LMFDB - Embedded newform 1859.2.a.l.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,2,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1859.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:	$14.8441897358$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.28561300.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 9x^{4} - x^{3} + 22x^{2} + 4x - 12 $ x^6 - 9x^4 - x^3 + 22x^2 + 4*x - 12
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.736891$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.45699 q^{2} -0.664116 q^{3} +4.03681 q^{4} +1.73689 q^{5} -1.63173 q^{6} +1.63580 q^{7} +5.00442 q^{8} -2.55895 q^{9} +O(q^{10})$	\(q+2.45699 q^{2} -0.664116 q^{3} +4.03681 q^{4} +1.73689 q^{5} -1.63173 q^{6} +1.63580 q^{7} +5.00442 q^{8} -2.55895 q^{9} +4.26753 q^{10} +1.00000 q^{11} -2.68091 q^{12} +4.01915 q^{14} -1.15350 q^{15} +4.22220 q^{16} +3.47465 q^{17} -6.28732 q^{18} -0.293781 q^{19} +7.01149 q^{20} -1.08636 q^{21} +2.45699 q^{22} +7.47820 q^{23} -3.32351 q^{24} -1.98321 q^{25} +3.69179 q^{27} +6.60341 q^{28} +6.61794 q^{29} -2.83413 q^{30} -0.799011 q^{31} +0.365068 q^{32} -0.664116 q^{33} +8.53719 q^{34} +2.84121 q^{35} -10.3300 q^{36} +1.62192 q^{37} -0.721818 q^{38} +8.69213 q^{40} -3.37711 q^{41} -2.66918 q^{42} -7.96758 q^{43} +4.03681 q^{44} -4.44462 q^{45} +18.3739 q^{46} +5.35709 q^{47} -2.80403 q^{48} -4.32416 q^{49} -4.87273 q^{50} -2.30757 q^{51} +9.28173 q^{53} +9.07069 q^{54} +1.73689 q^{55} +8.18623 q^{56} +0.195105 q^{57} +16.2602 q^{58} -9.51995 q^{59} -4.65644 q^{60} -5.55808 q^{61} -1.96316 q^{62} -4.18593 q^{63} -7.54743 q^{64} -1.63173 q^{66} -2.01055 q^{67} +14.0265 q^{68} -4.96639 q^{69} +6.98082 q^{70} -12.0286 q^{71} -12.8061 q^{72} -1.85800 q^{73} +3.98504 q^{74} +1.31708 q^{75} -1.18594 q^{76} +1.63580 q^{77} -14.2951 q^{79} +7.33350 q^{80} +5.22508 q^{81} -8.29753 q^{82} +15.5910 q^{83} -4.38543 q^{84} +6.03509 q^{85} -19.5763 q^{86} -4.39508 q^{87} +5.00442 q^{88} +16.3575 q^{89} -10.9204 q^{90} +30.1881 q^{92} +0.530636 q^{93} +13.1623 q^{94} -0.510266 q^{95} -0.242447 q^{96} -14.5648 q^{97} -10.6244 q^{98} -2.55895 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{3} + 8 q^{4} + 6 q^{5} + 12 q^{6} + 3 q^{7} - 3 q^{8} + 7 q^{9}+O(q^{10}) $ 6 * q + q^3 + 8 * q^4 + 6 * q^5 + 12 * q^6 + 3 * q^7 - 3 * q^8 + 7 * q^9	$ 6 q + q^{3} + 8 q^{4} + 6 q^{5} + 12 q^{6} + 3 q^{7} - 3 q^{8} + 7 q^{9} - 3 q^{10} + 6 q^{11} - 17 q^{12} + 12 q^{14} - 4 q^{15} + 8 q^{16} + 2 q^{17} - 6 q^{18} + 10 q^{19} + 15 q^{20} + 12 q^{21} + 3 q^{23} + 14 q^{24} - 6 q^{25} + 10 q^{27} + 16 q^{28} + 3 q^{29} + 19 q^{30} + 5 q^{31} - q^{32} + q^{33} - 5 q^{34} - 13 q^{35} + 20 q^{36} + 25 q^{37} - 27 q^{38} - 8 q^{40} + 24 q^{41} + 13 q^{42} - 8 q^{43} + 8 q^{44} + 27 q^{45} + 18 q^{46} + 10 q^{47} - 28 q^{48} - q^{49} - 26 q^{50} - 17 q^{51} + 10 q^{53} + 47 q^{54} + 6 q^{55} + 15 q^{56} + 6 q^{58} - 4 q^{59} - 61 q^{60} - 21 q^{61} - 5 q^{62} + 6 q^{63} - 27 q^{64} + 12 q^{66} + 21 q^{67} + 14 q^{68} + 5 q^{69} + 31 q^{70} - 3 q^{71} - 50 q^{72} + 13 q^{73} - 38 q^{74} - 23 q^{75} + 8 q^{76} + 3 q^{77} - 4 q^{79} + 44 q^{80} + 34 q^{81} - 33 q^{82} + 8 q^{83} + 47 q^{84} - 13 q^{85} - 11 q^{86} - 51 q^{87} - 3 q^{88} - 9 q^{89} - 70 q^{90} + 15 q^{92} - 21 q^{93} + 10 q^{94} + 27 q^{95} - 19 q^{96} + 15 q^{97} + 21 q^{98} + 7 q^{99}+O(q^{100}) $ 6 * q + q^3 + 8 * q^4 + 6 * q^5 + 12 * q^6 + 3 * q^7 - 3 * q^8 + 7 * q^9 - 3 * q^10 + 6 * q^11 - 17 * q^12 + 12 * q^14 - 4 * q^15 + 8 * q^16 + 2 * q^17 - 6 * q^18 + 10 * q^19 + 15 * q^20 + 12 * q^21 + 3 * q^23 + 14 * q^24 - 6 * q^25 + 10 * q^27 + 16 * q^28 + 3 * q^29 + 19 * q^30 + 5 * q^31 - q^32 + q^33 - 5 * q^34 - 13 * q^35 + 20 * q^36 + 25 * q^37 - 27 * q^38 - 8 * q^40 + 24 * q^41 + 13 * q^42 - 8 * q^43 + 8 * q^44 + 27 * q^45 + 18 * q^46 + 10 * q^47 - 28 * q^48 - q^49 - 26 * q^50 - 17 * q^51 + 10 * q^53 + 47 * q^54 + 6 * q^55 + 15 * q^56 + 6 * q^58 - 4 * q^59 - 61 * q^60 - 21 * q^61 - 5 * q^62 + 6 * q^63 - 27 * q^64 + 12 * q^66 + 21 * q^67 + 14 * q^68 + 5 * q^69 + 31 * q^70 - 3 * q^71 - 50 * q^72 + 13 * q^73 - 38 * q^74 - 23 * q^75 + 8 * q^76 + 3 * q^77 - 4 * q^79 + 44 * q^80 + 34 * q^81 - 33 * q^82 + 8 * q^83 + 47 * q^84 - 13 * q^85 - 11 * q^86 - 51 * q^87 - 3 * q^88 - 9 * q^89 - 70 * q^90 + 15 * q^92 - 21 * q^93 + 10 * q^94 + 27 * q^95 - 19 * q^96 + 15 * q^97 + 21 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.45699	1.73736	0.868678	−	0.495378i	$-0.164970\pi$
$2$	2.45699	1.73736	0.868678	+	0.495378i	$0.164970\pi$
$3$	−0.664116	−0.383427	−0.191714	−	0.981451i	$-0.561404\pi$
$3$	−0.664116	−0.383427	−0.191714	+	0.981451i	$0.561404\pi$
$4$	4.03681	2.01840
$5$	1.73689	0.776761	0.388381	−	0.921499i	$-0.373035\pi$
$5$	1.73689	0.776761	0.388381	+	0.921499i	$0.373035\pi$
$6$	−1.63173	−0.666149
$7$	1.63580	0.618274	0.309137	−	0.951017i	$-0.399960\pi$
$7$	1.63580	0.618274	0.309137	+	0.951017i	$0.399960\pi$
$8$	5.00442	1.76933
$9$	−2.55895	−0.852984
$10$	4.26753	1.34951
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.68091	−0.773911
$13$	0	0
$13$	0	0
$14$	4.01915	1.07416
$15$	−1.15350	−0.297831
$16$	4.22220	1.05555
$17$	3.47465	0.842727	0.421363	−	0.906892i	$-0.361552\pi$
$17$	3.47465	0.842727	0.421363	+	0.906892i	$0.361552\pi$
$18$	−6.28732	−1.48194
$19$	−0.293781	−0.0673980	−0.0336990	−	0.999432i	$-0.510729\pi$
$19$	−0.293781	−0.0673980	−0.0336990	+	0.999432i	$0.510729\pi$
$20$	7.01149	1.56782
$21$	−1.08636	−0.237063
$22$	2.45699	0.523832
$23$	7.47820	1.55931	0.779656	−	0.626208i	$-0.215394\pi$
$23$	7.47820	1.55931	0.779656	+	0.626208i	$0.215394\pi$
$24$	−3.32351	−0.678409
$25$	−1.98321	−0.396642
$26$	0	0
$27$	3.69179	0.710484
$28$	6.60341	1.24793
$29$	6.61794	1.22892	0.614460	−	0.788948i	$-0.289374\pi$
$29$	6.61794	1.22892	0.614460	+	0.788948i	$0.289374\pi$
$30$	−2.83413	−0.517439
$31$	−0.799011	−0.143507	−0.0717533	−	0.997422i	$-0.522859\pi$
$31$	−0.799011	−0.143507	−0.0717533	+	0.997422i	$0.522859\pi$
$32$	0.365068	0.0645355
