LMFDB - Embedded newform 2541.2.a.br.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2541,2,Mod(1,2541)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2541, 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("2541.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2541 = 3 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2541.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:	$20.2899871536$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 19x^{8} - x^{7} + 124x^{6} + 6x^{5} - 316x^{4} + 17x^{3} + 253x^{2} - 70x - 11 $ x^10 - 19x^8 - x^7 + 124x^6 + 6x^5 - 316x^4 + 17x^3 + 253x^2 - 70*x - 11
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 231)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.473713$ of defining polynomial
Character	$\chi$	$=$	2541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.473713 q^{2} +1.00000 q^{3} -1.77560 q^{4} +3.75881 q^{5} -0.473713 q^{6} +1.00000 q^{7} +1.78855 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.473713 q^{2} +1.00000 q^{3} -1.77560 q^{4} +3.75881 q^{5} -0.473713 q^{6} +1.00000 q^{7} +1.78855 q^{8} +1.00000 q^{9} -1.78060 q^{10} -1.77560 q^{12} -2.70774 q^{13} -0.473713 q^{14} +3.75881 q^{15} +2.70393 q^{16} -2.48283 q^{17} -0.473713 q^{18} +1.74466 q^{19} -6.67413 q^{20} +1.00000 q^{21} +3.79843 q^{23} +1.78855 q^{24} +9.12868 q^{25} +1.28269 q^{26} +1.00000 q^{27} -1.77560 q^{28} +5.80060 q^{29} -1.78060 q^{30} +2.24763 q^{31} -4.85799 q^{32} +1.17615 q^{34} +3.75881 q^{35} -1.77560 q^{36} -7.65311 q^{37} -0.826469 q^{38} -2.70774 q^{39} +6.72282 q^{40} +4.18500 q^{41} -0.473713 q^{42} -7.75162 q^{43} +3.75881 q^{45} -1.79937 q^{46} +12.4071 q^{47} +2.70393 q^{48} +1.00000 q^{49} -4.32437 q^{50} -2.48283 q^{51} +4.80786 q^{52} +8.83956 q^{53} -0.473713 q^{54} +1.78855 q^{56} +1.74466 q^{57} -2.74782 q^{58} +4.54166 q^{59} -6.67413 q^{60} +11.4825 q^{61} -1.06473 q^{62} +1.00000 q^{63} -3.10658 q^{64} -10.1779 q^{65} -12.2041 q^{67} +4.40849 q^{68} +3.79843 q^{69} -1.78060 q^{70} +7.75988 q^{71} +1.78855 q^{72} -15.6796 q^{73} +3.62538 q^{74} +9.12868 q^{75} -3.09781 q^{76} +1.28269 q^{78} +7.05380 q^{79} +10.1636 q^{80} +1.00000 q^{81} -1.98249 q^{82} -11.9004 q^{83} -1.77560 q^{84} -9.33248 q^{85} +3.67204 q^{86} +5.80060 q^{87} -1.69179 q^{89} -1.78060 q^{90} -2.70774 q^{91} -6.74448 q^{92} +2.24763 q^{93} -5.87739 q^{94} +6.55786 q^{95} -4.85799 q^{96} +6.99638 q^{97} -0.473713 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{3} + 18 q^{4} + 5 q^{5} + 10 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 10 * q^3 + 18 * q^4 + 5 * q^5 + 10 * q^7 - 3 * q^8 + 10 * q^9	$ 10 q + 10 q^{3} + 18 q^{4} + 5 q^{5} + 10 q^{7} - 3 q^{8} + 10 q^{9} - 6 q^{10} + 18 q^{12} + 6 q^{13} + 5 q^{15} + 38 q^{16} + 8 q^{17} + 7 q^{20} + 10 q^{21} - 3 q^{24} + 31 q^{25} + q^{26} + 10 q^{27} + 18 q^{28} - 14 q^{29} - 6 q^{30} + 26 q^{31} - 41 q^{32} + 21 q^{34} + 5 q^{35} + 18 q^{36} + 24 q^{37} + 8 q^{38} + 6 q^{39} - 5 q^{40} + 19 q^{41} - 6 q^{43} + 5 q^{45} - q^{46} + 15 q^{47} + 38 q^{48} + 10 q^{49} - q^{50} + 8 q^{51} - 25 q^{52} - q^{53} - 3 q^{56} + 11 q^{58} + 23 q^{59} + 7 q^{60} + 11 q^{62} + 10 q^{63} + 53 q^{64} - 29 q^{65} + 38 q^{67} + 87 q^{68} - 6 q^{70} + 26 q^{71} - 3 q^{72} - q^{73} - 39 q^{74} + 31 q^{75} - 2 q^{76} + q^{78} + 5 q^{79} + 6 q^{80} + 10 q^{81} + 5 q^{82} + 6 q^{83} + 18 q^{84} - q^{85} - 41 q^{86} - 14 q^{87} - 9 q^{89} - 6 q^{90} + 6 q^{91} - 48 q^{92} + 26 q^{93} - 42 q^{95} - 41 q^{96} + 24 q^{97}+O(q^{100}) $ 10 * q + 10 * q^3 + 18 * q^4 + 5 * q^5 + 10 * q^7 - 3 * q^8 + 10 * q^9 - 6 * q^10 + 18 * q^12 + 6 * q^13 + 5 * q^15 + 38 * q^16 + 8 * q^17 + 7 * q^20 + 10 * q^21 - 3 * q^24 + 31 * q^25 + q^26 + 10 * q^27 + 18 * q^28 - 14 * q^29 - 6 * q^30 + 26 * q^31 - 41 * q^32 + 21 * q^34 + 5 * q^35 + 18 * q^36 + 24 * q^37 + 8 * q^38 + 6 * q^39 - 5 * q^40 + 19 * q^41 - 6 * q^43 + 5 * q^45 - q^46 + 15 * q^47 + 38 * q^48 + 10 * q^49 - q^50 + 8 * q^51 - 25 * q^52 - q^53 - 3 * q^56 + 11 * q^58 + 23 * q^59 + 7 * q^60 + 11 * q^62 + 10 * q^63 + 53 * q^64 - 29 * q^65 + 38 * q^67 + 87 * q^68 - 6 * q^70 + 26 * q^71 - 3 * q^72 - q^73 - 39 * q^74 + 31 * q^75 - 2 * q^76 + q^78 + 5 * q^79 + 6 * q^80 + 10 * q^81 + 5 * q^82 + 6 * q^83 + 18 * q^84 - q^85 - 41 * q^86 - 14 * q^87 - 9 * q^89 - 6 * q^90 + 6 * q^91 - 48 * q^92 + 26 * q^93 - 42 * q^95 - 41 * q^96 + 24 * q^97

