LMFDB - Embedded newform 8673.2.a.s.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8673,2,Mod(1,8673)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8673, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8673.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8673 = 3 \cdot 7^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8673.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:	$69.2542536731$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.229.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 4x - 1 $ x^3 - 4*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 177)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.254102$ of defining polynomial
Character	$\chi$	$=$	8673.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.254102 q^{2} +1.00000 q^{3} -1.93543 q^{4} -1.68133 q^{5} -0.254102 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.254102 q^{2} +1.00000 q^{3} -1.93543 q^{4} -1.68133 q^{5} -0.254102 q^{6} +1.00000 q^{8} +1.00000 q^{9} +0.427229 q^{10} +2.18953 q^{11} -1.93543 q^{12} -4.18953 q^{13} -1.68133 q^{15} +3.61676 q^{16} +6.29809 q^{17} -0.254102 q^{18} -4.93543 q^{19} +3.25410 q^{20} -0.556364 q^{22} +3.44364 q^{23} +1.00000 q^{24} -2.17313 q^{25} +1.06457 q^{26} +1.00000 q^{27} -9.12497 q^{29} +0.427229 q^{30} +0.616763 q^{31} -2.91903 q^{32} +2.18953 q^{33} -1.60036 q^{34} -1.93543 q^{36} +1.44364 q^{37} +1.25410 q^{38} -4.18953 q^{39} -1.68133 q^{40} -4.10856 q^{41} +8.53579 q^{43} -4.23769 q^{44} -1.68133 q^{45} -0.875034 q^{46} +6.48763 q^{47} +3.61676 q^{48} +0.552195 q^{50} +6.29809 q^{51} +8.10856 q^{52} -0.664924 q^{53} -0.254102 q^{54} -3.68133 q^{55} -4.93543 q^{57} +2.31867 q^{58} -1.00000 q^{59} +3.25410 q^{60} +10.9958 q^{61} -0.156721 q^{62} -6.49180 q^{64} +7.04399 q^{65} -0.556364 q^{66} -9.93126 q^{67} -12.1895 q^{68} +3.44364 q^{69} +6.82687 q^{71} +1.00000 q^{72} -13.5040 q^{73} -0.366830 q^{74} -2.17313 q^{75} +9.55220 q^{76} +1.06457 q^{78} -1.17313 q^{79} -6.08097 q^{80} +1.00000 q^{81} +1.04399 q^{82} +15.3421 q^{83} -10.5892 q^{85} -2.16896 q^{86} -9.12497 q^{87} +2.18953 q^{88} -1.97942 q^{89} +0.427229 q^{90} -6.66492 q^{92} +0.616763 q^{93} -1.64852 q^{94} +8.29809 q^{95} -2.91903 q^{96} -3.33508 q^{97} +2.18953 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{3} + 2 q^{4} + 2 q^{5} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^3 + 2 * q^4 + 2 * q^5 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{3} + 2 q^{4} + 2 q^{5} + 3 q^{8} + 3 q^{9} - 5 q^{10} - 2 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{15} - 4 q^{16} - 3 q^{17} - 7 q^{19} + 9 q^{20} - 11 q^{22} + q^{23} + 3 q^{24} - q^{25} + 11 q^{26} + 3 q^{27} - 11 q^{29} - 5 q^{30} - 13 q^{31} - 4 q^{32} - 2 q^{33} + 7 q^{34} + 2 q^{36} - 5 q^{37} + 3 q^{38} - 4 q^{39} + 2 q^{40} + q^{41} + 6 q^{43} - 15 q^{44} + 2 q^{45} - 19 q^{46} - 11 q^{47} - 4 q^{48} - 21 q^{50} - 3 q^{51} + 11 q^{52} + 2 q^{53} - 4 q^{55} - 7 q^{57} + 14 q^{58} - 3 q^{59} + 9 q^{60} + q^{61} + 2 q^{62} - 21 q^{64} - 11 q^{66} + 10 q^{67} - 28 q^{68} + q^{69} + 26 q^{71} + 3 q^{72} - 7 q^{73} - 19 q^{74} - q^{75} + 6 q^{76} + 11 q^{78} + 2 q^{79} - 23 q^{80} + 3 q^{81} - 18 q^{82} + 3 q^{83} - 35 q^{85} + 31 q^{86} - 11 q^{87} - 2 q^{88} + 23 q^{89} - 5 q^{90} - 16 q^{92} - 13 q^{93} - 4 q^{94} + 3 q^{95} - 4 q^{96} - 14 q^{97} - 2 q^{99}+O(q^{100}) $ 3 * q + 3 * q^3 + 2 * q^4 + 2 * q^5 + 3 * q^8 + 3 * q^9 - 5 * q^10 - 2 * q^11 + 2 * q^12 - 4 * q^13 + 2 * q^15 - 4 * q^16 - 3 * q^17 - 7 * q^19 + 9 * q^20 - 11 * q^22 + q^23 + 3 * q^24 - q^25 + 11 * q^26 + 3 * q^27 - 11 * q^29 - 5 * q^30 - 13 * q^31 - 4 * q^32 - 2 * q^33 + 7 * q^34 + 2 * q^36 - 5 * q^37 + 3 * q^38 - 4 * q^39 + 2 * q^40 + q^41 + 6 * q^43 - 15 * q^44 + 2 * q^45 - 19 * q^46 - 11 * q^47 - 4 * q^48 - 21 * q^50 - 3 * q^51 + 11 * q^52 + 2 * q^53 - 4 * q^55 - 7 * q^57 + 14 * q^58 - 3 * q^59 + 9 * q^60 + q^61 + 2 * q^62 - 21 * q^64 - 11 * q^66 + 10 * q^67 - 28 * q^68 + q^69 + 26 * q^71 + 3 * q^72 - 7 * q^73 - 19 * q^74 - q^75 + 6 * q^76 + 11 * q^78 + 2 * q^79 - 23 * q^80 + 3 * q^81 - 18 * q^82 + 3 * q^83 - 35 * q^85 + 31 * q^86 - 11 * q^87 - 2 * q^88 + 23 * q^89 - 5 * q^90 - 16 * q^92 - 13 * q^93 - 4 * q^94 + 3 * q^95 - 4 * q^96 - 14 * q^97 - 2 * 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 $

$2$	−0.254102	−0.179677	−0.0898385	−	0.995956i	$-0.528635\pi$
$2$	−0.254102	−0.179677	−0.0898385	+	0.995956i	$0.528635\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.93543	−0.967716
$5$	−1.68133	−0.751914	−0.375957	−	0.926637i	$-0.622686\pi$
$5$	−1.68133	−0.751914	−0.375957	+	0.926637i	$0.622686\pi$
$6$	−0.254102	−0.103737
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.427229	0.135102
$11$	2.18953	0.660169	0.330085	−	0.943951i	$-0.392923\pi$
$11$	2.18953	0.660169	0.330085	+	0.943951i	$0.392923\pi$
$12$	−1.93543	−0.558711
$13$	−4.18953	−1.16197	−0.580984	−	0.813915i	$-0.697332\pi$
$13$	−4.18953	−1.16197	−0.580984	+	0.813915i	$0.697332\pi$
$14$	0	0
$15$	−1.68133	−0.434118
$16$	3.61676	0.904191
$17$	6.29809	1.52751	0.763756	−	0.645505i	$-0.223353\pi$
$17$	6.29809	1.52751	0.763756	+	0.645505i	$0.223353\pi$
$18$	−0.254102	−0.0598923
$19$	−4.93543	−1.13227	−0.566133	−	0.824314i	$-0.691561\pi$
$19$	−4.93543	−1.13227	−0.566133	+	0.824314i	$0.691561\pi$
$20$	3.25410	0.727639
$21$	0	0
$22$	−0.556364	−0.118617
$23$	3.44364	0.718048	0.359024	−	0.933328i	$-0.383110\pi$
$23$	3.44364	0.718048	0.359024	+	0.933328i	$0.383110\pi$
$24$	1.00000	0.204124
$25$	−2.17313	−0.434625
$26$	1.06457	0.208779
$27$	1.00000	0.192450
$28$	0	0
$29$	−9.12497	−1.69446	−0.847232	−	0.531223i	$-0.821733\pi$
$29$	−9.12497	−1.69446	−0.847232	+	0.531223i	$0.821733\pi$
$30$	0.427229	0.0780010
$31$	0.616763	0.110774	0.0553870	−	0.998465i	$-0.482361\pi$
$31$	0.616763	0.110774	0.0553870	+	0.998465i	$0.482361\pi$
