LMFDB - Embedded newform 1859.2.a.g.1.2

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:	$1$
Dimension:	$3$
Coefficient field:	3.3.361.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 6x + 7 $ x^3 - x^2 - 6*x + 7
Coefficient ring:	$\Z[a_1, a_2]$
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			1.2
Root			$-2.50702$ 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)

$f(q)$	$=$	$q+1.22188 q^{2} -2.50702 q^{3} -0.507019 q^{4} +2.28514 q^{5} -3.06327 q^{6} +0.285142 q^{7} -3.06327 q^{8} +3.28514 q^{9} +O(q^{10})$	\(q+1.22188 q^{2} -2.50702 q^{3} -0.507019 q^{4} +2.28514 q^{5} -3.06327 q^{6} +0.285142 q^{7} -3.06327 q^{8} +3.28514 q^{9} +2.79216 q^{10} -1.00000 q^{11} +1.27111 q^{12} +0.348409 q^{14} -5.72889 q^{15} -2.72889 q^{16} +0.507019 q^{17} +4.01404 q^{18} +3.95077 q^{19} -1.15861 q^{20} -0.714858 q^{21} -1.22188 q^{22} -0.0632663 q^{23} +7.67967 q^{24} +0.221876 q^{25} -0.714858 q^{27} -0.144573 q^{28} -10.7429 q^{29} -7.00000 q^{30} +3.57028 q^{31} +2.79216 q^{32} +2.50702 q^{33} +0.619514 q^{34} +0.651591 q^{35} -1.66563 q^{36} -7.72889 q^{37} +4.82735 q^{38} -7.00000 q^{40} +0.380486 q^{41} -0.873467 q^{42} -5.41168 q^{43} +0.507019 q^{44} +7.50702 q^{45} -0.0773036 q^{46} +11.3624 q^{47} +6.84139 q^{48} -6.91869 q^{49} +0.271105 q^{50} -1.27111 q^{51} -6.72889 q^{53} -0.873467 q^{54} -2.28514 q^{55} -0.873467 q^{56} -9.90466 q^{57} -13.1265 q^{58} -13.7289 q^{59} +2.90466 q^{60} -3.33437 q^{61} +4.36245 q^{62} +0.936734 q^{63} +8.86946 q^{64} +3.06327 q^{66} -0.207839 q^{67} -0.257068 q^{68} +0.158610 q^{69} +0.796164 q^{70} +2.77812 q^{71} -10.0633 q^{72} +2.00000 q^{73} -9.44375 q^{74} -0.556248 q^{75} -2.00311 q^{76} -0.285142 q^{77} -3.45779 q^{79} -6.23591 q^{80} -8.06327 q^{81} +0.464907 q^{82} -4.74293 q^{83} +0.362446 q^{84} +1.15861 q^{85} -6.61240 q^{86} +26.9327 q^{87} +3.06327 q^{88} +3.71486 q^{89} +9.17265 q^{90} +0.0320772 q^{92} -8.95077 q^{93} +13.8835 q^{94} +9.02807 q^{95} -7.00000 q^{96} -15.0281 q^{97} -8.45379 q^{98} -3.28514 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + q^{3} + 7 q^{4} + q^{5} - 6 q^{6} - 5 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) $ 3 * q + q^2 + q^3 + 7 * q^4 + q^5 - 6 * q^6 - 5 * q^7 - 6 * q^8 + 4 * q^9	$ 3 q + q^{2} + q^{3} + 7 q^{4} + q^{5} - 6 q^{6} - 5 q^{7} - 6 q^{8} + 4 q^{9} - 6 q^{10} - 3 q^{11} + 15 q^{12} - 8 q^{14} - 6 q^{15} + 3 q^{16} - 7 q^{17} - 5 q^{18} - 2 q^{19} - 4 q^{20} - 8 q^{21} - q^{22} + 3 q^{23} - 2 q^{24} - 2 q^{25} - 8 q^{27} - 18 q^{28} - 4 q^{29} - 21 q^{30} - q^{31} - 6 q^{32} - q^{33} + 4 q^{34} + 11 q^{35} + 3 q^{36} - 12 q^{37} + 31 q^{38} - 21 q^{40} - q^{41} - 9 q^{42} - 4 q^{43} - 7 q^{44} + 14 q^{45} + 20 q^{46} + 8 q^{47} + 20 q^{48} + 12 q^{50} - 15 q^{51} - 9 q^{53} - 9 q^{54} - q^{55} - 9 q^{56} - 26 q^{57} - 33 q^{58} - 30 q^{59} + 5 q^{60} - 18 q^{61} - 13 q^{62} + 6 q^{63} - 8 q^{64} + 6 q^{66} - 15 q^{67} - 29 q^{68} + q^{69} + 29 q^{70} + 11 q^{71} - 27 q^{72} + 6 q^{73} - 23 q^{74} - 7 q^{75} - 30 q^{76} + 5 q^{77} + 12 q^{79} + q^{80} - 21 q^{81} + 44 q^{82} + 14 q^{83} - 25 q^{84} + 4 q^{85} + 43 q^{86} + 43 q^{87} + 6 q^{88} + 17 q^{89} + 11 q^{90} + 7 q^{92} - 13 q^{93} - 10 q^{94} - 7 q^{95} - 21 q^{96} - 11 q^{97} + 38 q^{98} - 4 q^{99}+O(q^{100}) $ 3 * q + q^2 + q^3 + 7 * q^4 + q^5 - 6 * q^6 - 5 * q^7 - 6 * q^8 + 4 * q^9 - 6 * q^10 - 3 * q^11 + 15 * q^12 - 8 * q^14 - 6 * q^15 + 3 * q^16 - 7 * q^17 - 5 * q^18 - 2 * q^19 - 4 * q^20 - 8 * q^21 - q^22 + 3 * q^23 - 2 * q^24 - 2 * q^25 - 8 * q^27 - 18 * q^28 - 4 * q^29 - 21 * q^30 - q^31 - 6 * q^32 - q^33 + 4 * q^34 + 11 * q^35 + 3 * q^36 - 12 * q^37 + 31 * q^38 - 21 * q^40 - q^41 - 9 * q^42 - 4 * q^43 - 7 * q^44 + 14 * q^45 + 20 * q^46 + 8 * q^47 + 20 * q^48 + 12 * q^50 - 15 * q^51 - 9 * q^53 - 9 * q^54 - q^55 - 9 * q^56 - 26 * q^57 - 33 * q^58 - 30 * q^59 + 5 * q^60 - 18 * q^61 - 13 * q^62 + 6 * q^63 - 8 * q^64 + 6 * q^66 - 15 * q^67 - 29 * q^68 + q^69 + 29 * q^70 + 11 * q^71 - 27 * q^72 + 6 * q^73 - 23 * q^74 - 7 * q^75 - 30 * q^76 + 5 * q^77 + 12 * q^79 + q^80 - 21 * q^81 + 44 * q^82 + 14 * q^83 - 25 * q^84 + 4 * q^85 + 43 * q^86 + 43 * q^87 + 6 * q^88 + 17 * q^89 + 11 * q^90 + 7 * q^92 - 13 * q^93 - 10 * q^94 - 7 * q^95 - 21 * q^96 - 11 * q^97 + 38 * q^98 - 4 * 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 $

$2$	1.22188	0.863997	0.431998	−	0.901874i	$-0.357809\pi$
$2$	1.22188	0.863997	0.431998	+	0.901874i	$0.357809\pi$
$3$	−2.50702	−1.44743	−0.723714	−	0.690100i	$-0.757566\pi$
$3$	−2.50702	−1.44743	−0.723714	+	0.690100i	$0.757566\pi$
$4$	−0.507019	−0.253509
$5$	2.28514	1.02195	0.510973	−	0.859597i	$-0.329285\pi$
$5$	2.28514	1.02195	0.510973	+	0.859597i	$0.329285\pi$
$6$	−3.06327	−1.25057
$7$	0.285142	0.107774	0.0538869	−	0.998547i	$-0.482839\pi$
$7$	0.285142	0.107774	0.0538869	+	0.998547i	$0.482839\pi$
$8$	−3.06327	−1.08303
$9$	3.28514	1.09505
$10$	2.79216	0.882959
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.27111	0.366936
$13$	0	0
$13$	0	0
$14$	0.348409	0.0931162
$15$	−5.72889	−1.47919
$16$	−2.72889	−0.682224
$17$	0.507019	0.122970	0.0614850	−	0.998108i	$-0.480416\pi$
$17$	0.507019	0.122970	0.0614850	+	0.998108i	$0.480416\pi$
$18$	4.01404	0.946118
$19$	3.95077	0.906369	0.453185	−	0.891417i	$-0.350288\pi$
$19$	3.95077	0.906369	0.453185	+	0.891417i	$0.350288\pi$
$20$	−1.15861	−0.259073
$21$	−0.714858	−0.155995
$22$	−1.22188	−0.260505
$23$	−0.0632663	−0.0131919	−0.00659597	−	0.999978i	$-0.502100\pi$
$23$	−0.0632663	−0.0131919	−0.00659597	+	0.999978i	$0.502100\pi$
$24$	7.67967	1.56761
$25$	0.221876	0.0443752
$26$	0	0
$27$	−0.714858	−0.137574
$28$	−0.144573	−0.0273216
$29$	−10.7429	−1.99491	−0.997456	−	0.0712820i	$-0.977291\pi$
$29$	−10.7429	−1.99491	−0.997456	+	0.0712820i	$0.977291\pi$
$30$	−7.00000	−1.27802
$31$	3.57028	0.641242	0.320621	−	0.947208i	$-0.396108\pi$
$31$	3.57028	0.641242	0.320621	+	0.947208i	$0.396108\pi$
$32$	2.79216	0.493589
$33$	2.50702	0.436416
$34$	0.619514	0.106246
$35$	0.651591	0.110139