$33$	−0.664116	−0.115608
$34$	8.53719	1.46412
$35$	2.84121	0.480252
$36$	−10.3300	−1.72166
$37$	1.62192	0.266642	0.133321	−	0.991073i	$-0.457436\pi$
$37$	1.62192	0.266642	0.133321	+	0.991073i	$0.457436\pi$
$38$	−0.721818	−0.117094
$39$	0	0
$40$	8.69213	1.37435
$41$	−3.37711	−0.527416	−0.263708	−	0.964603i	$-0.584946\pi$
$41$	−3.37711	−0.527416	−0.263708	+	0.964603i	$0.584946\pi$
$42$	−2.66918	−0.411863
$43$	−7.96758	−1.21504	−0.607522	−	0.794303i	$-0.707836\pi$
$43$	−7.96758	−1.21504	−0.607522	+	0.794303i	$0.707836\pi$
$44$	4.03681	0.608572
$45$	−4.44462	−0.662565
$46$	18.3739	2.70908
$47$	5.35709	0.781412	0.390706	−	0.920515i	$-0.372231\pi$
$47$	5.35709	0.781412	0.390706	+	0.920515i	$0.372231\pi$
$48$	−2.80403	−0.404726
$49$	−4.32416	−0.617737
$50$	−4.87273	−0.689108
$51$	−2.30757	−0.323124
$52$	0	0
$53$	9.28173	1.27494	0.637472	−	0.770474i	$-0.279980\pi$
$53$	9.28173	1.27494	0.637472	+	0.770474i	$0.279980\pi$
$54$	9.07069	1.23436
$55$	1.73689	0.234202
$56$	8.18623	1.09393
$57$	0.195105	0.0258422
$58$	16.2602	2.13507
$59$	−9.51995	−1.23939	−0.619696	−	0.784842i	$-0.712744\pi$
$59$	−9.51995	−1.23939	−0.619696	+	0.784842i	$0.712744\pi$
$60$	−4.65644	−0.601144
$61$	−5.55808	−0.711639	−0.355820	−	0.934555i	$-0.615798\pi$
$61$	−5.55808	−0.711639	−0.355820	+	0.934555i	$0.615798\pi$
$62$	−1.96316	−0.249322
$63$	−4.18593	−0.527378
$64$	−7.54743	−0.943428
$65$	0	0
$66$	−1.63173	−0.200852
$67$	−2.01055	−0.245628	−0.122814	−	0.992430i	$-0.539192\pi$
$67$	−2.01055	−0.245628	−0.122814	+	0.992430i	$0.539192\pi$
$68$	14.0265	1.70096
$69$	−4.96639	−0.597883
$70$	6.98082	0.834368
$71$	−12.0286	−1.42754	−0.713768	−	0.700382i	$-0.753013\pi$
$71$	−12.0286	−1.42754	−0.713768	+	0.700382i	$0.753013\pi$
$72$	−12.8061	−1.50921
$73$	−1.85800	−0.217462	−0.108731	−	0.994071i	$-0.534679\pi$
$73$	−1.85800	−0.217462	−0.108731	+	0.994071i	$0.534679\pi$
$74$	3.98504	0.463252
$75$	1.31708	0.152083
$76$	−1.18594	−0.136036
$77$	1.63580	0.186417
$78$	0	0
$79$	−14.2951	−1.60833	−0.804164	−	0.594407i	$-0.797387\pi$
$79$	−14.2951	−1.60833	−0.804164	+	0.594407i	$0.797387\pi$
$80$	7.33350	0.819910
$81$	5.22508	0.580564
$82$	−8.29753	−0.916309
$83$	15.5910	1.71134	0.855668	−	0.517526i	$-0.173147\pi$
$83$	15.5910	1.71134	0.855668	+	0.517526i	$0.173147\pi$
$84$	−4.38543	−0.478489
$85$	6.03509	0.654597
$86$	−19.5763	−2.11096
$87$	−4.39508	−0.471202
$88$	5.00442	0.533473
$89$	16.3575	1.73389	0.866947	−	0.498400i	$-0.166079\pi$
$89$	16.3575	1.73389	0.866947	+	0.498400i	$0.166079\pi$
$90$	−10.9204	−1.15111
$91$	0	0
$92$	30.1881	3.14732
$93$	0.530636	0.0550243
$94$	13.1623	1.35759
$95$	−0.510266	−0.0523522
$96$	−0.242447	−0.0247447
$97$	−14.5648	−1.47883	−0.739413	−	0.673252i	$-0.764897\pi$
$97$	−14.5648	−1.47883	−0.739413	+	0.673252i	$0.764897\pi$
$98$	−10.6244	−1.07323
$99$	−2.55895	−0.257184
$100$	−8.00583	−0.800583
$101$	−17.5665	−1.74793	−0.873965	−	0.485990i	$-0.838459\pi$
$101$	−17.5665	−1.74793	−0.873965	+	0.485990i	$0.838459\pi$
$102$	−5.66968	−0.561382
$103$	9.04786	0.891512	0.445756	−	0.895155i	$-0.352935\pi$
$103$	9.04786	0.891512	0.445756	+	0.895155i	$0.352935\pi$
$104$	0	0
$105$	−1.88689	−0.184142
$106$	22.8051	2.21503
$107$	9.54797	0.923037	0.461519	−	0.887130i	$-0.347305\pi$
$107$	9.54797	0.923037	0.461519	+	0.887130i	$0.347305\pi$
$108$	14.9030	1.43404
$109$	−12.8592	−1.23169	−0.615843	−	0.787869i	$-0.711184\pi$
$109$	−12.8592	−1.23169	−0.615843	+	0.787869i	$0.711184\pi$
$110$	4.26753	0.406893
$111$	−1.07714	−0.102238
$112$	6.90667	0.652619
$113$	−0.468546	−0.0440771	−0.0220385	−	0.999757i	$-0.507016\pi$
$113$	−0.468546	−0.0440771	−0.0220385	+	0.999757i	$0.507016\pi$
$114$	0.479370	0.0448971
$115$	12.9888	1.21121
$116$	26.7153	2.48046
$117$	0	0
$118$	−23.3904	−2.15326
$119$	5.68384	0.521036
$120$	−5.77258	−0.526962
$121$	1.00000	0.0909091
$122$	−13.6562	−1.23637
$123$	2.24279	0.202226
$124$	−3.22545	−0.289654
$125$	−12.1291	−1.08486
$126$	−10.2848	−0.916243
$127$	9.97747	0.885357	0.442678	−	0.896680i	$-0.354028\pi$
$127$	9.97747	0.885357	0.442678	+	0.896680i	$0.354028\pi$
$128$	−19.2741	−1.70361
$129$	5.29139	0.465881
$130$	0	0
$131$	−5.28118	−0.461419	−0.230710	−	0.973023i	$-0.574105\pi$
$131$	−5.28118	−0.461419	−0.230710	+	0.973023i	$0.574105\pi$
$132$	−2.68091	−0.233343
$133$	−0.480567	−0.0416705
$134$	−4.93991	−0.426743
$135$	6.41223	0.551877
$136$	17.3886	1.49106
$137$	−2.69702	−0.230422	−0.115211	−	0.993341i	$-0.536754\pi$
$137$	−2.69702	−0.230422	−0.115211	+	0.993341i	$0.536754\pi$
$138$	−12.2024	−1.03874
$139$	−1.21930	−0.103420	−0.0517098	−	0.998662i	$-0.516467\pi$
$139$	−1.21930	−0.103420	−0.0517098	+	0.998662i	$0.516467\pi$
$140$	11.4694	0.969342
$141$	−3.55773	−0.299615
$142$	−29.5542	−2.48014
$143$	0	0
$144$	−10.8044	−0.900366
$145$	11.4946	0.954578
$146$	−4.56509	−0.377809
$147$	2.87174	0.236857
$148$	6.54737	0.538191
$149$	22.1031	1.81076	0.905379	−	0.424605i	$-0.139587\pi$
$149$	22.1031	1.81076	0.905379	+	0.424605i	$0.139587\pi$
$150$	3.23605	0.264223
$151$	0.270215	0.0219898	0.0109949	−	0.999940i	$-0.496500\pi$
$151$	0.270215	0.0219898	0.0109949	+	0.999940i	$0.496500\pi$
$152$	−1.47020	−0.119249
$153$	−8.89146	−0.718832
$154$	4.01915	0.323872
$155$	−1.38779	−0.111470
$156$	0	0
$157$	−12.2284	−0.975929	−0.487964	−	0.872864i	$-0.662260\pi$
$157$	−12.2284	−0.975929	−0.487964	+	0.872864i	$0.662260\pi$
$158$	−35.1230	−2.79424
$159$	−6.16414	−0.488848
$160$	0.634083	0.0501287
$161$	12.2328	0.964083
$162$	12.8380	1.00865
$163$	1.99597	0.156337	0.0781684	−	0.996940i	$-0.475093\pi$
$163$	1.99597	0.156337	0.0781684	+	0.996940i	$0.475093\pi$
$164$	−13.6327	−1.06454
$165$	−1.15350	−0.0897996
$166$	38.3070	2.97320
$167$	15.7282	1.21708	0.608542	−	0.793522i	$-0.291755\pi$
$167$	15.7282	1.21708	0.608542	+	0.793522i	$0.291755\pi$
$168$	−5.43660	−0.419443
$169$	0	0
$170$	14.8282	1.13727
$171$	0.751771	0.0574894
$172$	−32.1636	−2.45245
$173$	−10.6907	−0.812798	−0.406399	−	0.913696i	$-0.633216\pi$
$173$	−10.6907	−0.812798	−0.406399	+	0.913696i	$0.633216\pi$