$32$	−2.91903	−0.516016
$33$	2.18953	0.381149
$34$	−1.60036	−0.274459
$35$	0	0
$36$	−1.93543	−0.322572
$37$	1.44364	0.237332	0.118666	−	0.992934i	$-0.462138\pi$
$37$	1.44364	0.237332	0.118666	+	0.992934i	$0.462138\pi$
$38$	1.25410	0.203442
$39$	−4.18953	−0.670862
$40$	−1.68133	−0.265842
$41$	−4.10856	−0.641649	−0.320825	−	0.947139i	$-0.603960\pi$
$41$	−4.10856	−0.641649	−0.320825	+	0.947139i	$0.603960\pi$
$42$	0	0
$43$	8.53579	1.30170	0.650848	−	0.759208i	$-0.274414\pi$
$43$	8.53579	1.30170	0.650848	+	0.759208i	$0.274414\pi$
$44$	−4.23769	−0.638857
$45$	−1.68133	−0.250638
$46$	−0.875034	−0.129017
$47$	6.48763	0.946318	0.473159	−	0.880977i	$-0.343114\pi$
$47$	6.48763	0.946318	0.473159	+	0.880977i	$0.343114\pi$
$48$	3.61676	0.522035
$49$	0	0
$50$	0.552195	0.0780922
$51$	6.29809	0.881910
$52$	8.10856	1.12445
$53$	−0.664924	−0.0913343	−0.0456672	−	0.998957i	$-0.514541\pi$
$53$	−0.664924	−0.0913343	−0.0456672	+	0.998957i	$0.514541\pi$
$54$	−0.254102	−0.0345789
$55$	−3.68133	−0.496391
$56$	0	0
$57$	−4.93543	−0.653714
$58$	2.31867	0.304456
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	3.25410	0.420103
$61$	10.9958	1.40787	0.703936	−	0.710263i	$-0.251424\pi$
$61$	10.9958	1.40787	0.703936	+	0.710263i	$0.251424\pi$
$62$	−0.156721	−0.0199035
$63$	0	0
$64$	−6.49180	−0.811475
$65$	7.04399	0.873700
$66$	−0.556364	−0.0684837
$67$	−9.93126	−1.21330	−0.606648	−	0.794970i	$-0.707486\pi$
$67$	−9.93126	−1.21330	−0.606648	+	0.794970i	$0.707486\pi$
$68$	−12.1895	−1.47820
$69$	3.44364	0.414565
$70$	0	0
$71$	6.82687	0.810201	0.405100	−	0.914272i	$-0.367237\pi$
$71$	6.82687	0.810201	0.405100	+	0.914272i	$0.367237\pi$
$72$	1.00000	0.117851
$73$	−13.5040	−1.58053	−0.790264	−	0.612767i	$-0.790057\pi$
$73$	−13.5040	−1.58053	−0.790264	+	0.612767i	$0.790057\pi$
$74$	−0.366830	−0.0426432
$75$	−2.17313	−0.250931
$76$	9.55220	1.09571
$77$	0	0
$78$	1.06457	0.120539
$79$	−1.17313	−0.131987	−0.0659936	−	0.997820i	$-0.521022\pi$
$79$	−1.17313	−0.131987	−0.0659936	+	0.997820i	$0.521022\pi$
$80$	−6.08097	−0.679874
$81$	1.00000	0.111111
$82$	1.04399	0.115290
$83$	15.3421	1.68401	0.842006	−	0.539468i	$-0.181374\pi$
$83$	15.3421	1.68401	0.842006	+	0.539468i	$0.181374\pi$
$84$	0	0
$85$	−10.5892	−1.14856
$86$	−2.16896	−0.233885
$87$	−9.12497	−0.978299
$88$	2.18953	0.233405
$89$	−1.97942	−0.209819	−0.104909	−	0.994482i	$-0.533455\pi$
$89$	−1.97942	−0.209819	−0.104909	+	0.994482i	$0.533455\pi$
$90$	0.427229	0.0450339
$91$	0	0
$92$	−6.66492	−0.694866
$93$	0.616763	0.0639553
$94$	−1.64852	−0.170032
$95$	8.29809	0.851366
$96$	−2.91903	−0.297922
$97$	−3.33508	−0.338626	−0.169313	−	0.985562i	$-0.554155\pi$
$97$	−3.33508	−0.338626	−0.169313	+	0.985562i	$0.554155\pi$
$98$	0	0
$99$	2.18953	0.220056
$100$	4.20594	0.420594
$101$	3.49180	0.347447	0.173723	−	0.984794i	$-0.444420\pi$
$101$	3.49180	0.347447	0.173723	+	0.984794i	$0.444420\pi$
$102$	−1.60036	−0.158459
$103$	−8.21712	−0.809657	−0.404828	−	0.914393i	$-0.632669\pi$
$103$	−8.21712	−0.809657	−0.404828	+	0.914393i	$0.632669\pi$
$104$	−4.18953	−0.410818
$105$	0	0
$106$	0.168958	0.0164107
$107$	17.7899	1.71981	0.859907	−	0.510451i	$-0.170522\pi$
$107$	17.7899	1.71981	0.859907	+	0.510451i	$0.170522\pi$
$108$	−1.93543	−0.186237
$109$	−18.2981	−1.75264	−0.876320	−	0.481730i	$-0.840009\pi$
$109$	−18.2981	−1.75264	−0.876320	+	0.481730i	$0.840009\pi$
$110$	0.935432	0.0891900
$111$	1.44364	0.137024
$112$	0	0
$113$	−7.71414	−0.725686	−0.362843	−	0.931850i	$-0.618194\pi$
$113$	−7.71414	−0.725686	−0.362843	+	0.931850i	$0.618194\pi$
$114$	1.25410	0.117457
$115$	−5.78989	−0.539910
$116$	17.6608	1.63976
$117$	−4.18953	−0.387323
$118$	0.254102	0.0233920
$119$	0	0
$120$	−1.68133	−0.153484
$121$	−6.20594	−0.564176
$122$	−2.79406	−0.252962
$123$	−4.10856	−0.370456
$124$	−1.19370	−0.107198
$125$	12.0604	1.07871
$126$	0	0
$127$	6.18953	0.549232	0.274616	−	0.961554i	$-0.411449\pi$
$127$	6.18953	0.549232	0.274616	+	0.961554i	$0.411449\pi$
$128$	7.48763	0.661819
$129$	8.53579	0.751534
$130$	−1.78989	−0.156984
$131$	15.5798	1.36121	0.680606	−	0.732650i	$-0.261717\pi$
$131$	15.5798	1.36121	0.680606	+	0.732650i	$0.261717\pi$
$132$	−4.23769	−0.368844
$133$	0	0
$134$	2.52355	0.218002
$135$	−1.68133	−0.144706
$136$	6.29809	0.540057
$137$	0.664924	0.0568083	0.0284041	−	0.999597i	$-0.490957\pi$
$137$	0.664924	0.0568083	0.0284041	+	0.999597i	$0.490957\pi$
$138$	−0.875034	−0.0744878
$139$	18.7857	1.59338	0.796692	−	0.604385i	$-0.206581\pi$
$139$	18.7857	1.59338	0.796692	+	0.604385i	$0.206581\pi$
$140$	0	0
$141$	6.48763	0.546357
$142$	−1.73472	−0.145574
$143$	−9.17313	−0.767095
$144$	3.61676	0.301397
$145$	15.3421	1.27409
$146$	3.43140	0.283985
$147$	0	0
$148$	−2.79406	−0.229670
$149$	−8.04816	−0.659331	−0.329666	−	0.944098i	$-0.606936\pi$
$149$	−8.04816	−0.659331	−0.329666	+	0.944098i	$0.606936\pi$
$150$	0.552195	0.0450866
$151$	−17.8503	−1.45264	−0.726318	−	0.687359i	$-0.758770\pi$
$151$	−17.8503	−1.45264	−0.726318	+	0.687359i	$0.758770\pi$
$152$	−4.93543	−0.400316
$153$	6.29809	0.509171
$154$	0	0
$155$	−1.03698	−0.0832924
$156$	8.10856	0.649204
$157$	−10.4395	−0.833160	−0.416580	−	0.909099i	$-0.636771\pi$
$157$	−10.4395	−0.833160	−0.416580	+	0.909099i	$0.636771\pi$
$158$	0.298094	0.0237151
$159$	−0.664924	−0.0527319
$160$	4.90785	0.387999
$161$	0	0
$162$	−0.254102	−0.0199641
$163$	−3.76231	−0.294686	−0.147343	−	0.989085i	$-0.547072\pi$
$163$	−3.76231	−0.294686	−0.147343	+	0.989085i	$0.547072\pi$
$164$	7.95184	0.620934
$165$	−3.68133	−0.286591
$166$	−3.89845	−0.302578
$167$	−18.1086	−1.40128	−0.700641	−	0.713514i	$-0.747103\pi$
$167$	−18.1086	−1.40128	−0.700641	+	0.713514i	$0.747103\pi$
$168$	0	0
$169$	4.55220	0.350169
$170$	2.69073	0.206369
$171$	−4.93543	−0.377422
$172$	−16.5204	−1.25967
$173$	9.66598	0.734891	0.367446	−	0.930045i	$-0.380232\pi$
$173$	9.66598	0.734891	0.367446	+	0.930045i	$0.380232\pi$