$36$	−1.66563	−0.277605
$37$	−7.72889	−1.27062	−0.635311	−	0.772256i	$-0.719128\pi$
$37$	−7.72889	−1.27062	−0.635311	+	0.772256i	$0.719128\pi$
$38$	4.82735	0.783100
$39$	0	0
$40$	−7.00000	−1.10680
$41$	0.380486	0.0594219	0.0297110	−	0.999559i	$-0.490541\pi$
$41$	0.380486	0.0594219	0.0297110	+	0.999559i	$0.490541\pi$
$42$	−0.873467	−0.134779
$43$	−5.41168	−0.825273	−0.412636	−	0.910896i	$-0.635392\pi$
$43$	−5.41168	−0.825273	−0.412636	+	0.910896i	$0.635392\pi$
$44$	0.507019	0.0764359
$45$	7.50702	1.11908
$46$	−0.0773036	−0.0113978
$47$	11.3624	1.65738	0.828692	−	0.559706i	$-0.189086\pi$
$47$	11.3624	1.65738	0.828692	+	0.559706i	$0.189086\pi$
$48$	6.84139	0.987470
$49$	−6.91869	−0.988385
$50$	0.271105	0.0383401
$51$	−1.27111	−0.177990
$52$	0	0
$53$	−6.72889	−0.924285	−0.462142	−	0.886806i	$-0.652919\pi$
$53$	−6.72889	−0.924285	−0.462142	+	0.886806i	$0.652919\pi$
$54$	−0.873467	−0.118864
$55$	−2.28514	−0.308129
$56$	−0.873467	−0.116722
$57$	−9.90466	−1.31190
$58$	−13.1265	−1.72360
$59$	−13.7289	−1.78735	−0.893675	−	0.448715i	$-0.851882\pi$
$59$	−13.7289	−1.78735	−0.893675	+	0.448715i	$0.851882\pi$
$60$	2.90466	0.374990
$61$	−3.33437	−0.426923	−0.213461	−	0.976952i	$-0.568474\pi$
$61$	−3.33437	−0.426923	−0.213461	+	0.976952i	$0.568474\pi$
$62$	4.36245	0.554031
$63$	0.936734	0.118017
$64$	8.86946	1.10868
$65$	0	0
$66$	3.06327	0.377062
$67$	−0.207839	−0.0253916	−0.0126958	−	0.999919i	$-0.504041\pi$
$67$	−0.207839	−0.0253916	−0.0126958	+	0.999919i	$0.504041\pi$
$68$	−0.257068	−0.0311741
$69$	0.158610	0.0190944
$70$	0.796164	0.0951598
$71$	2.77812	0.329703	0.164851	−	0.986318i	$-0.447286\pi$
$71$	2.77812	0.329703	0.164851	+	0.986318i	$0.447286\pi$
$72$	−10.0633	−1.18597
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	−9.44375	−1.09781
$75$	−0.556248	−0.0642299
$76$	−2.00311	−0.229773
$77$	−0.285142	−0.0324950
$78$	0	0
$79$	−3.45779	−0.389032	−0.194516	−	0.980899i	$-0.562314\pi$
$79$	−3.45779	−0.389032	−0.194516	+	0.980899i	$0.562314\pi$
$80$	−6.23591	−0.697196
$81$	−8.06327	−0.895918
$82$	0.464907	0.0513404
$83$	−4.74293	−0.520604	−0.260302	−	0.965527i	$-0.583822\pi$
$83$	−4.74293	−0.520604	−0.260302	+	0.965527i	$0.583822\pi$
$84$	0.362446	0.0395461
$85$	1.15861	0.125669
$86$	−6.61240	−0.713033
$87$	26.9327	2.88749
$88$	3.06327	0.326545
$89$	3.71486	0.393774	0.196887	−	0.980426i	$-0.436917\pi$
$89$	3.71486	0.393774	0.196887	+	0.980426i	$0.436917\pi$
$90$	9.17265	0.966882
$91$	0	0
$92$	0.0320772	0.00334428
$93$	−8.95077	−0.928152
$94$	13.8835	1.43197
$95$	9.02807	0.926261
$96$	−7.00000	−0.714435
$97$	−15.0281	−1.52587	−0.762935	−	0.646475i	$-0.776242\pi$
$97$	−15.0281	−1.52587	−0.762935	+	0.646475i	$0.776242\pi$
$98$	−8.45379	−0.853961
$99$	−3.28514	−0.330169
$100$	−0.112495	−0.0112495
$101$	14.9327	1.48586	0.742931	−	0.669368i	$-0.233435\pi$
$101$	14.9327	1.48586	0.742931	+	0.669368i	$0.233435\pi$
$102$	−1.55313	−0.153783
$103$	−17.3905	−1.71354	−0.856769	−	0.515700i	$-0.827532\pi$
$103$	−17.3905	−1.71354	−0.856769	+	0.515700i	$0.827532\pi$
$104$	0	0
$105$	−1.63355	−0.159418
$106$	−8.22188	−0.798579
$107$	−15.7429	−1.52193	−0.760963	−	0.648795i	$-0.775273\pi$
$107$	−15.7429	−1.52193	−0.760963	+	0.648795i	$0.775273\pi$
$108$	0.362446	0.0348764
$109$	−18.9648	−1.81650	−0.908250	−	0.418429i	$-0.862581\pi$
$109$	−18.9648	−1.81650	−0.908250	+	0.418429i	$0.862581\pi$
$110$	−2.79216	−0.266222
$111$	19.3765	1.83913
$112$	−0.778124	−0.0735258
$113$	−14.6476	−1.37793	−0.688965	−	0.724795i	$-0.741934\pi$
$113$	−14.6476	−1.37793	−0.688965	+	0.724795i	$0.741934\pi$
$114$	−12.1023	−1.13348
$115$	−0.144573	−0.0134815
$116$	5.44687	0.505729
$117$	0	0
$118$	−16.7750	−1.54426
$119$	0.144573	0.0132529
$120$	17.5491	1.60201
$121$	1.00000	0.0909091
$122$	−4.07419	−0.368860
$123$	−0.953886	−0.0860090
$124$	−1.81020	−0.162561
$125$	−10.9187	−0.976598
$126$	1.14457	0.101967
$127$	0.841390	0.0746613	0.0373307	−	0.999303i	$-0.488115\pi$
$127$	0.841390	0.0746613	0.0373307	+	0.999303i	$0.488115\pi$
$128$	5.25307	0.464310
$129$	13.5672	1.19452
$130$	0	0
$131$	0.299180	0.0261395	0.0130697	−	0.999915i	$-0.495840\pi$
$131$	0.299180	0.0261395	0.0130697	+	0.999915i	$0.495840\pi$
$132$	−1.27111	−0.110636
$133$	1.12653	0.0976828
$134$	−0.253953	−0.0219382
$135$	−1.63355	−0.140594
$136$	−1.55313	−0.133180
$137$	10.7922	0.922037	0.461018	−	0.887391i	$-0.347484\pi$
$137$	10.7922	0.922037	0.461018	+	0.887391i	$0.347484\pi$
$138$	0.193802	0.0164975
$139$	3.68278	0.312369	0.156185	−	0.987728i	$-0.450081\pi$
$139$	3.68278	0.312369	0.156185	+	0.987728i	$0.450081\pi$
$140$	−0.330369	−0.0279213
$141$	−28.4859	−2.39894
$142$	3.39452	0.284862
$143$	0	0
$144$	−8.96481	−0.747067
$145$	−24.5491	−2.03869
$146$	2.44375	0.202246
$147$	17.3453	1.43062
$148$	3.91869	0.322115
$149$	−10.8695	−0.890461	−0.445231	−	0.895416i	$-0.646878\pi$
$149$	−10.8695	−0.890461	−0.445231	+	0.895416i	$0.646878\pi$
$150$	−0.679666	−0.0554945
$151$	−11.4749	−0.933817	−0.466909	−	0.884306i	$-0.654632\pi$
$151$	−11.4749	−0.933817	−0.466909	+	0.884306i	$0.654632\pi$
$152$	−12.1023	−0.981623
$153$	1.66563	0.134658
$154$	−0.348409	−0.0280756
$155$	8.15861	0.655315
$156$	0	0
$157$	16.1234	1.28679	0.643394	−	0.765535i	$-0.277526\pi$
$157$	16.1234	1.28679	0.643394	+	0.765535i	$0.277526\pi$
$158$	−4.22499	−0.336122
$159$	16.8695	1.33784
$160$	6.38049	0.504422
$161$	−0.0180399	−0.00142174
$162$	−9.85231	−0.774071
$163$	18.3132	1.43440	0.717201	−	0.696866i	$-0.245423\pi$
$163$	18.3132	1.43440	0.717201	+	0.696866i	$0.245423\pi$
$164$	−0.192913	−0.0150640
$165$	5.72889	0.445994
$166$	−5.79528	−0.449801
$167$	10.7741	0.833727	0.416863	−	0.908969i	$-0.363129\pi$
$167$	10.7741	0.833727	0.416863	+	0.908969i	$0.363129\pi$
$168$	2.18980	0.168947
$169$	0	0
$170$	1.41568	0.108578
$171$	12.9788	0.992517
$172$	2.74382	0.209214
$173$	−21.2500	−1.61560	−0.807802	−	0.589454i	$-0.799343\pi$
$173$	−21.2500	−1.61560	−0.807802	+	0.589454i	$0.799343\pi$
$174$	32.9085	2.49478
$175$	0.0632663	0.00478248
$176$	2.72889	0.205698