$174$	−10.7987	−0.818644
$175$	−3.24413	−0.245234
$176$	4.22220	0.318260
$177$	6.32235	0.475217
$178$	40.1903	3.01239
$179$	−24.9061	−1.86157	−0.930784	−	0.365569i	$-0.880874\pi$
$179$	−24.9061	−1.86157	−0.930784	+	0.365569i	$0.880874\pi$
$180$	−17.9421	−1.33732
$181$	5.01445	0.372721	0.186361	−	0.982481i	$-0.440331\pi$
$181$	5.01445	0.372721	0.186361	+	0.982481i	$0.440331\pi$
$182$	0	0
$183$	3.69121	0.272862
$184$	37.4240	2.75894
$185$	2.81710	0.207117
$186$	1.30377	0.0955968
$187$	3.47465	0.254092
$188$	21.6256	1.57721
$189$	6.03902	0.439274
$190$	−1.25372	−0.0909543
$191$	−21.8679	−1.58230	−0.791152	−	0.611620i	$-0.790518\pi$
$191$	−21.8679	−1.58230	−0.791152	+	0.611620i	$0.790518\pi$
$192$	5.01236	0.361736
$193$	18.7823	1.35198	0.675988	−	0.736913i	$-0.263717\pi$
$193$	18.7823	1.35198	0.675988	+	0.736913i	$0.263717\pi$
$194$	−35.7855	−2.56925
$195$	0	0
$196$	−17.4558	−1.24684
$197$	−13.7956	−0.982899	−0.491450	−	0.870906i	$-0.663533\pi$
$197$	−13.7956	−0.982899	−0.491450	+	0.870906i	$0.663533\pi$
$198$	−6.28732	−0.446820
$199$	−12.2468	−0.868149	−0.434075	−	0.900877i	$-0.642925\pi$
$199$	−12.2468	−0.868149	−0.434075	+	0.900877i	$0.642925\pi$
$200$	−9.92481	−0.701790
$201$	1.33524	0.0941805
$202$	−43.1607	−3.03677
$203$	10.8256	0.759810
$204$	−9.31521	−0.652195
$205$	−5.86567	−0.409676
$206$	22.2305	1.54887
$207$	−19.1363	−1.33007
$208$	0	0
$209$	−0.293781	−0.0203213
$210$	−4.63607	−0.319919
$211$	−13.8040	−0.950305	−0.475152	−	0.879903i	$-0.657607\pi$
$211$	−13.8040	−0.950305	−0.475152	+	0.879903i	$0.657607\pi$
$212$	37.4686	2.57335
$213$	7.98840	0.547356
$214$	23.4593	1.60364
$215$	−13.8388	−0.943800
$216$	18.4752	1.25708
$217$	−1.30702	−0.0887265
$218$	−31.5949	−2.13988
$219$	1.23393	0.0833810
$220$	7.01149	0.472715
$221$	0	0
$222$	−2.64653	−0.177623
$223$	−16.4057	−1.09861	−0.549305	−	0.835622i	$-0.685107\pi$
$223$	−16.4057	−1.09861	−0.549305	+	0.835622i	$0.685107\pi$
$224$	0.597178	0.0399007
$225$	5.07493	0.338329
$226$	−1.15121	−0.0765775
$227$	−10.0126	−0.664557	−0.332279	−	0.943181i	$-0.607817\pi$
$227$	−10.0126	−0.664557	−0.332279	+	0.943181i	$0.607817\pi$
$228$	0.787599	0.0521600
$229$	8.46067	0.559097	0.279548	−	0.960132i	$-0.409815\pi$
$229$	8.46067	0.559097	0.279548	+	0.960132i	$0.409815\pi$
$230$	31.9134	2.10431
$231$	−1.08636	−0.0714773
$232$	33.1189	2.17436
$233$	−11.5661	−0.757722	−0.378861	−	0.925454i	$-0.623684\pi$
$233$	−11.5661	−0.757722	−0.378861	+	0.925454i	$0.623684\pi$
$234$	0	0
$235$	9.30469	0.606971
$236$	−38.4302	−2.50159
$237$	9.49362	0.616677
$238$	13.9651	0.905225
$239$	−5.10653	−0.330314	−0.165157	−	0.986267i	$-0.552813\pi$
$239$	−5.10653	−0.330314	−0.165157	+	0.986267i	$0.552813\pi$
$240$	−4.87029	−0.314376
$241$	26.8317	1.72838	0.864191	−	0.503164i	$-0.167831\pi$
$241$	26.8317	1.72838	0.864191	+	0.503164i	$0.167831\pi$
$242$	2.45699	0.157941
$243$	−14.5454	−0.933089
$244$	−22.4369	−1.43638
$245$	−7.51059	−0.479834
$246$	5.51052	0.351338
$247$	0	0
$248$	−3.99858	−0.253910
$249$	−10.3542	−0.656173
$250$	−29.8010	−1.88478
$251$	−0.690964	−0.0436132	−0.0218066	−	0.999762i	$-0.506942\pi$
$251$	−0.690964	−0.0436132	−0.0218066	+	0.999762i	$0.506942\pi$
$252$	−16.8978	−1.06446
$253$	7.47820	0.470150
$254$	24.5146	1.53818
$255$	−4.00800	−0.250991
$256$	−32.2614	−2.01634
$257$	6.89490	0.430092	0.215046	−	0.976604i	$-0.431010\pi$
$257$	6.89490	0.430092	0.215046	+	0.976604i	$0.431010\pi$
$258$	13.0009	0.809401
$259$	2.65314	0.164858
$260$	0	0
$261$	−16.9350	−1.04825
$262$	−12.9758	−0.801649
$263$	2.44643	0.150853	0.0754266	−	0.997151i	$-0.475968\pi$
$263$	2.44643	0.150853	0.0754266	+	0.997151i	$0.475968\pi$
$264$	−3.32351	−0.204548
$265$	16.1214	0.990327
$266$	−1.18075	−0.0723964
$267$	−10.8633	−0.664823
$268$	−8.11621	−0.495777
$269$	21.6219	1.31831	0.659154	−	0.752008i	$-0.270915\pi$
$269$	21.6219	1.31831	0.659154	+	0.752008i	$0.270915\pi$
$270$	15.7548	0.958806
$271$	−1.87121	−0.113668	−0.0568341	−	0.998384i	$-0.518101\pi$
$271$	−1.87121	−0.113668	−0.0568341	+	0.998384i	$0.518101\pi$
$272$	14.6707	0.889540
$273$	0	0
$274$	−6.62656	−0.400325
$275$	−1.98321	−0.119592
$276$	−20.0484	−1.20677
$277$	−6.28819	−0.377821	−0.188910	−	0.981994i	$-0.560496\pi$
$277$	−6.28819	−0.377821	−0.188910	+	0.981994i	$0.560496\pi$
$278$	−2.99581	−0.179676
$279$	2.04463	0.122409
$280$	14.2186	0.849723
$281$	7.68890	0.458681	0.229341	−	0.973346i	$-0.426343\pi$
$281$	7.68890	0.458681	0.229341	+	0.973346i	$0.426343\pi$
$282$	−8.74131	−0.520537
$283$	27.7138	1.64741	0.823707	−	0.567015i	$-0.191902\pi$
$283$	27.7138	1.64741	0.823707	+	0.567015i	$0.191902\pi$
$284$	−48.5573	−2.88134
$285$	0.338875	0.0200732
$286$	0	0
$287$	−5.52428	−0.326088
$288$	−0.934191	−0.0550477
$289$	−4.92680	−0.289812
$290$	28.2422	1.65844
$291$	9.67268	0.567022
$292$	−7.50038	−0.438927
$293$	16.2391	0.948699	0.474349	−	0.880337i	$-0.342683\pi$
$293$	16.2391	0.948699	0.474349	+	0.880337i	$0.342683\pi$
$294$	7.05584	0.411505
$295$	−16.5351	−0.962712
$296$	8.11676	0.471777
$297$	3.69179	0.214219
$298$	54.3072	3.14593
$299$	0	0
$300$	5.31680	0.306965
$301$	−13.0334	−0.751231
$302$	0.663917	0.0382041
$303$	11.6662	0.670204
$304$	−1.24040	−0.0711419
$305$	−9.65378	−0.552774
$306$	−21.8462	−1.24887
$307$	5.80030	0.331041	0.165520	−	0.986206i	$-0.447070\pi$
$307$	5.80030	0.331041	0.165520	+	0.986206i	$0.447070\pi$
$308$	6.60341	0.376264
$309$	−6.00882	−0.341830
$310$	−3.40980	−0.193664
$311$	−8.39017	−0.475763	−0.237881	−	0.971294i	$-0.576453\pi$
$311$	−8.39017	−0.475763	−0.237881	+	0.971294i	$0.576453\pi$
$312$	0	0
$313$	2.73695	0.154702	0.0773508	−	0.997004i	$-0.475354\pi$
$313$	2.73695	0.154702	0.0773508	+	0.997004i	$0.475354\pi$
$314$	−30.0450	−1.69554
$315$	−7.27051	−0.409647
$316$	−57.7067	−3.24626
$317$	−9.07707	−0.509819	−0.254910	−	0.966965i	$-0.582046\pi$
$317$	−9.07707	−0.509819	−0.254910	+	0.966965i	$0.582046\pi$
$318$	−15.1452	−0.849303
$319$	6.61794	0.370533
$320$	−13.1091	−0.732819
$321$	−6.34096	−0.353918