$174$	2.31867	0.175778
$175$	0	0
$176$	7.91903	0.596919
$177$	−1.00000	−0.0751646
$178$	0.502975	0.0376996
$179$	−8.95601	−0.669403	−0.334702	−	0.942324i	$-0.608636\pi$
$179$	−8.95601	−0.669403	−0.334702	+	0.942324i	$0.608636\pi$
$180$	3.25410	0.242546
$181$	0.487628	0.0362451	0.0181225	−	0.999836i	$-0.494231\pi$
$181$	0.487628	0.0362451	0.0181225	+	0.999836i	$0.494231\pi$
$182$	0	0
$183$	10.9958	0.812835
$184$	3.44364	0.253868
$185$	−2.42723	−0.178453
$186$	−0.156721	−0.0114913
$187$	13.7899	1.00842
$188$	−12.5564	−0.915767
$189$	0	0
$190$	−2.10856	−0.152971
$191$	5.07681	0.367345	0.183672	−	0.982988i	$-0.441201\pi$
$191$	5.07681	0.367345	0.183672	+	0.982988i	$0.441201\pi$
$192$	−6.49180	−0.468505
$193$	9.36266	0.673939	0.336970	−	0.941516i	$-0.390598\pi$
$193$	9.36266	0.673939	0.336970	+	0.941516i	$0.390598\pi$
$194$	0.847448	0.0608433
$195$	7.04399	0.504431
$196$	0	0
$197$	−16.2499	−1.15776	−0.578880	−	0.815413i	$-0.696510\pi$
$197$	−16.2499	−1.15776	−0.578880	+	0.815413i	$0.696510\pi$
$198$	−0.556364	−0.0395391
$199$	−6.64958	−0.471376	−0.235688	−	0.971829i	$-0.575734\pi$
$199$	−6.64958	−0.471376	−0.235688	+	0.971829i	$0.575734\pi$
$200$	−2.17313	−0.153663
$201$	−9.93126	−0.700497
$202$	−0.887271	−0.0624282
$203$	0	0
$204$	−12.1895	−0.853438
$205$	6.90785	0.482465
$206$	2.08798	0.145477
$207$	3.44364	0.239349
$208$	−15.1526	−1.05064
$209$	−10.8063	−0.747487
$210$	0	0
$211$	13.1526	0.905459	0.452729	−	0.891648i	$-0.350450\pi$
$211$	13.1526	0.905459	0.452729	+	0.891648i	$0.350450\pi$
$212$	1.28692	0.0883857
$213$	6.82687	0.467770
$214$	−4.52044	−0.309011
$215$	−14.3515	−0.978763
$216$	1.00000	0.0680414
$217$	0	0
$218$	4.64958	0.314909
$219$	−13.5040	−0.912518
$220$	7.12497	0.480365
$221$	−26.3861	−1.77492
$222$	−0.366830	−0.0246200
$223$	9.70892	0.650157	0.325079	−	0.945687i	$-0.394609\pi$
$223$	9.70892	0.650157	0.325079	+	0.945687i	$0.394609\pi$
$224$	0	0
$225$	−2.17313	−0.144875
$226$	1.96018	0.130389
$227$	−6.16896	−0.409448	−0.204724	−	0.978820i	$-0.565630\pi$
$227$	−6.16896	−0.409448	−0.204724	+	0.978820i	$0.565630\pi$
$228$	9.55220	0.632610
$229$	−25.8175	−1.70607	−0.853033	−	0.521856i	$-0.825240\pi$
$229$	−25.8175	−1.70607	−0.853033	+	0.521856i	$0.825240\pi$
$230$	1.47122	0.0970094
$231$	0	0
$232$	−9.12497	−0.599083
$233$	12.2499	0.802520	0.401260	−	0.915964i	$-0.368572\pi$
$233$	12.2499	0.802520	0.401260	+	0.915964i	$0.368572\pi$
$234$	1.06457	0.0695930
$235$	−10.9078	−0.711549
$236$	1.93543	0.125986
$237$	−1.17313	−0.0762028
$238$	0	0
$239$	−22.9477	−1.48436	−0.742181	−	0.670200i	$-0.766208\pi$
$239$	−22.9477	−1.48436	−0.742181	+	0.670200i	$0.766208\pi$
$240$	−6.08097	−0.392525
$241$	−4.67015	−0.300831	−0.150415	−	0.988623i	$-0.548061\pi$
$241$	−4.67015	−0.300831	−0.150415	+	0.988623i	$0.548061\pi$
$242$	1.57694	0.101370
$243$	1.00000	0.0641500
$244$	−21.2817	−1.36242
$245$	0	0
$246$	1.04399	0.0665625
$247$	20.6772	1.31566
$248$	0.616763	0.0391645
$249$	15.3421	0.972265
$250$	−3.06457	−0.193820
$251$	−22.4067	−1.41430	−0.707148	−	0.707066i	$-0.750018\pi$
$251$	−22.4067	−1.41430	−0.707148	+	0.707066i	$0.750018\pi$
$252$	0	0
$253$	7.53996	0.474033
$254$	−1.57277	−0.0986844
$255$	−10.5892	−0.663120
$256$	11.0810	0.692561
$257$	−31.1372	−1.94229	−0.971143	−	0.238499i	$-0.923345\pi$
$257$	−31.1372	−1.94229	−0.971143	+	0.238499i	$0.923345\pi$
$258$	−2.16896	−0.135033
$259$	0	0
$260$	−13.6332	−0.845493
$261$	−9.12497	−0.564821
$262$	−3.95885	−0.244578
$263$	24.9547	1.53877	0.769386	−	0.638784i	$-0.220562\pi$
$263$	24.9547	1.53877	0.769386	+	0.638784i	$0.220562\pi$
$264$	2.18953	0.134757
$265$	1.11796	0.0686755
$266$	0	0
$267$	−1.97942	−0.121139
$268$	19.2213	1.17413
$269$	−5.99477	−0.365508	−0.182754	−	0.983159i	$-0.558501\pi$
$269$	−5.99477	−0.365508	−0.182754	+	0.983159i	$0.558501\pi$
$270$	0.427229	0.0260003
$271$	1.97241	0.119816	0.0599078	−	0.998204i	$-0.480919\pi$
$271$	1.97241	0.119816	0.0599078	+	0.998204i	$0.480919\pi$
$272$	22.7787	1.38116
$273$	0	0
$274$	−0.168958	−0.0102071
$275$	−4.75814	−0.286926
$276$	−6.66492	−0.401181
$277$	−2.53579	−0.152361	−0.0761804	−	0.997094i	$-0.524272\pi$
$277$	−2.53579	−0.152361	−0.0761804	+	0.997094i	$0.524272\pi$
$278$	−4.77348	−0.286295
$279$	0.616763	0.0369246
$280$	0	0
$281$	−18.8545	−1.12476	−0.562381	−	0.826878i	$-0.690115\pi$
$281$	−18.8545	−1.12476	−0.562381	+	0.826878i	$0.690115\pi$
$282$	−1.64852	−0.0981678
$283$	5.78989	0.344173	0.172087	−	0.985082i	$-0.444949\pi$
$283$	5.78989	0.344173	0.172087	+	0.985082i	$0.444949\pi$
$284$	−13.2130	−0.784044
$285$	8.29809	0.491537
$286$	2.33091	0.137829
$287$	0	0
$288$	−2.91903	−0.172005
$289$	22.6660	1.33329
$290$	−3.89845	−0.228925
$291$	−3.33508	−0.195506
$292$	26.1361	1.52950
$293$	−7.73472	−0.451867	−0.225934	−	0.974143i	$-0.572543\pi$
$293$	−7.73472	−0.451867	−0.225934	+	0.974143i	$0.572543\pi$
$294$	0	0
$295$	1.68133	0.0978909
$296$	1.44364	0.0839096
$297$	2.18953	0.127050
$298$	2.04505	0.118467
$299$	−14.4272	−0.834348
$300$	4.20594	0.242830
$301$	0	0
$302$	4.53579	0.261005
$303$	3.49180	0.200598
$304$	−17.8503	−1.02378
$305$	−18.4876	−1.05860
$306$	−1.60036	−0.0914863
$307$	−16.4999	−0.941697	−0.470849	−	0.882214i	$-0.656052\pi$
$307$	−16.4999	−0.941697	−0.470849	+	0.882214i	$0.656052\pi$
$308$	0	0
$309$	−8.21712	−0.467456
$310$	0.263499	0.0149657
$311$	−24.9354	−1.41396	−0.706979	−	0.707234i	$-0.749943\pi$
$311$	−24.9354	−1.41396	−0.706979	+	0.707234i	$0.749943\pi$
$312$	−4.18953	−0.237186
$313$	24.1690	1.36611	0.683055	−	0.730367i	$-0.260651\pi$
$313$	24.1690	1.36611	0.683055	+	0.730367i	$0.260651\pi$
$314$	2.65269	0.149700
$315$	0	0
$316$	2.27051	0.127726
$317$	−18.1812	−1.02116	−0.510579	−	0.859831i	$-0.670569\pi$
$317$	−18.1812	−1.02116	−0.510579	+	0.859831i	$0.670569\pi$
$318$	0.168958	0.00947471
$319$	−19.9794	−1.11863
$320$	10.9149	0.610159
