LMFDB - Embedded newform 931.2.a.n.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(1,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, 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("931.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.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:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 6x^{5} + 18x^{4} + 4x^{3} - 12x^{2} - x + 1 $ x^7 - 3x^6 - 6x^5 + 18x^4 + 4x^3 - 12*x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 133)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-2.29398$ of defining polynomial
Character	$\chi$	$=$	931.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.59421 q^{2} -2.89925 q^{3} +4.72991 q^{4} +1.85806 q^{5} -7.52126 q^{6} +7.08194 q^{8} +5.40568 q^{9} +O(q^{10})$	\(q+2.59421 q^{2} -2.89925 q^{3} +4.72991 q^{4} +1.85806 q^{5} -7.52126 q^{6} +7.08194 q^{8} +5.40568 q^{9} +4.82019 q^{10} -3.51514 q^{11} -13.7132 q^{12} +3.68871 q^{13} -5.38698 q^{15} +8.91219 q^{16} +4.85806 q^{17} +14.0234 q^{18} +1.00000 q^{19} +8.78844 q^{20} -9.11899 q^{22} +1.71956 q^{23} -20.5323 q^{24} -1.54762 q^{25} +9.56927 q^{26} -6.97467 q^{27} +3.20098 q^{29} -13.9749 q^{30} +0.627857 q^{31} +8.95619 q^{32} +10.1913 q^{33} +12.6028 q^{34} +25.5683 q^{36} +1.62286 q^{37} +2.59421 q^{38} -10.6945 q^{39} +13.1587 q^{40} -5.18841 q^{41} +6.18419 q^{43} -16.6263 q^{44} +10.0441 q^{45} +4.46089 q^{46} -5.43568 q^{47} -25.8387 q^{48} -4.01484 q^{50} -14.0847 q^{51} +17.4472 q^{52} +5.81446 q^{53} -18.0937 q^{54} -6.53133 q^{55} -2.89925 q^{57} +8.30400 q^{58} -4.88969 q^{59} -25.4799 q^{60} -7.36829 q^{61} +1.62879 q^{62} +5.40982 q^{64} +6.85384 q^{65} +26.4383 q^{66} -0.0879948 q^{67} +22.9782 q^{68} -4.98544 q^{69} +15.7990 q^{71} +38.2827 q^{72} +3.01818 q^{73} +4.21003 q^{74} +4.48694 q^{75} +4.72991 q^{76} -27.7438 q^{78} -14.7534 q^{79} +16.5594 q^{80} +4.00431 q^{81} -13.4598 q^{82} -4.03094 q^{83} +9.02656 q^{85} +16.0431 q^{86} -9.28045 q^{87} -24.8940 q^{88} -1.32673 q^{89} +26.0564 q^{90} +8.13335 q^{92} -1.82032 q^{93} -14.1013 q^{94} +1.85806 q^{95} -25.9663 q^{96} -4.69587 q^{97} -19.0017 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 2 q^{2} - 2 q^{3} + 10 q^{4} - 2 q^{5} - 4 q^{6} + 12 q^{8} + 15 q^{9}+O(q^{10}) $ 7 * q + 2 * q^2 - 2 * q^3 + 10 * q^4 - 2 * q^5 - 4 * q^6 + 12 * q^8 + 15 * q^9	$ 7 q + 2 q^{2} - 2 q^{3} + 10 q^{4} - 2 q^{5} - 4 q^{6} + 12 q^{8} + 15 q^{9} + 7 q^{11} - 22 q^{12} + 6 q^{13} + 2 q^{15} + 24 q^{16} + 19 q^{17} - 12 q^{18} + 7 q^{19} - 8 q^{20} - 6 q^{22} - q^{23} + 20 q^{24} - 3 q^{25} + 12 q^{26} - 14 q^{27} + 24 q^{29} - 20 q^{30} + 26 q^{32} - 14 q^{33} + 6 q^{34} + 46 q^{36} + 8 q^{37} + 2 q^{38} + 16 q^{39} - 10 q^{40} - 4 q^{41} + 4 q^{43} + 26 q^{44} + 14 q^{45} - 16 q^{46} + 5 q^{47} - 28 q^{48} + 16 q^{50} - 4 q^{51} + 42 q^{52} + 20 q^{53} - 24 q^{54} - 30 q^{55} - 2 q^{57} - 16 q^{59} - 44 q^{60} + 5 q^{61} + 24 q^{62} + 32 q^{64} + 26 q^{65} + 68 q^{66} - 4 q^{67} + 22 q^{68} - 36 q^{69} + 12 q^{71} + 3 q^{73} - 4 q^{74} + 18 q^{75} + 10 q^{76} - 14 q^{78} - 20 q^{79} - 4 q^{80} + 27 q^{81} - 48 q^{82} - 11 q^{83} + 26 q^{85} + 36 q^{86} - 16 q^{87} - 32 q^{88} - 10 q^{89} + 32 q^{90} - 30 q^{92} - 4 q^{93} + 16 q^{94} - 2 q^{95} - 12 q^{96} - 4 q^{97} + 15 q^{99}+O(q^{100}) $ 7 * q + 2 * q^2 - 2 * q^3 + 10 * q^4 - 2 * q^5 - 4 * q^6 + 12 * q^8 + 15 * q^9 + 7 * q^11 - 22 * q^12 + 6 * q^13 + 2 * q^15 + 24 * q^16 + 19 * q^17 - 12 * q^18 + 7 * q^19 - 8 * q^20 - 6 * q^22 - q^23 + 20 * q^24 - 3 * q^25 + 12 * q^26 - 14 * q^27 + 24 * q^29 - 20 * q^30 + 26 * q^32 - 14 * q^33 + 6 * q^34 + 46 * q^36 + 8 * q^37 + 2 * q^38 + 16 * q^39 - 10 * q^40 - 4 * q^41 + 4 * q^43 + 26 * q^44 + 14 * q^45 - 16 * q^46 + 5 * q^47 - 28 * q^48 + 16 * q^50 - 4 * q^51 + 42 * q^52 + 20 * q^53 - 24 * q^54 - 30 * q^55 - 2 * q^57 - 16 * q^59 - 44 * q^60 + 5 * q^61 + 24 * q^62 + 32 * q^64 + 26 * q^65 + 68 * q^66 - 4 * q^67 + 22 * q^68 - 36 * q^69 + 12 * q^71 + 3 * q^73 - 4 * q^74 + 18 * q^75 + 10 * q^76 - 14 * q^78 - 20 * q^79 - 4 * q^80 + 27 * q^81 - 48 * q^82 - 11 * q^83 + 26 * q^85 + 36 * q^86 - 16 * q^87 - 32 * q^88 - 10 * q^89 + 32 * q^90 - 30 * q^92 - 4 * q^93 + 16 * q^94 - 2 * q^95 - 12 * q^96 - 4 * q^97 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.59421	1.83438	0.917190	−	0.398449i	$-0.130452\pi$
$2$	2.59421	1.83438	0.917190	+	0.398449i	$0.130452\pi$
$3$	−2.89925	−1.67389	−0.836943	−	0.547291i	$-0.815659\pi$
$3$	−2.89925	−1.67389	−0.836943	+	0.547291i	$0.815659\pi$
$4$	4.72991	2.36495
$5$	1.85806	0.830949	0.415475	−	0.909605i	$-0.363616\pi$
$5$	1.85806	0.830949	0.415475	+	0.909605i	$0.363616\pi$
$6$	−7.52126	−3.07054
$7$	0	0
$7$	0	0
$8$	7.08194	2.50384
$9$	5.40568	1.80189
$10$	4.82019	1.52428
$11$	−3.51514	−1.05985	−0.529927	−	0.848043i	$-0.677781\pi$
$11$	−3.51514	−1.05985	−0.529927	+	0.848043i	$0.677781\pi$
$12$	−13.7132	−3.95866
$13$	3.68871	1.02306	0.511532	−	0.859264i	$-0.329078\pi$
$13$	3.68871	1.02306	0.511532	+	0.859264i	$0.329078\pi$
$14$	0	0
$15$	−5.38698	−1.39091
$16$	8.91219	2.22805
$17$	4.85806	1.17825	0.589126	−	0.808041i	$-0.299472\pi$
$17$	4.85806	1.17825	0.589126	+	0.808041i	$0.299472\pi$
$18$	14.0234	3.30536
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	8.78844	1.96516
$21$	0	0
$22$	−9.11899	−1.94418
$23$	1.71956	0.358553	0.179276	−	0.983799i	$-0.442624\pi$
$23$	1.71956	0.358553	0.179276	+	0.983799i	$0.442624\pi$
$24$	−20.5323	−4.19115
$25$	−1.54762	−0.309524
$26$	9.56927	1.87669
$27$	−6.97467	−1.34228
$28$	0	0
$29$	3.20098	0.594407	0.297203	−	0.954814i	$-0.403946\pi$
$29$	3.20098	0.594407	0.297203	+	0.954814i	$0.403946\pi$
$30$	−13.9749	−2.55146
$31$	0.627857	0.112766	0.0563832	−	0.998409i	$-0.482043\pi$
$31$	0.627857	0.112766	0.0563832	+	0.998409i	$0.482043\pi$
$32$	8.95619	1.58325
$33$	10.1913	1.77407