$322$	30.0560	1.67495
$323$	−1.02079	−0.0567981
$324$	21.0926	1.17181
$325$	0	0
$326$	4.90409	0.271613
$327$	8.53998	0.472262
$328$	−16.9005	−0.933172
$329$	8.76314	0.483127
$330$	−2.83413	−0.156014
$331$	−18.0591	−0.992615	−0.496308	−	0.868147i	$-0.665311\pi$
$331$	−18.0591	−0.992615	−0.496308	+	0.868147i	$0.665311\pi$
$332$	62.9379	3.45417
$333$	−4.15041	−0.227441
$334$	38.6440	2.11451
$335$	−3.49211	−0.190794
$336$	−4.58683	−0.250232
$337$	−14.4529	−0.787298	−0.393649	−	0.919261i	$-0.628788\pi$
$337$	−14.4529	−0.787298	−0.393649	+	0.919261i	$0.628788\pi$
$338$	0	0
$339$	0.311168	0.0169003
$340$	24.3625	1.32124
$341$	−0.799011	−0.0432689
$342$	1.84710	0.0998795
$343$	−18.5241	−1.00021
$344$	−39.8731	−2.14981
$345$	−8.62608	−0.464412
$346$	−26.2669	−1.41212
$347$	−3.51763	−0.188836	−0.0944182	−	0.995533i	$-0.530099\pi$
$347$	−3.51763	−0.188836	−0.0944182	+	0.995533i	$0.530099\pi$
$348$	−17.7421	−0.951075
$349$	24.3041	1.30097	0.650484	−	0.759520i	$-0.274566\pi$
$349$	24.3041	1.30097	0.650484	+	0.759520i	$0.274566\pi$
$350$	−7.97081	−0.426058
$351$	0	0
$352$	0.365068	0.0194582
$353$	10.1403	0.539712	0.269856	−	0.962901i	$-0.413024\pi$
$353$	10.1403	0.539712	0.269856	+	0.962901i	$0.413024\pi$
$354$	15.5340	0.825620
$355$	−20.8924	−1.10885
$356$	66.0322	3.49970
$357$	−3.77472	−0.199780
$358$	−61.1941	−3.23421
$359$	−4.78700	−0.252648	−0.126324	−	0.991989i	$-0.540318\pi$
$359$	−4.78700	−0.252648	−0.126324	+	0.991989i	$0.540318\pi$
$360$	−22.2427	−1.17229
$361$	−18.9137	−0.995458
$362$	12.3205	0.647549
$363$	−0.664116	−0.0348570
$364$	0	0
$365$	−3.22714	−0.168916
$366$	9.06927	0.474058
$367$	9.74833	0.508859	0.254429	−	0.967091i	$-0.418112\pi$
$367$	9.74833	0.508859	0.254429	+	0.967091i	$0.418112\pi$
$368$	31.5744	1.64593
$369$	8.64186	0.449877
$370$	6.92158	0.359836
$371$	15.1831	0.788265
$372$	2.14207	0.111061
$373$	0.583716	0.0302237	0.0151118	−	0.999886i	$-0.495190\pi$
$373$	0.583716	0.0302237	0.0151118	+	0.999886i	$0.495190\pi$
$374$	8.53719	0.441447
$375$	8.05511	0.415964
$376$	26.8091	1.38258
$377$	0	0
$378$	14.8378	0.763176
$379$	31.4481	1.61538	0.807691	−	0.589606i	$-0.200717\pi$
$379$	31.4481	1.61538	0.807691	+	0.589606i	$0.200717\pi$
$380$	−2.05984	−0.105668
$381$	−6.62619	−0.339470
$382$	−53.7292	−2.74902
$383$	−5.21147	−0.266294	−0.133147	−	0.991096i	$-0.542508\pi$
$383$	−5.21147	−0.266294	−0.133147	+	0.991096i	$0.542508\pi$
$384$	12.8002	0.653209
$385$	2.84121	0.144801
$386$	46.1478	2.34886
$387$	20.3886	1.03641
$388$	−58.7951	−2.98487
$389$	−2.19164	−0.111121	−0.0555603	−	0.998455i	$-0.517695\pi$
$389$	−2.19164	−0.111121	−0.0555603	+	0.998455i	$0.517695\pi$
$390$	0	0
$391$	25.9841	1.31407
$392$	−21.6399	−1.09298
$393$	3.50732	0.176921
$394$	−33.8958	−1.70765
$395$	−24.8291	−1.24929
$396$	−10.3300	−0.519102
$397$	−4.17369	−0.209471	−0.104736	−	0.994500i	$-0.533400\pi$
$397$	−4.17369	−0.209471	−0.104736	+	0.994500i	$0.533400\pi$
$398$	−30.0902	−1.50828
$399$	0.319152	0.0159776
$400$	−8.37350	−0.418675
$401$	−22.4330	−1.12025	−0.560125	−	0.828408i	$-0.689247\pi$
$401$	−22.4330	−1.12025	−0.560125	+	0.828408i	$0.689247\pi$
$402$	3.28067	0.163625
$403$	0	0
$404$	−70.9125	−3.52803
$405$	9.07539	0.450960
$406$	26.5985	1.32006
$407$	1.62192	0.0803955
$408$	−11.5480	−0.571713
$409$	−12.9812	−0.641879	−0.320939	−	0.947100i	$-0.603999\pi$
$409$	−12.9812	−0.641879	−0.320939	+	0.947100i	$0.603999\pi$
$410$	−14.4119	−0.711753
$411$	1.79113	0.0883501
$412$	36.5244	1.79943
$413$	−15.5727	−0.766284
$414$	−47.0178	−2.31080
$415$	27.0799	1.32930
$416$	0	0
$417$	0.809755	0.0396539
$418$	−0.721818	−0.0353052
$419$	11.6411	0.568703	0.284351	−	0.958720i	$-0.408222\pi$
$419$	11.6411	0.568703	0.284351	+	0.958720i	$0.408222\pi$
$420$	−7.61701	−0.371672
$421$	14.7033	0.716594	0.358297	−	0.933608i	$-0.383358\pi$
$421$	14.7033	0.716594	0.358297	+	0.933608i	$0.383358\pi$
$422$	−33.9163	−1.65102
$423$	−13.7085	−0.666532
$424$	46.4497	2.25580
$425$	−6.89096	−0.334261
$426$	19.6274	0.950952
$427$	−9.09191	−0.439989
$428$	38.5433	1.86306
$429$	0	0
$430$	−34.0019	−1.63972
$431$	−31.1519	−1.50054	−0.750268	−	0.661133i	$-0.770076\pi$
$431$	−31.1519	−1.50054	−0.750268	+	0.661133i	$0.770076\pi$
$432$	15.5874	0.749951
$433$	34.0486	1.63627	0.818135	−	0.575027i	$-0.195008\pi$
$433$	34.0486	1.63627	0.818135	+	0.575027i	$0.195008\pi$
$434$	−3.21134	−0.154149
$435$	−7.63377	−0.366011
$436$	−51.9100	−2.48604
$437$	−2.19695	−0.105095
$438$	3.03174	0.144862
$439$	−26.0916	−1.24528	−0.622642	−	0.782507i	$-0.713941\pi$
$439$	−26.0916	−1.24528	−0.622642	+	0.782507i	$0.713941\pi$
$440$	8.69213	0.414381
$441$	11.0653	0.526919
$442$	0	0
$443$	26.8402	1.27522	0.637608	−	0.770361i	$-0.279924\pi$
$443$	26.8402	1.27522	0.637608	+	0.770361i	$0.279924\pi$
$444$	−4.34821	−0.206357
$445$	28.4112	1.34682
$446$	−40.3088	−1.90868
$447$	−14.6790	−0.694294
$448$	−12.3461	−0.583298
$449$	18.7199	0.883446	0.441723	−	0.897151i	$-0.354367\pi$
$449$	18.7199	0.883446	0.441723	+	0.897151i	$0.354367\pi$
$450$	12.4691	0.587798
$451$	−3.37711	−0.159022
$452$	−1.89143	−0.0889653
$453$	−0.179454	−0.00843149
$454$	−24.6008	−1.15457
$455$	0	0
$456$	0.976385	0.0457234
$457$	7.38799	0.345596	0.172798	−	0.984957i	$-0.444719\pi$
$457$	7.38799	0.345596	0.172798	+	0.984957i	$0.444719\pi$
$458$	20.7878	0.971350
$459$	12.8277	0.598744
$460$	52.4334	2.44472
$461$	20.8874	0.972822	0.486411	−	0.873730i	$-0.338306\pi$
$461$	20.8874	0.972822	0.486411	+	0.873730i	$0.338306\pi$
$462$	−2.66918	−0.124181
$463$	26.4800	1.23063	0.615315	−	0.788281i	$-0.289029\pi$
$463$	26.4800	1.23063	0.615315	+	0.788281i	$0.289029\pi$
$464$	27.9422	1.29719
$465$	0.921656	0.0427408
$466$	−28.4179	−1.31643
$467$	23.2677	1.07670	0.538351	−	0.842721i	$-0.319047\pi$
$467$	23.2677	1.07670	0.538351	+	0.842721i	$0.319047\pi$
$468$	0	0
$469$	−3.28886	−0.151866
$470$	22.8615	1.05452
$471$	8.12104	0.374198
$472$	−47.6418	−2.19289
$473$	−7.96758	−0.366350
$474$	23.3257	1.07139
$475$	0.582629	0.0267329
$476$	22.9445	1.05166