$177$	34.4186	2.58706
$178$	4.53910	0.340220
$179$	4.14457	0.309780	0.154890	−	0.987932i	$-0.450498\pi$
$179$	4.14457	0.309780	0.154890	+	0.987932i	$0.450498\pi$
$180$	−3.80620	−0.283697
$181$	20.2811	1.50749	0.753743	−	0.657170i	$-0.228247\pi$
$181$	20.2811	1.50749	0.753743	+	0.657170i	$0.228247\pi$
$182$	0	0
$183$	8.35933	0.617940
$184$	0.193802	0.0142872
$185$	−17.6616	−1.29851
$186$	−10.9367	−0.801920
$187$	−0.507019	−0.0370769
$188$	−5.76097	−0.420162
$189$	−0.203836	−0.0148269
$190$	11.0312	0.800287
$191$	4.61951	0.334256	0.167128	−	0.985935i	$-0.446551\pi$
$191$	4.61951	0.334256	0.167128	+	0.985935i	$0.446551\pi$
$192$	−22.2359	−1.60474
$193$	5.69682	0.410066	0.205033	−	0.978755i	$-0.434270\pi$
$193$	5.69682	0.410066	0.205033	+	0.978755i	$0.434270\pi$
$194$	−18.3624	−1.31835
$195$	0	0
$196$	3.50791	0.250565
$197$	1.85943	0.132479	0.0662395	−	0.997804i	$-0.478900\pi$
$197$	1.85943	0.132479	0.0662395	+	0.997804i	$0.478900\pi$
$198$	−4.01404	−0.285265
$199$	8.26710	0.586039	0.293020	−	0.956106i	$-0.405340\pi$
$199$	8.26710	0.586039	0.293020	+	0.956106i	$0.405340\pi$
$200$	−0.679666	−0.0480596
$201$	0.521056	0.0367525
$202$	18.2459	1.28378
$203$	−3.06327	−0.214999
$204$	0.644474	0.0451222
$205$	0.869465	0.0607261
$206$	−21.2491	−1.48049
$207$	−0.207839	−0.0144458
$208$	0	0
$209$	−3.95077	−0.273281
$210$	−1.99600	−0.137737
$211$	2.81020	0.193462	0.0967311	−	0.995311i	$-0.469161\pi$
$211$	2.81020	0.193462	0.0967311	+	0.995311i	$0.469161\pi$
$212$	3.41168	0.234315
$213$	−6.96481	−0.477221
$214$	−19.2359	−1.31494
$215$	−12.3664	−0.843385
$216$	2.18980	0.148997
$217$	1.01804	0.0691091
$218$	−23.1726	−1.56945
$219$	−5.01404	−0.338817
$220$	1.15861	0.0781135
$221$	0	0
$222$	23.6757	1.58901
$223$	14.0602	0.941537	0.470769	−	0.882257i	$-0.343977\pi$
$223$	14.0602	0.941537	0.470769	+	0.882257i	$0.343977\pi$
$224$	0.796164	0.0531959
$225$	0.728895	0.0485930
$226$	−17.8975	−1.19053
$227$	19.2038	1.27460	0.637302	−	0.770614i	$-0.280051\pi$
$227$	19.2038	1.27460	0.637302	+	0.770614i	$0.280051\pi$
$228$	5.02185	0.332580
$229$	−12.4789	−0.824632	−0.412316	−	0.911041i	$-0.635280\pi$
$229$	−12.4789	−0.824632	−0.412316	+	0.911041i	$0.635280\pi$
$230$	−0.176650	−0.0116479
$231$	0.714858	0.0470342
$232$	32.9085	2.16055
$233$	−7.97193	−0.522258	−0.261129	−	0.965304i	$-0.584095\pi$
$233$	−7.97193	−0.522258	−0.261129	+	0.965304i	$0.584095\pi$
$234$	0	0
$235$	25.9648	1.69376
$236$	6.96081	0.453110
$237$	8.66874	0.563095
$238$	0.176650	0.0114505
$239$	18.9468	1.22556	0.612782	−	0.790252i	$-0.290050\pi$
$239$	18.9468	1.22556	0.612782	+	0.790252i	$0.290050\pi$
$240$	15.6336	1.00914
$241$	−15.6336	−1.00705	−0.503523	−	0.863982i	$-0.667963\pi$
$241$	−15.6336	−1.00705	−0.503523	+	0.863982i	$0.667963\pi$
$242$	1.22188	0.0785452
$243$	22.3593	1.43435
$244$	1.69059	0.108229
$245$	−15.8102	−1.01008
$246$	−1.16553	−0.0743115
$247$	0	0
$248$	−10.9367	−0.694483
$249$	11.8906	0.753537
$250$	−13.3413	−0.843777
$251$	3.88750	0.245377	0.122689	−	0.992445i	$-0.460848\pi$
$251$	3.88750	0.245377	0.122689	+	0.992445i	$0.460848\pi$
$252$	−0.474941	−0.0299185
$253$	0.0632663	0.00397752
$254$	1.02807	0.0645071
$255$	−2.90466	−0.181897
$256$	−11.3203	−0.707521
$257$	14.0452	0.876117	0.438059	−	0.898946i	$-0.355666\pi$
$257$	14.0452	0.876117	0.438059	+	0.898946i	$0.355666\pi$
$258$	16.5774	1.03206
$259$	−2.20384	−0.136940
$260$	0	0
$261$	−35.2921	−2.18452
$262$	0.365561	0.0225844
$263$	20.1194	1.24062	0.620308	−	0.784358i	$-0.287008\pi$
$263$	20.1194	1.24062	0.620308	+	0.784358i	$0.287008\pi$
$264$	−7.67967	−0.472651
$265$	−15.3765	−0.944570
$266$	1.37648	0.0843976
$267$	−9.31322	−0.569960
$268$	0.105378	0.00643700
$269$	−6.28514	−0.383212	−0.191606	−	0.981472i	$-0.561370\pi$
$269$	−6.28514	−0.383212	−0.191606	+	0.981472i	$0.561370\pi$
$270$	−1.99600	−0.121473
$271$	−31.7922	−1.93124	−0.965618	−	0.259965i	$-0.916289\pi$
$271$	−31.7922	−1.93124	−0.965618	+	0.259965i	$0.916289\pi$
$272$	−1.38360	−0.0838931
$273$	0	0
$274$	13.1867	0.796637
$275$	−0.221876	−0.0133796
$276$	−0.0804181	−0.00484060
$277$	16.8343	1.01147	0.505737	−	0.862688i	$-0.331221\pi$
$277$	16.8343	1.01147	0.505737	+	0.862688i	$0.331221\pi$
$278$	4.49990	0.269886
$279$	11.7289	0.702191
$280$	−1.99600	−0.119284
$281$	9.09134	0.542344	0.271172	−	0.962531i	$-0.412589\pi$
$281$	9.09134	0.542344	0.271172	+	0.962531i	$0.412589\pi$
$282$	−34.8062	−2.07268
$283$	23.1546	1.37640	0.688199	−	0.725522i	$-0.258401\pi$
$283$	23.1546	1.37640	0.688199	+	0.725522i	$0.258401\pi$
$284$	−1.40856	−0.0835827
$285$	−22.6336	−1.34070
$286$	0	0
$287$	0.108493	0.00640412
$288$	9.17265	0.540503
$289$	−16.7429	−0.984878
$290$	−29.9960	−1.76143
$291$	37.6757	2.20859
$292$	−1.01404	−0.0593420
$293$	−22.3734	−1.30707	−0.653533	−	0.756898i	$-0.726714\pi$
$293$	−22.3734	−1.30707	−0.653533	+	0.756898i	$0.726714\pi$
$294$	21.1938	1.23605
$295$	−31.3725	−1.82658
$296$	23.6757	1.37612
$297$	0.714858	0.0414802
$298$	−13.2811	−0.769356
$299$	0	0
$300$	0.282028	0.0162829
$301$	−1.54310	−0.0889427
$302$	−14.0210	−0.806815
$303$	−37.4366	−2.15068
$304$	−10.7812	−0.618346
$305$	−7.61951	−0.436292
$306$	2.03519	0.116344
$307$	−7.72889	−0.441111	−0.220556	−	0.975374i	$-0.570787\pi$
$307$	−7.72889	−0.441111	−0.220556	+	0.975374i	$0.570787\pi$
$308$	0.144573	0.00823779
$309$	43.5984	2.48022
$310$	9.96881	0.566190
$311$	−23.7218	−1.34514	−0.672569	−	0.740034i	$-0.734809\pi$
$311$	−23.7218	−1.34514	−0.672569	+	0.740034i	$0.734809\pi$
$312$	0	0
$313$	2.48987	0.140736	0.0703678	−	0.997521i	$-0.477583\pi$
$313$	2.48987	0.140736	0.0703678	+	0.997521i	$0.477583\pi$
$314$	19.7008	1.11178
$315$	2.14057	0.120607
$316$	1.75316	0.0986232
$317$	5.53910	0.311107	0.155553	−	0.987827i	$-0.450284\pi$
$317$	5.53910	0.311107	0.155553	+	0.987827i	$0.450284\pi$
$318$	20.6124	1.15589
$319$	10.7429	0.601489
$320$	20.2680	1.13302
$321$	39.4678	2.20288
$322$	−0.0220425	−0.00122838
$323$	2.00311	0.111456
$324$	4.08823	0.227124
$325$	0	0
$326$	22.3765	1.23932
$327$	47.5451	2.62925