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 $

$2$	−0.473713	−0.334966	−0.167483	−	0.985875i	$-0.553564\pi$
$2$	−0.473713	−0.334966	−0.167483	+	0.985875i	$0.553564\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.77560	−0.887798
$5$	3.75881	1.68099	0.840496	−	0.541818i	$-0.182264\pi$
$5$	3.75881	1.68099	0.840496	+	0.541818i	$0.182264\pi$
$6$	−0.473713	−0.193393
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.78855	0.632348
$9$	1.00000	0.333333
$10$	−1.78060	−0.563075
$11$	0	0
$11$	0	0
$12$	−1.77560	−0.512570
$13$	−2.70774	−0.750993	−0.375496	−	0.926824i	$-0.622528\pi$
$13$	−2.70774	−0.750993	−0.375496	+	0.926824i	$0.622528\pi$
$14$	−0.473713	−0.126605
$15$	3.75881	0.970521
$16$	2.70393	0.675983
$17$	−2.48283	−0.602174	−0.301087	−	0.953597i	$-0.597349\pi$
$17$	−2.48283	−0.602174	−0.301087	+	0.953597i	$0.597349\pi$
$18$	−0.473713	−0.111655
$19$	1.74466	0.400253	0.200126	−	0.979770i	$-0.435865\pi$
$19$	1.74466	0.400253	0.200126	+	0.979770i	$0.435865\pi$
$20$	−6.67413	−1.49238
$21$	1.00000	0.218218
$22$	0	0
$23$	3.79843	0.792028	0.396014	−	0.918244i	$-0.370393\pi$
$23$	3.79843	0.792028	0.396014	+	0.918244i	$0.370393\pi$
$24$	1.78855	0.365086
$25$	9.12868	1.82574
$26$	1.28269	0.251557
$27$	1.00000	0.192450
$28$	−1.77560	−0.335556
$29$	5.80060	1.07714	0.538572	−	0.842580i	$-0.318964\pi$
$29$	5.80060	1.07714	0.538572	+	0.842580i	$0.318964\pi$
$30$	−1.78060	−0.325091
$31$	2.24763	0.403686	0.201843	−	0.979418i	$-0.435307\pi$
$31$	2.24763	0.403686	0.201843	+	0.979418i	$0.435307\pi$
$32$	−4.85799	−0.858779
$33$	0	0
$34$	1.17615	0.201707
$35$	3.75881	0.635355
$36$	−1.77560	−0.295933
$37$	−7.65311	−1.25816	−0.629082	−	0.777339i	$-0.716569\pi$
$37$	−7.65311	−1.25816	−0.629082	+	0.777339i	$0.716569\pi$
$38$	−0.826469	−0.134071
$39$	−2.70774	−0.433586
$40$	6.72282	1.06297
$41$	4.18500	0.653587	0.326793	−	0.945096i	$-0.394032\pi$
$41$	4.18500	0.653587	0.326793	+	0.945096i	$0.394032\pi$
$42$	−0.473713	−0.0730955
$43$	−7.75162	−1.18211	−0.591056	−	0.806631i	$-0.701289\pi$
$43$	−7.75162	−1.18211	−0.591056	+	0.806631i	$0.701289\pi$
$44$	0	0
$45$	3.75881	0.560331
$46$	−1.79937	−0.265302
$47$	12.4071	1.80976	0.904878	−	0.425670i	$-0.139962\pi$
$47$	12.4071	1.80976	0.904878	+	0.425670i	$0.139962\pi$
$48$	2.70393	0.390279
$49$	1.00000	0.142857
$50$	−4.32437	−0.611559
$51$	−2.48283	−0.347665
$52$	4.80786	0.666730
$53$	8.83956	1.21421	0.607103	−	0.794623i	$-0.292331\pi$
$53$	8.83956	1.21421	0.607103	+	0.794623i	$0.292331\pi$
$54$	−0.473713	−0.0644642
$55$	0	0
$56$	1.78855	0.239005
$57$	1.74466	0.231086
$58$	−2.74782	−0.360806
$59$	4.54166	0.591274	0.295637	−	0.955300i	$-0.404468\pi$
$59$	4.54166	0.591274	0.295637	+	0.955300i	$0.404468\pi$
$60$	−6.67413	−0.861627
$61$	11.4825	1.47019	0.735093	−	0.677967i	$-0.237139\pi$
$61$	11.4825	1.47019	0.735093	+	0.677967i	$0.237139\pi$
$62$	−1.06473	−0.135221
$63$	1.00000	0.125988
$64$	−3.10658	−0.388322
$65$	−10.1779	−1.26241
$66$	0	0
$67$	−12.2041	−1.49096	−0.745481	−	0.666527i	$-0.767780\pi$
$67$	−12.2041	−1.49096	−0.745481	+	0.666527i	$0.767780\pi$
$68$	4.40849	0.534609
$69$	3.79843	0.457278
$70$	−1.78060	−0.212822
$71$	7.75988	0.920928	0.460464	−	0.887678i	$-0.347683\pi$
$71$	7.75988	0.920928	0.460464	+	0.887678i	$0.347683\pi$
$72$	1.78855	0.210783