$477$	−23.7515	−1.08751
$478$	−12.5467	−0.573873
$479$	−10.3364	−0.472284	−0.236142	−	0.971719i	$-0.575883\pi$
$479$	−10.3364	−0.472284	−0.236142	+	0.971719i	$0.575883\pi$
$480$	−0.421105	−0.0192207
$481$	0	0
$482$	65.9253	3.00281
$483$	−8.12402	−0.369656
$484$	4.03681	0.183491
$485$	−25.2974	−1.14870
$486$	−35.7380	−1.62111
$487$	−27.3650	−1.24003	−0.620014	−	0.784591i	$-0.712873\pi$
$487$	−27.3650	−1.24003	−0.620014	+	0.784591i	$0.712873\pi$
$488$	−27.8150	−1.25912
$489$	−1.32556	−0.0599438
$490$	−18.4535	−0.833642
$491$	−24.9289	−1.12502	−0.562512	−	0.826789i	$-0.690165\pi$
$491$	−24.9289	−1.12502	−0.562512	+	0.826789i	$0.690165\pi$
$492$	9.05371	0.408173
$493$	22.9950	1.03564
$494$	0	0
$495$	−4.44462	−0.199771
$496$	−3.37358	−0.151478
$497$	−19.6764	−0.882609
$498$	−25.4403	−1.14001
$499$	−11.7972	−0.528117	−0.264058	−	0.964507i	$-0.585061\pi$
$499$	−11.7972	−0.528117	−0.264058	+	0.964507i	$0.585061\pi$
$500$	−48.9627	−2.18968
$501$	−10.4453	−0.466663
$502$	−1.69769	−0.0757717
$503$	−2.38701	−0.106432	−0.0532158	−	0.998583i	$-0.516947\pi$
$503$	−2.38701	−0.106432	−0.0532158	+	0.998583i	$0.516947\pi$
$504$	−20.9482	−0.933105
$505$	−30.5110	−1.35772
$506$	18.3739	0.816818
$507$	0	0
$508$	40.2771	1.78701
$509$	31.6718	1.40383	0.701914	−	0.712261i	$-0.252329\pi$
$509$	31.6718	1.40383	0.701914	+	0.712261i	$0.252329\pi$
$510$	−9.84761	−0.436060
$511$	−3.03931	−0.134451
$512$	−40.7179	−1.79949
$513$	−1.08458	−0.0478852
$514$	16.9407	0.747223
$515$	15.7151	0.692492
$516$	21.3603	0.940336
$517$	5.35709	0.235605
$518$	6.51873	0.286417
$519$	7.09985	0.311649
$520$	0	0
$521$	16.5505	0.725091	0.362546	−	0.931966i	$-0.381908\pi$
$521$	16.5505	0.725091	0.362546	+	0.931966i	$0.381908\pi$
$522$	−41.6091	−1.82118
$523$	−30.4983	−1.33360	−0.666798	−	0.745238i	$-0.732336\pi$
$523$	−30.4983	−1.33360	−0.666798	+	0.745238i	$0.732336\pi$
$524$	−21.3191	−0.931330
$525$	2.15448	0.0940292
$526$	6.01085	0.262086
$527$	−2.77628	−0.120937
$528$	−2.80403	−0.122030
$529$	32.9235	1.43146
$530$	39.6100	1.72055
$531$	24.3611	1.05718
$532$	−1.93996	−0.0841078
$533$	0	0
$534$	−26.6910	−1.15503
$535$	16.5838	0.716980
$536$	−10.0616	−0.434597
$537$	16.5405	0.713776
$538$	53.1247	2.29037
$539$	−4.32416	−0.186255
$540$	25.8849	1.11391
$541$	12.2536	0.526824	0.263412	−	0.964683i	$-0.415152\pi$
$541$	12.2536	0.526824	0.263412	+	0.964683i	$0.415152\pi$
$542$	−4.59756	−0.197482
$543$	−3.33018	−0.142912
$544$	1.26848	0.0543858
$545$	−22.3350	−0.956726
$546$	0	0
$547$	−19.1291	−0.817903	−0.408952	−	0.912556i	$-0.634106\pi$
$547$	−19.1291	−0.817903	−0.408952	+	0.912556i	$0.634106\pi$
$548$	−10.8874	−0.465085
$549$	14.2229	0.607017
$550$	−4.87273	−0.207774
$551$	−1.94422	−0.0828268
$552$	−24.8539	−1.05785
$553$	−23.3840	−0.994388
$554$	−15.4500	−0.656409
$555$	−1.87088	−0.0794143
$556$	−4.92207	−0.208742
$557$	4.13852	0.175355	0.0876773	−	0.996149i	$-0.472056\pi$
$557$	4.13852	0.175355	0.0876773	+	0.996149i	$0.472056\pi$
$558$	5.02364	0.212668
$559$	0	0
$560$	11.9961	0.506929
$561$	−2.30757	−0.0974257
$562$	18.8916	0.796893
$563$	7.23626	0.304972	0.152486	−	0.988306i	$-0.451272\pi$
$563$	7.23626	0.304972	0.152486	+	0.988306i	$0.451272\pi$
$564$	−14.3619	−0.604744
$565$	−0.813813	−0.0342374
$566$	68.0926	2.86214
$567$	8.54719	0.358948
$568$	−60.1963	−2.52578
$569$	−6.17369	−0.258814	−0.129407	−	0.991592i	$-0.541307\pi$
$569$	−6.17369	−0.258814	−0.129407	+	0.991592i	$0.541307\pi$
$570$	0.832614	0.0348744
$571$	5.47725	0.229216	0.114608	−	0.993411i	$-0.463439\pi$
$571$	5.47725	0.229216	0.114608	+	0.993411i	$0.463439\pi$
$572$	0	0
$573$	14.5228	0.606698
$574$	−13.5731	−0.566530
$575$	−14.8308	−0.618489
$576$	19.3135	0.804729
$577$	36.9750	1.53929	0.769644	−	0.638473i	$-0.220434\pi$
$577$	36.9750	1.53929	0.769644	+	0.638473i	$0.220434\pi$
$578$	−12.1051	−0.503506
$579$	−12.4736	−0.518385
$580$	46.4016	1.92672
$581$	25.5038	1.05808
$582$	23.7657	0.985120
$583$	9.28173	0.384410
$584$	−9.29820	−0.384762
$585$	0	0
$586$	39.8993	1.64823
$587$	−30.9816	−1.27875	−0.639374	−	0.768896i	$-0.720806\pi$
$587$	−30.9816	−1.27875	−0.639374	+	0.768896i	$0.720806\pi$
$588$	11.5927	0.478073
$589$	0.234734	0.00967206
$590$	−40.6266	−1.67257
$591$	9.16191	0.376870
$592$	6.84806	0.281454
$593$	30.0100	1.23236	0.616181	−	0.787604i	$-0.288679\pi$
$593$	30.0100	1.23236	0.616181	+	0.787604i	$0.288679\pi$
$594$	9.07069	0.372175
$595$	9.87220	0.404721
$596$	89.2260	3.65484
$597$	8.13326	0.332872
$598$	0	0
$599$	−10.2955	−0.420664	−0.210332	−	0.977630i	$-0.567455\pi$
$599$	−10.2955	−0.420664	−0.210332	+	0.977630i	$0.567455\pi$
$600$	6.59122	0.269085
$601$	27.5257	1.12280	0.561398	−	0.827546i	$-0.310264\pi$
$601$	27.5257	1.12280	0.561398	+	0.827546i	$0.310264\pi$
$602$	−32.0229	−1.30516
$603$	5.14491	0.209517
$604$	1.09081	0.0443843
$605$	1.73689	0.0706147
$606$	28.6637	1.16438
$607$	−6.94324	−0.281817	−0.140909	−	0.990023i	$-0.545002\pi$
$607$	−6.94324	−0.281817	−0.140909	+	0.990023i	$0.545002\pi$
$608$	−0.107250	−0.00434956
$609$	−7.18947	−0.291332
$610$	−23.7193	−0.960365
$611$	0	0
$612$	−35.8931	−1.45089
$613$	14.7624	0.596249	0.298125	−	0.954527i	$-0.403639\pi$
$613$	14.7624	0.596249	0.298125	+	0.954527i	$0.403639\pi$
$614$	14.2513	0.575136
$615$	3.89548	0.157081
$616$	8.18623	0.329833
$617$	32.2238	1.29728	0.648642	−	0.761094i	$-0.275337\pi$
$617$	32.2238	1.29728	0.648642	+	0.761094i	$0.275337\pi$
$618$	−14.7636	−0.593880
$619$	−16.4101	−0.659579	−0.329789	−	0.944055i	$-0.606978\pi$
$619$	−16.4101	−0.659579	−0.329789	+	0.944055i	$0.606978\pi$
$620$	−5.60226	−0.224992
$621$	27.6079	1.10787
$622$	−20.6146	−0.826569
$623$	26.7577	1.07202
$624$	0	0
$625$	−11.1508	−0.446033
$626$	6.72466	0.268772
$627$	0.195105	0.00779173
$628$	−49.3635	−1.96982
$629$	5.63560	0.224706
$630$	−17.8636	−0.711702
$631$	14.4791	0.576404	0.288202	−	0.957570i	$-0.406942\pi$
$631$	14.4791	0.576404	0.288202	+	0.957570i	$0.406942\pi$
$632$	−71.5388	−2.84566
$633$	9.16743	0.364373
$634$	−22.3023	−0.885737
$635$	17.3298	0.687711