$34$	12.6028	2.16136
$35$	0	0
$36$	25.5683	4.26139
$37$	1.62286	0.266797	0.133398	−	0.991063i	$-0.457411\pi$
$37$	1.62286	0.266797	0.133398	+	0.991063i	$0.457411\pi$
$38$	2.59421	0.420836
$39$	−10.6945	−1.71249
$40$	13.1587	2.08057
$41$	−5.18841	−0.810294	−0.405147	−	0.914252i	$-0.632780\pi$
$41$	−5.18841	−0.810294	−0.405147	+	0.914252i	$0.632780\pi$
$42$	0	0
$43$	6.18419	0.943080	0.471540	−	0.881845i	$-0.343698\pi$
$43$	6.18419	0.943080	0.471540	+	0.881845i	$0.343698\pi$
$44$	−16.6263	−2.50650
$45$	10.0441	1.49728
$46$	4.46089	0.657722
$47$	−5.43568	−0.792875	−0.396437	−	0.918062i	$-0.629754\pi$
$47$	−5.43568	−0.792875	−0.396437	+	0.918062i	$0.629754\pi$
$48$	−25.8387	−3.72950
$49$	0	0
$50$	−4.01484	−0.567784
$51$	−14.0847	−1.97226
$52$	17.4472	2.41950
$53$	5.81446	0.798677	0.399338	−	0.916804i	$-0.369240\pi$
$53$	5.81446	0.798677	0.399338	+	0.916804i	$0.369240\pi$
$54$	−18.0937	−2.46224
$55$	−6.53133	−0.880685
$56$	0	0
$57$	−2.89925	−0.384016
$58$	8.30400	1.09037
$59$	−4.88969	−0.636583	−0.318292	−	0.947993i	$-0.603109\pi$
$59$	−4.88969	−0.636583	−0.318292	+	0.947993i	$0.603109\pi$
$60$	−25.4799	−3.28944
$61$	−7.36829	−0.943413	−0.471707	−	0.881756i	$-0.656362\pi$
$61$	−7.36829	−0.943413	−0.471707	+	0.881756i	$0.656362\pi$
$62$	1.62879	0.206856
$63$	0	0
$64$	5.40982	0.676227
$65$	6.85384	0.850114
$66$	26.4383	3.25433
$67$	−0.0879948	−0.0107503	−0.00537514	−	0.999986i	$-0.501711\pi$
$67$	−0.0879948	−0.0107503	−0.00537514	+	0.999986i	$0.501711\pi$
$68$	22.9782	2.78651
$69$	−4.98544	−0.600176
$70$	0	0
$71$	15.7990	1.87499	0.937496	−	0.347995i	$-0.113137\pi$
$71$	15.7990	1.87499	0.937496	+	0.347995i	$0.113137\pi$
$72$	38.2827	4.51165
$73$	3.01818	0.353251	0.176626	−	0.984278i	$-0.443482\pi$
$73$	3.01818	0.353251	0.176626	+	0.984278i	$0.443482\pi$
$74$	4.21003	0.489406
$75$	4.48694	0.518107
$76$	4.72991	0.542557
$77$	0	0
$78$	−27.7438	−3.14136
$79$	−14.7534	−1.65988	−0.829942	−	0.557850i	$-0.811627\pi$
$79$	−14.7534	−1.65988	−0.829942	+	0.557850i	$0.811627\pi$
$80$	16.5594	1.85139
$81$	4.00431	0.444924
$82$	−13.4598	−1.48639
$83$	−4.03094	−0.442454	−0.221227	−	0.975222i	$-0.571006\pi$
$83$	−4.03094	−0.442454	−0.221227	+	0.975222i	$0.571006\pi$
$84$	0	0
$85$	9.02656	0.979068
$86$	16.0431	1.72997
$87$	−9.28045	−0.994969
$88$	−24.8940	−2.65371
$89$	−1.32673	−0.140633	−0.0703163	−	0.997525i	$-0.522401\pi$
$89$	−1.32673	−0.140633	−0.0703163	+	0.997525i	$0.522401\pi$
$90$	26.0564	2.74658
$91$	0	0
$92$	8.13335	0.847960
$93$	−1.82032	−0.188758
$94$	−14.1013	−1.45443
$95$	1.85806	0.190633
$96$	−25.9663	−2.65017
$97$	−4.69587	−0.476793	−0.238397	−	0.971168i	$-0.576622\pi$
$97$	−4.69587	−0.476793	−0.238397	+	0.971168i	$0.576622\pi$
$98$	0	0
$99$	−19.0017	−1.90974
$100$	−7.32009	−0.732009
$101$	0.569938	0.0567110	0.0283555	−	0.999598i	$-0.490973\pi$
$101$	0.569938	0.0567110	0.0283555	+	0.999598i	$0.490973\pi$
$102$	−36.5387	−3.61787
$103$	−12.2276	−1.20482	−0.602409	−	0.798188i	$-0.705792\pi$
$103$	−12.2276	−1.20482	−0.602409	+	0.798188i	$0.705792\pi$
$104$	26.1232	2.56159
$105$	0	0
$106$	15.0839	1.46508
$107$	−18.3739	−1.77627	−0.888136	−	0.459580i	$-0.848000\pi$
$107$	−18.3739	−1.77627	−0.888136	+	0.459580i	$0.848000\pi$
$108$	−32.9895	−3.17442
$109$	−13.9624	−1.33735	−0.668677	−	0.743553i	$-0.733139\pi$
$109$	−13.9624	−1.33735	−0.668677	+	0.743553i	$0.733139\pi$
$110$	−16.9436	−1.61551
$111$	−4.70508	−0.446587
$112$	0	0
$113$	−19.2840	−1.81409	−0.907044	−	0.421035i	$-0.861667\pi$
$113$	−19.2840	−1.81409	−0.907044	+	0.421035i	$0.861667\pi$
$114$	−7.52126	−0.704431
$115$	3.19504	0.297939
$116$	15.1403	1.40574
$117$	19.9400	1.84345
$118$	−12.6849	−1.16774
$119$	0	0
$120$	−38.1503	−3.48263
$121$	1.35620	0.123291
$122$	−19.1149	−1.73058
$123$	15.0425	1.35634
$124$	2.96970	0.266687
$125$	−12.1659	−1.08815
$126$	0	0
$127$	−5.98199	−0.530816	−0.265408	−	0.964136i	$-0.585507\pi$
$127$	−5.98199	−0.530816	−0.265408	+	0.964136i	$0.585507\pi$
$128$	−3.87820	−0.342788
$129$	−17.9295	−1.57861
$130$	17.7803	1.55943
$131$	18.5645	1.62198	0.810992	−	0.585057i	$-0.198928\pi$
$131$	18.5645	1.62198	0.810992	+	0.585057i	$0.198928\pi$
$132$	48.2038	4.19560
$133$	0	0
$134$	−0.228277	−0.0197201
$135$	−12.9593	−1.11536
$136$	34.4045	2.95016
$137$	−0.392832	−0.0335619	−0.0167810	−	0.999859i	$-0.505342\pi$
$137$	−0.392832	−0.0335619	−0.0167810	+	0.999859i	$0.505342\pi$
$138$	−12.9333	−1.10095
$139$	2.20935	0.187395	0.0936973	−	0.995601i	$-0.470131\pi$
$139$	2.20935	0.187395	0.0936973	+	0.995601i	$0.470131\pi$
$140$	0	0
$141$	15.7594	1.32718
$142$	40.9858	3.43945
$143$	−12.9663	−1.08430
$144$	48.1764	4.01470
$145$	5.94761	0.493922
$146$	7.82978	0.647997
$147$	0	0
$148$	7.67597	0.630961
$149$	14.7422	1.20772	0.603862	−	0.797089i	$-0.293628\pi$
$149$	14.7422	1.20772	0.603862	+	0.797089i	$0.293628\pi$
$150$	11.6400	0.950406
$151$	−8.64356	−0.703403	−0.351701	−	0.936112i	$-0.614397\pi$
$151$	−8.64356	−0.703403	−0.351701	+	0.936112i	$0.614397\pi$
$152$	7.08194	0.574421
$153$	26.2611	2.12308
$154$	0	0
$155$	1.16659	0.0937031
$156$	−50.5840	−4.04996
$157$	23.0605	1.84043	0.920213	−	0.391417i	$-0.128015\pi$
$157$	23.0605	1.84043	0.920213	+	0.391417i	$0.128015\pi$
$158$	−38.2733	−3.04486
$159$	−16.8576	−1.33689
$160$	16.6411	1.31560
$161$	0	0
$162$	10.3880	0.816159
$163$	−1.56192	−0.122339	−0.0611694	−	0.998127i	$-0.519483\pi$
$163$	−1.56192	−0.122339	−0.0611694	+	0.998127i	$0.519483\pi$
$164$	−24.5407	−1.91631
$165$	18.9360	1.47417
$166$	−10.4571	−0.811628
$167$	−15.6485	−1.21092	−0.605458	−	0.795877i	$-0.707010\pi$
$167$	−15.6485	−1.21092	−0.605458	+	0.795877i	$0.707010\pi$
$168$	0	0
$169$	0.606574	0.0466595
$170$	23.4167	1.79598
$171$	5.40568	0.413382
$172$	29.2506	2.23034
$173$	−9.98245	−0.758952	−0.379476	−	0.925202i	$-0.623896\pi$
$173$	−9.98245	−0.758952	−0.379476	+	0.925202i	$0.623896\pi$