$73$	−15.6796	−1.83516	−0.917580	−	0.397552i	$-0.869860\pi$
$73$	−15.6796	−1.83516	−0.917580	+	0.397552i	$0.869860\pi$
$74$	3.62538	0.421441
$75$	9.12868	1.05409
$76$	−3.09781	−0.355344
$77$	0	0
$78$	1.28269	0.145236
$79$	7.05380	0.793615	0.396807	−	0.917902i	$-0.370118\pi$
$79$	7.05380	0.793615	0.396807	+	0.917902i	$0.370118\pi$
$80$	10.1636	1.13632
$81$	1.00000	0.111111
$82$	−1.98249	−0.218929
$83$	−11.9004	−1.30624	−0.653122	−	0.757253i	$-0.726541\pi$
$83$	−11.9004	−1.30624	−0.653122	+	0.757253i	$0.726541\pi$
$84$	−1.77560	−0.193733
$85$	−9.33248	−1.01225
$86$	3.67204	0.395967
$87$	5.80060	0.621889
$88$	0	0
$89$	−1.69179	−0.179329	−0.0896647	−	0.995972i	$-0.528580\pi$
$89$	−1.69179	−0.179329	−0.0896647	+	0.995972i	$0.528580\pi$
$90$	−1.78060	−0.187692
$91$	−2.70774	−0.283848
$92$	−6.74448	−0.703161
$93$	2.24763	0.233068
$94$	−5.87739	−0.606206
$95$	6.55786	0.672822
$96$	−4.85799	−0.495816
$97$	6.99638	0.710375	0.355188	−	0.934795i	$-0.384417\pi$
$97$	6.99638	0.710375	0.355188	+	0.934795i	$0.384417\pi$
$98$	−0.473713	−0.0478522
$99$	0	0
$100$	−16.2088	−1.62088
$101$	−2.71683	−0.270335	−0.135167	−	0.990823i	$-0.543157\pi$
$101$	−2.71683	−0.270335	−0.135167	+	0.990823i	$0.543157\pi$
$102$	1.17615	0.116456
$103$	−0.255788	−0.0252036	−0.0126018	−	0.999921i	$-0.504011\pi$
$103$	−0.255788	−0.0252036	−0.0126018	+	0.999921i	$0.504011\pi$
$104$	−4.84293	−0.474888
$105$	3.75881	0.366823
$106$	−4.18741	−0.406717
$107$	−11.8608	−1.14662	−0.573311	−	0.819338i	$-0.694341\pi$
$107$	−11.8608	−1.14662	−0.573311	+	0.819338i	$0.694341\pi$
$108$	−1.77560	−0.170857
$109$	15.8720	1.52026	0.760129	−	0.649772i	$-0.225136\pi$
$109$	15.8720	1.52026	0.760129	+	0.649772i	$0.225136\pi$
$110$	0	0
$111$	−7.65311	−0.726401
$112$	2.70393	0.255498
$113$	−5.11650	−0.481320	−0.240660	−	0.970609i	$-0.577364\pi$
$113$	−5.11650	−0.481320	−0.240660	+	0.970609i	$0.577364\pi$
$114$	−0.826469	−0.0774059
$115$	14.2776	1.33139
$116$	−10.2995	−0.956286
$117$	−2.70774	−0.250331
$118$	−2.15144	−0.198056
$119$	−2.48283	−0.227600
$120$	6.72282	0.613707
$121$	0	0
$122$	−5.43942	−0.492462
$123$	4.18500	0.377348
$124$	−3.99088	−0.358392
$125$	15.5189	1.38805
$126$	−0.473713	−0.0422017
$127$	−0.203338	−0.0180433	−0.00902166	−	0.999959i	$-0.502872\pi$
$127$	−0.203338	−0.0180433	−0.00902166	+	0.999959i	$0.502872\pi$
$128$	11.1876	0.988853
$129$	−7.75162	−0.682492
$130$	4.82140	0.422865
$131$	10.2788	0.898067	0.449034	−	0.893515i	$-0.351768\pi$
$131$	10.2788	0.898067	0.449034	+	0.893515i	$0.351768\pi$
$132$	0	0
$133$	1.74466	0.151281
$134$	5.78122	0.499421
$135$	3.75881	0.323507
$136$	−4.44065	−0.380783
$137$	−17.1096	−1.46177	−0.730887	−	0.682499i	$-0.760893\pi$
$137$	−17.1096	−1.46177	−0.730887	+	0.682499i	$0.760893\pi$
$138$	−1.79937	−0.153172
$139$	−19.5009	−1.65405	−0.827023	−	0.562168i	$-0.809968\pi$
$139$	−19.5009	−1.65405	−0.827023	+	0.562168i	$0.809968\pi$
$140$	−6.67413	−0.564067
$141$	12.4071	1.04486
$142$	−3.67596	−0.308479
$143$	0	0
$144$	2.70393	0.225328
$145$	21.8034	1.81067
$146$	7.42763	0.614715
$147$	1.00000	0.0824786
$148$	13.5888	1.11699
$149$	9.89037	0.810251	0.405125	−	0.914261i	$-0.367228\pi$
$149$	9.89037	0.810251	0.405125	+	0.914261i	$0.367228\pi$
$150$	−4.32437	−0.353084
$151$	15.5014	1.26148	0.630741	−	0.775993i	$-0.282751\pi$
$151$	15.5014	1.26148	0.630741	+	0.775993i	$0.282751\pi$
$152$	3.12041	0.253099
$153$	−2.48283	−0.200725
$154$	0	0
$155$	8.44843	0.678594
$156$	4.80786	0.384937
$157$	16.9536	1.35305	0.676523	−	0.736422i	$-0.263486\pi$
$157$	16.9536	1.35305	0.676523	+	0.736422i	$0.263486\pi$
$158$	−3.34148	−0.265834
$159$	8.83956	0.701022
$160$	−18.2603	−1.44360
$161$	3.79843	0.299359
$162$	−0.473713	−0.0372184
$163$	19.9739	1.56447	0.782237	−	0.622981i	$-0.214079\pi$
$163$	19.9739	1.56447	0.782237	+	0.622981i	$0.214079\pi$
$164$	−7.43086	−0.580253
$165$	0	0
$166$	5.63739	0.437547