$636$	−24.8835	−0.986693
$637$	0	0
$638$	16.2602	0.643748
$639$	30.7807	1.21766
$640$	−33.4770	−1.32330
$641$	47.6860	1.88348	0.941742	−	0.336335i	$-0.109188\pi$
$641$	47.6860	1.88348	0.941742	+	0.336335i	$0.109188\pi$
$642$	−15.5797	−0.614881
$643$	41.8558	1.65063	0.825315	−	0.564673i	$-0.190998\pi$
$643$	41.8558	1.65063	0.825315	+	0.564673i	$0.190998\pi$
$644$	49.3816	1.94591
$645$	9.19058	0.361879
$646$	−2.50806	−0.0986785
$647$	38.0018	1.49400	0.747002	−	0.664822i	$-0.231493\pi$
$647$	38.0018	1.49400	0.747002	+	0.664822i	$0.231493\pi$
$648$	26.1485	1.02721
$649$	−9.51995	−0.373691
$650$	0	0
$651$	0.868014	0.0340201
$652$	8.05736	0.315551
$653$	34.7892	1.36141	0.680704	−	0.732559i	$-0.261674\pi$
$653$	34.7892	1.36141	0.680704	+	0.732559i	$0.261674\pi$
$654$	20.9827	0.820487
$655$	−9.17284	−0.358413
$656$	−14.2588	−0.556714
$657$	4.75453	0.185492
$658$	21.5309	0.839364
$659$	−20.4952	−0.798381	−0.399190	−	0.916868i	$-0.630709\pi$
$659$	−20.4952	−0.798381	−0.399190	+	0.916868i	$0.630709\pi$
$660$	−4.65644	−0.181252
$661$	1.94183	0.0755283	0.0377642	−	0.999287i	$-0.487976\pi$
$661$	1.94183	0.0755283	0.0377642	+	0.999287i	$0.487976\pi$
$662$	−44.3709	−1.72453
$663$	0	0
$664$	78.0239	3.02792
$665$	−0.834693	−0.0323680
$666$	−10.1975	−0.395146
$667$	49.4903	1.91627
$668$	63.4917	2.45657
$669$	10.8953	0.421237
$670$	−8.58009	−0.331478
$671$	−5.55808	−0.214567
$672$	−0.396595	−0.0152990
$673$	32.3547	1.24718	0.623591	−	0.781751i	$-0.285673\pi$
$673$	32.3547	1.24718	0.623591	+	0.781751i	$0.285673\pi$
$674$	−35.5106	−1.36782
$675$	−7.32158	−0.281808
$676$	0	0
$677$	17.5181	0.673274	0.336637	−	0.941634i	$-0.390710\pi$
$677$	17.5181	0.673274	0.336637	+	0.941634i	$0.390710\pi$
$678$	0.764538	0.0293619
$679$	−23.8250	−0.914321
$680$	30.2021	1.15820
$681$	6.64950	0.254809
$682$	−1.96316	−0.0751734
$683$	20.4573	0.782776	0.391388	−	0.920226i	$-0.371995\pi$
$683$	20.4573	0.782776	0.391388	+	0.920226i	$0.371995\pi$
$684$	3.03476	0.116037
$685$	−4.68443	−0.178983
$686$	−45.5135	−1.73771
$687$	−5.61886	−0.214373
$688$	−33.6407	−1.28254
$689$	0	0
$690$	−21.1942	−0.806849
$691$	−18.1261	−0.689551	−0.344775	−	0.938685i	$-0.612045\pi$
$691$	−18.1261	−0.689551	−0.344775	+	0.938685i	$0.612045\pi$
$692$	−43.1562	−1.64055
$693$	−4.18593	−0.159010
$694$	−8.64279	−0.328076
$695$	−2.11779	−0.0803323
$696$	−21.9948	−0.833710
$697$	−11.7343	−0.444467
$698$	59.7150	2.26025
$699$	7.68124	0.290531
$700$	−13.0959	−0.494980
$701$	9.99654	0.377564	0.188782	−	0.982019i	$-0.439546\pi$
$701$	9.99654	0.377564	0.188782	+	0.982019i	$0.439546\pi$
$702$	0	0
$703$	−0.476489	−0.0179711
$704$	−7.54743	−0.284454
$705$	−6.17939	−0.232729
$706$	24.9146	0.937672
$707$	−28.7352	−1.08070
$708$	25.5221	0.959179
$709$	23.3554	0.877131	0.438565	−	0.898699i	$-0.355487\pi$
$709$	23.3554	0.877131	0.438565	+	0.898699i	$0.355487\pi$
$710$	−51.3325	−1.92647
$711$	36.5805	1.37188
$712$	81.8599	3.06783
$713$	−5.97516	−0.223772
$714$	−9.27446	−0.347088
$715$	0	0
$716$	−100.541	−3.75740
$717$	3.39133	0.126651
$718$	−11.7616	−0.438940
$719$	8.88520	0.331362	0.165681	−	0.986179i	$-0.447018\pi$
$719$	8.88520	0.331362	0.165681	+	0.986179i	$0.447018\pi$
$720$	−18.7661	−0.699370
$721$	14.8005	0.551199
$722$	−46.4708	−1.72946
$723$	−17.8194	−0.662709
$724$	20.2424	0.752302
$725$	−13.1248	−0.487441
$726$	−1.63173	−0.0605590
$727$	−22.6584	−0.840353	−0.420177	−	0.907442i	$-0.638032\pi$
$727$	−22.6584	−0.840353	−0.420177	+	0.907442i	$0.638032\pi$
$728$	0	0
$729$	−6.01541	−0.222793
$730$	−7.92906	−0.293468
$731$	−27.6846	−1.02395
$732$	14.9007	0.550746
$733$	40.9147	1.51122	0.755609	−	0.655023i	$-0.227341\pi$
$733$	40.9147	1.51122	0.755609	+	0.655023i	$0.227341\pi$
$734$	23.9516	0.884068
$735$	4.98790	0.183981
$736$	2.73005	0.100631
$737$	−2.01055	−0.0740597
$738$	21.2330	0.781596
$739$	−13.2217	−0.486368	−0.243184	−	0.969980i	$-0.578192\pi$
$739$	−13.2217	−0.486368	−0.243184	+	0.969980i	$0.578192\pi$
$740$	11.3721	0.418046
$741$	0	0
$742$	37.3047	1.36950
$743$	22.5580	0.827574	0.413787	−	0.910374i	$-0.364206\pi$
$743$	22.5580	0.827574	0.413787	+	0.910374i	$0.364206\pi$
$744$	2.65552	0.0973562
$745$	38.3907	1.40653
$746$	1.43419	0.0525093
$747$	−39.8966	−1.45974
$748$	14.0265	0.512859
$749$	15.6186	0.570690
$750$	19.7913	0.722677
$751$	39.9520	1.45787	0.728935	−	0.684582i	$-0.240015\pi$
$751$	39.9520	1.45787	0.728935	+	0.684582i	$0.240015\pi$
$752$	22.6187	0.824819
$753$	0.458880	0.0167225
$754$	0	0
$755$	0.469335	0.0170808
$756$	24.3784	0.886633
$757$	−48.3591	−1.75764	−0.878822	−	0.477151i	$-0.841670\pi$
$757$	−48.3591	−1.75764	−0.878822	+	0.477151i	$0.841670\pi$
$758$	77.2678	2.80649
$759$	−4.96639	−0.180268
$760$	−2.55358	−0.0926282
$761$	−21.7929	−0.789990	−0.394995	−	0.918683i	$-0.629254\pi$
$761$	−21.7929	−0.789990	−0.394995	+	0.918683i	$0.629254\pi$
$762$	−16.2805	−0.589780
$763$	−21.0351	−0.761520
$764$	−88.2764	−3.19373
$765$	−15.4435	−0.558361
$766$	−12.8045	−0.462647
$767$	0	0
$768$	21.4253	0.773120
$769$	−6.42559	−0.231713	−0.115856	−	0.993266i	$-0.536961\pi$
$769$	−6.42559	−0.231713	−0.115856	+	0.993266i	$0.536961\pi$
$770$	6.98082	0.251571
$771$	−4.57901	−0.164909
$772$	75.8203	2.72883
$773$	36.2953	1.30545	0.652725	−	0.757595i	$-0.273626\pi$
$773$	36.2953	1.30545	0.652725	+	0.757595i	$0.273626\pi$
$774$	50.0947	1.80062
$775$	1.58461	0.0569207
$776$	−72.8881	−2.61653
$777$	−1.76199	−0.0632110
$778$	−5.38484	−0.193056
$779$	0.992131	0.0355468
$780$	0	0
$781$	−12.0286	−0.430418
$782$	63.8428	2.28301
$783$	24.4320	0.873129
$784$	−18.2574	−0.652052
$785$	−21.2393	−0.758064
$786$	8.61745	0.307374
$787$	33.7328	1.20245	0.601223	−	0.799081i	$-0.294680\pi$
$787$	33.7328	1.20245	0.601223	+	0.799081i	$0.294680\pi$
$788$	−55.6904	−1.98389
$789$	−1.62471	−0.0578413
$790$	−61.0049	−2.17046
$791$	−0.766447	−0.0272517
$792$	−12.8061	−0.455043
$793$	0	0
$794$	−10.2547	−0.363926
$795$	−10.7064	−0.379718
$796$	−49.4378	−1.75228
$797$	−50.3349	−1.78296	−0.891478	−	0.453065i	$-0.850331\pi$