$174$	−24.0754	−1.82515
$175$	0	0
$176$	−31.3276	−2.36141
$177$	14.1764	1.06557
$178$	−3.44180	−0.257974
$179$	15.6761	1.17169	0.585845	−	0.810423i	$-0.300763\pi$
$179$	15.6761	1.17169	0.585845	+	0.810423i	$0.300763\pi$
$180$	47.5075	3.54100
$181$	−14.0629	−1.04529	−0.522645	−	0.852550i	$-0.675055\pi$
$181$	−14.0629	−1.04529	−0.522645	+	0.852550i	$0.675055\pi$
$182$	0	0
$183$	21.3626	1.57917
$184$	12.1778	0.897759
$185$	3.01537	0.221694
$186$	−4.72228	−0.346254
$187$	−17.0767	−1.24878
$188$	−25.7102	−1.87511
$189$	0	0
$190$	4.82019	0.349693
$191$	14.2579	1.03166	0.515832	−	0.856690i	$-0.327483\pi$
$191$	14.2579	1.03166	0.515832	+	0.856690i	$0.327483\pi$
$192$	−15.6844	−1.13193
$193$	−6.26005	−0.450608	−0.225304	−	0.974288i	$-0.572338\pi$
$193$	−6.26005	−0.450608	−0.225304	+	0.974288i	$0.572338\pi$
$194$	−12.1821	−0.874620
$195$	−19.8710	−1.42299
$196$	0	0
$197$	−4.46741	−0.318290	−0.159145	−	0.987255i	$-0.550874\pi$
$197$	−4.46741	−0.318290	−0.159145	+	0.987255i	$0.550874\pi$
$198$	−49.2943	−3.50320
$199$	15.8836	1.12596	0.562980	−	0.826471i	$-0.309655\pi$
$199$	15.8836	1.12596	0.562980	+	0.826471i	$0.309655\pi$
$200$	−10.9601	−0.774999
$201$	0.255119	0.0179947
$202$	1.47854	0.104030
$203$	0	0
$204$	−66.6195	−4.66430
$205$	−9.64037	−0.673313
$206$	−31.7208	−2.21009
$207$	9.29538	0.646073
$208$	32.8745	2.27944
$209$	−3.51514	−0.243147
$210$	0	0
$211$	8.71958	0.600281	0.300140	−	0.953895i	$-0.402966\pi$
$211$	8.71958	0.600281	0.300140	+	0.953895i	$0.402966\pi$
$212$	27.5018	1.88883
$213$	−45.8052	−3.13852
$214$	−47.6657	−3.25836
$215$	11.4906	0.783652
$216$	−49.3942	−3.36085
$217$	0	0
$218$	−36.2213	−2.45322
$219$	−8.75047	−0.591302
$220$	−30.8926	−2.08278
$221$	17.9200	1.20543
$222$	−12.2060	−0.819210
$223$	−5.10334	−0.341745	−0.170872	−	0.985293i	$-0.554659\pi$
$223$	−5.10334	−0.341745	−0.170872	+	0.985293i	$0.554659\pi$
$224$	0	0
$225$	−8.36593	−0.557728
$226$	−50.0267	−3.32773
$227$	−2.16600	−0.143763	−0.0718813	−	0.997413i	$-0.522900\pi$
$227$	−2.16600	−0.143763	−0.0718813	+	0.997413i	$0.522900\pi$
$228$	−13.7132	−0.908179
$229$	24.2488	1.60240	0.801202	−	0.598394i	$-0.204194\pi$
$229$	24.2488	1.60240	0.801202	+	0.598394i	$0.204194\pi$
$230$	8.28859	0.546534
$231$	0	0
$232$	22.6691	1.48830
$233$	2.79368	0.183020	0.0915101	−	0.995804i	$-0.470831\pi$
$233$	2.79368	0.183020	0.0915101	+	0.995804i	$0.470831\pi$
$234$	51.7284	3.38159
$235$	−10.0998	−0.658838
$236$	−23.1278	−1.50549
$237$	42.7738	2.77846
$238$	0	0
$239$	28.1576	1.82136	0.910682	−	0.413109i	$-0.135557\pi$
$239$	28.1576	1.82136	0.910682	+	0.413109i	$0.135557\pi$
$240$	−48.0098	−3.09902
$241$	17.2881	1.11362	0.556812	−	0.830639i	$-0.312025\pi$
$241$	17.2881	1.11362	0.556812	+	0.830639i	$0.312025\pi$
$242$	3.51825	0.226162
$243$	9.31449	0.597525
$244$	−34.8513	−2.23113
$245$	0	0
$246$	39.0234	2.48804
$247$	3.68871	0.234707
$248$	4.44644	0.282349
$249$	11.6867	0.740617
$250$	−31.5607	−1.99608
$251$	3.30974	0.208909	0.104455	−	0.994530i	$-0.466690\pi$
$251$	3.30974	0.208909	0.104455	+	0.994530i	$0.466690\pi$
$252$	0	0
$253$	−6.04448	−0.380013
$254$	−15.5185	−0.973718
$255$	−26.1703	−1.63885
$256$	−20.8805	−1.30503
$257$	−2.20124	−0.137310	−0.0686548	−	0.997640i	$-0.521871\pi$
$257$	−2.20124	−0.137310	−0.0686548	+	0.997640i	$0.521871\pi$
$258$	−46.5129	−2.89577
$259$	0	0
$260$	32.4180	2.01048
$261$	17.3035	1.07106
$262$	48.1600	2.97534
$263$	1.42703	0.0879945	0.0439972	−	0.999032i	$-0.485991\pi$
$263$	1.42703	0.0879945	0.0439972	+	0.999032i	$0.485991\pi$
$264$	72.1740	4.44200
$265$	10.8036	0.663660
$266$	0	0
$267$	3.84652	0.235403
$268$	−0.416207	−0.0254239
$269$	−2.26935	−0.138365	−0.0691823	−	0.997604i	$-0.522039\pi$
$269$	−2.26935	−0.138365	−0.0691823	+	0.997604i	$0.522039\pi$
$270$	−33.6192	−2.04600
$271$	3.43963	0.208943	0.104471	−	0.994528i	$-0.466685\pi$
$271$	3.43963	0.208943	0.104471	+	0.994528i	$0.466685\pi$
$272$	43.2959	2.62520
$273$	0	0
$274$	−1.01909	−0.0615653
$275$	5.44009	0.328050
$276$	−23.5806	−1.41939
$277$	5.91649	0.355487	0.177744	−	0.984077i	$-0.443120\pi$
$277$	5.91649	0.355487	0.177744	+	0.984077i	$0.443120\pi$
$278$	5.73151	0.343753
$279$	3.39399	0.203193
$280$	0	0
$281$	−24.4540	−1.45880	−0.729402	−	0.684086i	$-0.760201\pi$
$281$	−24.4540	−1.45880	−0.729402	+	0.684086i	$0.760201\pi$
$282$	40.8831	2.43456
$283$	−23.6926	−1.40838	−0.704188	−	0.710013i	$-0.748689\pi$
$283$	−23.6926	−1.40838	−0.704188	+	0.710013i	$0.748689\pi$
$284$	74.7276	4.43427
$285$	−5.38698	−0.319097
$286$	−33.6373	−1.98902
$287$	0	0
$288$	48.4143	2.85284
$289$	6.60073	0.388278
$290$	15.4293	0.906041
$291$	13.6145	0.798097
$292$	14.2757	0.835423
$293$	14.8606	0.868164	0.434082	−	0.900873i	$-0.357073\pi$
$293$	14.8606	0.868164	0.434082	+	0.900873i	$0.357073\pi$
$294$	0	0
$295$	−9.08533	−0.528968
$296$	11.4930	0.668017
$297$	24.5169	1.42262
$298$	38.2442	2.21543
$299$	6.34295	0.366822
$300$	21.2228	1.22530
$301$	0	0
$302$	−22.4232	−1.29031
$303$	−1.65240	−0.0949277
$304$	8.91219	0.511149
$305$	−13.6907	−0.783928
$306$	68.1267	3.89454
$307$	23.0610	1.31616	0.658080	−	0.752948i	$-0.271369\pi$
$307$	23.0610	1.31616	0.658080	+	0.752948i	$0.271369\pi$
$308$	0	0
$309$	35.4508	2.01673
$310$	3.02639	0.171887
$311$	7.36533	0.417650	0.208825	−	0.977953i	$-0.433036\pi$
$311$	7.36533	0.417650	0.208825	+	0.977953i	$0.433036\pi$
$312$	−75.7378	−4.28781
$313$	−6.60341	−0.373247	−0.186623	−	0.982432i	$-0.559754\pi$
$313$	−6.60341	−0.373247	−0.186623	+	0.982432i	$0.559754\pi$
$314$	59.8236	3.37604
$315$	0	0
$316$	−69.7820	−3.92555
$317$	−19.7434	−1.10890	−0.554451	−	0.832217i	$-0.687072\pi$
$317$	−19.7434	−1.10890	−0.554451	+	0.832217i	$0.687072\pi$
$318$	−43.7321	−2.45237
$319$	−11.2519	−0.629985
$320$	10.0518	0.561910
$321$	53.2706	2.97328
$322$	0	0
$323$	4.85806	0.270310
$324$	18.9400	1.05222