$167$	−17.4516	−1.35044	−0.675222	−	0.737615i	$-0.735952\pi$
$167$	−17.4516	−1.35044	−0.675222	+	0.737615i	$0.735952\pi$
$168$	1.78855	0.137990
$169$	−5.66813	−0.436010
$170$	4.42092	0.339069
$171$	1.74466	0.133418
$172$	13.7637	1.04948
$173$	9.35944	0.711585	0.355793	−	0.934565i	$-0.384211\pi$
$173$	9.35944	0.711585	0.355793	+	0.934565i	$0.384211\pi$
$174$	−2.74782	−0.208312
$175$	9.12868	0.690063
$176$	0	0
$177$	4.54166	0.341372
$178$	0.801423	0.0600692
$179$	5.49347	0.410602	0.205301	−	0.978699i	$-0.434183\pi$
$179$	5.49347	0.410602	0.205301	+	0.978699i	$0.434183\pi$
$180$	−6.67413	−0.497461
$181$	−11.1844	−0.831332	−0.415666	−	0.909517i	$-0.636451\pi$
$181$	−11.1844	−0.831332	−0.415666	+	0.909517i	$0.636451\pi$
$182$	1.28269	0.0950795
$183$	11.4825	0.848812
$184$	6.79369	0.500837
$185$	−28.7666	−2.11496
$186$	−1.06473	−0.0780699
$187$	0	0
$188$	−22.0299	−1.60670
$189$	1.00000	0.0727393
$190$	−3.10654	−0.225372
$191$	−5.75822	−0.416650	−0.208325	−	0.978060i	$-0.566801\pi$
$191$	−5.75822	−0.416650	−0.208325	+	0.978060i	$0.566801\pi$
$192$	−3.10658	−0.224198
$193$	14.8846	1.07142	0.535708	−	0.844404i	$-0.320045\pi$
$193$	14.8846	1.07142	0.535708	+	0.844404i	$0.320045\pi$
$194$	−3.31428	−0.237951
$195$	−10.1779	−0.728854
$196$	−1.77560	−0.126828
$197$	−12.5476	−0.893978	−0.446989	−	0.894540i	$-0.647504\pi$
$197$	−12.5476	−0.893978	−0.446989	+	0.894540i	$0.647504\pi$
$198$	0	0
$199$	0.834418	0.0591503	0.0295752	−	0.999563i	$-0.490585\pi$
$199$	0.834418	0.0591503	0.0295752	+	0.999563i	$0.490585\pi$
$200$	16.3271	1.15450
$201$	−12.2041	−0.860808
$202$	1.28700	0.0905528
$203$	5.80060	0.407122
$204$	4.40849	0.308656
$205$	15.7306	1.09867
$206$	0.121170	0.00844233
$207$	3.79843	0.264009
$208$	−7.32155	−0.507658
$209$	0	0
$210$	−1.78060	−0.122873
$211$	26.8703	1.84983	0.924914	−	0.380176i	$-0.124137\pi$
$211$	26.8703	1.84983	0.924914	+	0.380176i	$0.124137\pi$
$212$	−15.6955	−1.07797
$213$	7.75988	0.531698
$214$	5.61859	0.384079
$215$	−29.1369	−1.98712
$216$	1.78855	0.121695
$217$	2.24763	0.152579
$218$	−7.51876	−0.509234
$219$	−15.6796	−1.05953
$220$	0	0
$221$	6.72285	0.452228
$222$	3.62538	0.243319
$223$	4.01918	0.269144	0.134572	−	0.990904i	$-0.457034\pi$
$223$	4.01918	0.269144	0.134572	+	0.990904i	$0.457034\pi$
$224$	−4.85799	−0.324588
$225$	9.12868	0.608578
$226$	2.42375	0.161226
$227$	11.7020	0.776690	0.388345	−	0.921514i	$-0.373047\pi$
$227$	11.7020	0.776690	0.388345	+	0.921514i	$0.373047\pi$
$228$	−3.09781	−0.205158
$229$	−6.54504	−0.432508	−0.216254	−	0.976337i	$-0.569384\pi$
$229$	−6.54504	−0.432508	−0.216254	+	0.976337i	$0.569384\pi$
$230$	−6.76349	−0.445971
$231$	0	0
$232$	10.3746	0.681129
$233$	−0.172567	−0.0113052	−0.00565262	−	0.999984i	$-0.501799\pi$
$233$	−0.172567	−0.0113052	−0.00565262	+	0.999984i	$0.501799\pi$
$234$	1.28269	0.0838522
$235$	46.6358	3.04219
$236$	−8.06415	−0.524932
$237$	7.05380	0.458194
$238$	1.17615	0.0762383
$239$	10.4504	0.675982	0.337991	−	0.941149i	$-0.390253\pi$
$239$	10.4504	0.675982	0.337991	+	0.941149i	$0.390253\pi$
$240$	10.1636	0.656056
$241$	3.41821	0.220186	0.110093	−	0.993921i	$-0.464885\pi$
$241$	3.41821	0.220186	0.110093	+	0.993921i	$0.464885\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	−20.3883	−1.30523
$245$	3.75881	0.240142
$246$	−1.98249	−0.126399
$247$	−4.72409	−0.300587
$248$	4.02000	0.255270
$249$	−11.9004	−0.754160
$250$	−7.35151	−0.464951
$251$	12.6751	0.800047	0.400024	−	0.916505i	$-0.369002\pi$
$251$	12.6751	0.800047	0.400024	+	0.916505i	$0.369002\pi$
$252$	−1.77560	−0.111852
$253$	0	0
$254$	0.0963238	0.00604389
$255$	−9.33248	−0.584422
$256$	0.913441	0.0570901
$257$	−18.1852	−1.13436	−0.567182	−	0.823593i	$-0.691966\pi$
$257$	−18.1852	−1.13436	−0.567182	+	0.823593i	$0.691966\pi$
$258$	3.67204	0.228611
$259$	−7.65311	−0.475541
$260$	18.0718	1.12077
$261$	5.80060	0.359048