$328$	−1.16553	−0.0643556
$329$	3.23992	0.178622
$330$	7.00000	0.385337
$331$	19.7750	1.08693	0.543466	−	0.839431i	$-0.317112\pi$
$331$	19.7750	1.08693	0.543466	+	0.839431i	$0.317112\pi$
$332$	2.40475	0.131978
$333$	−25.3905	−1.39139
$334$	13.1646	0.720337
$335$	−0.474941	−0.0259488
$336$	1.95077	0.106423
$337$	19.1858	1.04512	0.522558	−	0.852603i	$-0.324978\pi$
$337$	19.1858	1.04512	0.522558	+	0.852603i	$0.324978\pi$
$338$	0	0
$339$	36.7218	1.99445
$340$	−0.587437	−0.0318582
$341$	−3.57028	−0.193342
$342$	15.8585	0.857532
$343$	−3.96881	−0.214296
$344$	16.5774	0.893794
$345$	0.362446	0.0195134
$346$	−25.9648	−1.39588
$347$	−1.39452	−0.0748619	−0.0374310	−	0.999299i	$-0.511917\pi$
$347$	−1.39452	−0.0748619	−0.0374310	+	0.999299i	$0.511917\pi$
$348$	−13.6554	−0.732006
$349$	8.18668	0.438223	0.219112	−	0.975700i	$-0.429684\pi$
$349$	8.18668	0.438223	0.219112	+	0.975700i	$0.429684\pi$
$350$	0.0773036	0.00413205
$351$	0	0
$352$	−2.79216	−0.148823
$353$	24.8171	1.32088	0.660441	−	0.750878i	$-0.270369\pi$
$353$	24.8171	1.32088	0.660441	+	0.750878i	$0.270369\pi$
$354$	42.0553	2.23521
$355$	6.34841	0.336939
$356$	−1.88350	−0.0998254
$357$	−0.362446	−0.0191827
$358$	5.06415	0.267649
$359$	2.06327	0.108895	0.0544475	−	0.998517i	$-0.482660\pi$
$359$	2.06327	0.108895	0.0544475	+	0.998517i	$0.482660\pi$
$360$	−22.9960	−1.21200
$361$	−3.39141	−0.178495
$362$	24.7810	1.30246
$363$	−2.50702	−0.131584
$364$	0	0
$365$	4.57028	0.239220
$366$	10.2141	0.533898
$367$	25.5803	1.33528	0.667641	−	0.744483i	$-0.267304\pi$
$367$	25.5803	1.33528	0.667641	+	0.744483i	$0.267304\pi$
$368$	0.172647	0.00899985
$369$	1.24995	0.0650698
$370$	−21.5803	−1.12191
$371$	−1.91869	−0.0996136
$372$	4.53821	0.235295
$373$	12.0913	0.626066	0.313033	−	0.949742i	$-0.398655\pi$
$373$	12.0913	0.626066	0.313033	+	0.949742i	$0.398655\pi$
$374$	−0.619514	−0.0320343
$375$	27.3734	1.41355
$376$	−34.8062	−1.79499
$377$	0	0
$378$	−0.249063	−0.0128104
$379$	−15.7781	−0.810468	−0.405234	−	0.914213i	$-0.632810\pi$
$379$	−15.7781	−0.810468	−0.405234	+	0.914213i	$0.632810\pi$
$380$	−4.57740	−0.234816
$381$	−2.10938	−0.108067
$382$	5.64447	0.288796
$383$	−21.7601	−1.11189	−0.555944	−	0.831220i	$-0.687643\pi$
$383$	−21.7601	−1.11189	−0.555944	+	0.831220i	$0.687643\pi$
$384$	−13.1695	−0.672055
$385$	−0.651591	−0.0332082
$386$	6.96081	0.354296
$387$	−17.7781	−0.903713
$388$	7.61951	0.386822
$389$	4.54913	0.230650	0.115325	−	0.993328i	$-0.463209\pi$
$389$	4.54913	0.230650	0.115325	+	0.993328i	$0.463209\pi$
$390$	0	0
$391$	−0.0320772	−0.00162221
$392$	21.1938	1.07045
$393$	−0.750049	−0.0378350
$394$	2.27199	0.114461
$395$	−7.90154	−0.397570
$396$	1.66563	0.0837010
$397$	−13.8726	−0.696245	−0.348122	−	0.937449i	$-0.613181\pi$
$397$	−13.8726	−0.696245	−0.348122	+	0.937449i	$0.613181\pi$
$398$	10.1014	0.506336
$399$	−2.82424	−0.141389
$400$	−0.605477	−0.0302738
$401$	−12.0241	−0.600453	−0.300227	−	0.953868i	$-0.597062\pi$
$401$	−12.0241	−0.600453	−0.300227	+	0.953868i	$0.597062\pi$
$402$	0.636666	0.0317540
$403$	0	0
$404$	−7.57117	−0.376680
$405$	−18.4257	−0.915581
$406$	−3.74293	−0.185759
$407$	7.72889	0.383107
$408$	3.89373	0.192769
$409$	17.4678	0.863728	0.431864	−	0.901939i	$-0.357856\pi$
$409$	17.4678	0.863728	0.431864	+	0.901939i	$0.357856\pi$
$410$	1.06238	0.0524671
$411$	−27.0561	−1.33458
$412$	8.81732	0.434398
$413$	−3.91469	−0.192629
$414$	−0.253953	−0.0124811
$415$	−10.8383	−0.532030
$416$	0	0
$417$	−9.23280	−0.452132
$418$	−4.82735	−0.236114
$419$	23.4999	1.14805	0.574023	−	0.818839i	$-0.305382\pi$
$419$	23.4999	1.14805	0.574023	+	0.818839i	$0.305382\pi$
$420$	0.828241	0.0404140
$421$	−1.87347	−0.0913072	−0.0456536	−	0.998957i	$-0.514537\pi$
$421$	−1.87347	−0.0913072	−0.0456536	+	0.998957i	$0.514537\pi$
$422$	3.43372	0.167151
$423$	37.3273	1.81491
$424$	20.6124	1.00103
$425$	0.112495	0.00545683
$426$	−8.51013	−0.412317
$427$	−0.950771	−0.0460110
$428$	7.98196	0.385823
$429$	0	0
$430$	−15.1103	−0.728682
$431$	−6.15772	−0.296607	−0.148304	−	0.988942i	$-0.547381\pi$
$431$	−6.15772	−0.296607	−0.148304	+	0.988942i	$0.547381\pi$
$432$	1.95077	0.0938565
$433$	22.3624	1.07467	0.537335	−	0.843369i	$-0.319431\pi$
$433$	22.3624	1.07467	0.537335	+	0.843369i	$0.319431\pi$
$434$	1.24392	0.0597100
$435$	61.5451	2.95086
$436$	9.61551	0.460499
$437$	−0.249951	−0.0119568
$438$	−6.12653	−0.292737
$439$	−38.5632	−1.84052	−0.920260	−	0.391308i	$-0.872023\pi$
$439$	−38.5632	−1.84052	−0.920260	+	0.391308i	$0.872023\pi$
$440$	7.00000	0.333712
$441$	−22.7289	−1.08233
$442$	0	0
$443$	−25.4819	−1.21068	−0.605340	−	0.795967i	$-0.706963\pi$
$443$	−25.4819	−1.21068	−0.605340	+	0.795967i	$0.706963\pi$
$444$	−9.82424	−0.466238
$445$	8.48898	0.402416
$446$	17.1798	0.813485
$447$	27.2500	1.28888
$448$	2.52906	0.119487
$449$	−36.3553	−1.71571	−0.857857	−	0.513888i	$-0.828205\pi$
$449$	−36.3553	−1.71571	−0.857857	+	0.513888i	$0.828205\pi$
$450$	0.890619	0.0419842
$451$	−0.380486	−0.0179164
$452$	7.42660	0.349318
$453$	28.7679	1.35163
$454$	23.4647	1.10125
$455$	0	0
$456$	30.3406	1.42083
$457$	−16.2780	−0.761454	−0.380727	−	0.924688i	$-0.624326\pi$
$457$	−16.2780	−0.761454	−0.380727	+	0.924688i	$0.624326\pi$
$458$	−15.2477	−0.712479
$459$	−0.362446	−0.0169175
$460$	0.0733010	0.00341768
$461$	−2.80620	−0.130698	−0.0653488	−	0.997862i	$-0.520816\pi$
$461$	−2.80620	−0.130698	−0.0653488	+	0.997862i	$0.520816\pi$
$462$	0.873467	0.0406374
$463$	−18.8835	−0.877591	−0.438795	−	0.898587i	$-0.644595\pi$
$463$	−18.8835	−0.877591	−0.438795	+	0.898587i	$0.644595\pi$
$464$	29.3163	1.36098
$465$	−20.4538	−0.948522
$466$	−9.74071	−0.451229
$467$	−25.6295	−1.18599	−0.592997	−	0.805205i	$-0.702055\pi$
$467$	−25.6295	−1.18599	−0.592997	+	0.805205i	$0.702055\pi$
$468$	0	0
$469$	−0.0592637	−0.00273654
$470$	31.7258	1.46340
$471$	−40.4217	−1.86253
$472$	42.0553	1.93575
$473$	5.41168	0.248829
$474$	10.5921	0.486513
$475$	0.876582	0.0402203
$476$	−0.0733010	−0.00335974
$477$	−22.1054	−1.01214
$478$	23.1506	1.05888