$325$	−5.70871	−0.316662
$326$	−4.05194	−0.224416
$327$	40.4805	2.23858
$328$	−36.7440	−2.02885
$329$	0	0
$330$	49.1239	2.70418
$331$	34.9018	1.91838	0.959189	−	0.282765i	$-0.0912516\pi$
$331$	34.9018	1.91838	0.959189	+	0.282765i	$0.0912516\pi$
$332$	−19.0660	−1.04638
$333$	8.77266	0.480739
$334$	−40.5954	−2.22128
$335$	−0.163500	−0.00893293
$336$	0	0
$337$	−22.4312	−1.22191	−0.610953	−	0.791667i	$-0.709213\pi$
$337$	−22.4312	−1.22191	−0.610953	+	0.791667i	$0.709213\pi$
$338$	1.57358	0.0855914
$339$	55.9093	3.03658
$340$	42.6948	2.31545
$341$	−2.20700	−0.119516
$342$	14.0234	0.758301
$343$	0	0
$344$	43.7960	2.36132
$345$	−9.26323	−0.498716
$346$	−25.8965	−1.39221
$347$	3.43777	0.184549	0.0922745	−	0.995734i	$-0.470586\pi$
$347$	3.43777	0.184549	0.0922745	+	0.995734i	$0.470586\pi$
$348$	−43.8957	−2.35305
$349$	−15.9690	−0.854802	−0.427401	−	0.904062i	$-0.640571\pi$
$349$	−15.9690	−0.854802	−0.427401	+	0.904062i	$0.640571\pi$
$350$	0	0
$351$	−25.7275	−1.37323
$352$	−31.4822	−1.67801
$353$	23.4843	1.24994	0.624970	−	0.780648i	$-0.285111\pi$
$353$	23.4843	1.24994	0.624970	+	0.780648i	$0.285111\pi$
$354$	36.7766	1.95466
$355$	29.3554	1.55802
$356$	−6.27529	−0.332590
$357$	0	0
$358$	40.6671	2.14933
$359$	−7.48850	−0.395228	−0.197614	−	0.980280i	$-0.563319\pi$
$359$	−7.48850	−0.395228	−0.197614	+	0.980280i	$0.563319\pi$
$360$	71.1314	3.74896
$361$	1.00000	0.0526316
$362$	−36.4822	−1.91746
$363$	−3.93196	−0.206374
$364$	0	0
$365$	5.60796	0.293534
$366$	55.4189	2.89679
$367$	−1.32190	−0.0690027	−0.0345013	−	0.999405i	$-0.510984\pi$
$367$	−1.32190	−0.0690027	−0.0345013	+	0.999405i	$0.510984\pi$
$368$	15.3250	0.798873
$369$	−28.0469	−1.46006
$370$	7.82249	0.406672
$371$	0	0
$372$	−8.60992	−0.446404
$373$	16.0606	0.831588	0.415794	−	0.909459i	$-0.363504\pi$
$373$	16.0606	0.831588	0.415794	+	0.909459i	$0.363504\pi$
$374$	−44.3006	−2.29073
$375$	35.2719	1.82143
$376$	−38.4951	−1.98523
$377$	11.8075	0.608116
$378$	0	0
$379$	29.7184	1.52653	0.763265	−	0.646085i	$-0.223595\pi$
$379$	29.7184	1.52653	0.763265	+	0.646085i	$0.223595\pi$
$380$	8.78844	0.450837
$381$	17.3433	0.888525
$382$	36.9879	1.89247
$383$	−8.81894	−0.450627	−0.225313	−	0.974286i	$-0.572341\pi$
$383$	−8.81894	−0.450627	−0.225313	+	0.974286i	$0.572341\pi$
$384$	11.2439	0.573787
$385$	0	0
$386$	−16.2399	−0.826587
$387$	33.4297	1.69933
$388$	−22.2110	−1.12759
$389$	−2.69383	−0.136583	−0.0682913	−	0.997665i	$-0.521755\pi$
$389$	−2.69383	−0.136583	−0.0682913	+	0.997665i	$0.521755\pi$
$390$	−51.5495	−2.61031
$391$	8.35371	0.422465
$392$	0	0
$393$	−53.8231	−2.71502
$394$	−11.5894	−0.583864
$395$	−27.4126	−1.37928
$396$	−89.8762	−4.51645
$397$	−12.6488	−0.634824	−0.317412	−	0.948288i	$-0.602814\pi$
$397$	−12.6488	−0.634824	−0.317412	+	0.948288i	$0.602814\pi$
$398$	41.2054	2.06544
$399$	0	0
$400$	−13.7927	−0.689634
$401$	14.0325	0.700750	0.350375	−	0.936610i	$-0.386054\pi$
$401$	14.0325	0.700750	0.350375	+	0.936610i	$0.386054\pi$
$402$	0.661832	0.0330092
$403$	2.31598	0.115367
$404$	2.69575	0.134119
$405$	7.44025	0.369709
$406$	0	0
$407$	−5.70458	−0.282765
$408$	−99.7473	−4.93823
$409$	−19.1589	−0.947345	−0.473672	−	0.880701i	$-0.657072\pi$
$409$	−19.1589	−0.947345	−0.473672	+	0.880701i	$0.657072\pi$
$410$	−25.0091	−1.23511
$411$	1.13892	0.0561788
$412$	−57.8352	−2.84934
$413$	0	0
$414$	24.1141	1.18514
$415$	−7.48973	−0.367656
$416$	33.0368	1.61976
$417$	−6.40547	−0.313677
$418$	−9.11899	−0.446025
$419$	−19.9035	−0.972350	−0.486175	−	0.873861i	$-0.661608\pi$
$419$	−19.9035	−0.972350	−0.486175	+	0.873861i	$0.661608\pi$
$420$	0	0
$421$	−1.62383	−0.0791408	−0.0395704	−	0.999217i	$-0.512599\pi$
$421$	−1.62383	−0.0791408	−0.0395704	+	0.999217i	$0.512599\pi$
$422$	22.6204	1.10114
$423$	−29.3835	−1.42867
$424$	41.1776	1.99976
$425$	−7.51842	−0.364697
$426$	−118.828	−5.75725
$427$	0	0
$428$	−86.9068	−4.20080
$429$	37.5927	1.81499
$430$	29.8090	1.43752
$431$	−9.50653	−0.457913	−0.228957	−	0.973437i	$-0.573531\pi$
$431$	−9.50653	−0.457913	−0.228957	+	0.973437i	$0.573531\pi$
$432$	−62.1596	−2.99065
$433$	32.9746	1.58466	0.792328	−	0.610095i	$-0.208869\pi$
$433$	32.9746	1.58466	0.792328	+	0.610095i	$0.208869\pi$
$434$	0	0
$435$	−17.2436	−0.826769
$436$	−66.0407	−3.16278
$437$	1.71956	0.0822576
$438$	−22.7005	−1.08467
$439$	−28.5020	−1.36032	−0.680162	−	0.733061i	$-0.738091\pi$
$439$	−28.5020	−1.36032	−0.680162	+	0.733061i	$0.738091\pi$
$440$	−46.2545	−2.20510
$441$	0	0
$442$	46.4881	2.21121
$443$	−4.93266	−0.234358	−0.117179	−	0.993111i	$-0.537385\pi$
$443$	−4.93266	−0.234358	−0.117179	+	0.993111i	$0.537385\pi$
$444$	−22.2546	−1.05616
$445$	−2.46513	−0.116859
$446$	−13.2391	−0.626890
$447$	−42.7413	−2.02159
$448$	0	0
$449$	23.8243	1.12434	0.562170	−	0.827022i	$-0.309967\pi$
$449$	23.8243	1.12434	0.562170	+	0.827022i	$0.309967\pi$
$450$	−21.7029	−1.02309
$451$	18.2380	0.858793
$452$	−91.2116	−4.29023
$453$	25.0599	1.17742
$454$	−5.61905	−0.263715
$455$	0	0
$456$	−20.5323	−0.961515
$457$	16.5346	0.773455	0.386727	−	0.922194i	$-0.373605\pi$
$457$	16.5346	0.773455	0.386727	+	0.922194i	$0.373605\pi$
$458$	62.9063	2.93942
$459$	−33.8834	−1.58154
$460$	15.1122	0.704612
$461$	−28.5520	−1.32980	−0.664899	−	0.746933i	$-0.731525\pi$
$461$	−28.5520	−1.32980	−0.664899	+	0.746933i	$0.731525\pi$
$462$	0	0
$463$	−23.7870	−1.10548	−0.552739	−	0.833355i	$-0.686417\pi$
$463$	−23.7870	−1.10548	−0.552739	+	0.833355i	$0.686417\pi$
$464$	28.5277	1.32437
$465$	−3.38225	−0.156848
$466$	7.24739	0.335729
$467$	24.0932	1.11490	0.557451	−	0.830210i	$-0.311780\pi$
$467$	24.0932	1.11490	0.557451	+	0.830210i	$0.311780\pi$
$468$	94.3142	4.35967
$469$	0	0
$470$	−26.2010	−1.20856
$471$	−66.8582	−3.08066
$472$	−34.6285	−1.59390
$473$	−21.7383	−0.999527
$474$	110.964	5.09674
$475$	−1.54762	−0.0710096
$476$	0	0
$477$	31.4311	1.43913
$478$	73.0466	3.34107