$262$	−4.86922	−0.300822
$263$	−15.7837	−0.973264	−0.486632	−	0.873607i	$-0.661775\pi$
$263$	−15.7837	−0.973264	−0.486632	+	0.873607i	$0.661775\pi$
$264$	0	0
$265$	33.2262	2.04107
$266$	−0.826469	−0.0506741
$267$	−1.69179	−0.103536
$268$	21.6695	1.32367
$269$	22.9896	1.40170	0.700851	−	0.713308i	$-0.252804\pi$
$269$	22.9896	1.40170	0.700851	+	0.713308i	$0.252804\pi$
$270$	−1.78060	−0.108364
$271$	−9.34021	−0.567377	−0.283689	−	0.958916i	$-0.591558\pi$
$271$	−9.34021	−0.567377	−0.283689	+	0.958916i	$0.591558\pi$
$272$	−6.71339	−0.407059
$273$	−2.70774	−0.163880
$274$	8.10505	0.489644
$275$	0	0
$276$	−6.74448	−0.405970
$277$	−19.4367	−1.16784	−0.583918	−	0.811813i	$-0.698481\pi$
$277$	−19.4367	−1.16784	−0.583918	+	0.811813i	$0.698481\pi$
$278$	9.23784	0.554049
$279$	2.24763	0.134562
$280$	6.72282	0.401765
$281$	4.44358	0.265082	0.132541	−	0.991178i	$-0.457686\pi$
$281$	4.44358	0.265082	0.132541	+	0.991178i	$0.457686\pi$
$282$	−5.87739	−0.349993
$283$	−13.8486	−0.823216	−0.411608	−	0.911361i	$-0.635033\pi$
$283$	−13.8486	−0.823216	−0.411608	+	0.911361i	$0.635033\pi$
$284$	−13.7784	−0.817598
$285$	6.55786	0.388454
$286$	0	0
$287$	4.18500	0.247033
$288$	−4.85799	−0.286260
$289$	−10.8356	−0.637387
$290$	−10.3285	−0.606512
$291$	6.99638	0.410135
$292$	27.8406	1.62925
$293$	19.2359	1.12377	0.561887	−	0.827214i	$-0.310076\pi$
$293$	19.2359	1.12377	0.561887	+	0.827214i	$0.310076\pi$
$294$	−0.473713	−0.0276275
$295$	17.0713	0.993927
$296$	−13.6880	−0.795596
$297$	0	0
$298$	−4.68520	−0.271406
$299$	−10.2852	−0.594807
$300$	−16.2088	−0.935818
$301$	−7.75162	−0.446796
$302$	−7.34319	−0.422553
$303$	−2.71683	−0.156078
$304$	4.71745	0.270564
$305$	43.1606	2.47137
$306$	1.17615	0.0672358
$307$	−2.24474	−0.128114	−0.0640571	−	0.997946i	$-0.520404\pi$
$307$	−2.24474	−0.128114	−0.0640571	+	0.997946i	$0.520404\pi$
$308$	0	0
$309$	−0.255788	−0.0145513
$310$	−4.00213	−0.227306
$311$	12.6291	0.716129	0.358065	−	0.933697i	$-0.383437\pi$
$311$	12.6291	0.716129	0.358065	+	0.933697i	$0.383437\pi$
$312$	−4.84293	−0.274177
$313$	1.06646	0.0602797	0.0301398	−	0.999546i	$-0.490405\pi$
$313$	1.06646	0.0602797	0.0301398	+	0.999546i	$0.490405\pi$
$314$	−8.03115	−0.453224
$315$	3.75881	0.211785
$316$	−12.5247	−0.704569
$317$	−25.1710	−1.41374	−0.706872	−	0.707342i	$-0.749894\pi$
$317$	−25.1710	−1.41374	−0.706872	+	0.707342i	$0.749894\pi$
$318$	−4.18741	−0.234818
$319$	0	0
$320$	−11.6770	−0.652766
$321$	−11.8608	−0.662003
$322$	−1.79937	−0.100275
$323$	−4.33169	−0.241022
$324$	−1.77560	−0.0986442
$325$	−24.7181	−1.37111
$326$	−9.46188	−0.524045
$327$	15.8720	0.877722
$328$	7.48507	0.413294
$329$	12.4071	0.684024
$330$	0	0
$331$	−8.53640	−0.469203	−0.234601	−	0.972092i	$-0.575378\pi$
$331$	−8.53640	−0.469203	−0.234601	+	0.972092i	$0.575378\pi$
$332$	21.1304	1.15968
$333$	−7.65311	−0.419388
$334$	8.26704	0.452352
$335$	−45.8728	−2.50630
$336$	2.70393	0.147512
$337$	17.2565	0.940020	0.470010	−	0.882661i	$-0.344250\pi$
$337$	17.2565	0.940020	0.470010	+	0.882661i	$0.344250\pi$
$338$	2.68507	0.146048
$339$	−5.11650	−0.277890
$340$	16.5707	0.898673
$341$	0	0
$342$	−0.826469	−0.0446903
$343$	1.00000	0.0539949
$344$	−13.8642	−0.747505
$345$	14.2776	0.768680
$346$	−4.43369	−0.238357
$347$	−4.15698	−0.223159	−0.111579	−	0.993756i	$-0.535591\pi$
$347$	−4.15698	−0.223159	−0.111579	+	0.993756i	$0.535591\pi$
$348$	−10.2995	−0.552112
$349$	−7.70785	−0.412592	−0.206296	−	0.978490i	$-0.566141\pi$
$349$	−7.70785	−0.412592	−0.206296	+	0.978490i	$0.566141\pi$
$350$	−4.32437	−0.231147
$351$	−2.70774	−0.144529
$352$	0	0
$353$	−4.84242	−0.257736	−0.128868	−	0.991662i	$-0.541134\pi$
$353$	−4.84242	−0.257736	−0.128868	+	0.991662i	$0.541134\pi$
$354$	−2.15144	−0.114348
$355$	29.1679	1.54807
$356$	3.00393	0.159208
$357$	−2.48283	−0.131405
$358$	−2.60233	−0.137537
