215\pi$
$938$	11.1977	0.365618
$939$	−27.1598	−0.886326
$940$	−0.447662	−0.0146011
$941$	−28.3881	−0.925426	−0.462713	−	0.886508i	$-0.653124\pi$
$941$	−28.3881	−0.925426	−0.462713	+	0.886508i	$0.653124\pi$
$942$	11.0804	0.361020
$943$	13.7748	0.448570
$944$	−55.7235	−1.81364
$945$	3.84535	0.125089
$946$	0	0
$947$	25.9316	0.842664	0.421332	−	0.906906i	$-0.361563\pi$
$947$	25.9316	0.842664	0.421332	+	0.906906i	$0.361563\pi$
$948$	−24.4508	−0.794125
$949$	−8.41840	−0.273273
$950$	38.2716	1.24169
$951$	−5.85498	−0.189861
$952$	−31.0721	−1.00705
$953$	−16.6331	−0.538798	−0.269399	−	0.963029i	$-0.586825\pi$
$953$	−16.6331	−0.538798	−0.269399	+	0.963029i	$0.586825\pi$
$954$	−5.14641	−0.166621
$955$	2.53089	0.0818976
$956$	−21.8390	−0.706325
$957$	−1.64603	−0.0532085
$958$	47.0946	1.52156
$959$	−20.6479	−0.666756
$960$	−0.373344	−0.0120496
$961$	43.7028	1.40977
$962$	22.0774	0.711805
$963$	14.5410	0.468578
$964$	2.30254	0.0741598
$965$	3.43850	0.110689
$966$	37.0111	1.19081
$967$	37.5232	1.20667	0.603333	−	0.797489i	$-0.293839\pi$
$967$	37.5232	1.20667	0.603333	+	0.797489i	$0.293839\pi$
$968$	13.7862	0.443104
$969$	30.4415	0.977923
$970$	0.615540	0.0197638
$971$	−14.6351	−0.469662	−0.234831	−	0.972036i	$-0.575454\pi$
$971$	−14.6351	−0.469662	−0.234831	+	0.972036i	$0.575454\pi$
$972$	17.3729	0.557236
$973$	10.4489	0.334976
$974$	6.64353	0.212872
$975$	−10.5366	−0.337442
$976$	−27.7228	−0.887387
$977$	−3.59770	−0.115101	−0.0575503	−	0.998343i	$-0.518329\pi$
$977$	−3.59770	−0.115101	−0.0575503	+	0.998343i	$0.518329\pi$
$978$	28.4260	0.908963
$979$	1.23604	0.0395039
$980$	2.44376	0.0780631
$981$	19.7476	0.630491
$982$	−58.3147	−1.86090
$983$	−25.2914	−0.806670	−0.403335	−	0.915052i	$-0.632149\pi$
$983$	−25.2914	−0.806670	−0.403335	+	0.915052i	$0.632149\pi$
$984$	5.78848	0.184530
$985$	−2.48976	−0.0793303
$986$	−92.1511	−2.93469
$987$	11.5531	0.367739
$988$	−9.34288	−0.297236
$989$	0	0
$990$	0.0615810	0.00195717
$991$	33.2741	1.05699	0.528494	−	0.848937i	$-0.322757\pi$
$991$	33.2741	1.05699	0.528494	+	0.848937i	$0.322757\pi$
$992$	−55.4039	−1.75908
$993$	8.50251	0.269819
$994$	59.3854	1.88359
$995$	1.30575	0.0413951
$996$	−10.0654	−0.318933
$997$	−18.2842	−0.579067	−0.289533	−	0.957168i	$-0.593500\pi$
$997$	−18.2842	−0.579067	−0.289533	+	0.957168i	$0.593500\pi$
$998$	29.2768	0.926742
$999$	−39.9609	−1.26431

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.m.1.9	yes	10
43.42	odd	2	inner	1849.2.a.m.1.2	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.2.a.m.1.2	✓	10	43.42	odd	2	inner