$479$	−4.49298	−0.205290	−0.102645	−	0.994718i	$-0.532730\pi$
$479$	−4.49298	−0.205290	−0.102645	+	0.994718i	$0.532730\pi$
$480$	−15.9960	−0.730114
$481$	0	0
$482$	−19.1023	−0.870084
$483$	0.0452264	0.00205787
$484$	−0.507019	−0.0230463
$485$	−34.3413	−1.55936
$486$	27.3203	1.23928
$487$	21.8093	0.988274	0.494137	−	0.869384i	$-0.335484\pi$
$487$	21.8093	0.988274	0.494137	+	0.869384i	$0.335484\pi$
$488$	10.2141	0.462369
$489$	−45.9116	−2.07619
$490$	−19.3181	−0.872703
$491$	0.359332	0.0162164	0.00810820	−	0.999967i	$-0.497419\pi$
$491$	0.359332	0.0162164	0.00810820	+	0.999967i	$0.497419\pi$
$492$	0.483638	0.0218041
$493$	−5.44687	−0.245315
$494$	0	0
$495$	−7.50702	−0.337415
$496$	−9.74293	−0.437471
$497$	0.792161	0.0355333
$498$	14.5289	0.651054
$499$	0.394523	0.0176613	0.00883064	−	0.999961i	$-0.497189\pi$
$499$	0.394523	0.0176613	0.00883064	+	0.999961i	$0.497189\pi$
$500$	5.53598	0.247577
$501$	−27.0109	−1.20676
$502$	4.75005	0.212005
$503$	−25.5812	−1.14061	−0.570305	−	0.821433i	$-0.693175\pi$
$503$	−25.5812	−1.14061	−0.570305	+	0.821433i	$0.693175\pi$
$504$	−2.86946	−0.127816
$505$	34.1234	1.51847
$506$	0.0773036	0.00343656
$507$	0	0
$508$	−0.426600	−0.0189273
$509$	8.88350	0.393754	0.196877	−	0.980428i	$-0.436920\pi$
$509$	8.88350	0.393754	0.196877	+	0.980428i	$0.436920\pi$
$510$	−3.54913	−0.157158
$511$	0.570285	0.0252279
$512$	−24.3382	−1.07561
$513$	−2.82424	−0.124693
$514$	17.1615	0.756963
$515$	−39.7398	−1.75115
$516$	−6.87881	−0.302823
$517$	−11.3624	−0.499720
$518$	−2.69281	−0.118315
$519$	53.2740	2.33847
$520$	0	0
$521$	38.5803	1.69023	0.845117	−	0.534581i	$-0.179531\pi$
$521$	38.5803	1.69023	0.845117	+	0.534581i	$0.179531\pi$
$522$	−43.1225	−1.88742
$523$	24.2359	1.05976	0.529881	−	0.848072i	$-0.322236\pi$
$523$	24.2359	1.05976	0.529881	+	0.848072i	$0.322236\pi$
$524$	−0.151690	−0.00662660
$525$	−0.158610	−0.00692230
$526$	24.5834	1.07189
$527$	1.81020	0.0788536
$528$	−6.84139	−0.297733
$529$	−22.9960	−0.999826
$530$	−18.7882	−0.816105
$531$	−45.1014	−1.95723
$532$	−0.571173	−0.0247635
$533$	0	0
$534$	−11.3796	−0.492443
$535$	−35.9748	−1.55533
$536$	0.636666	0.0274998
$537$	−10.3905	−0.448384
$538$	−7.67967	−0.331094
$539$	6.91869	0.298009
$540$	0.828241	0.0356418
$541$	−9.10538	−0.391471	−0.195735	−	0.980657i	$-0.562709\pi$
$541$	−9.10538	−0.391471	−0.195735	+	0.980657i	$0.562709\pi$
$542$	−38.8461	−1.66858
$543$	−50.8452	−2.18198
$544$	1.41568	0.0606967
$545$	−43.3373	−1.85637
$546$	0	0
$547$	−42.0109	−1.79626	−0.898129	−	0.439733i	$-0.855073\pi$
$547$	−42.0109	−1.79626	−0.898129	+	0.439733i	$0.855073\pi$
$548$	−5.47183	−0.233745
$549$	−10.9539	−0.467500
$550$	−0.271105	−0.0115600
$551$	−42.4429	−1.80813
$552$	−0.485864	−0.0206798
$553$	−0.985963	−0.0419274
$554$	20.5694	0.873910
$555$	44.2780	1.87950
$556$	−1.86724	−0.0791885
$557$	−10.6124	−0.449662	−0.224831	−	0.974398i	$-0.572183\pi$
$557$	−10.6124	−0.449662	−0.224831	+	0.974398i	$0.572183\pi$
$558$	14.3313	0.606690
$559$	0	0
$560$	−1.77812	−0.0751394
$561$	1.27111	0.0536661
$562$	11.1085	0.468583
$563$	−19.3945	−0.817382	−0.408691	−	0.912673i	$-0.634015\pi$
$563$	−19.3945	−0.817382	−0.408691	+	0.912673i	$0.634015\pi$
$564$	14.4429	0.608154
$565$	−33.4718	−1.40817
$566$	28.2921	1.18920
$567$	−2.29918	−0.0965565
$568$	−8.51013	−0.357077
$569$	33.6625	1.41121	0.705603	−	0.708607i	$-0.250676\pi$
$569$	33.6625	1.41121	0.705603	+	0.708607i	$0.250676\pi$
$570$	−27.6554	−1.15836
$571$	−11.0250	−0.461380	−0.230690	−	0.973027i	$-0.574098\pi$
$571$	−11.0250	−0.461380	−0.230690	+	0.973027i	$0.574098\pi$
$572$	0	0
$573$	−11.5812	−0.483812
$574$	0.132565	0.00553314
$575$	−0.0140373	−0.000585395 0
$576$	29.1375	1.21406
$577$	−11.1898	−0.465837	−0.232919	−	0.972496i	$-0.574828\pi$
$577$	−11.1898	−0.465837	−0.232919	+	0.972496i	$0.574828\pi$
$578$	−20.4578	−0.850932
$579$	−14.2820	−0.593541
$580$	12.4469	0.516828
$581$	−1.35241	−0.0561075
$582$	46.0350	1.90821
$583$	6.72889	0.278682
$584$	−6.12653	−0.253518
$585$	0	0
$586$	−27.3375	−1.12930
$587$	−4.45779	−0.183993	−0.0919963	−	0.995759i	$-0.529325\pi$
$587$	−4.45779	−0.183993	−0.0919963	+	0.995759i	$0.529325\pi$
$588$	−8.79439	−0.362674
$589$	14.1054	0.581202
$590$	−38.3333	−1.57816
$591$	−4.66163	−0.191754
$592$	21.0913	0.866849
$593$	28.0733	1.15283	0.576416	−	0.817156i	$-0.304451\pi$
$593$	28.0733	1.15283	0.576416	+	0.817156i	$0.304451\pi$
$594$	0.873467	0.0358388
$595$	0.330369	0.0135438
$596$	5.51102	0.225740
$597$	−20.7258	−0.848250
$598$	0	0
$599$	17.6304	0.720360	0.360180	−	0.932883i	$-0.382715\pi$
$599$	17.6304	0.720360	0.360180	+	0.932883i	$0.382715\pi$
$600$	1.70393	0.0695628
$601$	6.69771	0.273205	0.136603	−	0.990626i	$-0.456382\pi$
$601$	6.69771	0.273205	0.136603	+	0.990626i	$0.456382\pi$
$602$	−1.88548	−0.0768462
$603$	−0.682780	−0.0278050
$604$	5.81801	0.236731
$605$	2.28514	0.0929043
$606$	−45.7429	−1.85818
$607$	−11.1546	−0.452752	−0.226376	−	0.974040i	$-0.572688\pi$
$607$	−11.1546	−0.452752	−0.226376	+	0.974040i	$0.572688\pi$
$608$	11.0312	0.447374
$609$	7.67967	0.311196
$610$	−9.31010	−0.376955
$611$	0	0
$612$	−0.844505	−0.0341371
$613$	15.3203	0.618782	0.309391	−	0.950935i	$-0.399875\pi$
$613$	15.3203	0.618782	0.309391	+	0.950935i	$0.399875\pi$
$614$	−9.44375	−0.381119
$615$	−2.17976	−0.0878966
$616$	0.873467	0.0351930
$617$	−24.4819	−0.985603	−0.492801	−	0.870142i	$-0.664027\pi$
$617$	−24.4819	−0.985603	−0.492801	+	0.870142i	$0.664027\pi$
$618$	53.2718	2.14291
$619$	−14.3624	−0.577275	−0.288638	−	0.957438i	$-0.593202\pi$
$619$	−14.3624	−0.577275	−0.288638	+	0.957438i	$0.593202\pi$
$620$	−4.13657	−0.166129
$621$	0.0452264	0.00181487
$622$	−28.9851	−1.16220
$623$	1.05926	0.0424385
$624$	0	0
$625$	−26.0602	−1.04241
$626$	3.04231	0.121595
$627$	9.90466	0.395554
$628$	−8.17487	−0.326213
$629$	−3.91869	−0.156249
$630$	2.61551	0.104204
$631$	−25.4186	−1.01190	−0.505949	−	0.862563i	$-0.668858\pi$
$631$	−25.4186	−1.01190	−0.505949	+	0.862563i	$0.668858\pi$
$632$	10.5921	0.421332
$633$	−7.04523	−0.280023
$634$	6.76809	0.268795