$359$	−4.41834	−0.233191	−0.116596	−	0.993179i	$-0.537198\pi$
$359$	−4.41834	−0.233191	−0.116596	+	0.993179i	$0.537198\pi$
$360$	6.72282	0.354324
$361$	−15.9562	−0.839798
$362$	5.29821	0.278468
$363$	0	0
$364$	4.80786	0.252000
$365$	−58.9367	−3.08489
$366$	−5.43942	−0.284323
$367$	−29.5315	−1.54153	−0.770766	−	0.637118i	$-0.780126\pi$
$367$	−29.5315	−1.54153	−0.770766	+	0.637118i	$0.780126\pi$
$368$	10.2707	0.535398
$369$	4.18500	0.217862
$370$	13.6271	0.708440
$371$	8.83956	0.458927
$372$	−3.99088	−0.206918
$373$	−7.64965	−0.396084	−0.198042	−	0.980194i	$-0.563458\pi$
$373$	−7.64965	−0.396084	−0.198042	+	0.980194i	$0.563458\pi$
$374$	0	0
$375$	15.5189	0.801394
$376$	22.1906	1.14440
$377$	−15.7065	−0.808927
$378$	−0.473713	−0.0243652
$379$	−11.2094	−0.575788	−0.287894	−	0.957662i	$-0.592955\pi$
$379$	−11.2094	−0.575788	−0.287894	+	0.957662i	$0.592955\pi$
$380$	−11.6441	−0.597330
$381$	−0.203338	−0.0104173
$382$	2.72774	0.139563
$383$	−24.7447	−1.26440	−0.632199	−	0.774806i	$-0.717847\pi$
$383$	−24.7447	−1.26440	−0.632199	+	0.774806i	$0.717847\pi$
$384$	11.1876	0.570915
$385$	0	0
$386$	−7.05102	−0.358887
$387$	−7.75162	−0.394037
$388$	−12.4228	−0.630670
$389$	−29.0347	−1.47212	−0.736060	−	0.676917i	$-0.763316\pi$
$389$	−29.0347	−1.47212	−0.736060	+	0.676917i	$0.763316\pi$
$390$	4.82140	0.244141
$391$	−9.43085	−0.476939
$392$	1.78855	0.0903354
$393$	10.2788	0.518499
$394$	5.94395	0.299452
$395$	26.5139	1.33406
$396$	0	0
$397$	−8.27461	−0.415291	−0.207645	−	0.978204i	$-0.566580\pi$
$397$	−8.27461	−0.415291	−0.207645	+	0.978204i	$0.566580\pi$
$398$	−0.395275	−0.0198133
$399$	1.74466	0.0873423
$400$	24.6833	1.23417
$401$	−26.7390	−1.33528	−0.667642	−	0.744483i	$-0.732696\pi$
$401$	−26.7390	−1.33528	−0.667642	+	0.744483i	$0.732696\pi$
$402$	5.78122	0.288341
$403$	−6.08601	−0.303166
$404$	4.82399	0.240003
$405$	3.75881	0.186777
$406$	−2.74782	−0.136372
$407$	0	0
$408$	−4.44065	−0.219845
$409$	−34.6829	−1.71496	−0.857479	−	0.514519i	$-0.827970\pi$
$409$	−34.6829	−1.71496	−0.857479	+	0.514519i	$0.827970\pi$
$410$	−7.45180	−0.368018
$411$	−17.1096	−0.843955
$412$	0.454177	0.0223757
$413$	4.54166	0.223480
$414$	−1.79937	−0.0884341
$415$	−44.7315	−2.19578
$416$	13.1542	0.644936
$417$	−19.5009	−0.954964
$418$	0	0
$419$	−4.34546	−0.212290	−0.106145	−	0.994351i	$-0.533851\pi$
$419$	−4.34546	−0.212290	−0.106145	+	0.994351i	$0.533851\pi$
$420$	−6.67413	−0.325664
$421$	−4.73841	−0.230936	−0.115468	−	0.993311i	$-0.536837\pi$
$421$	−4.73841	−0.230936	−0.115468	+	0.993311i	$0.536837\pi$
$422$	−12.7288	−0.619629
$423$	12.4071	0.603252
$424$	15.8100	0.767800
$425$	−22.6649	−1.09941
$426$	−3.67596	−0.178101
$427$	11.4825	0.555678
$428$	21.0599	1.01797
$429$	0	0
$430$	13.8025	0.665617
$431$	29.8622	1.43841	0.719206	−	0.694797i	$-0.244506\pi$
$431$	29.8622	1.43841	0.719206	+	0.694797i	$0.244506\pi$
$432$	2.70393	0.130093
$433$	−21.7239	−1.04399	−0.521993	−	0.852950i	$-0.674811\pi$
$433$	−21.7239	−1.04399	−0.521993	+	0.852950i	$0.674811\pi$
$434$	−1.06473	−0.0511088
$435$	21.8034	1.04539
$436$	−28.1822	−1.34968
$437$	6.62698	0.317012
$438$	7.42763	0.354906
$439$	40.3447	1.92555	0.962773	−	0.270313i	$-0.0871271\pi$
$439$	40.3447	1.92555	0.962773	+	0.270313i	$0.0871271\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	−3.18470	−0.151481
$443$	−13.8789	−0.659408	−0.329704	−	0.944084i	$-0.606949\pi$
$443$	−13.8789	−0.659408	−0.329704	+	0.944084i	$0.606949\pi$
$444$	13.5888	0.644897
$445$	−6.35912	−0.301451
$446$	−1.90394	−0.0901540
$447$	9.89037	0.467799
$448$	−3.10658	−0.146772
$449$	−14.3023	−0.674966	−0.337483	−	0.941332i	$-0.609575\pi$
$449$	−14.3023	−0.674966	−0.337483	+	0.941332i	$0.609575\pi$
$450$	−4.32437	−0.203853
$451$	0	0
$452$	9.08484	0.427315
$453$	15.5014	0.728317
$454$	−5.54340	−0.260164
$455$	−10.1779	−0.477147
$456$	3.12041	0.146127
$457$	14.1278	0.660869	0.330435	−	0.943829i	$-0.392805\pi$