$479$	21.5096	0.982797	0.491398	−	0.870935i	$-0.336486\pi$
$479$	21.5096	0.982797	0.491398	+	0.870935i	$0.336486\pi$
$480$	−48.2469	−2.20216
$481$	5.98626	0.272950
$482$	44.8489	2.04281
$483$	0	0
$484$	6.41468	0.291576
$485$	−8.72520	−0.396191
$486$	24.1637	1.09609
$487$	−30.8062	−1.39596	−0.697982	−	0.716115i	$-0.745918\pi$
$487$	−30.8062	−1.39596	−0.697982	+	0.716115i	$0.745918\pi$
$488$	−52.1818	−2.36216
$489$	4.52840	0.204781
$490$	0	0
$491$	17.1395	0.773495	0.386747	−	0.922186i	$-0.373599\pi$
$491$	17.1395	0.773495	0.386747	+	0.922186i	$0.373599\pi$
$492$	71.1497	3.20768
$493$	15.5505	0.700361
$494$	9.56927	0.430542
$495$	−35.3063	−1.58690
$496$	5.59558	0.251249
$497$	0	0
$498$	30.3178	1.35857
$499$	−23.9337	−1.07142	−0.535711	−	0.844402i	$-0.679956\pi$
$499$	−23.9337	−1.07142	−0.535711	+	0.844402i	$0.679956\pi$
$500$	−57.5434	−2.57342
$501$	45.3689	2.02694
$502$	8.58615	0.383219
$503$	6.98088	0.311262	0.155631	−	0.987815i	$-0.450259\pi$
$503$	6.98088	0.311262	0.155631	+	0.987815i	$0.450259\pi$
$504$	0	0
$505$	1.05898	0.0471239
$506$	−15.6806	−0.697089
$507$	−1.75861	−0.0781027
$508$	−28.2942	−1.25535
$509$	−10.4918	−0.465039	−0.232520	−	0.972592i	$-0.574697\pi$
$509$	−10.4918	−0.465039	−0.232520	+	0.972592i	$0.574697\pi$
$510$	−67.8911	−3.00627
$511$	0	0
$512$	−46.4119	−2.05113
$513$	−6.97467	−0.307939
$514$	−5.71047	−0.251878
$515$	−22.7195	−1.00114
$516$	−84.8050	−3.73333
$517$	19.1071	0.840331
$518$	0	0
$519$	28.9417	1.27040
$520$	48.5384	2.12855
$521$	1.21564	0.0532580	0.0266290	−	0.999645i	$-0.491523\pi$
$521$	1.21564	0.0532580	0.0266290	+	0.999645i	$0.491523\pi$
$522$	44.8887	1.96473
$523$	−4.25228	−0.185939	−0.0929697	−	0.995669i	$-0.529636\pi$
$523$	−4.25228	−0.185939	−0.0929697	+	0.995669i	$0.529636\pi$
$524$	87.8081	3.83592
$525$	0	0
$526$	3.70201	0.161415
$527$	3.05016	0.132867
$528$	90.8266	3.95272
$529$	−20.0431	−0.871440
$530$	28.0268	1.21740
$531$	−26.4321	−1.14705
$532$	0	0
$533$	−19.1385	−0.828982
$534$	9.97866	0.431819
$535$	−34.1398	−1.47599
$536$	−0.623174	−0.0269170
$537$	−45.4491	−1.96127
$538$	−5.88716	−0.253813
$539$	0	0
$540$	−61.2965	−2.63778
$541$	32.2316	1.38575	0.692873	−	0.721060i	$-0.256345\pi$
$541$	32.2316	1.38575	0.692873	+	0.721060i	$0.256345\pi$
$542$	8.92310	0.383280
$543$	40.7721	1.74970
$544$	43.5097	1.86546
$545$	−25.9429	−1.11127
$546$	0	0
$547$	−1.39956	−0.0598407	−0.0299204	−	0.999552i	$-0.509525\pi$
$547$	−1.39956	−0.0598407	−0.0299204	+	0.999552i	$0.509525\pi$
$548$	−1.85806	−0.0793723
$549$	−39.8306	−1.69993
$550$	14.1127	0.601768
$551$	3.20098	0.136366
$552$	−35.3065	−1.50275
$553$	0	0
$554$	15.3486	0.652099
$555$	−8.74232	−0.371091
$556$	10.4500	0.443179
$557$	26.4429	1.12042	0.560212	−	0.828349i	$-0.310720\pi$
$557$	26.4429	1.12042	0.560212	+	0.828349i	$0.310720\pi$
$558$	8.80471	0.372733
$559$	22.8117	0.964831
$560$	0	0
$561$	49.5098	2.09031
$562$	−63.4387	−2.67600
$563$	27.1771	1.14538	0.572689	−	0.819772i	$-0.305900\pi$
$563$	27.1771	1.14538	0.572689	+	0.819772i	$0.305900\pi$
$564$	74.5405	3.13872
$565$	−35.8308	−1.50742
$566$	−61.4634	−2.58350
$567$	0	0
$568$	111.887	4.69469
$569$	−16.2384	−0.680748	−0.340374	−	0.940290i	$-0.610554\pi$
$569$	−16.2384	−0.680748	−0.340374	+	0.940290i	$0.610554\pi$
$570$	−13.9749	−0.585346
$571$	−22.8445	−0.956011	−0.478005	−	0.878357i	$-0.658640\pi$
$571$	−22.8445	−0.956011	−0.478005	+	0.878357i	$0.658640\pi$
$572$	−61.3295	−2.56431
$573$	−41.3372	−1.72689
$574$	0	0
$575$	−2.66122	−0.110981
$576$	29.2437	1.21849
$577$	−47.6337	−1.98302	−0.991509	−	0.130041i	$-0.958489\pi$
$577$	−47.6337	−1.98302	−0.991509	+	0.130041i	$0.958489\pi$
$578$	17.1237	0.712250
$579$	18.1495	0.754267
$580$	28.1316	1.16810
$581$	0	0
$582$	35.3189	1.46401
$583$	−20.4386	−0.846481
$584$	21.3746	0.884486
$585$	37.0496	1.53181
$586$	38.5514	1.59254
$587$	−21.9802	−0.907221	−0.453611	−	0.891200i	$-0.649864\pi$
$587$	−21.9802	−0.907221	−0.453611	+	0.891200i	$0.649864\pi$
$588$	0	0
$589$	0.627857	0.0258704
$590$	−23.5692	−0.970329
$591$	12.9522	0.532780
$592$	14.4632	0.594436
$593$	−9.04871	−0.371586	−0.185793	−	0.982589i	$-0.559485\pi$
$593$	−9.04871	−0.371586	−0.185793	+	0.982589i	$0.559485\pi$
$594$	63.6020	2.60962
$595$	0	0
$596$	69.7290	2.85621
$597$	−46.0506	−1.88473
$598$	16.4549	0.672892
$599$	3.14651	0.128563	0.0642814	−	0.997932i	$-0.479524\pi$
$599$	3.14651	0.128563	0.0642814	+	0.997932i	$0.479524\pi$
$600$	31.7762	1.29726
$601$	34.2901	1.39872	0.699361	−	0.714769i	$-0.253468\pi$
$601$	34.2901	1.39872	0.699361	+	0.714769i	$0.253468\pi$
$602$	0	0
$603$	−0.475672	−0.0193708
$604$	−40.8832	−1.66351
$605$	2.51989	0.102448
$606$	−4.28666	−0.174134
$607$	−3.90479	−0.158491	−0.0792454	−	0.996855i	$-0.525251\pi$
$607$	−3.90479	−0.158491	−0.0792454	+	0.996855i	$0.525251\pi$
$608$	8.95619	0.363221
$609$	0	0
$610$	−35.5165	−1.43802
$611$	−20.0506	−0.811161
$612$	124.212	5.02099
$613$	−17.5869	−0.710330	−0.355165	−	0.934804i	$-0.615575\pi$
$613$	−17.5869	−0.710330	−0.355165	+	0.934804i	$0.615575\pi$
$614$	59.8250	2.41434
$615$	27.9499	1.12705
$616$	0	0
$617$	43.3913	1.74687	0.873434	−	0.486943i	$-0.161888\pi$
$617$	43.3913	1.74687	0.873434	+	0.486943i	$0.161888\pi$
$618$	91.9667	3.69944
$619$	−26.8786	−1.08034	−0.540172	−	0.841555i	$-0.681641\pi$
$619$	−26.8786	−1.08034	−0.540172	+	0.841555i	$0.681641\pi$
$620$	5.51788	0.221603
$621$	−11.9934	−0.481277
$622$	19.1072	0.766128
$623$	0	0
$624$	−95.3115	−3.81551
$625$	−14.8668	−0.594671
$626$	−17.1306	−0.684677
$627$	10.1913	0.407001
$628$	109.074	4.35252
$629$	7.88395	0.314354
$630$	0	0
$631$	−29.5102	−1.17478	−0.587391	−	0.809303i	$-0.699845\pi$
$631$	−29.5102	−1.17478	−0.587391	+	0.809303i	$0.699845\pi$
$632$	−104.482	−4.15609
$633$	−25.2803	−1.00480
$634$	−51.2185	−2.03415
$635$	−11.1149	−0.441081
$636$	−79.7348	−3.16169
$637$	0	0
$638$	−29.1897	−1.15563