$797$	−50.3349	−1.78296	−0.891478	+	0.453065i	$0.850331\pi$
$798$	0.784154	0.0277588
$799$	18.6140	0.658517
$800$	−0.724006	−0.0255975
$801$	−41.8581	−1.47898
$802$	−55.1177	−1.94627
$803$	−1.85800	−0.0655673
$804$	5.39010	0.190094
$805$	21.2471	0.748862
$806$	0	0
$807$	−14.3594	−0.505475
$808$	−87.9100	−3.09266
$809$	−39.9535	−1.40469	−0.702345	−	0.711837i	$-0.747864\pi$
$809$	−39.9535	−1.40469	−0.702345	+	0.711837i	$0.747864\pi$
$810$	22.2982	0.783478
$811$	−36.4511	−1.27997	−0.639986	−	0.768386i	$-0.721060\pi$
$811$	−36.4511	−1.27997	−0.639986	+	0.768386i	$0.721060\pi$
$812$	43.7010	1.53360
$813$	1.24270	0.0435835
$814$	3.98504	0.139676
$815$	3.46679	0.121436
$816$	−9.74301	−0.341074
$817$	2.34072	0.0818916
$818$	−31.8947	−1.11517
$819$	0	0
$820$	−23.6786	−0.826892
$821$	−27.9954	−0.977047	−0.488523	−	0.872551i	$-0.662464\pi$
$821$	−27.9954	−0.977047	−0.488523	+	0.872551i	$0.662464\pi$
$822$	4.40080	0.153496
$823$	16.5118	0.575564	0.287782	−	0.957696i	$-0.407082\pi$
$823$	16.5118	0.575564	0.287782	+	0.957696i	$0.407082\pi$
$824$	45.2792	1.57738
$825$	1.31708	0.0458548
$826$	−38.2621	−1.33131
$827$	17.9889	0.625534	0.312767	−	0.949830i	$-0.398744\pi$
$827$	17.9889	0.625534	0.312767	+	0.949830i	$0.398744\pi$
$828$	−77.2497	−2.68461
$829$	−45.2546	−1.57176	−0.785879	−	0.618380i	$-0.787789\pi$
$829$	−45.2546	−1.57176	−0.785879	+	0.618380i	$0.787789\pi$
$830$	66.5350	2.30947
$831$	4.17609	0.144867
$832$	0	0
$833$	−15.0249	−0.520583
$834$	1.98956	0.0688929
$835$	27.3182	0.945384
$836$	−1.18594	−0.0410165
$837$	−2.94978	−0.101959
$838$	28.6020	0.988039
$839$	−7.15907	−0.247158	−0.123579	−	0.992335i	$-0.539437\pi$
$839$	−7.15907	−0.247158	−0.123579	+	0.992335i	$0.539437\pi$
$840$	−9.44279	−0.325807
$841$	14.7971	0.510245
$842$	36.1258	1.24498
$843$	−5.10632	−0.175871
$844$	−55.7240	−1.91810
$845$	0	0
$846$	−33.6818	−1.15800
$847$	1.63580	0.0562068
$848$	39.1893	1.34577
$849$	−18.4052	−0.631664
$850$	−16.9310	−0.580729
$851$	12.1290	0.415778
$852$	32.2476	1.10479
$853$	36.2660	1.24172	0.620862	−	0.783920i	$-0.286783\pi$
$853$	36.2660	1.24172	0.620862	+	0.783920i	$0.286783\pi$
$854$	−22.3388	−0.764416
$855$	1.30574	0.0446555
$856$	47.7820	1.63316
$857$	52.3196	1.78720	0.893601	−	0.448861i	$-0.148170\pi$
$857$	52.3196	1.78720	0.893601	+	0.448861i	$0.148170\pi$
$858$	0	0
$859$	17.1259	0.584329	0.292165	−	0.956368i	$-0.405625\pi$
$859$	17.1259	0.584329	0.292165	+	0.956368i	$0.405625\pi$
$860$	−55.8646	−1.90497
$861$	3.66876	0.125031
$862$	−76.5401	−2.60697
$863$	15.4074	0.524473	0.262236	−	0.965004i	$-0.415540\pi$
$863$	15.4074	0.524473	0.262236	+	0.965004i	$0.415540\pi$
$864$	1.34775	0.0458515
$865$	−18.5686	−0.631350
$866$	83.6570	2.84278
$867$	3.27197	0.111122
$868$	−5.27620	−0.179086
$869$	−14.2951	−0.484929
$870$	−18.7561	−0.635891
$871$	0	0
$872$	−64.3527	−2.17926
$873$	37.2705	1.26141
$874$	−5.39790	−0.182587
$875$	−19.8407	−0.670740
$876$	4.98112	0.168296
$877$	17.5157	0.591463	0.295731	−	0.955271i	$-0.404437\pi$
$877$	17.5157	0.591463	0.295731	+	0.955271i	$0.404437\pi$
$878$	−64.1069	−2.16350
$879$	−10.7846	−0.363757
$880$	7.33350	0.247212
$881$	−3.38159	−0.113929	−0.0569643	−	0.998376i	$-0.518142\pi$
$881$	−3.38159	−0.113929	−0.0569643	+	0.998376i	$0.518142\pi$
$882$	27.1874	0.915446
$883$	−27.7476	−0.933780	−0.466890	−	0.884315i	$-0.654626\pi$
$883$	−27.7476	−0.933780	−0.466890	+	0.884315i	$0.654626\pi$
$884$	0	0
$885$	10.9812	0.369130
$886$	65.9461	2.21550
$887$	−40.6413	−1.36460	−0.682301	−	0.731071i	$-0.739021\pi$
$887$	−40.6413	−1.36460	−0.682301	+	0.731071i	$0.739021\pi$
$888$	−5.39047	−0.180892
$889$	16.3211	0.547394
$890$	69.8062	2.33991
$891$	5.22508	0.175047
$892$	−66.2268	−2.21744
$893$	−1.57381	−0.0526656
$894$	−36.0662	−1.20624
$895$	−43.2592	−1.44599
$896$	−31.5286	−1.05330
$897$	0	0
$898$	45.9946	1.53486
$899$	−5.28780	−0.176358
$900$	20.4865	0.682884
$901$	32.2508	1.07443
$902$	−8.29753	−0.276277
$903$	8.65567	0.288042
$904$	−2.34480	−0.0779868
$905$	8.70956	0.289516
$906$	−0.440917	−0.0146485
$907$	−0.523526	−0.0173834	−0.00869171	−	0.999962i	$-0.502767\pi$
$907$	−0.523526	−0.0173834	−0.00869171	+	0.999962i	$0.502767\pi$
$908$	−40.4188	−1.34134
$909$	44.9517	1.49095
$910$	0	0
$911$	11.1021	0.367828	0.183914	−	0.982942i	$-0.441123\pi$
$911$	11.1021	0.367828	0.183914	+	0.982942i	$0.441123\pi$
$912$	0.823770	0.0272778
$913$	15.5910	0.515987
$914$	18.1522	0.600422
$915$	6.41123	0.211949
$916$	34.1541	1.12848
$917$	−8.63896	−0.285284
$918$	31.5175	1.04023
$919$	3.68284	0.121486	0.0607429	−	0.998153i	$-0.480653\pi$
$919$	3.68284	0.121486	0.0607429	+	0.998153i	$0.480653\pi$
$920$	65.0015	2.14304
$921$	−3.85207	−0.126930
$922$	51.3201	1.69014
$923$	0	0
$924$	−4.38543	−0.144270
$925$	−3.21660	−0.105761
$926$	65.0611	2.13804
$927$	−23.1530	−0.760445
$928$	2.41600	0.0793090
$929$	33.2563	1.09110	0.545552	−	0.838077i	$-0.316320\pi$
$929$	33.2563	1.09110	0.545552	+	0.838077i	$0.316320\pi$
$930$	2.26450	0.0742559
$931$	1.27036	0.0416342
$932$	−46.6902	−1.52939
$933$	5.57204	0.182420
$934$	57.1686	1.87061
$935$	6.03509	0.197369
$936$	0	0
$937$	0.0211062	0.000689510 0	0.000344755	−	1.00000i	$-0.499890\pi$
$937$	0.0211062	0.000689510 0	0.000344755		1.00000i	$0.499890\pi$
$938$	−8.08071	−0.263845
$939$	−1.81765	−0.0593168
$940$	37.5612	1.22511
$941$	−27.4643	−0.895310	−0.447655	−	0.894206i	$-0.647741\pi$
$941$	−27.4643	−0.895310	−0.447655	+	0.894206i	$0.647741\pi$
$942$	19.9533	0.650114
$943$	−25.2547	−0.822406
$944$	−40.1951	−1.30824
$945$	10.4891	0.341211
$946$	−19.5763	−0.636480
$947$	−10.7984	−0.350900	−0.175450	−	0.984488i	$-0.556138\pi$
$947$	−10.7984	−0.350900	−0.175450	+	0.984488i	$0.556138\pi$
$948$	38.3239	1.24470
$949$	0	0
$950$	1.43152	0.0464445
$951$	6.02822	0.195479
$952$	28.4443	0.921885
$953$	−35.7546	−1.15820	−0.579102	−	0.815255i	$-0.696597\pi$
$953$	−35.7546	−1.15820	−0.579102	+	0.815255i	$0.696597\pi$
$954$	−58.3572	−1.88938
$955$	−37.9821	−1.22907
$956$	−20.6141	−0.666707