$321$	17.7899	0.992935
$322$	0	0
$323$	−31.0838	−1.72955
$324$	−1.93543	−0.107524
$325$	9.10439	0.505021
$326$	0.956008	0.0529484
$327$	−18.2981	−1.01189
$328$	−4.10856	−0.226857
$329$	0	0
$330$	0.935432	0.0514939
$331$	−14.6290	−0.804083	−0.402041	−	0.915622i	$-0.631699\pi$
$331$	−14.6290	−0.804083	−0.402041	+	0.915622i	$0.631699\pi$
$332$	−29.6936	−1.62965
$333$	1.44364	0.0791107
$334$	4.60142	0.251778
$335$	16.6977	0.912295
$336$	0	0
$337$	−19.1526	−1.04331	−0.521653	−	0.853158i	$-0.674684\pi$
$337$	−19.1526	−1.04331	−0.521653	+	0.853158i	$0.674684\pi$
$338$	−1.15672	−0.0629173
$339$	−7.71414	−0.418975
$340$	20.4946	1.11148
$341$	1.35042	0.0731295
$342$	1.25410	0.0678141
$343$	0	0
$344$	8.53579	0.460219
$345$	−5.78989	−0.311717
$346$	−2.45614	−0.132043
$347$	29.4301	1.57989	0.789944	−	0.613178i	$-0.210109\pi$
$347$	29.4301	1.57989	0.789944	+	0.613178i	$0.210109\pi$
$348$	17.6608	0.946716
$349$	−28.9065	−1.54733	−0.773665	−	0.633595i	$-0.781579\pi$
$349$	−28.9065	−1.54733	−0.773665	+	0.633595i	$0.781579\pi$
$350$	0	0
$351$	−4.18953	−0.223621
$352$	−6.39131	−0.340658
$353$	−0.0481609	−0.00256335	−0.00128167	−	0.999999i	$-0.500408\pi$
$353$	−0.0481609	−0.00256335	−0.00128167	+	0.999999i	$0.500408\pi$
$354$	0.254102	0.0135054
$355$	−11.4782	−0.609201
$356$	3.83104	0.203045
$357$	0	0
$358$	2.27574	0.120276
$359$	11.7417	0.619705	0.309852	−	0.950785i	$-0.399720\pi$
$359$	11.7417	0.619705	0.309852	+	0.950785i	$0.399720\pi$
$360$	−1.68133	−0.0886139
$361$	5.35849	0.282026
$362$	−0.123907	−0.00651241
$363$	−6.20594	−0.325727
$364$	0	0
$365$	22.7047	1.18842
$366$	−2.79406	−0.146048
$367$	7.04399	0.367693	0.183847	−	0.982955i	$-0.441145\pi$
$367$	7.04399	0.367693	0.183847	+	0.982955i	$0.441145\pi$
$368$	12.4548	0.649252
$369$	−4.10856	−0.213883
$370$	0.616763	0.0320640
$371$	0	0
$372$	−1.19370	−0.0618906
$373$	31.5316	1.63265	0.816323	−	0.577596i	$-0.196009\pi$
$373$	31.5316	1.63265	0.816323	+	0.577596i	$0.196009\pi$
$374$	−3.50403	−0.181189
$375$	12.0604	0.622796
$376$	6.48763	0.334574
$377$	38.2294	1.96891
$378$	0	0
$379$	−10.5030	−0.539502	−0.269751	−	0.962930i	$-0.586941\pi$
$379$	−10.5030	−0.539502	−0.269751	+	0.962930i	$0.586941\pi$
$380$	−16.0604	−0.823881
$381$	6.18953	0.317099
$382$	−1.29002	−0.0660034
$383$	−23.3023	−1.19069	−0.595345	−	0.803470i	$-0.702985\pi$
$383$	−23.3023	−1.19069	−0.595345	+	0.803470i	$0.702985\pi$
$384$	7.48763	0.382101
$385$	0	0
$386$	−2.37907	−0.121091
$387$	8.53579	0.433899
$388$	6.45481	0.327694
$389$	−33.4835	−1.69768	−0.848839	−	0.528651i	$-0.822698\pi$
$389$	−33.4835	−1.69768	−0.848839	+	0.528651i	$0.822698\pi$
$390$	−1.78989	−0.0906346
$391$	21.6883	1.09683
$392$	0	0
$393$	15.5798	0.785896
$394$	4.12914	0.208023
$395$	1.97241	0.0992430
$396$	−4.23769	−0.212952
$397$	10.6977	0.536904	0.268452	−	0.963293i	$-0.413488\pi$
$397$	10.6977	0.536904	0.268452	+	0.963293i	$0.413488\pi$
$398$	1.68967	0.0846954
$399$	0	0
$400$	−7.85969	−0.392984
$401$	−23.3145	−1.16427	−0.582135	−	0.813092i	$-0.697783\pi$
$401$	−23.3145	−1.16427	−0.582135	+	0.813092i	$0.697783\pi$
$402$	2.52355	0.125863
$403$	−2.58395	−0.128716
$404$	−6.75814	−0.336230
$405$	−1.68133	−0.0835460
$406$	0	0
$407$	3.16089	0.156679
$408$	6.29809	0.311802
$409$	8.65970	0.428194	0.214097	−	0.976812i	$-0.431319\pi$
$409$	8.65970	0.428194	0.214097	+	0.976812i	$0.431319\pi$
$410$	−1.75530	−0.0866879
$411$	0.664924	0.0327983
$412$	15.9037	0.783518
$413$	0	0
$414$	−0.875034	−0.0430056
$415$	−25.7951	−1.26623
$416$	12.2294	0.599594
$417$	18.7857	0.919941
$418$	2.74590	0.134306
$419$	−4.63734	−0.226549	−0.113274	−	0.993564i	$-0.536134\pi$
$419$	−4.63734	−0.226549	−0.113274	+	0.993564i	$0.536134\pi$
$420$	0	0
$421$	1.68133	0.0819430	0.0409715	−	0.999160i	$-0.486955\pi$
$421$	1.68133	0.0819430	0.0409715	+	0.999160i	$0.486955\pi$
$422$	−3.34209	−0.162690
$423$	6.48763	0.315439
$424$	−0.664924	−0.0322916
$425$	−13.6866	−0.663896
$426$	−1.73472	−0.0840475
$427$	0	0
$428$	−34.4311	−1.66429
$429$	−9.17313	−0.442883
$430$	3.64674	0.175861
$431$	11.5040	0.554130	0.277065	−	0.960851i	$-0.410638\pi$
$431$	11.5040	0.554130	0.277065	+	0.960851i	$0.410638\pi$
$432$	3.61676	0.174012
$433$	−24.5069	−1.17773	−0.588863	−	0.808233i	$-0.700424\pi$
$433$	−24.5069	−1.17773	−0.588863	+	0.808233i	$0.700424\pi$
$434$	0	0
$435$	15.3421	0.735597
$436$	35.4147	1.69606
$437$	−16.9958	−0.813021
$438$	3.43140	0.163959
$439$	5.63840	0.269106	0.134553	−	0.990906i	$-0.457040\pi$
$439$	5.63840	0.269106	0.134553	+	0.990906i	$0.457040\pi$
$440$	−3.68133	−0.175501
$441$	0	0
$442$	6.70475	0.318912
$443$	−38.0070	−1.80577	−0.902884	−	0.429885i	$-0.858554\pi$
$443$	−38.0070	−1.80577	−0.902884	+	0.429885i	$0.858554\pi$
$444$	−2.79406	−0.132600
$445$	3.32807	0.157765
$446$	−2.46705	−0.116818
$447$	−8.04816	−0.380665
$448$	0	0
$449$	−11.0357	−0.520805	−0.260402	−	0.965500i	$-0.583855\pi$
$449$	−11.0357	−0.520805	−0.260402	+	0.965500i	$0.583855\pi$
$450$	0.552195	0.0260307
$451$	−8.99583	−0.423597
$452$	14.9302	0.702258
$453$	−17.8503	−0.838680
$454$	1.56754	0.0735684
$455$	0	0
$456$	−4.93543	−0.231123
$457$	−32.3913	−1.51520	−0.757601	−	0.652718i	$-0.773629\pi$
$457$	−32.3913	−1.51520	−0.757601	+	0.652718i	$0.773629\pi$
$458$	6.56026	0.306541
$459$	6.29809	0.293970
$460$	11.2059	0.522480
$461$	−34.9599	−1.62825	−0.814123	−	0.580693i	$-0.802782\pi$
$461$	−34.9599	−1.62825	−0.814123	+	0.580693i	$0.802782\pi$
$462$	0	0
$463$	−22.8063	−1.05990	−0.529949	−	0.848029i	$-0.677789\pi$
$463$	−22.8063	−1.05990	−0.529949	+	0.848029i	$0.677789\pi$
$464$	−33.0028	−1.53212
$465$	−1.03698	−0.0480889
$466$	−3.11273	−0.144194
$467$	36.2416	1.67706	0.838530	−	0.544855i	$-0.183415\pi$
$467$	36.2416	1.67706	0.838530	+	0.544855i	$0.183415\pi$
$468$	8.10856	0.374818
$469$	0	0
$470$	2.77170	0.127849
$471$	−10.4395	−0.481025
$472$	−1.00000	−0.0460287