$635$	1.92270	0.0762999
$636$	−8.55313	−0.339154
$637$	0	0
$638$	13.1265	0.519684
$639$	9.12653	0.361040
$640$	12.0040	0.474500
$641$	−18.6897	−0.738199	−0.369099	−	0.929390i	$-0.620334\pi$
$641$	−18.6897	−0.738199	−0.369099	+	0.929390i	$0.620334\pi$
$642$	48.2248	1.90328
$643$	−0.221876	−0.00874994	−0.00437497	−	0.999990i	$-0.501393\pi$
$643$	−0.221876	−0.00874994	−0.00437497	+	0.999990i	$0.501393\pi$
$644$	0.00914657	0.000360425 0
$645$	31.0029	1.22074
$646$	2.44756	0.0962979
$647$	−10.0602	−0.395505	−0.197753	−	0.980252i	$-0.563364\pi$
$647$	−10.0602	−0.395505	−0.197753	+	0.980252i	$0.563364\pi$
$648$	24.6999	0.970305
$649$	13.7289	0.538906
$650$	0	0
$651$	−2.55225	−0.100030
$652$	−9.28514	−0.363634
$653$	25.1375	0.983705	0.491852	−	0.870679i	$-0.336320\pi$
$653$	25.1375	0.983705	0.491852	+	0.870679i	$0.336320\pi$
$654$	58.0943	2.27167
$655$	0.683668	0.0267131
$656$	−1.03831	−0.0405390
$657$	6.57028	0.256331
$658$	3.95878	0.154329
$659$	−30.7530	−1.19797	−0.598983	−	0.800762i	$-0.704428\pi$
$659$	−30.7530	−1.19797	−0.598983	+	0.800762i	$0.704428\pi$
$660$	−2.90466	−0.113064
$661$	−44.1335	−1.71659	−0.858296	−	0.513155i	$-0.828477\pi$
$661$	−44.1335	−1.71659	−0.858296	+	0.513155i	$0.828477\pi$
$662$	24.1626	0.939107
$663$	0	0
$664$	14.5289	0.563829
$665$	2.57429	0.0998266
$666$	−31.0241	−1.20216
$667$	0.679666	0.0263168
$668$	−5.46268	−0.211357
$669$	−35.2491	−1.36281
$670$	−0.580320	−0.0224197
$671$	3.33437	0.128722
$672$	−1.99600	−0.0769973
$673$	19.6516	0.757513	0.378757	−	0.925496i	$-0.376352\pi$
$673$	19.6516	0.757513	0.378757	+	0.925496i	$0.376352\pi$
$674$	23.4427	0.902978
$675$	−0.158610	−0.00610490
$676$	0	0
$677$	26.0250	1.00022	0.500110	−	0.865962i	$-0.333293\pi$
$677$	26.0250	1.00022	0.500110	+	0.865962i	$0.333293\pi$
$678$	44.8695	1.72320
$679$	−4.28514	−0.164449
$680$	−3.54913	−0.136103
$681$	−48.1444	−1.84490
$682$	−4.36245	−0.167047
$683$	−14.4609	−0.553331	−0.276666	−	0.960966i	$-0.589229\pi$
$683$	−14.4609	−0.553331	−0.276666	+	0.960966i	$0.589229\pi$
$684$	−6.58052	−0.251612
$685$	24.6616	0.942272
$686$	−4.84940	−0.185151
$687$	31.2849	1.19360
$688$	14.7679	0.563021
$689$	0	0
$690$	0.442864	0.0168596
$691$	8.71085	0.331377	0.165688	−	0.986178i	$-0.447015\pi$
$691$	8.71085	0.331377	0.165688	+	0.986178i	$0.447015\pi$
$692$	10.7741	0.409571
$693$	−0.936734	−0.0355836
$694$	−1.70393	−0.0646805
$695$	8.41568	0.319225
$696$	−82.5021	−3.12724
$697$	0.192913	0.00730712
$698$	10.0031	0.378623
$699$	19.9858	0.755931
$700$	−0.0320772	−0.00121240
$701$	37.5732	1.41912	0.709560	−	0.704645i	$-0.248894\pi$
$701$	37.5732	1.41912	0.709560	+	0.704645i	$0.248894\pi$
$702$	0	0
$703$	−30.5351	−1.15165
$704$	−8.86946	−0.334281
$705$	−65.0943	−2.45159
$706$	30.3234	1.14124
$707$	4.25796	0.160137
$708$	−17.4509	−0.655844
$709$	−10.9196	−0.410094	−0.205047	−	0.978752i	$-0.565735\pi$
$709$	−10.9196	−0.410094	−0.205047	+	0.978752i	$0.565735\pi$
$710$	7.75697	0.291114
$711$	−11.3593	−0.426008
$712$	−11.3796	−0.426468
$713$	−0.225879	−0.00845923
$714$	−0.442864	−0.0165738
$715$	0	0
$716$	−2.10138	−0.0785321
$717$	−47.4999	−1.77392
$718$	2.52106	0.0940850
$719$	34.6093	1.29071	0.645354	−	0.763883i	$-0.276710\pi$
$719$	34.6093	1.29071	0.645354	+	0.763883i	$0.276710\pi$
$720$	−20.4859	−0.763463
$721$	−4.95878	−0.184674
$722$	−4.14388	−0.154219
$723$	39.1936	1.45763
$724$	−10.2829	−0.382162
$725$	−2.38360	−0.0885247
$726$	−3.06327	−0.113688
$727$	19.3281	0.716841	0.358421	−	0.933560i	$-0.383315\pi$
$727$	19.3281	0.716841	0.358421	+	0.933560i	$0.383315\pi$
$728$	0	0
$729$	−31.8655	−1.18020
$730$	5.58432	0.206685
$731$	−2.74382	−0.101484
$732$	−4.23834	−0.156653
$733$	−8.03519	−0.296787	−0.148393	−	0.988928i	$-0.547410\pi$
$733$	−8.03519	−0.296787	−0.148393	+	0.988928i	$0.547410\pi$
$734$	31.2560	1.15368
$735$	39.6365	1.46201
$736$	−0.176650	−0.00651140
$737$	0.207839	0.00765584
$738$	1.52729	0.0562201
$739$	15.0290	0.552849	0.276425	−	0.961036i	$-0.410850\pi$
$739$	15.0290	0.552849	0.276425	+	0.961036i	$0.410850\pi$
$740$	8.95477	0.329184
$741$	0	0
$742$	−2.34441	−0.0860659
$743$	41.7006	1.52985	0.764924	−	0.644121i	$-0.222777\pi$
$743$	41.7006	1.52985	0.764924	+	0.644121i	$0.222777\pi$
$744$	27.4186	1.00521
$745$	−24.8383	−0.910004
$746$	14.7741	0.540919
$747$	−15.5812	−0.570087
$748$	0.257068	0.00939933
$749$	−4.48898	−0.164024
$750$	33.4469	1.22131
$751$	−26.1827	−0.955420	−0.477710	−	0.878518i	$-0.658533\pi$
$751$	−26.1827	−0.955420	−0.477710	+	0.878518i	$0.658533\pi$
$752$	−31.0069	−1.13071
$753$	−9.74605	−0.355166
$754$	0	0
$755$	−26.2219	−0.954312
$756$	0.103349	0.00375876
$757$	50.3734	1.83085	0.915426	−	0.402487i	$-0.131854\pi$
$757$	50.3734	1.83085	0.915426	+	0.402487i	$0.131854\pi$
$758$	−19.2789	−0.700242
$759$	−0.158610	−0.00575717
$760$	−27.6554	−1.00317
$761$	15.0882	0.546948	0.273474	−	0.961879i	$-0.411827\pi$
$761$	15.0882	0.546948	0.273474	+	0.961879i	$0.411827\pi$
$762$	−2.57740	−0.0933694
$763$	−5.40767	−0.195771
$764$	−2.34218	−0.0847371
$765$	3.80620	0.137613
$766$	−26.5881	−0.960668
$767$	0	0
$768$	28.3803	1.02409
$769$	−34.1094	−1.23002	−0.615008	−	0.788521i	$-0.710847\pi$
$769$	−34.1094	−1.23002	−0.615008	+	0.788521i	$0.710847\pi$
$770$	−0.796164	−0.0286918
$771$	−35.2116	−1.26812
$772$	−2.88839	−0.103956
$773$	−16.5772	−0.596241	−0.298120	−	0.954528i	$-0.596360\pi$
$773$	−16.5772	−0.596241	−0.298120	+	0.954528i	$0.596360\pi$
$774$	−21.7227	−0.780805
$775$	0.792161	0.0284553
$776$	46.0350	1.65256
$777$	5.52506	0.198210
$778$	5.55847	0.199281
$779$	1.50321	0.0538582
$780$	0	0
$781$	−2.77812	−0.0994091
$782$	−0.0391944	−0.00140159
$783$	7.67967	0.274449
$784$	18.8804	0.674300
$785$	36.8443	1.31503
$786$	−0.916467	−0.0326893
$787$	−21.7670	−0.775910	−0.387955	−	0.921678i	$-0.626818\pi$
$787$	−21.7670	−0.775910	−0.387955	+	0.921678i	$0.626818\pi$
$788$	−0.942766	−0.0335846
$789$	−50.4397	−1.79570
$790$	−9.65471	−0.343499
$791$	−4.17665	−0.148505
$792$	10.0633	0.357583
$793$	0	0
$794$	−16.9506	−0.601553