$639$	85.4041	3.37854
$640$	−7.20592	−0.284839
$641$	−11.1538	−0.440548	−0.220274	−	0.975438i	$-0.570695\pi$
$641$	−11.1538	−0.440548	−0.220274	+	0.975438i	$0.570695\pi$
$642$	138.195	5.45412
$643$	−30.3635	−1.19742	−0.598710	−	0.800966i	$-0.704320\pi$
$643$	−30.3635	−1.19742	−0.598710	+	0.800966i	$0.704320\pi$
$644$	0	0
$645$	−33.3141	−1.31174
$646$	12.6028	0.495851
$647$	−11.1611	−0.438790	−0.219395	−	0.975636i	$-0.570408\pi$
$647$	−11.1611	−0.438790	−0.219395	+	0.975636i	$0.570408\pi$
$648$	28.3583	1.11402
$649$	17.1879	0.674685
$650$	−14.8096	−0.580880
$651$	0	0
$652$	−7.38773	−0.289326
$653$	40.0307	1.56652	0.783262	−	0.621692i	$-0.213554\pi$
$653$	40.0307	1.56652	0.783262	+	0.621692i	$0.213554\pi$
$654$	105.015	4.10640
$655$	34.4938	1.34779
$656$	−46.2401	−1.80537
$657$	16.3153	0.636521
$658$	0	0
$659$	−19.9271	−0.776248	−0.388124	−	0.921607i	$-0.626877\pi$
$659$	−19.9271	−0.776248	−0.388124	+	0.921607i	$0.626877\pi$
$660$	89.5655	3.48633
$661$	−22.4030	−0.871375	−0.435687	−	0.900098i	$-0.643495\pi$
$661$	−22.4030	−0.871375	−0.435687	+	0.900098i	$0.643495\pi$
$662$	90.5426	3.51904
$663$	−51.9545	−2.01775
$664$	−28.5469	−1.10783
$665$	0	0
$666$	22.7581	0.881858
$667$	5.50427	0.213126
$668$	−74.0159	−2.86376
$669$	14.7959	0.572041
$670$	−0.424151	−0.0163864
$671$	25.9006	0.999880
$672$	0	0
$673$	21.4386	0.826399	0.413200	−	0.910640i	$-0.364411\pi$
$673$	21.4386	0.826399	0.413200	+	0.910640i	$0.364411\pi$
$674$	−58.1912	−2.24144
$675$	10.7941	0.415466
$676$	2.86904	0.110348
$677$	1.63459	0.0628223	0.0314111	−	0.999507i	$-0.490000\pi$
$677$	1.63459	0.0628223	0.0314111	+	0.999507i	$0.490000\pi$
$678$	145.040	5.57024
$679$	0	0
$680$	63.9255	2.45143
$681$	6.27979	0.240642
$682$	−5.72542	−0.219238
$683$	−32.3500	−1.23784	−0.618920	−	0.785454i	$-0.712430\pi$
$683$	−32.3500	−1.23784	−0.618920	+	0.785454i	$0.712430\pi$
$684$	25.5683	0.977630
$685$	−0.729905	−0.0278882
$686$	0	0
$687$	−70.3034	−2.68224
$688$	55.1147	2.10123
$689$	21.4478	0.817098
$690$	−24.0307	−0.914834
$691$	25.5852	0.973308	0.486654	−	0.873595i	$-0.338217\pi$
$691$	25.5852	0.973308	0.486654	+	0.873595i	$0.338217\pi$
$692$	−47.2161	−1.79489
$693$	0	0
$694$	8.91828	0.338533
$695$	4.10510	0.155715
$696$	−65.7236	−2.49125
$697$	−25.2056	−0.954731
$698$	−41.4269	−1.56803
$699$	−8.09960	−0.306355
$700$	0	0
$701$	27.2978	1.03102	0.515511	−	0.856883i	$-0.327602\pi$
$701$	27.2978	1.03102	0.515511	+	0.856883i	$0.327602\pi$
$702$	−66.7425	−2.51903
$703$	1.62286	0.0612073
$704$	−19.0163	−0.716702
$705$	29.2819	1.10282
$706$	60.9230	2.29287
$707$	0	0
$708$	67.0533	2.52002
$709$	25.8953	0.972520	0.486260	−	0.873814i	$-0.338361\pi$
$709$	25.8953	0.972520	0.486260	+	0.873814i	$0.338361\pi$
$710$	76.1540	2.85801
$711$	−79.7520	−2.99093
$712$	−9.39579	−0.352122
$713$	1.07964	0.0404327
$714$	0	0
$715$	−24.0922	−0.900997
$716$	74.1467	2.77099
$717$	−81.6360	−3.04875
$718$	−19.4267	−0.724998
$719$	−7.38755	−0.275509	−0.137755	−	0.990466i	$-0.543989\pi$
$719$	−7.38755	−0.275509	−0.137755	+	0.990466i	$0.543989\pi$
$720$	89.5146	3.33601
$721$	0	0
$722$	2.59421	0.0965464
$723$	−50.1226	−1.86408
$724$	−66.5164	−2.47206
$725$	−4.95389	−0.183983
$726$	−10.2003	−0.378569
$727$	−29.7644	−1.10390	−0.551950	−	0.833877i	$-0.686116\pi$
$727$	−29.7644	−1.10390	−0.551950	+	0.833877i	$0.686116\pi$
$728$	0	0
$729$	−39.0180	−1.44511
$730$	14.5482	0.538453
$731$	30.0432	1.11119
$732$	101.043	3.73465
$733$	−45.3928	−1.67662	−0.838312	−	0.545191i	$-0.816457\pi$
$733$	−45.3928	−1.67662	−0.838312	+	0.545191i	$0.816457\pi$
$734$	−3.42928	−0.126577
$735$	0	0
$736$	15.4007	0.567677
$737$	0.309314	0.0113937
$738$	−72.7594	−2.67831
$739$	48.1394	1.77084	0.885418	−	0.464796i	$-0.153872\pi$
$739$	48.1394	1.77084	0.885418	+	0.464796i	$0.153872\pi$
$740$	14.2624	0.524297
$741$	−10.6945	−0.392873
$742$	0	0
$743$	−7.43426	−0.272737	−0.136368	−	0.990658i	$-0.543543\pi$
$743$	−7.43426	−0.272737	−0.136368	+	0.990658i	$0.543543\pi$
$744$	−12.8914	−0.472620
$745$	27.3918	1.00356
$746$	41.6646	1.52545
$747$	−21.7900	−0.797254
$748$	−80.7714	−2.95329
$749$	0	0
$750$	91.5026	3.34120
$751$	−16.1586	−0.589636	−0.294818	−	0.955553i	$-0.595259\pi$
$751$	−16.1586	−0.589636	−0.294818	+	0.955553i	$0.595259\pi$
$752$	−48.4438	−1.76656
$753$	−9.59578	−0.349690
$754$	30.6310	1.11552
$755$	−16.0602	−0.584492
$756$	0	0
$757$	33.5836	1.22062	0.610308	−	0.792164i	$-0.291046\pi$
$757$	33.5836	1.22062	0.610308	+	0.792164i	$0.291046\pi$
$758$	77.0956	2.80024
$759$	17.5245	0.636099
$760$	13.1587	0.477314
$761$	29.4504	1.06757	0.533787	−	0.845619i	$-0.320768\pi$
$761$	29.4504	1.06757	0.533787	+	0.845619i	$0.320768\pi$
$762$	44.9921	1.62989
$763$	0	0
$764$	67.4385	2.43984
$765$	48.7947	1.76417
$766$	−22.8781	−0.826621
$767$	−18.0366	−0.651265
$768$	60.5378	2.18447
$769$	−38.9622	−1.40501	−0.702506	−	0.711678i	$-0.747936\pi$
$769$	−38.9622	−1.40501	−0.702506	+	0.711678i	$0.747936\pi$
$770$	0	0
$771$	6.38196	0.229841
$772$	−29.6094	−1.06567
$773$	9.94169	0.357578	0.178789	−	0.983887i	$-0.442782\pi$
$773$	9.94169	0.357578	0.178789	+	0.983887i	$0.442782\pi$
$774$	86.7236	3.11722
$775$	−0.971682	−0.0349039
$776$	−33.2558	−1.19382
$777$	0	0
$778$	−6.98835	−0.250545
$779$	−5.18841	−0.185894
$780$	−93.9880	−3.36531
$781$	−55.5356	−1.98722
$782$	21.6713	0.774963
$783$	−22.3258	−0.797858
$784$	0	0
$785$	42.8477	1.52930
$786$	−139.628	−4.98037
$787$	48.5087	1.72915	0.864575	−	0.502505i	$-0.167588\pi$
$787$	48.5087	1.72915	0.864575	+	0.502505i	$0.167588\pi$
$788$	−21.1304	−0.752740
$789$	−4.13732	−0.147293
$790$	−71.1140	−2.53012
$791$	0	0
$792$	−134.569	−4.78170
$793$	−27.1795	−0.965172
$794$	−32.8135	−1.16451
$795$	−31.3224	−1.11089
$796$	75.1280	2.66284
$797$	−33.5790	−1.18943	−0.594715	−	0.803936i	$-0.702735\pi$
$797$	−33.5790	−1.18943	−0.594715	+	0.803936i	$0.702735\pi$