$473$	18.6894	0.859340
$474$	0.298094	0.0136919
$475$	10.7253	0.492112
$476$	0	0
$477$	−0.664924	−0.0304448
$478$	5.83104	0.266706
$479$	−17.0562	−0.779319	−0.389660	−	0.920959i	$-0.627407\pi$
$479$	−17.0562	−0.779319	−0.389660	+	0.920959i	$0.627407\pi$
$480$	4.90785	0.224012
$481$	−6.04816	−0.275772
$482$	1.18669	0.0540524
$483$	0	0
$484$	12.0112	0.545963
$485$	5.60737	0.254617
$486$	−0.254102	−0.0115263
$487$	15.3473	0.695453	0.347727	−	0.937596i	$-0.386954\pi$
$487$	15.3473	0.695453	0.347727	+	0.937596i	$0.386954\pi$
$488$	10.9958	0.497758
$489$	−3.76231	−0.170137
$490$	0	0
$491$	18.0122	0.812881	0.406440	−	0.913677i	$-0.366770\pi$
$491$	18.0122	0.812881	0.406440	+	0.913677i	$0.366770\pi$
$492$	7.95184	0.358497
$493$	−57.4699	−2.58831
$494$	−5.25410	−0.236393
$495$	−3.68133	−0.165464
$496$	2.23069	0.100161
$497$	0	0
$498$	−3.89845	−0.174694
$499$	−21.6074	−0.967279	−0.483639	−	0.875267i	$-0.660685\pi$
$499$	−21.6074	−0.967279	−0.483639	+	0.875267i	$0.660685\pi$
$500$	−23.3421	−1.04389
$501$	−18.1086	−0.809031
$502$	5.69357	0.254116
$503$	−7.76231	−0.346104	−0.173052	−	0.984913i	$-0.555363\pi$
$503$	−7.76231	−0.346104	−0.173052	+	0.984913i	$0.555363\pi$
$504$	0	0
$505$	−5.87086	−0.261250
$506$	−1.91592	−0.0851729
$507$	4.55220	0.202170
$508$	−11.9794	−0.531501
$509$	−40.7704	−1.80712	−0.903558	−	0.428467i	$-0.859054\pi$
$509$	−40.7704	−1.80712	−0.903558	+	0.428467i	$0.859054\pi$
$510$	2.69073	0.119147
$511$	0	0
$512$	−17.7909	−0.786256
$513$	−4.93543	−0.217905
$514$	7.91202	0.348984
$515$	13.8157	0.608792
$516$	−16.5204	−0.727272
$517$	14.2049	0.624730
$518$	0	0
$519$	9.66598	0.424290
$520$	7.04399	0.308899
$521$	−41.0427	−1.79811	−0.899056	−	0.437834i	$-0.855746\pi$
$521$	−41.0427	−1.79811	−0.899056	+	0.437834i	$0.855746\pi$
$522$	2.31867	0.101485
$523$	22.5686	0.986856	0.493428	−	0.869787i	$-0.335744\pi$
$523$	22.5686	0.986856	0.493428	+	0.869787i	$0.335744\pi$
$524$	−30.1536	−1.31727
$525$	0	0
$526$	−6.34103	−0.276482
$527$	3.88443	0.169208
$528$	7.91903	0.344631
$529$	−11.1414	−0.484408
$530$	−0.284075	−0.0123394
$531$	−1.00000	−0.0433963
$532$	0	0
$533$	17.2130	0.745576
$534$	0.502975	0.0217659
$535$	−29.9107	−1.29315
$536$	−9.93126	−0.428965
$537$	−8.95601	−0.386480
$538$	1.52328	0.0656733
$539$	0	0
$540$	3.25410	0.140034
$541$	35.0357	1.50630	0.753150	−	0.657849i	$-0.228533\pi$
$541$	35.0357	1.50630	0.753150	+	0.657849i	$0.228533\pi$
$542$	−0.501194	−0.0215281
$543$	0.487628	0.0209261
$544$	−18.3843	−0.788220
$545$	30.7651	1.31783
$546$	0	0
$547$	3.70191	0.158282	0.0791410	−	0.996863i	$-0.474782\pi$
$547$	3.70191	0.158282	0.0791410	+	0.996863i	$0.474782\pi$
$548$	−1.28692	−0.0549743
$549$	10.9958	0.469291
$550$	1.20905	0.0515541
$551$	45.0357	1.91858
$552$	3.44364	0.146571
$553$	0	0
$554$	0.644348	0.0273757
$555$	−2.42723	−0.103030
$556$	−36.3585	−1.54194
$557$	−16.7253	−0.708675	−0.354337	−	0.935118i	$-0.615294\pi$
$557$	−16.7253	−0.708675	−0.354337	+	0.935118i	$0.615294\pi$
$558$	−0.156721	−0.00663451
$559$	−35.7610	−1.51253
$560$	0	0
$561$	13.7899	0.582210
$562$	4.79095	0.202094
$563$	−24.9149	−1.05004	−0.525018	−	0.851091i	$-0.675941\pi$
$563$	−24.9149	−1.05004	−0.525018	+	0.851091i	$0.675941\pi$
$564$	−12.5564	−0.528718
$565$	12.9700	0.545653
$566$	−1.47122	−0.0618400
$567$	0	0
$568$	6.82687	0.286449
$569$	42.4548	1.77980	0.889899	−	0.456157i	$-0.150775\pi$
$569$	42.4548	1.77980	0.889899	+	0.456157i	$0.150775\pi$
$570$	−2.10856	−0.0883178
$571$	−32.6977	−1.36836	−0.684179	−	0.729314i	$-0.739839\pi$
$571$	−32.6977	−1.36836	−0.684179	+	0.729314i	$0.739839\pi$
$572$	17.7540	0.742331
$573$	5.07681	0.212087
$574$	0	0
$575$	−7.48346	−0.312082
$576$	−6.49180	−0.270492
$577$	13.2716	0.552503	0.276251	−	0.961085i	$-0.410908\pi$
$577$	13.2716	0.552503	0.276251	+	0.961085i	$0.410908\pi$
$578$	−5.75946	−0.239562
$579$	9.36266	0.389099
$580$	−29.6936	−1.23296
$581$	0	0
$582$	0.847448	0.0351279
$583$	−1.45587	−0.0602961
$584$	−13.5040	−0.558801
$585$	7.04399	0.291233
$586$	1.96541	0.0811901
$587$	14.4067	0.594626	0.297313	−	0.954780i	$-0.403909\pi$
$587$	14.4067	0.594626	0.297313	+	0.954780i	$0.403909\pi$
$588$	0	0
$589$	−3.04399	−0.125426
$590$	−0.427229	−0.0175887
$591$	−16.2499	−0.668433
$592$	5.22129	0.214594
$593$	1.85863	0.0763247	0.0381623	−	0.999272i	$-0.487850\pi$
$593$	1.85863	0.0763247	0.0381623	+	0.999272i	$0.487850\pi$
$594$	−0.556364	−0.0228279
$595$	0	0
$596$	15.5767	0.638045
$597$	−6.64958	−0.272149
$598$	3.66598	0.149913
$599$	−20.2171	−0.826049	−0.413025	−	0.910720i	$-0.635528\pi$
$599$	−20.2171	−0.826049	−0.413025	+	0.910720i	$0.635528\pi$
$600$	−2.17313	−0.0887175
$601$	29.6608	1.20989	0.604944	−	0.796268i	$-0.293196\pi$
$601$	29.6608	1.20989	0.604944	+	0.796268i	$0.293196\pi$
$602$	0	0
$603$	−9.93126	−0.404432
$604$	34.5480	1.40574
$605$	10.4342	0.424212
$606$	−0.887271	−0.0360429
$607$	−8.06040	−0.327161	−0.163581	−	0.986530i	$-0.552304\pi$
$607$	−8.06040	−0.327161	−0.163581	+	0.986530i	$0.552304\pi$
$608$	14.4067	0.584267
$609$	0	0
$610$	4.69774	0.190206
$611$	−27.1801	−1.09959
$612$	−12.1895	−0.492733
$613$	−35.7886	−1.44549	−0.722743	−	0.691117i	$-0.757119\pi$
$613$	−35.7886	−1.44549	−0.722743	+	0.691117i	$0.757119\pi$
$614$	4.19264	0.169201
$615$	6.90785	0.278551
$616$	0	0
$617$	21.7159	0.874250	0.437125	−	0.899401i	$-0.355997\pi$
$617$	21.7159	0.874250	0.437125	+	0.899401i	$0.355997\pi$
$618$	2.08798	0.0839910
$619$	15.3679	0.617688	0.308844	−	0.951113i	$-0.400058\pi$
$619$	15.3679	0.617688	0.308844	+	0.951113i	$0.400058\pi$
$620$	2.00701	0.0806034
$621$	3.44364	0.138188
$622$	6.33614	0.254056
$623$	0	0
$624$	−15.1526	−0.606588
$625$	−9.41188	−0.376475
$626$	−6.14137	−0.245459
$627$	−10.8063	−0.431562
$628$	20.2049	0.806263
$629$	9.09215	0.362528
$630$	0	0
$631$	−24.5358	−0.976754	−0.488377	−	0.872633i	$-0.662411\pi$
$631$	−24.5358	−0.976754	−0.488377	+	0.872633i	$0.662411\pi$