$795$	38.5491	1.36720
$796$	−4.19158	−0.148566
$797$	−28.9717	−1.02623	−0.513116	−	0.858319i	$-0.671509\pi$
$797$	−28.9717	−1.02623	−0.513116	+	0.858319i	$0.671509\pi$
$798$	−3.45087	−0.122159
$799$	5.76097	0.203809
$800$	0.619514	0.0219031
$801$	12.2038	0.431201
$802$	−14.6919	−0.518790
$803$	−2.00000	−0.0705785
$804$	−0.264185	−0.00931709
$805$	−0.0412238	−0.00145295
$806$	0	0
$807$	15.7570	0.554672
$808$	−45.7429	−1.60923
$809$	−48.4257	−1.70256	−0.851279	−	0.524714i	$-0.824172\pi$
$809$	−48.4257	−1.70256	−0.851279	+	0.524714i	$0.824172\pi$
$810$	−22.5139	−0.791059
$811$	−50.7499	−1.78207	−0.891034	−	0.453936i	$-0.850019\pi$
$811$	−50.7499	−1.78207	−0.891034	+	0.453936i	$0.850019\pi$
$812$	1.55313	0.0545043
$813$	79.7035	2.79533
$814$	9.44375	0.331003
$815$	41.8483	1.46588
$816$	3.46871	0.121429
$817$	−21.3803	−0.748002
$818$	21.3435	0.746259
$819$	0	0
$820$	−0.440835	−0.0153946
$821$	24.2600	0.846679	0.423340	−	0.905971i	$-0.360858\pi$
$821$	24.2600	0.846679	0.423340	+	0.905971i	$0.360858\pi$
$822$	−33.0593	−1.15307
$823$	25.5171	0.889469	0.444734	−	0.895663i	$-0.353298\pi$
$823$	25.5171	0.889469	0.444734	+	0.895663i	$0.353298\pi$
$824$	53.2718	1.85581
$825$	0.556248	0.0193661
$826$	−4.78327	−0.166431
$827$	−8.82112	−0.306741	−0.153370	−	0.988169i	$-0.549013\pi$
$827$	−8.82112	−0.306741	−0.153370	+	0.988169i	$0.549013\pi$
$828$	0.105378	0.00366215
$829$	−19.4718	−0.676285	−0.338142	−	0.941095i	$-0.609799\pi$
$829$	−19.4718	−0.676285	−0.338142	+	0.941095i	$0.609799\pi$
$830$	−13.2430	−0.459672
$831$	−42.2038	−1.46403
$832$	0	0
$833$	−3.50791	−0.121542
$834$	−11.2813	−0.390641
$835$	24.6204	0.852024
$836$	2.00311	0.0692792
$837$	−2.55225	−0.0882185
$838$	28.7140	0.991908
$839$	24.3905	0.842054	0.421027	−	0.907048i	$-0.361670\pi$
$839$	24.3905	0.842054	0.421027	+	0.907048i	$0.361670\pi$
$840$	5.00400	0.172654
$841$	86.4106	2.97968
$842$	−2.28915	−0.0788892
$843$	−22.7922	−0.785004
$844$	−1.42482	−0.0490445
$845$	0	0
$846$	45.6093	1.56808
$847$	0.285142	0.00979761
$848$	18.3624	0.630569
$849$	−58.0490	−1.99224
$850$	0.137455	0.00471468
$851$	0.488979	0.0167620
$852$	3.53129	0.120980
$853$	11.8984	0.407394	0.203697	−	0.979034i	$-0.434704\pi$
$853$	11.8984	0.407394	0.203697	+	0.979034i	$0.434704\pi$
$854$	−1.16172	−0.0397534
$855$	29.6585	1.01430
$856$	48.2248	1.64829
$857$	38.5030	1.31524	0.657619	−	0.753351i	$-0.271564\pi$
$857$	38.5030	1.31524	0.657619	+	0.753351i	$0.271564\pi$
$858$	0	0
$859$	23.8804	0.814788	0.407394	−	0.913252i	$-0.366438\pi$
$859$	23.8804	0.814788	0.407394	+	0.913252i	$0.366438\pi$
$860$	6.27002	0.213806
$861$	−0.271993	−0.00926951
$862$	−7.52397	−0.256268
$863$	32.7289	1.11410	0.557052	−	0.830477i	$-0.311932\pi$
$863$	32.7289	1.11410	0.557052	+	0.830477i	$0.311932\pi$
$864$	−1.99600	−0.0679052
$865$	−48.5592	−1.65106
$866$	27.3241	0.928512
$867$	41.9748	1.42554
$868$	−0.516165	−0.0175198
$869$	3.45779	0.117297
$870$	75.2005	2.54954
$871$	0	0
$872$	58.0943	1.96732
$873$	−49.3694	−1.67090
$874$	−0.305409	−0.0103306
$875$	−3.11338	−0.105252
$876$	2.54221	0.0858933
$877$	−26.6344	−0.899381	−0.449691	−	0.893184i	$-0.648466\pi$
$877$	−26.6344	−0.899381	−0.449691	+	0.893184i	$0.648466\pi$
$878$	−47.1194	−1.59020
$879$	56.0905	1.89188
$880$	6.23591	0.210213
$881$	0.349297	0.0117681	0.00588406	−	0.999983i	$-0.498127\pi$
$881$	0.349297	0.0117681	0.00588406	+	0.999983i	$0.498127\pi$
$882$	−27.7719	−0.935128
$883$	−32.5039	−1.09384	−0.546922	−	0.837184i	$-0.684200\pi$
$883$	−32.5039	−1.09384	−0.546922	+	0.837184i	$0.684200\pi$
$884$	0	0
$885$	78.6514	2.64384
$886$	−31.1357	−1.04602
$887$	29.1375	0.978340	0.489170	−	0.872188i	$-0.337300\pi$
$887$	29.1375	0.978340	0.489170	+	0.872188i	$0.337300\pi$
$888$	−59.3553	−1.99183
$889$	0.239916	0.00804653
$890$	10.3725	0.347686
$891$	8.06327	0.270130
$892$	−7.12876	−0.238689
$893$	44.8904	1.50220
$894$	33.2961	1.11359
$895$	9.47094	0.316579
$896$	1.49787	0.0500404
$897$	0	0
$898$	−44.4217	−1.48237
$899$	−38.3553	−1.27922
$900$	−0.369563	−0.0123188
$901$	−3.41168	−0.113659
$902$	−0.464907	−0.0154797
$903$	3.86858	0.128738
$904$	44.8695	1.49234
$905$	46.3453	1.54057
$906$	35.1508	1.16781
$907$	−0.664740	−0.0220723	−0.0110362	−	0.999939i	$-0.503513\pi$
$907$	−0.664740	−0.0220723	−0.0110362	+	0.999939i	$0.503513\pi$
$908$	−9.73670	−0.323124
$909$	49.0561	1.62709
$910$	0	0
$911$	24.5522	0.813452	0.406726	−	0.913550i	$-0.366670\pi$
$911$	24.5522	0.813452	0.406726	+	0.913550i	$0.366670\pi$
$912$	27.0288	0.895012
$913$	4.74293	0.156968
$914$	−19.8897	−0.657894
$915$	19.1023	0.631501
$916$	6.32706	0.209052
$917$	0.0853089	0.00281715
$918$	−0.442864	−0.0146167
$919$	−21.0561	−0.694578	−0.347289	−	0.937758i	$-0.612898\pi$
$919$	−21.0561	−0.694578	−0.347289	+	0.937758i	$0.612898\pi$
$920$	0.442864	0.0146008
$921$	19.3765	0.638477
$922$	−3.42883	−0.112922
$923$	0	0
$924$	−0.362446	−0.0119236
$925$	−1.71486	−0.0563842
$926$	−23.0733	−0.758236
$927$	−57.1303	−1.87641
$928$	−29.9960	−0.984667
$929$	2.97104	0.0974766	0.0487383	−	0.998812i	$-0.484480\pi$
$929$	2.97104	0.0974766	0.0487383	+	0.998812i	$0.484480\pi$
$930$	−24.9920	−0.819520
$931$	−27.3342	−0.895841
$932$	4.04191	0.132397
$933$	59.4709	1.94699
$934$	−31.3161	−1.02470
$935$	−1.15861	−0.0378906
$936$	0	0
$937$	52.0350	1.69991	0.849955	−	0.526856i	$-0.176629\pi$
$937$	52.0350	1.69991	0.849955	+	0.526856i	$0.176629\pi$
$938$	−0.0724129	−0.00236436
$939$	−6.24214	−0.203705
$940$	−13.1646	−0.429383
$941$	44.2108	1.44123	0.720615	−	0.693336i	$-0.243860\pi$
$941$	44.2108	1.44123	0.720615	+	0.693336i	$0.243860\pi$
$942$	−49.3903	−1.60922
$943$	−0.0240719	−0.000783891 0
$944$	37.4647	1.21937
$945$	−0.465795	−0.0151523
$946$	6.61240	0.214988
$947$	17.9969	0.584820	0.292410	−	0.956293i	$-0.405543\pi$
$947$	17.9969	0.584820	0.292410	+	0.956293i	$0.405543\pi$
$948$	−4.39521	−0.142750
$949$	0	0
$950$	1.07107	0.0347502
$951$	−13.8866	−0.450304
$952$	−0.442864	−0.0143533
$953$	6.50390	0.210682	0.105341	−	0.994436i	$-0.466407\pi$