$457$	14.1278	0.660869	0.330435	+	0.943829i	$0.392805\pi$
$458$	3.10047	0.144875
$459$	−2.48283	−0.115888
$460$	−25.3513	−1.18201
$461$	0.966736	0.0450254	0.0225127	−	0.999747i	$-0.492833\pi$
$461$	0.966736	0.0450254	0.0225127	+	0.999747i	$0.492833\pi$
$462$	0	0
$463$	31.8119	1.47842	0.739212	−	0.673473i	$-0.235198\pi$
$463$	31.8119	1.47842	0.739212	+	0.673473i	$0.235198\pi$
$464$	15.6844	0.728131
$465$	8.44843	0.391786
$466$	0.0817473	0.00378687
$467$	−29.6133	−1.37034	−0.685169	−	0.728384i	$-0.740272\pi$
$467$	−29.6133	−1.37034	−0.685169	+	0.728384i	$0.740272\pi$
$468$	4.80786	0.222243
$469$	−12.2041	−0.563531
$470$	−22.0920	−1.01903
$471$	16.9536	0.781181
$472$	8.12298	0.373891
$473$	0	0
$474$	−3.34148	−0.153479
$475$	15.9264	0.730756
$476$	4.40849	0.202063
$477$	8.83956	0.404735
$478$	−4.95051	−0.226431
$479$	26.5853	1.21471	0.607356	−	0.794430i	$-0.292230\pi$
$479$	26.5853	1.21471	0.607356	+	0.794430i	$0.292230\pi$
$480$	−18.2603	−0.833463
$481$	20.7226	0.944871
$482$	−1.61925	−0.0737548
$483$	3.79843	0.172835
$484$	0	0
$485$	26.2981	1.19414
$486$	−0.473713	−0.0214881
$487$	14.1343	0.640486	0.320243	−	0.947335i	$-0.396235\pi$
$487$	14.1343	0.640486	0.320243	+	0.947335i	$0.396235\pi$
$488$	20.5370	0.929668
$489$	19.9739	0.903249
$490$	−1.78060	−0.0804392
$491$	−15.4186	−0.695831	−0.347916	−	0.937526i	$-0.613110\pi$
$491$	−15.4186	−0.695831	−0.347916	+	0.937526i	$0.613110\pi$
$492$	−7.43086	−0.335009
$493$	−14.4019	−0.648627
$494$	2.23786	0.100686
$495$	0	0
$496$	6.07744	0.272885
$497$	7.75988	0.348078
$498$	5.63739	0.252618
$499$	30.7024	1.37443	0.687214	−	0.726455i	$-0.258833\pi$
$499$	30.7024	1.37443	0.687214	+	0.726455i	$0.258833\pi$
$500$	−27.5553	−1.23231
$501$	−17.4516	−0.779679
$502$	−6.00438	−0.267988
$503$	18.1890	0.811005	0.405503	−	0.914094i	$-0.367096\pi$
$503$	18.1890	0.811005	0.405503	+	0.914094i	$0.367096\pi$
$504$	1.78855	0.0796683
$505$	−10.2121	−0.454431
$506$	0	0
$507$	−5.66813	−0.251731
$508$	0.361046	0.0160188
$509$	−32.1744	−1.42611	−0.713054	−	0.701110i	$-0.752688\pi$
$509$	−32.1744	−1.42611	−0.713054	+	0.701110i	$0.752688\pi$
$510$	4.42092	0.195761
$511$	−15.6796	−0.693625
$512$	−22.8079	−1.00798
$513$	1.74466	0.0770287
$514$	8.61458	0.379973
$515$	−0.961461	−0.0423670
$516$	13.7637	0.605915
$517$	0	0
$518$	3.62538	0.159290
$519$	9.35944	0.410834
$520$	−18.2037	−0.798284
$521$	−27.8238	−1.21898	−0.609490	−	0.792793i	$-0.708626\pi$
$521$	−27.8238	−1.21898	−0.609490	+	0.792793i	$0.708626\pi$
$522$	−2.74782	−0.120269
$523$	19.1282	0.836419	0.418209	−	0.908351i	$-0.362658\pi$
$523$	19.1282	0.836419	0.418209	+	0.908351i	$0.362658\pi$
$524$	−18.2511	−0.797302
$525$	9.12868	0.398408
$526$	7.47694	0.326010
$527$	−5.58048	−0.243089
$528$	0	0
$529$	−8.57190	−0.372691
$530$	−15.7397	−0.683689
$531$	4.54166	0.197091
$532$	−3.09781	−0.134307
$533$	−11.3319	−0.490839
$534$	0.801423	0.0346810
$535$	−44.5824	−1.92746
$536$	−21.8275	−0.942806
$537$	5.49347	0.237061
$538$	−10.8905	−0.469522
$539$	0	0
$540$	−6.67413	−0.287209
$541$	−42.6820	−1.83504	−0.917521	−	0.397688i	$-0.869813\pi$
$541$	−42.6820	−1.83504	−0.917521	+	0.397688i	$0.869813\pi$
$542$	4.42458	0.190052
$543$	−11.1844	−0.479970
$544$	12.0615	0.517134
$545$	59.6597	2.55554
$546$	1.28269	0.0548942
$547$	25.1162	1.07389	0.536946	−	0.843617i	$-0.319578\pi$
$547$	25.1162	1.07389	0.536946	+	0.843617i	$0.319578\pi$
$548$	30.3798	1.29776
$549$	11.4825	0.490062
$550$	0	0
$551$	10.1201	0.431130
$552$	6.79369	0.289158
$553$	7.05380	0.299958
$554$	9.20740	0.391185
$555$	−28.7666	−1.22107
$556$	34.6258	1.46846
$557$	4.25720	0.180383	0.0901917	−	0.995924i	$-0.471252\pi$
$557$	4.25720	0.180383	0.0901917	+	0.995924i	$0.471252\pi$
$558$	−1.06473	−0.0450737
$559$	20.9894	0.887757
$560$	10.1636	0.429490
$561$	0	0
$562$	−2.10498	−0.0887933