$632$	−1.17313	−0.0466645
$633$	13.1526	0.522767
$634$	4.61987	0.183479
$635$	−10.4067	−0.412975
$636$	1.28692	0.0510295
$637$	0	0
$638$	5.07681	0.200993
$639$	6.82687	0.270067
$640$	−12.5892	−0.497631
$641$	−16.0521	−0.634018	−0.317009	−	0.948422i	$-0.602679\pi$
$641$	−16.0521	−0.634018	−0.317009	+	0.948422i	$0.602679\pi$
$642$	−4.52044	−0.178408
$643$	9.47645	0.373715	0.186857	−	0.982387i	$-0.440170\pi$
$643$	9.47645	0.373715	0.186857	+	0.982387i	$0.440170\pi$
$644$	0	0
$645$	−14.3515	−0.565089
$646$	7.89845	0.310760
$647$	−41.1924	−1.61944	−0.809720	−	0.586817i	$-0.800381\pi$
$647$	−41.1924	−1.61944	−0.809720	+	0.586817i	$0.800381\pi$
$648$	1.00000	0.0392837
$649$	−2.18953	−0.0859467
$650$	−2.31344	−0.0907406
$651$	0	0
$652$	7.28169	0.285173
$653$	14.0757	0.550827	0.275413	−	0.961326i	$-0.411185\pi$
$653$	14.0757	0.550827	0.275413	+	0.961326i	$0.411185\pi$
$654$	4.64958	0.181813
$655$	−26.1948	−1.02351
$656$	−14.8597	−0.580173
$657$	−13.5040	−0.526843
$658$	0	0
$659$	−20.6220	−0.803319	−0.401659	−	0.915789i	$-0.631566\pi$
$659$	−20.6220	−0.803319	−0.401659	+	0.915789i	$0.631566\pi$
$660$	7.12497	0.277339
$661$	30.1414	1.17236	0.586182	−	0.810180i	$-0.300630\pi$
$661$	30.1414	1.17236	0.586182	+	0.810180i	$0.300630\pi$
$662$	3.71725	0.144475
$663$	−26.3861	−1.02475
$664$	15.3421	0.595388
$665$	0	0
$666$	−0.366830	−0.0142144
$667$	−31.4231	−1.21671
$668$	35.0479	1.35604
$669$	9.70892	0.375368
$670$	−4.24292	−0.163918
$671$	24.0757	0.929434
$672$	0	0
$673$	3.27468	0.126230	0.0631148	−	0.998006i	$-0.479897\pi$
$673$	3.27468	0.126230	0.0631148	+	0.998006i	$0.479897\pi$
$674$	4.86670	0.187458
$675$	−2.17313	−0.0836437
$676$	−8.81047	−0.338864
$677$	−19.6126	−0.753773	−0.376887	−	0.926259i	$-0.623005\pi$
$677$	−19.6126	−0.753773	−0.376887	+	0.926259i	$0.623005\pi$
$678$	1.96018	0.0752801
$679$	0	0
$680$	−10.5892	−0.406076
$681$	−6.16896	−0.236395
$682$	−0.343145	−0.0131397
$683$	12.1812	0.466101	0.233050	−	0.972465i	$-0.425129\pi$
$683$	12.1812	0.466101	0.233050	+	0.972465i	$0.425129\pi$
$684$	9.55220	0.365237
$685$	−1.11796	−0.0427149
$686$	0	0
$687$	−25.8175	−0.984998
$688$	30.8719	1.17698
$689$	2.78572	0.106128
$690$	1.47122	0.0560084
$691$	13.8052	0.525176	0.262588	−	0.964908i	$-0.415424\pi$
$691$	13.8052	0.525176	0.262588	+	0.964908i	$0.415424\pi$
$692$	−18.7079	−0.711166
$693$	0	0
$694$	−7.47823	−0.283870
$695$	−31.5850	−1.19809
$696$	−9.12497	−0.345881
$697$	−25.8761	−0.980127
$698$	7.34520	0.278020
$699$	12.2499	0.463335
$700$	0	0
$701$	−9.06980	−0.342561	−0.171281	−	0.985222i	$-0.554791\pi$
$701$	−9.06980	−0.342561	−0.171281	+	0.985222i	$0.554791\pi$
$702$	1.06457	0.0401795
$703$	−7.12497	−0.268723
$704$	−14.2140	−0.535711
$705$	−10.9078	−0.410813
$706$	0.0122378	0.000460575 0
$707$	0	0
$708$	1.93543	0.0727380
$709$	26.2171	0.984605	0.492302	−	0.870424i	$-0.336155\pi$
$709$	26.2171	0.984605	0.492302	+	0.870424i	$0.336155\pi$
$710$	2.91664	0.109459
$711$	−1.17313	−0.0439957
$712$	−1.97942	−0.0741821
$713$	2.12391	0.0795409
$714$	0	0
$715$	15.4231	0.576790
$716$	17.3337	0.647793
$717$	−22.9477	−0.856996
$718$	−2.98359	−0.111347
$719$	37.5972	1.40214	0.701070	−	0.713092i	$-0.252706\pi$
$719$	37.5972	1.40214	0.701070	+	0.713092i	$0.252706\pi$
$720$	−6.08097	−0.226625
$721$	0	0
$722$	−1.36160	−0.0506736
$723$	−4.67015	−0.173685
$724$	−0.943770	−0.0350749
$725$	19.8297	0.736457
$726$	1.57694	0.0585257
$727$	−42.3463	−1.57054	−0.785268	−	0.619156i	$-0.787475\pi$
$727$	−42.3463	−1.57054	−0.785268	+	0.619156i	$0.787475\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−5.76931	−0.213532
$731$	53.7592	1.98836
$732$	−21.2817	−0.786594
$733$	5.96408	0.220288	0.110144	−	0.993916i	$-0.464869\pi$
$733$	5.96408	0.220288	0.110144	+	0.993916i	$0.464869\pi$
$734$	−1.78989	−0.0660661
$735$	0	0
$736$	−10.0521	−0.370524
$737$	−21.7448	−0.800981
$738$	1.04399	0.0384299
$739$	39.9435	1.46935	0.734673	−	0.678422i	$-0.237336\pi$
$739$	39.9435	1.46935	0.734673	+	0.678422i	$0.237336\pi$
$740$	4.69774	0.172692
$741$	20.6772	0.759595
$742$	0	0
$743$	22.7407	0.834274	0.417137	−	0.908844i	$-0.363033\pi$
$743$	22.7407	0.834274	0.417137	+	0.908844i	$0.363033\pi$
$744$	0.616763	0.0226116
$745$	13.5316	0.495760
$746$	−8.01224	−0.293349
$747$	15.3421	0.561338
$748$	−26.6894	−0.975861
$749$	0	0
$750$	−3.06457	−0.111902
$751$	17.8052	0.649722	0.324861	−	0.945762i	$-0.394682\pi$
$751$	17.8052	0.649722	0.324861	+	0.945762i	$0.394682\pi$
$752$	23.4642	0.855652
$753$	−22.4067	−0.816544
$754$	−9.71414	−0.353768
$755$	30.0122	1.09226
$756$	0	0
$757$	27.4353	0.997153	0.498576	−	0.866846i	$-0.333856\pi$
$757$	27.4353	0.997153	0.498576	+	0.866846i	$0.333856\pi$
$758$	2.66882	0.0969360
$759$	7.53996	0.273683
$760$	8.29809	0.301003
$761$	−10.1812	−0.369068	−0.184534	−	0.982826i	$-0.559078\pi$
$761$	−10.1812	−0.369068	−0.184534	+	0.982826i	$0.559078\pi$
$762$	−1.57277	−0.0569755
$763$	0	0
$764$	−9.82581	−0.355485
$765$	−10.5892	−0.382853
$766$	5.92114	0.213940
$767$	4.18953	0.151275
$768$	11.0810	0.399850
$769$	−38.0398	−1.37175	−0.685876	−	0.727719i	$-0.740581\pi$
$769$	−38.0398	−1.37175	−0.685876	+	0.727719i	$0.740581\pi$
$770$	0	0
$771$	−31.1372	−1.12138
$772$	−18.1208	−0.652182
$773$	44.1676	1.58860	0.794300	−	0.607526i	$-0.207838\pi$
$773$	44.1676	1.58860	0.794300	+	0.607526i	$0.207838\pi$
$774$	−2.16896	−0.0779616
$775$	−1.34030	−0.0481452
$776$	−3.33508	−0.119722
$777$	0	0
$778$	8.50820	0.305034
$779$	20.2775	0.726517
$780$	−13.6332	−0.488146
$781$	14.9477	0.534870
$782$	−5.51104	−0.197075
$783$	−9.12497	−0.326100
$784$	0	0
$785$	17.5522	0.626465
$786$	−3.95885	−0.141207
$787$	16.3379	0.582384	0.291192	−	0.956665i	$-0.405948\pi$
$787$	16.3379	0.582384	0.291192	+	0.956665i	$0.405948\pi$
$788$	31.4506	1.12038
$789$	24.9547	0.888410
$790$	−0.501194	−0.0178317
$791$	0	0