$957$	−4.39508	−0.142073
$958$	−25.3966	−0.820525
$959$	−4.41179	−0.142464
$960$	8.70593	0.280983
$961$	−30.3616	−0.979406
$962$	0	0
$963$	−24.4328	−0.787336
$964$	108.314	3.48857
$965$	32.6227	1.05016
$966$	−19.9607	−0.642223
$967$	−48.5134	−1.56009	−0.780043	−	0.625726i	$-0.784803\pi$
$967$	−48.5134	−1.56009	−0.780043	+	0.625726i	$0.784803\pi$
$968$	5.00442	0.160848
$969$	0.677920	0.0217779
$970$	−62.1555	−1.99569
$971$	17.9561	0.576239	0.288119	−	0.957595i	$-0.406970\pi$
$971$	17.9561	0.576239	0.288119	+	0.957595i	$0.406970\pi$
$972$	−58.7170	−1.88335
$973$	−1.99453	−0.0639417
$974$	−67.2356	−2.15437
$975$	0	0
$976$	−23.4673	−0.751171
$977$	−13.9178	−0.445271	−0.222636	−	0.974902i	$-0.571466\pi$
$977$	−13.9178	−0.445271	−0.222636	+	0.974902i	$0.571466\pi$
$978$	−3.25688	−0.104144
$979$	16.3575	0.522789
$980$	−30.3188	−0.968499
$981$	32.9060	1.05061
$982$	−61.2500	−1.95457
$983$	−11.1702	−0.356275	−0.178137	−	0.984006i	$-0.557007\pi$
$983$	−11.1702	−0.356275	−0.178137	+	0.984006i	$0.557007\pi$
$984$	11.2239	0.357804
$985$	−23.9615	−0.763478
$986$	56.4986	1.79928
$987$	−5.81973	−0.185244
$988$	0	0
$989$	−59.5832	−1.89463
$990$	−10.9204	−0.347073
$991$	−16.1153	−0.511921	−0.255960	−	0.966687i	$-0.582392\pi$
$991$	−16.1153	−0.511921	−0.255960	+	0.966687i	$0.582392\pi$
$992$	−0.291693	−0.00926127
$993$	11.9933	0.380596
$994$	−48.3448	−1.53341
$995$	−21.2713	−0.674345
$996$	−41.7980	−1.32442
$997$	−43.9898	−1.39317	−0.696586	−	0.717474i	$-0.745298\pi$
$997$	−43.9898	−1.39317	−0.696586	+	0.717474i	$0.745298\pi$
$998$	−28.9857	−0.917527
$999$	5.98778	0.189445

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.l.1.6		6
13.4	even	6		143.2.e.c.133.6	yes	12
13.10	even	6		143.2.e.c.100.6	✓	12
13.12	even	2		1859.2.a.k.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.e.c.100.6	✓	12	13.10	even	6
143.2.e.c.133.6	yes	12	13.4	even	6
1859.2.a.k.1.1		6	13.12	even	2
1859.2.a.l.1.6		6	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:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q+2.45699 q^{2} -0.664116 q^{3} +4.03681 q^{4} +1.73689 q^{5} -1.63173 q^{6} +1.63580 q^{7} +5.00442 q^{8} -2.55895 q^{9} +O(q^{10})\)	\(q+2.45699 q^{2} -0.664116 q^{3} +4.03681 q^{4} +1.73689 q^{5} -1.63173 q^{6} +1.63580 q^{7} +5.00442 q^{8} -2.55895 q^{9} +4.26753 q^{10} +1.00000 q^{11} -2.68091 q^{12} +4.01915 q^{14} -1.15350 q^{15} +4.22220 q^{16} +3.47465 q^{17} -6.28732 q^{18} -0.293781 q^{19} +7.01149 q^{20} -1.08636 q^{21} +2.45699 q^{22} +7.47820 q^{23} -3.32351 q^{24} -1.98321 q^{25} +3.69179 q^{27} +6.60341 q^{28} +6.61794 q^{29} -2.83413 q^{30} -0.799011 q^{31} +0.365068 q^{32} -0.664116 q^{33} +8.53719 q^{34} +2.84121 q^{35} -10.3300 q^{36} +1.62192 q^{37} -0.721818 q^{38} +8.69213 q^{40} -3.37711 q^{41} -2.66918 q^{42} -7.96758 q^{43} +4.03681 q^{44} -4.44462 q^{45} +18.3739 q^{46} +5.35709 q^{47} -2.80403 q^{48} -4.32416 q^{49} -4.87273 q^{50} -2.30757 q^{51} +9.28173 q^{53} +9.07069 q^{54} +1.73689 q^{55} +8.18623 q^{56} +0.195105 q^{57} +16.2602 q^{58} -9.51995 q^{59} -4.65644 q^{60} -5.55808 q^{61} -1.96316 q^{62} -4.18593 q^{63} -7.54743 q^{64} -1.63173 q^{66} -2.01055 q^{67} +14.0265 q^{68} -4.96639 q^{69} +6.98082 q^{70} -12.0286 q^{71} -12.8061 q^{72} -1.85800 q^{73} +3.98504 q^{74} +1.31708 q^{75} -1.18594 q^{76} +1.63580 q^{77} -14.2951 q^{79} +7.33350 q^{80} +5.22508 q^{81} -8.29753 q^{82} +15.5910 q^{83} -4.38543 q^{84} +6.03509 q^{85} -19.5763 q^{86} -4.39508 q^{87} +5.00442 q^{88} +16.3575 q^{89} -10.9204 q^{90} +30.1881 q^{92} +0.530636 q^{93} +13.1623 q^{94} -0.510266 q^{95} -0.242447 q^{96} -14.5648 q^{97} -10.6244 q^{98} -2.55895 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{3} + 8 q^{4} + 6 q^{5} + 12 q^{6} + 3 q^{7} - 3 q^{8} + 7 q^{9}+O(q^{10}) \) 6 * q + q^3 + 8 * q^4 + 6 * q^5 + 12 * q^6 + 3 * q^7 - 3 * q^8 + 7 * q^9	\( 6 q + q^{3} + 8 q^{4} + 6 q^{5} + 12 q^{6} + 3 q^{7} - 3 q^{8} + 7 q^{9} - 3 q^{10} + 6 q^{11} - 17 q^{12} + 12 q^{14} - 4 q^{15} + 8 q^{16} + 2 q^{17} - 6 q^{18} + 10 q^{19} + 15 q^{20} + 12 q^{21} + 3 q^{23} + 14 q^{24} - 6 q^{25} + 10 q^{27} + 16 q^{28} + 3 q^{29} + 19 q^{30} + 5 q^{31} - q^{32} + q^{33} - 5 q^{34} - 13 q^{35} + 20 q^{36} + 25 q^{37} - 27 q^{38} - 8 q^{40} + 24 q^{41} + 13 q^{42} - 8 q^{43} + 8 q^{44} + 27 q^{45} + 18 q^{46} + 10 q^{47} - 28 q^{48} - q^{49} - 26 q^{50} - 17 q^{51} + 10 q^{53} + 47 q^{54} + 6 q^{55} + 15 q^{56} + 6 q^{58} - 4 q^{59} - 61 q^{60} - 21 q^{61} - 5 q^{62} + 6 q^{63} - 27 q^{64} + 12 q^{66} + 21 q^{67} + 14 q^{68} + 5 q^{69} + 31 q^{70} - 3 q^{71} - 50 q^{72} + 13 q^{73} - 38 q^{74} - 23 q^{75} + 8 q^{76} + 3 q^{77} - 4 q^{79} + 44 q^{80} + 34 q^{81} - 33 q^{82} + 8 q^{83} + 47 q^{84} - 13 q^{85} - 11 q^{86} - 51 q^{87} - 3 q^{88} - 9 q^{89} - 70 q^{90} + 15 q^{92} - 21 q^{93} + 10 q^{94} + 27 q^{95} - 19 q^{96} + 15 q^{97} + 21 q^{98} + 7 q^{99}+O(q^{100}) \) 6 * q + q^3 + 8 * q^4 + 6 * q^5 + 12 * q^6 + 3 * q^7 - 3 * q^8 + 7 * q^9 - 3 * q^10 + 6 * q^11 - 17 * q^12 + 12 * q^14 - 4 * q^15 + 8 * q^16 + 2 * q^17 - 6 * q^18 + 10 * q^19 + 15 * q^20 + 12 * q^21 + 3 * q^23 + 14 * q^24 - 6 * q^25 + 10 * q^27 + 16 * q^28 + 3 * q^29 + 19 * q^30 + 5 * q^31 - q^32 + q^33 - 5 * q^34 - 13 * q^35 + 20 * q^36 + 25 * q^37 - 27 * q^38 - 8 * q^40 + 24 * q^41 + 13 * q^42 - 8 * q^43 + 8 * q^44 + 27 * q^45 + 18 * q^46 + 10 * q^47 - 28 * q^48 - q^49 - 26 * q^50 - 17 * q^51 + 10 * q^53 + 47 * q^54 + 6 * q^55 + 15 * q^56 + 6 * q^58 - 4 * q^59 - 61 * q^60 - 21 * q^61 - 5 * q^62 + 6 * q^63 - 27 * q^64 + 12 * q^66 + 21 * q^67 + 14 * q^68 + 5 * q^69 + 31 * q^70 - 3 * q^71 - 50 * q^72 + 13 * q^73 - 38 * q^74 - 23 * q^75 + 8 * q^76 + 3 * q^77 - 4 * q^79 + 44 * q^80 + 34 * q^81 - 33 * q^82 + 8 * q^83 + 47 * q^84 - 13 * q^85 - 11 * q^86 - 51 * q^87 - 3 * q^88 - 9 * q^89 - 70 * q^90 + 15 * q^92 - 21 * q^93 + 10 * q^94 + 27 * q^95 - 19 * q^96 + 15 * q^97 + 21 * q^98 + 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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