1849.2.a.m.1.9	yes	10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q+1.81926 q^{2} +1.25580 q^{3} +1.30972 q^{4} +0.160379 q^{5} +2.28463 q^{6} -4.31672 q^{7} -1.25580 q^{8} -1.42297 q^{9} +O(q^{10})\)	\(q+1.81926 q^{2} +1.25580 q^{3} +1.30972 q^{4} +0.160379 q^{5} +2.28463 q^{6} -4.31672 q^{7} -1.25580 q^{8} -1.42297 q^{9} +0.291772 q^{10} -0.148323 q^{11} +1.64475 q^{12} +1.68675 q^{13} -7.85326 q^{14} +0.201404 q^{15} -4.90407 q^{16} -5.73187 q^{17} -2.58876 q^{18} -4.22912 q^{19} +0.210052 q^{20} -5.42094 q^{21} -0.269839 q^{22} -3.75285 q^{23} -1.57703 q^{24} -4.97428 q^{25} +3.06865 q^{26} -5.55436 q^{27} -5.65371 q^{28} +8.83708 q^{29} +0.366406 q^{30} +8.64308 q^{31} -6.41020 q^{32} -0.186264 q^{33} -10.4278 q^{34} -0.692311 q^{35} -1.86369 q^{36} +7.19452 q^{37} -7.69389 q^{38} +2.11822 q^{39} -0.201404 q^{40} -3.67049 q^{41} -9.86211 q^{42} -0.194262 q^{44} -0.228214 q^{45} -6.82743 q^{46} -2.13120 q^{47} -6.15853 q^{48} +11.6341 q^{49} -9.04953 q^{50} -7.19807 q^{51} +2.20918 q^{52} +1.98798 q^{53} -10.1048 q^{54} -0.0237879 q^{55} +5.42094 q^{56} -5.31093 q^{57} +16.0770 q^{58} +11.3627 q^{59} +0.263783 q^{60} +5.65302 q^{61} +15.7240 q^{62} +6.14256 q^{63} -1.85371 q^{64} +0.270519 q^{65} -0.338863 q^{66} -1.42587 q^{67} -7.50715 q^{68} -4.71283 q^{69} -1.25950 q^{70} -7.56187 q^{71} +1.78696 q^{72} -4.99089 q^{73} +13.0887 q^{74} -6.24669 q^{75} -5.53898 q^{76} +0.640269 q^{77} +3.85360 q^{78} -14.8660 q^{79} -0.786510 q^{80} -2.70625 q^{81} -6.67759 q^{82} -6.11970 q^{83} -7.09992 q^{84} -0.919270 q^{85} +11.0976 q^{87} +0.186264 q^{88} -8.33340 q^{89} -0.415182 q^{90} -7.28124 q^{91} -4.91519 q^{92} +10.8540 q^{93} -3.87721 q^{94} -0.678262 q^{95} -8.04993 q^{96} +2.10967 q^{97} +21.1655 q^{98} +0.211059 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{4} + 22 q^{6} + 14 q^{9}+O(q^{10}) \) 10 * q + 2 * q^4 + 22 * q^6 + 14 * q^9	\( 10 q + 2 q^{4} + 22 q^{6} + 14 q^{9} - 22 q^{10} - 10 q^{11} - 14 q^{13} - 22 q^{14} - 22 q^{15} - 26 q^{16} - 16 q^{17} - 44 q^{21} - 18 q^{23} - 44 q^{24} - 6 q^{25} - 2 q^{31} - 28 q^{36} - 22 q^{38} + 22 q^{40} - 2 q^{44} - 18 q^{47} + 18 q^{49} + 28 q^{52} + 2 q^{53} + 44 q^{56} - 22 q^{57} - 22 q^{58} + 14 q^{59} + 8 q^{64} - 22 q^{66} + 26 q^{67} + 32 q^{68} + 44 q^{74} - 44 q^{78} - 56 q^{79} + 2 q^{81} - 38 q^{83} - 22 q^{87} - 22 q^{90} - 74 q^{92} + 22 q^{96} + 34 q^{97} - 36 q^{99}+O(q^{100}) \) 10 * q + 2 * q^4 + 22 * q^6 + 14 * q^9 - 22 * q^10 - 10 * q^11 - 14 * q^13 - 22 * q^14 - 22 * q^15 - 26 * q^16 - 16 * q^17 - 44 * q^21 - 18 * q^23 - 44 * q^24 - 6 * q^25 - 2 * q^31 - 28 * q^36 - 22 * q^38 + 22 * q^40 - 2 * q^44 - 18 * q^47 + 18 * q^49 + 28 * q^52 + 2 * q^53 + 44 * q^56 - 22 * q^57 - 22 * q^58 + 14 * q^59 + 8 * q^64 - 22 * q^66 + 26 * q^67 + 32 * q^68 + 44 * q^74 - 44 * q^78 - 56 * q^79 + 2 * q^81 - 38 * q^83 - 22 * q^87 - 22 * q^90 - 74 * q^92 + 22 * q^96 + 34 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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