$792$	2.18953	0.0778017
$793$	−46.0674	−1.63590
$794$	−2.71831	−0.0964693
$795$	1.11796	0.0396498
$796$	12.8698	0.456158
$797$	32.9424	1.16688	0.583441	−	0.812156i	$-0.301706\pi$
$797$	32.9424	1.16688	0.583441	+	0.812156i	$0.301706\pi$
$798$	0	0
$799$	40.8597	1.44551
$800$	6.34341	0.224274
$801$	−1.97942	−0.0699395
$802$	5.92425	0.209193
$803$	−29.5675	−1.04342
$804$	19.2213	0.677883
$805$	0	0
$806$	0.656586	0.0231273
$807$	−5.99477	−0.211026
$808$	3.49180	0.122841
$809$	−51.9659	−1.82702	−0.913511	−	0.406814i	$-0.866640\pi$
$809$	−51.9659	−1.82702	−0.913511	+	0.406814i	$0.866640\pi$
$810$	0.427229	0.0150113
$811$	−26.9424	−0.946077	−0.473039	−	0.881042i	$-0.656843\pi$
$811$	−26.9424	−0.946077	−0.473039	+	0.881042i	$0.656843\pi$
$812$	0	0
$813$	1.97241	0.0691756
$814$	−0.803187	−0.0281517
$815$	6.32568	0.221579
$816$	22.7787	0.797414
$817$	−42.1278	−1.47387
$818$	−2.20044	−0.0769367
$819$	0	0
$820$	−13.3697	−0.466889
$821$	−27.8914	−0.973418	−0.486709	−	0.873564i	$-0.661803\pi$
$821$	−27.8914	−0.973418	−0.486709	+	0.873564i	$0.661803\pi$
$822$	−0.168958	−0.00589310
$823$	18.3103	0.638258	0.319129	−	0.947711i	$-0.396610\pi$
$823$	18.3103	0.638258	0.319129	+	0.947711i	$0.396610\pi$
$824$	−8.21712	−0.286257
$825$	−4.75814	−0.165657
$826$	0	0
$827$	−4.37384	−0.152093	−0.0760467	−	0.997104i	$-0.524230\pi$
$827$	−4.37384	−0.152093	−0.0760467	+	0.997104i	$0.524230\pi$
$828$	−6.66492	−0.231622
$829$	−30.5204	−1.06002	−0.530009	−	0.847992i	$-0.677812\pi$
$829$	−30.5204	−1.06002	−0.530009	+	0.847992i	$0.677812\pi$
$830$	6.55458	0.227513
$831$	−2.53579	−0.0879655
$832$	27.1976	0.942907
$833$	0	0
$834$	−4.77348	−0.165292
$835$	30.4465	1.05364
$836$	20.9149	0.723355
$837$	0.616763	0.0213184
$838$	1.17836	0.0407056
$839$	0.859686	0.0296797	0.0148398	−	0.999890i	$-0.495276\pi$
$839$	0.859686	0.0296797	0.0148398	+	0.999890i	$0.495276\pi$
$840$	0	0
$841$	54.2650	1.87121
$842$	−0.427229	−0.0147233
$843$	−18.8545	−0.649382
$844$	−25.4559	−0.876227
$845$	−7.65375	−0.263297
$846$	−1.64852	−0.0566772
$847$	0	0
$848$	−2.40487	−0.0825836
$849$	5.78989	0.198709
$850$	3.47778	0.119287
$851$	4.97136	0.170416
$852$	−13.2130	−0.452668
$853$	−50.4741	−1.72820	−0.864099	−	0.503321i	$-0.832111\pi$
$853$	−50.4741	−1.72820	−0.864099	+	0.503321i	$0.832111\pi$
$854$	0	0
$855$	8.29809	0.283789
$856$	17.7899	0.608046
$857$	−38.4946	−1.31495	−0.657476	−	0.753476i	$-0.728376\pi$
$857$	−38.4946	−1.31495	−0.657476	+	0.753476i	$0.728376\pi$
$858$	2.33091	0.0795759
$859$	27.1044	0.924790	0.462395	−	0.886674i	$-0.346990\pi$
$859$	27.1044	0.924790	0.462395	+	0.886674i	$0.346990\pi$
$860$	27.7763	0.947165
$861$	0	0
$862$	−2.92319	−0.0995644
$863$	10.6443	0.362338	0.181169	−	0.983452i	$-0.442012\pi$
$863$	10.6443	0.362338	0.181169	+	0.983452i	$0.442012\pi$
$864$	−2.91903	−0.0993073
$865$	−16.2517	−0.552575
$866$	6.22724	0.211610
$867$	22.6660	0.769777
$868$	0	0
$869$	−2.56860	−0.0871339
$870$	−3.89845	−0.132170
$871$	41.6074	1.40981
$872$	−18.2981	−0.619652
$873$	−3.33508	−0.112875
$874$	4.31867	0.146081
$875$	0	0
$876$	26.1361	0.883058
$877$	40.0328	1.35181	0.675906	−	0.736988i	$-0.263753\pi$
$877$	40.0328	1.35181	0.675906	+	0.736988i	$0.263753\pi$
$878$	−1.43273	−0.0483522
$879$	−7.73472	−0.260886
$880$	−13.3145	−0.448832
$881$	−29.9588	−1.00934	−0.504670	−	0.863313i	$-0.668386\pi$
$881$	−29.9588	−1.00934	−0.504670	+	0.863313i	$0.668386\pi$
$882$	0	0
$883$	−12.3239	−0.414732	−0.207366	−	0.978263i	$-0.566489\pi$
$883$	−12.3239	−0.414732	−0.207366	+	0.978263i	$0.566489\pi$
$884$	51.0685	1.71762
$885$	1.68133	0.0565173
$886$	9.65765	0.324455
$887$	−25.4559	−0.854725	−0.427362	−	0.904080i	$-0.640557\pi$
$887$	−25.4559	−0.854725	−0.427362	+	0.904080i	$0.640557\pi$
$888$	1.44364	0.0484452
$889$	0	0
$890$	−0.845667	−0.0283468
$891$	2.18953	0.0733521
$892$	−18.7909	−0.629168
$893$	−32.0192	−1.07148
$894$	2.04505	0.0683967
$895$	15.0580	0.503334
$896$	0	0
$897$	−14.4272	−0.481711
$898$	2.80418	0.0935766
$899$	−5.62794	−0.187702
$900$	4.20594	0.140198
$901$	−4.18775	−0.139514
$902$	2.28586	0.0761107
$903$	0	0
$904$	−7.71414	−0.256569
$905$	−0.819863	−0.0272532
$906$	4.53579	0.150691
$907$	38.4863	1.27792	0.638958	−	0.769241i	$-0.279366\pi$
$907$	38.4863	1.27792	0.638958	+	0.769241i	$0.279366\pi$
$908$	11.9396	0.396230
$909$	3.49180	0.115816
$910$	0	0
$911$	21.2234	0.703163	0.351581	−	0.936157i	$-0.385644\pi$
$911$	21.2234	0.703163	0.351581	+	0.936157i	$0.385644\pi$
$912$	−17.8503	−0.591082
$913$	33.5920	1.11173
$914$	8.23069	0.272247
$915$	−18.4876	−0.611182
$916$	49.9680	1.65099
$917$	0	0
$918$	−1.60036	−0.0528196
$919$	46.3051	1.52746	0.763732	−	0.645533i	$-0.223365\pi$
$919$	46.3051	1.52746	0.763732	+	0.645533i	$0.223365\pi$
$920$	−5.78989	−0.190887
$921$	−16.4999	−0.543689
$922$	8.88337	0.292558
$923$	−28.6014	−0.941427
$924$	0	0
$925$	−3.13720	−0.103151
$926$	5.79512	0.190439
$927$	−8.21712	−0.269886
$928$	26.6360	0.874370
$929$	−31.9313	−1.04763	−0.523815	−	0.851832i	$-0.675492\pi$
$929$	−31.9313	−1.04763	−0.523815	+	0.851832i	$0.675492\pi$
$930$	0.263499	0.00864047
$931$	0	0
$932$	−23.7089	−0.776611
$933$	−24.9354	−0.816349
$934$	−9.20905	−0.301329
$935$	−23.1854	−0.758243
$936$	−4.18953	−0.136939
$937$	33.6813	1.10032	0.550161	−	0.835059i	$-0.314567\pi$
$937$	33.6813	1.10032	0.550161	+	0.835059i	$0.314567\pi$
$938$	0	0
$939$	24.1690	0.788724
$940$	21.1114	0.688578
$941$	22.6977	0.739925	0.369963	−	0.929047i	$-0.379371\pi$
$941$	22.6977	0.739925	0.369963	+	0.929047i	$0.379371\pi$
$942$	2.65269	0.0864292
$943$	−14.1484	−0.460735
$944$	−3.61676	−0.117716
$945$	0	0
$946$	−4.74901	−0.154404
$947$	22.5533	0.732882	0.366441	−	0.930441i	$-0.380576\pi$
$947$	22.5533	0.732882	0.366441	+	0.930441i	$0.380576\pi$
$948$	2.27051	0.0737427
$949$	56.5756	1.83652
$950$	−2.72532	−0.0884211
$951$	−18.1812	−0.589566
$952$	0	0