$798$	0	0
$799$	−26.4068	−0.934206
$800$	−13.8608	−0.490052
$801$	−7.17185	−0.253405
$802$	36.4032	1.28544
$803$	−10.6093	−0.374395
$804$	1.20669	0.0425567
$805$	0	0
$806$	6.00813	0.211627
$807$	6.57942	0.231606
$808$	4.03627	0.141995
$809$	53.5849	1.88395	0.941973	−	0.335689i	$-0.108969\pi$
$809$	53.5849	1.88395	0.941973	+	0.335689i	$0.108969\pi$
$810$	19.3015	0.678187
$811$	44.4587	1.56116	0.780579	−	0.625057i	$-0.214924\pi$
$811$	44.4587	1.56116	0.780579	+	0.625057i	$0.214924\pi$
$812$	0	0
$813$	−9.97236	−0.349746
$814$	−14.7988	−0.518699
$815$	−2.90214	−0.101657
$816$	−125.526	−4.39429
$817$	6.18419	0.216357
$818$	−49.7020	−1.73779
$819$	0	0
$820$	−45.5981	−1.59235
$821$	0.257745	0.00899535	0.00449767	−	0.999990i	$-0.498568\pi$
$821$	0.257745	0.00899535	0.00449767	+	0.999990i	$0.498568\pi$
$822$	2.95459	0.103053
$823$	9.75380	0.339996	0.169998	−	0.985444i	$-0.445624\pi$
$823$	9.75380	0.339996	0.169998	+	0.985444i	$0.445624\pi$
$824$	−86.5948	−3.01667
$825$	−15.7722	−0.549118
$826$	0	0
$827$	29.5627	1.02800	0.513998	−	0.857791i	$-0.328164\pi$
$827$	29.5627	1.02800	0.513998	+	0.857791i	$0.328164\pi$
$828$	43.9662	1.52793
$829$	40.7861	1.41656	0.708280	−	0.705931i	$-0.249471\pi$
$829$	40.7861	1.41656	0.708280	+	0.705931i	$0.249471\pi$
$830$	−19.4299	−0.674422
$831$	−17.1534	−0.595045
$832$	19.9552	0.691823
$833$	0	0
$834$	−16.6171	−0.575403
$835$	−29.0758	−1.00621
$836$	−16.6263	−0.575032
$837$	−4.37909	−0.151364
$838$	−51.6338	−1.78366
$839$	13.7643	0.475195	0.237597	−	0.971364i	$-0.423640\pi$
$839$	13.7643	0.475195	0.237597	+	0.971364i	$0.423640\pi$
$840$	0	0
$841$	−18.7537	−0.646680
$842$	−4.21256	−0.145174
$843$	70.8984	2.44187
$844$	41.2428	1.41964
$845$	1.12705	0.0387717
$846$	−76.2269	−2.62073
$847$	0	0
$848$	51.8195	1.77949
$849$	68.6908	2.35746
$850$	−19.5043	−0.668993
$851$	2.79060	0.0956606
$852$	−216.654	−7.42246
$853$	−11.6913	−0.400303	−0.200152	−	0.979765i	$-0.564143\pi$
$853$	−11.6913	−0.400303	−0.200152	+	0.979765i	$0.564143\pi$
$854$	0	0
$855$	10.0441	0.343500
$856$	−130.123	−4.44751
$857$	3.07531	0.105051	0.0525253	−	0.998620i	$-0.483273\pi$
$857$	3.07531	0.105051	0.0525253	+	0.998620i	$0.483273\pi$
$858$	97.5231	3.32938
$859$	52.3984	1.78781	0.893906	−	0.448255i	$-0.147954\pi$
$859$	52.3984	1.78781	0.893906	+	0.448255i	$0.147954\pi$
$860$	54.3494	1.85330
$861$	0	0
$862$	−24.6619	−0.839987
$863$	29.0479	0.988802	0.494401	−	0.869234i	$-0.335388\pi$
$863$	29.0479	0.988802	0.494401	+	0.869234i	$0.335388\pi$
$864$	−62.4665	−2.12515
$865$	−18.5480	−0.630650
$866$	85.5428	2.90686
$867$	−19.1372	−0.649934
$868$	0	0
$869$	51.8601	1.75923
$870$	−44.7335	−1.51661
$871$	−0.324587	−0.0109982
$872$	−98.8807	−3.34852
$873$	−25.3844	−0.859130
$874$	4.46089	0.150892
$875$	0	0
$876$	−41.3889	−1.39840
$877$	−37.2859	−1.25906	−0.629528	−	0.776978i	$-0.716752\pi$
$877$	−37.2859	−1.25906	−0.629528	+	0.776978i	$0.716752\pi$
$878$	−73.9400	−2.49535
$879$	−43.0846	−1.45321
$880$	−58.2085	−1.96221
$881$	13.6326	0.459295	0.229648	−	0.973274i	$-0.426243\pi$
$881$	13.6326	0.459295	0.229648	+	0.973274i	$0.426243\pi$
$882$	0	0
$883$	−47.2253	−1.58926	−0.794629	−	0.607096i	$-0.792335\pi$
$883$	−47.2253	−1.58926	−0.794629	+	0.607096i	$0.792335\pi$
$884$	84.7597	2.85078
$885$	26.3407	0.885432
$886$	−12.7963	−0.429901
$887$	47.8778	1.60758	0.803789	−	0.594914i	$-0.202814\pi$
$887$	47.8778	1.60758	0.803789	+	0.594914i	$0.202814\pi$
$888$	−33.3211	−1.11818
$889$	0	0
$890$	−6.39507	−0.214363
$891$	−14.0757	−0.471554
$892$	−24.1383	−0.808210
$893$	−5.43568	−0.181898
$894$	−110.880	−3.70837
$895$	29.1272	0.973615
$896$	0	0
$897$	−18.3898	−0.614018
$898$	61.8052	2.06247
$899$	2.00976	0.0670291
$900$	−39.5700	−1.31900
$901$	28.2470	0.941043
$902$	47.3131	1.57535
$903$	0	0
$904$	−136.568	−4.54219
$905$	−26.1298	−0.868583
$906$	65.0105	2.15983
$907$	4.27946	0.142097	0.0710485	−	0.997473i	$-0.477365\pi$
$907$	4.27946	0.142097	0.0710485	+	0.997473i	$0.477365\pi$
$908$	−10.2450	−0.339991
$909$	3.08090	0.102187
$910$	0	0
$911$	−2.50426	−0.0829697	−0.0414848	−	0.999139i	$-0.513209\pi$
$911$	−2.50426	−0.0829697	−0.0414848	+	0.999139i	$0.513209\pi$
$912$	−25.8387	−0.855605
$913$	14.1693	0.468936
$914$	42.8941	1.41881
$915$	39.6929	1.31221
$916$	114.694	3.78961
$917$	0	0
$918$	−87.9004	−2.90115
$919$	7.25451	0.239304	0.119652	−	0.992816i	$-0.461822\pi$
$919$	7.25451	0.239304	0.119652	+	0.992816i	$0.461822\pi$
$920$	22.6271	0.745992
$921$	−66.8597	−2.20310
$922$	−74.0697	−2.43936
$923$	58.2778	1.91824
$924$	0	0
$925$	−2.51157	−0.0825799
$926$	−61.7085	−2.02787
$927$	−66.0982	−2.17095
$928$	28.6686	0.941092
$929$	8.75357	0.287195	0.143598	−	0.989636i	$-0.454133\pi$
$929$	8.75357	0.287195	0.143598	+	0.989636i	$0.454133\pi$
$930$	−8.77426	−0.287719
$931$	0	0
$932$	13.2139	0.432834
$933$	−21.3540	−0.699098
$934$	62.5028	2.04515
$935$	−31.7296	−1.03767
$936$	141.214	4.61571
$937$	28.4821	0.930469	0.465235	−	0.885187i	$-0.345970\pi$
$937$	28.4821	0.930469	0.465235	+	0.885187i	$0.345970\pi$
$938$	0	0
$939$	19.1450	0.624772
$940$	−47.7711	−1.55812
$941$	31.6167	1.03068	0.515338	−	0.856987i	$-0.327666\pi$
$941$	31.6167	1.03068	0.515338	+	0.856987i	$0.327666\pi$
$942$	−173.444	−5.65111
$943$	−8.92178	−0.290533
$944$	−43.5778	−1.41834
$945$	0	0
$946$	−56.3936	−1.83351
$947$	16.1626	0.525215	0.262607	−	0.964903i	$-0.415418\pi$
$947$	16.1626	0.525215	0.262607	+	0.964903i	$0.415418\pi$
$948$	202.316	6.57091
$949$	11.1332	0.361399
$950$	−4.01484	−0.130259
$951$	57.2412	1.85617
$952$	0	0
$953$	31.5802	1.02298	0.511492	−	0.859288i	$-0.329093\pi$
$953$	31.5802	1.02298	0.511492	+	0.859288i	$0.329093\pi$
$954$	81.5387	2.63991
$955$	26.4920	0.857261
$956$	133.183	4.30744
$957$	32.6221	1.05452
$958$	55.8002	1.80282
$959$	0	0
$960$	−29.1426	−0.940573
$961$	−30.6058	−0.987284
$962$	15.5296	0.500694