$953$	6.50390	0.210682	0.105341	+	0.994436i	$0.466407\pi$
$954$	−27.0100	−0.874482
$955$	10.5562	0.341592
$956$	−9.60636	−0.310692
$957$	−26.9327	−0.870612
$958$	−5.48987	−0.177370
$959$	3.07730	0.0993713
$960$	−50.8122	−1.63996
$961$	−18.2531	−0.588809
$962$	0	0
$963$	−51.7178	−1.66658
$964$	7.92650	0.255295
$965$	13.0180	0.419066
$966$	0.0552611	0.00177800
$967$	27.4429	0.882503	0.441252	−	0.897383i	$-0.354535\pi$
$967$	27.4429	0.882503	0.441252	+	0.897383i	$0.354535\pi$
$968$	−3.06327	−0.0984571
$969$	−5.02185	−0.161325
$970$	−41.9608	−1.34728
$971$	27.2780	0.875393	0.437697	−	0.899123i	$-0.355794\pi$
$971$	27.2780	0.875393	0.437697	+	0.899123i	$0.355794\pi$
$972$	−11.3366	−0.363622
$973$	1.05012	0.0336652
$974$	26.6483	0.853866
$975$	0	0
$976$	9.09915	0.291257
$977$	7.17665	0.229601	0.114801	−	0.993389i	$-0.463377\pi$
$977$	7.17665	0.229601	0.114801	+	0.993389i	$0.463377\pi$
$978$	−56.0983	−1.79382
$979$	−3.71486	−0.118727
$980$	8.01607	0.256064
$981$	−62.3021	−1.98915
$982$	0.439059	0.0140109
$983$	28.4326	0.906860	0.453430	−	0.891292i	$-0.350200\pi$
$983$	28.4326	0.906860	0.453430	+	0.891292i	$0.350200\pi$
$984$	2.92201	0.0931501
$985$	4.24906	0.135386
$986$	−6.65540	−0.211951
$987$	−8.12253	−0.258543
$988$	0	0
$989$	0.342377	0.0108869
$990$	−9.17265	−0.291526
$991$	42.7490	1.35797	0.678983	−	0.734154i	$-0.262421\pi$
$991$	42.7490	1.35797	0.678983	+	0.734154i	$0.262421\pi$
$992$	9.96881	0.316510
$993$	−49.5763	−1.57326
$994$	0.967923	0.0307006
$995$	18.8915	0.598901
$996$	−6.02877	−0.191029
$997$	−28.7859	−0.911660	−0.455830	−	0.890067i	$-0.650657\pi$
$997$	−28.7859	−0.911660	−0.455830	+	0.890067i	$0.650657\pi$
$998$	0.482059	0.0152593
$999$	5.52506	0.174805

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.g.1.2		3
13.4	even	6		143.2.e.b.133.2	yes	6
13.10	even	6		143.2.e.b.100.2	✓	6
13.12	even	2		1859.2.a.f.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.e.b.100.2	✓	6	13.10	even	6
143.2.e.b.133.2	yes	6	13.4	even	6
1859.2.a.f.1.2		3	13.12	even	2
1859.2.a.g.1.2		3	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)

\(f(q)\)	\(=\)	\(q+1.22188 q^{2} -2.50702 q^{3} -0.507019 q^{4} +2.28514 q^{5} -3.06327 q^{6} +0.285142 q^{7} -3.06327 q^{8} +3.28514 q^{9} +O(q^{10})\)	\(q+1.22188 q^{2} -2.50702 q^{3} -0.507019 q^{4} +2.28514 q^{5} -3.06327 q^{6} +0.285142 q^{7} -3.06327 q^{8} +3.28514 q^{9} +2.79216 q^{10} -1.00000 q^{11} +1.27111 q^{12} +0.348409 q^{14} -5.72889 q^{15} -2.72889 q^{16} +0.507019 q^{17} +4.01404 q^{18} +3.95077 q^{19} -1.15861 q^{20} -0.714858 q^{21} -1.22188 q^{22} -0.0632663 q^{23} +7.67967 q^{24} +0.221876 q^{25} -0.714858 q^{27} -0.144573 q^{28} -10.7429 q^{29} -7.00000 q^{30} +3.57028 q^{31} +2.79216 q^{32} +2.50702 q^{33} +0.619514 q^{34} +0.651591 q^{35} -1.66563 q^{36} -7.72889 q^{37} +4.82735 q^{38} -7.00000 q^{40} +0.380486 q^{41} -0.873467 q^{42} -5.41168 q^{43} +0.507019 q^{44} +7.50702 q^{45} -0.0773036 q^{46} +11.3624 q^{47} +6.84139 q^{48} -6.91869 q^{49} +0.271105 q^{50} -1.27111 q^{51} -6.72889 q^{53} -0.873467 q^{54} -2.28514 q^{55} -0.873467 q^{56} -9.90466 q^{57} -13.1265 q^{58} -13.7289 q^{59} +2.90466 q^{60} -3.33437 q^{61} +4.36245 q^{62} +0.936734 q^{63} +8.86946 q^{64} +3.06327 q^{66} -0.207839 q^{67} -0.257068 q^{68} +0.158610 q^{69} +0.796164 q^{70} +2.77812 q^{71} -10.0633 q^{72} +2.00000 q^{73} -9.44375 q^{74} -0.556248 q^{75} -2.00311 q^{76} -0.285142 q^{77} -3.45779 q^{79} -6.23591 q^{80} -8.06327 q^{81} +0.464907 q^{82} -4.74293 q^{83} +0.362446 q^{84} +1.15861 q^{85} -6.61240 q^{86} +26.9327 q^{87} +3.06327 q^{88} +3.71486 q^{89} +9.17265 q^{90} +0.0320772 q^{92} -8.95077 q^{93} +13.8835 q^{94} +9.02807 q^{95} -7.00000 q^{96} -15.0281 q^{97} -8.45379 q^{98} -3.28514 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + q^{3} + 7 q^{4} + q^{5} - 6 q^{6} - 5 q^{7} - 6 q^{8} + 4 q^{9}+O(q^{10}) \) 3 * q + q^2 + q^3 + 7 * q^4 + q^5 - 6 * q^6 - 5 * q^7 - 6 * q^8 + 4 * q^9	\( 3 q + q^{2} + q^{3} + 7 q^{4} + q^{5} - 6 q^{6} - 5 q^{7} - 6 q^{8} + 4 q^{9} - 6 q^{10} - 3 q^{11} + 15 q^{12} - 8 q^{14} - 6 q^{15} + 3 q^{16} - 7 q^{17} - 5 q^{18} - 2 q^{19} - 4 q^{20} - 8 q^{21} - q^{22} + 3 q^{23} - 2 q^{24} - 2 q^{25} - 8 q^{27} - 18 q^{28} - 4 q^{29} - 21 q^{30} - q^{31} - 6 q^{32} - q^{33} + 4 q^{34} + 11 q^{35} + 3 q^{36} - 12 q^{37} + 31 q^{38} - 21 q^{40} - q^{41} - 9 q^{42} - 4 q^{43} - 7 q^{44} + 14 q^{45} + 20 q^{46} + 8 q^{47} + 20 q^{48} + 12 q^{50} - 15 q^{51} - 9 q^{53} - 9 q^{54} - q^{55} - 9 q^{56} - 26 q^{57} - 33 q^{58} - 30 q^{59} + 5 q^{60} - 18 q^{61} - 13 q^{62} + 6 q^{63} - 8 q^{64} + 6 q^{66} - 15 q^{67} - 29 q^{68} + q^{69} + 29 q^{70} + 11 q^{71} - 27 q^{72} + 6 q^{73} - 23 q^{74} - 7 q^{75} - 30 q^{76} + 5 q^{77} + 12 q^{79} + q^{80} - 21 q^{81} + 44 q^{82} + 14 q^{83} - 25 q^{84} + 4 q^{85} + 43 q^{86} + 43 q^{87} + 6 q^{88} + 17 q^{89} + 11 q^{90} + 7 q^{92} - 13 q^{93} - 10 q^{94} - 7 q^{95} - 21 q^{96} - 11 q^{97} + 38 q^{98} - 4 q^{99}+O(q^{100}) \) 3 * q + q^2 + q^3 + 7 * q^4 + q^5 - 6 * q^6 - 5 * q^7 - 6 * q^8 + 4 * q^9 - 6 * q^10 - 3 * q^11 + 15 * q^12 - 8 * q^14 - 6 * q^15 + 3 * q^16 - 7 * q^17 - 5 * q^18 - 2 * q^19 - 4 * q^20 - 8 * q^21 - q^22 + 3 * q^23 - 2 * q^24 - 2 * q^25 - 8 * q^27 - 18 * q^28 - 4 * q^29 - 21 * q^30 - q^31 - 6 * q^32 - q^33 + 4 * q^34 + 11 * q^35 + 3 * q^36 - 12 * q^37 + 31 * q^38 - 21 * q^40 - q^41 - 9 * q^42 - 4 * q^43 - 7 * q^44 + 14 * q^45 + 20 * q^46 + 8 * q^47 + 20 * q^48 + 12 * q^50 - 15 * q^51 - 9 * q^53 - 9 * q^54 - q^55 - 9 * q^56 - 26 * q^57 - 33 * q^58 - 30 * q^59 + 5 * q^60 - 18 * q^61 - 13 * q^62 + 6 * q^63 - 8 * q^64 + 6 * q^66 - 15 * q^67 - 29 * q^68 + q^69 + 29 * q^70 + 11 * q^71 - 27 * q^72 + 6 * q^73 - 23 * q^74 - 7 * q^75 - 30 * q^76 + 5 * q^77 + 12 * q^79 + q^80 - 21 * q^81 + 44 * q^82 + 14 * q^83 - 25 * q^84 + 4 * q^85 + 43 * q^86 + 43 * q^87 + 6 * q^88 + 17 * q^89 + 11 * q^90 + 7 * q^92 - 13 * q^93 - 10 * q^94 - 7 * q^95 - 21 * q^96 - 11 * q^97 + 38 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more