$953$	−10.3791	−0.336211	−0.168105	−	0.985769i	$-0.553765\pi$
$953$	−10.3791	−0.336211	−0.168105	+	0.985769i	$0.553765\pi$
$954$	0.168958	0.00547023
$955$	−8.53579	−0.276212
$956$	44.4137	1.43644
$957$	−19.9794	−0.645843
$958$	4.33402	0.140026
$959$	0	0
$960$	10.9149	0.352275
$961$	−30.6196	−0.987729
$962$	1.53685	0.0495500
$963$	17.7899	0.573271
$964$	9.03876	0.291119
$965$	−15.7417	−0.506744
$966$	0	0
$967$	32.1913	1.03520	0.517601	−	0.855622i	$-0.326825\pi$
$967$	32.1913	1.03520	0.517601	+	0.855622i	$0.326825\pi$
$968$	−6.20594	−0.199466
$969$	−31.0838	−0.998556
$970$	−1.42484	−0.0457489
$971$	33.1114	1.06260	0.531298	−	0.847185i	$-0.321705\pi$
$971$	33.1114	1.06260	0.531298	+	0.847185i	$0.321705\pi$
$972$	−1.93543	−0.0620790
$973$	0	0
$974$	−3.89978	−0.124957
$975$	9.10439	0.291574
$976$	39.7693	1.27298
$977$	12.2307	0.391294	0.195647	−	0.980674i	$-0.437319\pi$
$977$	12.2307	0.391294	0.195647	+	0.980674i	$0.437319\pi$
$978$	0.956008	0.0305698
$979$	−4.33402	−0.138516
$980$	0	0
$981$	−18.2981	−0.584213
$982$	−4.57694	−0.146056
$983$	7.26111	0.231593	0.115797	−	0.993273i	$-0.463058\pi$
$983$	7.26111	0.231593	0.115797	+	0.993273i	$0.463058\pi$
$984$	−4.10856	−0.130976
$985$	27.3215	0.870536
$986$	14.6032	0.465061
$987$	0	0
$988$	−40.0192	−1.27318
$989$	29.3941	0.934679
$990$	0.935432	0.0297300
$991$	−20.1054	−0.638671	−0.319335	−	0.947642i	$-0.603460\pi$
$991$	−20.1054	−0.638671	−0.319335	+	0.947642i	$0.603460\pi$
$992$	−1.80035	−0.0571611
$993$	−14.6290	−0.464237
$994$	0	0
$995$	11.1801	0.354434
$996$	−29.6936	−0.940877
$997$	42.3173	1.34020	0.670102	−	0.742269i	$-0.266250\pi$
$997$	42.3173	1.34020	0.670102	+	0.742269i	$0.266250\pi$
$998$	5.49047	0.173798
$999$	1.44364	0.0456746

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8673.2.a.s.1.2		3
7.6	odd	2		177.2.a.d.1.2	✓	3
21.20	even	2		531.2.a.d.1.2		3
28.27	even	2		2832.2.a.t.1.3		3
35.34	odd	2		4425.2.a.w.1.2		3
84.83	odd	2		8496.2.a.bl.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.a.d.1.2	✓	3	7.6	odd	2
531.2.a.d.1.2		3	21.20	even	2
2832.2.a.t.1.3		3	28.27	even	2
4425.2.a.w.1.2		3	35.34	odd	2
8496.2.a.bl.1.1		3	84.83	odd	2
8673.2.a.s.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:	\( N \)	\(=\)	\( 8673 = 3 \cdot 7^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8673.a (trivial)

\(f(q)\)	\(=\)	\(q-0.254102 q^{2} +1.00000 q^{3} -1.93543 q^{4} -1.68133 q^{5} -0.254102 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.254102 q^{2} +1.00000 q^{3} -1.93543 q^{4} -1.68133 q^{5} -0.254102 q^{6} +1.00000 q^{8} +1.00000 q^{9} +0.427229 q^{10} +2.18953 q^{11} -1.93543 q^{12} -4.18953 q^{13} -1.68133 q^{15} +3.61676 q^{16} +6.29809 q^{17} -0.254102 q^{18} -4.93543 q^{19} +3.25410 q^{20} -0.556364 q^{22} +3.44364 q^{23} +1.00000 q^{24} -2.17313 q^{25} +1.06457 q^{26} +1.00000 q^{27} -9.12497 q^{29} +0.427229 q^{30} +0.616763 q^{31} -2.91903 q^{32} +2.18953 q^{33} -1.60036 q^{34} -1.93543 q^{36} +1.44364 q^{37} +1.25410 q^{38} -4.18953 q^{39} -1.68133 q^{40} -4.10856 q^{41} +8.53579 q^{43} -4.23769 q^{44} -1.68133 q^{45} -0.875034 q^{46} +6.48763 q^{47} +3.61676 q^{48} +0.552195 q^{50} +6.29809 q^{51} +8.10856 q^{52} -0.664924 q^{53} -0.254102 q^{54} -3.68133 q^{55} -4.93543 q^{57} +2.31867 q^{58} -1.00000 q^{59} +3.25410 q^{60} +10.9958 q^{61} -0.156721 q^{62} -6.49180 q^{64} +7.04399 q^{65} -0.556364 q^{66} -9.93126 q^{67} -12.1895 q^{68} +3.44364 q^{69} +6.82687 q^{71} +1.00000 q^{72} -13.5040 q^{73} -0.366830 q^{74} -2.17313 q^{75} +9.55220 q^{76} +1.06457 q^{78} -1.17313 q^{79} -6.08097 q^{80} +1.00000 q^{81} +1.04399 q^{82} +15.3421 q^{83} -10.5892 q^{85} -2.16896 q^{86} -9.12497 q^{87} +2.18953 q^{88} -1.97942 q^{89} +0.427229 q^{90} -6.66492 q^{92} +0.616763 q^{93} -1.64852 q^{94} +8.29809 q^{95} -2.91903 q^{96} -3.33508 q^{97} +2.18953 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{3} + 2 q^{4} + 2 q^{5} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^3 + 2 * q^4 + 2 * q^5 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{3} + 2 q^{4} + 2 q^{5} + 3 q^{8} + 3 q^{9} - 5 q^{10} - 2 q^{11} + 2 q^{12} - 4 q^{13} + 2 q^{15} - 4 q^{16} - 3 q^{17} - 7 q^{19} + 9 q^{20} - 11 q^{22} + q^{23} + 3 q^{24} - q^{25} + 11 q^{26} + 3 q^{27} - 11 q^{29} - 5 q^{30} - 13 q^{31} - 4 q^{32} - 2 q^{33} + 7 q^{34} + 2 q^{36} - 5 q^{37} + 3 q^{38} - 4 q^{39} + 2 q^{40} + q^{41} + 6 q^{43} - 15 q^{44} + 2 q^{45} - 19 q^{46} - 11 q^{47} - 4 q^{48} - 21 q^{50} - 3 q^{51} + 11 q^{52} + 2 q^{53} - 4 q^{55} - 7 q^{57} + 14 q^{58} - 3 q^{59} + 9 q^{60} + q^{61} + 2 q^{62} - 21 q^{64} - 11 q^{66} + 10 q^{67} - 28 q^{68} + q^{69} + 26 q^{71} + 3 q^{72} - 7 q^{73} - 19 q^{74} - q^{75} + 6 q^{76} + 11 q^{78} + 2 q^{79} - 23 q^{80} + 3 q^{81} - 18 q^{82} + 3 q^{83} - 35 q^{85} + 31 q^{86} - 11 q^{87} - 2 q^{88} + 23 q^{89} - 5 q^{90} - 16 q^{92} - 13 q^{93} - 4 q^{94} + 3 q^{95} - 4 q^{96} - 14 q^{97} - 2 q^{99}+O(q^{100}) \) 3 * q + 3 * q^3 + 2 * q^4 + 2 * q^5 + 3 * q^8 + 3 * q^9 - 5 * q^10 - 2 * q^11 + 2 * q^12 - 4 * q^13 + 2 * q^15 - 4 * q^16 - 3 * q^17 - 7 * q^19 + 9 * q^20 - 11 * q^22 + q^23 + 3 * q^24 - q^25 + 11 * q^26 + 3 * q^27 - 11 * q^29 - 5 * q^30 - 13 * q^31 - 4 * q^32 - 2 * q^33 + 7 * q^34 + 2 * q^36 - 5 * q^37 + 3 * q^38 - 4 * q^39 + 2 * q^40 + q^41 + 6 * q^43 - 15 * q^44 + 2 * q^45 - 19 * q^46 - 11 * q^47 - 4 * q^48 - 21 * q^50 - 3 * q^51 + 11 * q^52 + 2 * q^53 - 4 * q^55 - 7 * q^57 + 14 * q^58 - 3 * q^59 + 9 * q^60 + q^61 + 2 * q^62 - 21 * q^64 - 11 * q^66 + 10 * q^67 - 28 * q^68 + q^69 + 26 * q^71 + 3 * q^72 - 7 * q^73 - 19 * q^74 - q^75 + 6 * q^76 + 11 * q^78 + 2 * q^79 - 23 * q^80 + 3 * q^81 - 18 * q^82 + 3 * q^83 - 35 * q^85 + 31 * q^86 - 11 * q^87 - 2 * q^88 + 23 * q^89 - 5 * q^90 - 16 * q^92 - 13 * q^93 - 4 * q^94 + 3 * q^95 - 4 * q^96 - 14 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more