$963$	−99.3234	−3.20065
$964$	81.7710	2.63367
$965$	−11.6315	−0.374432
$966$	0	0
$967$	−47.3998	−1.52427	−0.762137	−	0.647415i	$-0.775850\pi$
$967$	−47.3998	−1.52427	−0.762137	+	0.647415i	$0.775850\pi$
$968$	9.60450	0.308700
$969$	−14.0847	−0.452467
$970$	−22.6350	−0.726765
$971$	27.0996	0.869669	0.434835	−	0.900510i	$-0.356807\pi$
$971$	27.0996	0.869669	0.434835	+	0.900510i	$0.356807\pi$
$972$	44.0566	1.41312
$973$	0	0
$974$	−79.9177	−2.56073
$975$	16.5510	0.530057
$976$	−65.6676	−2.10197
$977$	29.9068	0.956804	0.478402	−	0.878141i	$-0.341216\pi$
$977$	29.9068	0.956804	0.478402	+	0.878141i	$0.341216\pi$
$978$	11.7476	0.375647
$979$	4.66363	0.149050
$980$	0	0
$981$	−75.4761	−2.40977
$982$	44.4634	1.41888
$983$	−17.8375	−0.568928	−0.284464	−	0.958687i	$-0.591816\pi$
$983$	−17.8375	−0.568928	−0.284464	+	0.958687i	$0.591816\pi$
$984$	106.530	3.39606
$985$	−8.30071	−0.264483
$986$	40.3413	1.28473
$987$	0	0
$988$	17.4472	0.555071
$989$	10.6341	0.338144
$990$	−91.5917	−2.91098
$991$	−27.9506	−0.887881	−0.443940	−	0.896056i	$-0.646420\pi$
$991$	−27.9506	−0.887881	−0.443940	+	0.896056i	$0.646420\pi$
$992$	5.62320	0.178537
$993$	−101.189	−3.21115
$994$	0	0
$995$	29.5127	0.935615
$996$	55.2771	1.75152
$997$	29.8690	0.945960	0.472980	−	0.881073i	$-0.343178\pi$
$997$	29.8690	0.945960	0.472980	+	0.881073i	$0.343178\pi$
$998$	−62.0891	−1.96539
$999$	−11.3189	−0.358115

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.a.n.1.6		7
3.2	odd	2		8379.2.a.cl.1.2		7
7.2	even	3		133.2.f.d.39.2	✓	14
7.3	odd	6		931.2.f.p.324.2		14
7.4	even	3		133.2.f.d.58.2	yes	14
7.5	odd	6		931.2.f.p.704.2		14
7.6	odd	2		931.2.a.o.1.6		7
21.2	odd	6		1197.2.j.l.172.6		14
21.11	odd	6		1197.2.j.l.856.6		14
21.20	even	2		8379.2.a.ck.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.f.d.39.2	✓	14	7.2	even	3
133.2.f.d.58.2	yes	14	7.4	even	3
931.2.a.n.1.6		7	1.1	even	1	trivial
931.2.a.o.1.6		7	7.6	odd	2
931.2.f.p.324.2		14	7.3	odd	6
931.2.f.p.704.2		14	7.5	odd	6
1197.2.j.l.172.6		14	21.2	odd	6
1197.2.j.l.856.6		14	21.11	odd	6
8379.2.a.ck.1.2		7	21.20	even	2
8379.2.a.cl.1.2		7	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.a (trivial)

\(f(q)\)	\(=\)	\(q+2.59421 q^{2} -2.89925 q^{3} +4.72991 q^{4} +1.85806 q^{5} -7.52126 q^{6} +7.08194 q^{8} +5.40568 q^{9} +O(q^{10})\)	\(q+2.59421 q^{2} -2.89925 q^{3} +4.72991 q^{4} +1.85806 q^{5} -7.52126 q^{6} +7.08194 q^{8} +5.40568 q^{9} +4.82019 q^{10} -3.51514 q^{11} -13.7132 q^{12} +3.68871 q^{13} -5.38698 q^{15} +8.91219 q^{16} +4.85806 q^{17} +14.0234 q^{18} +1.00000 q^{19} +8.78844 q^{20} -9.11899 q^{22} +1.71956 q^{23} -20.5323 q^{24} -1.54762 q^{25} +9.56927 q^{26} -6.97467 q^{27} +3.20098 q^{29} -13.9749 q^{30} +0.627857 q^{31} +8.95619 q^{32} +10.1913 q^{33} +12.6028 q^{34} +25.5683 q^{36} +1.62286 q^{37} +2.59421 q^{38} -10.6945 q^{39} +13.1587 q^{40} -5.18841 q^{41} +6.18419 q^{43} -16.6263 q^{44} +10.0441 q^{45} +4.46089 q^{46} -5.43568 q^{47} -25.8387 q^{48} -4.01484 q^{50} -14.0847 q^{51} +17.4472 q^{52} +5.81446 q^{53} -18.0937 q^{54} -6.53133 q^{55} -2.89925 q^{57} +8.30400 q^{58} -4.88969 q^{59} -25.4799 q^{60} -7.36829 q^{61} +1.62879 q^{62} +5.40982 q^{64} +6.85384 q^{65} +26.4383 q^{66} -0.0879948 q^{67} +22.9782 q^{68} -4.98544 q^{69} +15.7990 q^{71} +38.2827 q^{72} +3.01818 q^{73} +4.21003 q^{74} +4.48694 q^{75} +4.72991 q^{76} -27.7438 q^{78} -14.7534 q^{79} +16.5594 q^{80} +4.00431 q^{81} -13.4598 q^{82} -4.03094 q^{83} +9.02656 q^{85} +16.0431 q^{86} -9.28045 q^{87} -24.8940 q^{88} -1.32673 q^{89} +26.0564 q^{90} +8.13335 q^{92} -1.82032 q^{93} -14.1013 q^{94} +1.85806 q^{95} -25.9663 q^{96} -4.69587 q^{97} -19.0017 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 2 q^{2} - 2 q^{3} + 10 q^{4} - 2 q^{5} - 4 q^{6} + 12 q^{8} + 15 q^{9}+O(q^{10}) \) 7 * q + 2 * q^2 - 2 * q^3 + 10 * q^4 - 2 * q^5 - 4 * q^6 + 12 * q^8 + 15 * q^9	\( 7 q + 2 q^{2} - 2 q^{3} + 10 q^{4} - 2 q^{5} - 4 q^{6} + 12 q^{8} + 15 q^{9} + 7 q^{11} - 22 q^{12} + 6 q^{13} + 2 q^{15} + 24 q^{16} + 19 q^{17} - 12 q^{18} + 7 q^{19} - 8 q^{20} - 6 q^{22} - q^{23} + 20 q^{24} - 3 q^{25} + 12 q^{26} - 14 q^{27} + 24 q^{29} - 20 q^{30} + 26 q^{32} - 14 q^{33} + 6 q^{34} + 46 q^{36} + 8 q^{37} + 2 q^{38} + 16 q^{39} - 10 q^{40} - 4 q^{41} + 4 q^{43} + 26 q^{44} + 14 q^{45} - 16 q^{46} + 5 q^{47} - 28 q^{48} + 16 q^{50} - 4 q^{51} + 42 q^{52} + 20 q^{53} - 24 q^{54} - 30 q^{55} - 2 q^{57} - 16 q^{59} - 44 q^{60} + 5 q^{61} + 24 q^{62} + 32 q^{64} + 26 q^{65} + 68 q^{66} - 4 q^{67} + 22 q^{68} - 36 q^{69} + 12 q^{71} + 3 q^{73} - 4 q^{74} + 18 q^{75} + 10 q^{76} - 14 q^{78} - 20 q^{79} - 4 q^{80} + 27 q^{81} - 48 q^{82} - 11 q^{83} + 26 q^{85} + 36 q^{86} - 16 q^{87} - 32 q^{88} - 10 q^{89} + 32 q^{90} - 30 q^{92} - 4 q^{93} + 16 q^{94} - 2 q^{95} - 12 q^{96} - 4 q^{97} + 15 q^{99}+O(q^{100}) \) 7 * q + 2 * q^2 - 2 * q^3 + 10 * q^4 - 2 * q^5 - 4 * q^6 + 12 * q^8 + 15 * q^9 + 7 * q^11 - 22 * q^12 + 6 * q^13 + 2 * q^15 + 24 * q^16 + 19 * q^17 - 12 * q^18 + 7 * q^19 - 8 * q^20 - 6 * q^22 - q^23 + 20 * q^24 - 3 * q^25 + 12 * q^26 - 14 * q^27 + 24 * q^29 - 20 * q^30 + 26 * q^32 - 14 * q^33 + 6 * q^34 + 46 * q^36 + 8 * q^37 + 2 * q^38 + 16 * q^39 - 10 * q^40 - 4 * q^41 + 4 * q^43 + 26 * q^44 + 14 * q^45 - 16 * q^46 + 5 * q^47 - 28 * q^48 + 16 * q^50 - 4 * q^51 + 42 * q^52 + 20 * q^53 - 24 * q^54 - 30 * q^55 - 2 * q^57 - 16 * q^59 - 44 * q^60 + 5 * q^61 + 24 * q^62 + 32 * q^64 + 26 * q^65 + 68 * q^66 - 4 * q^67 + 22 * q^68 - 36 * q^69 + 12 * q^71 + 3 * q^73 - 4 * q^74 + 18 * q^75 + 10 * q^76 - 14 * q^78 - 20 * q^79 - 4 * q^80 + 27 * q^81 - 48 * q^82 - 11 * q^83 + 26 * q^85 + 36 * q^86 - 16 * q^87 - 32 * q^88 - 10 * q^89 + 32 * q^90 - 30 * q^92 - 4 * q^93 + 16 * q^94 - 2 * q^95 - 12 * q^96 - 4 * q^97 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more