$563$	7.43714	0.313438	0.156719	−	0.987643i	$-0.449908\pi$
$563$	7.43714	0.313438	0.156719	+	0.987643i	$0.449908\pi$
$564$	−22.0299	−0.927628
$565$	−19.2320	−0.809096
$566$	6.56028	0.275749
$567$	1.00000	0.0419961
$568$	13.8789	0.582347
$569$	−43.6293	−1.82904	−0.914518	−	0.404546i	$-0.867430\pi$
$569$	−43.6293	−1.82904	−0.914518	+	0.404546i	$0.867430\pi$
$570$	−3.10654	−0.130119
$571$	34.1074	1.42735	0.713676	−	0.700476i	$-0.247029\pi$
$571$	34.1074	1.42735	0.713676	+	0.700476i	$0.247029\pi$
$572$	0	0
$573$	−5.75822	−0.240553
$574$	−1.98249	−0.0827474
$575$	34.6747	1.44603
$576$	−3.10658	−0.129441
$577$	28.0804	1.16900	0.584501	−	0.811393i	$-0.301290\pi$
$577$	28.0804	1.16900	0.584501	+	0.811393i	$0.301290\pi$
$578$	5.13295	0.213503
$579$	14.8846	0.618582
$580$	−38.7140	−1.60751
$581$	−11.9004	−0.493713
$582$	−3.31428	−0.137381
$583$	0	0
$584$	−28.0437	−1.16046
$585$	−10.1779	−0.420804
$586$	−9.11230	−0.376426
$587$	−6.72735	−0.277668	−0.138834	−	0.990316i	$-0.544335\pi$
$587$	−6.72735	−0.277668	−0.138834	+	0.990316i	$0.544335\pi$
$588$	−1.77560	−0.0732243
$589$	3.92136	0.161577
$590$	−8.08687	−0.332931
$591$	−12.5476	−0.516138
$592$	−20.6935	−0.850497
$593$	−20.8442	−0.855969	−0.427984	−	0.903786i	$-0.640776\pi$
$593$	−20.8442	−0.855969	−0.427984	+	0.903786i	$0.640776\pi$
$594$	0	0
$595$	−9.33248	−0.382594
$596$	−17.5613	−0.719339
$597$	0.834418	0.0341504
$598$	4.87222	0.199240
$599$	0.180675	0.00738218	0.00369109	−	0.999993i	$-0.498825\pi$
$599$	0.180675	0.00738218	0.00369109	+	0.999993i	$0.498825\pi$
$600$	16.3271	0.666550
$601$	−27.6043	−1.12600	−0.563001	−	0.826456i	$-0.690353\pi$
$601$	−27.6043	−1.12600	−0.563001	+	0.826456i	$0.690353\pi$
$602$	3.67204	0.149661
$603$	−12.2041	−0.496988
$604$	−27.5241	−1.11994
$605$	0	0
$606$	1.28700	0.0522807
$607$	−23.3280	−0.946854	−0.473427	−	0.880833i	$-0.656983\pi$
$607$	−23.3280	−0.946854	−0.473427	+	0.880833i	$0.656983\pi$
$608$	−8.47554	−0.343729
$609$	5.80060	0.235052
$610$	−20.4457	−0.827824
$611$	−33.5951	−1.35911
$612$	4.40849	0.178203
$613$	19.5003	0.787608	0.393804	−	0.919194i	$-0.371159\pi$
$613$	19.5003	0.787608	0.393804	+	0.919194i	$0.371159\pi$
$614$	1.06336	0.0429139
$615$	15.7306	0.634320
$616$	0	0
$617$	−23.2566	−0.936276	−0.468138	−	0.883655i	$-0.655075\pi$
$617$	−23.2566	−0.936276	−0.468138	+	0.883655i	$0.655075\pi$
$618$	0.121170	0.00487418
$619$	−28.5491	−1.14749	−0.573743	−	0.819035i	$-0.694509\pi$
$619$	−28.5491	−1.14749	−0.573743	+	0.819035i	$0.694509\pi$
$620$	−15.0010	−0.602454
$621$	3.79843	0.152426
$622$	−5.98256	−0.239879
$623$	−1.69179	−0.0677801
$624$	−7.32155	−0.293097
$625$	12.6893	0.507574
$626$	−0.505194	−0.0201916
$627$	0	0
$628$	−30.1028	−1.20123
$629$	19.0013	0.757633
$630$	−1.78060	−0.0709407
$631$	5.30112	0.211034	0.105517	−	0.994417i	$-0.466350\pi$
$631$	5.30112	0.211034	0.105517	+	0.994417i	$0.466350\pi$
$632$	12.6161	0.501840
$633$	26.8703	1.06800
$634$	11.9238	0.473556
$635$	−0.764309	−0.0303307
$636$	−15.6955	−0.622366
$637$	−2.70774	−0.107285
$638$	0	0
$639$	7.75988	0.306976
$640$	42.0521	1.66225
$641$	−29.8881	−1.18051	−0.590255	−	0.807217i	$-0.700973\pi$
$641$	−29.8881	−1.18051	−0.590255	+	0.807217i	$0.700973\pi$
$642$	5.61859	0.221748
$643$	38.4403	1.51594	0.757969	−	0.652291i	$-0.226192\pi$
$643$	38.4403	1.51594	0.757969	+	0.652291i	$0.226192\pi$
$644$	−6.74448	−0.265770
$645$	−29.1369	−1.14726
$646$	2.05198	0.0807340
$647$	−32.3602	−1.27221	−0.636105	−	0.771603i	$-0.719455\pi$
$647$	−32.3602	−1.27221	−0.636105	+	0.771603i	$0.719455\pi$
$648$	1.78855	0.0702608
$649$	0	0
$650$	11.7093	0.459276
$651$	2.24763	0.0880916
$652$	−35.4655	−1.38894
$653$	23.9046	0.935459	0.467729	−	0.883872i	$-0.345072\pi$
$653$	23.9046	0.935459	0.467729	+	0.883872i	$0.345072\pi$
$654$	−7.51876	−0.294007
$655$	38.6363	1.50964
$656$	11.3160	0.441814
$657$	−15.6796	−0.611720
$658$	−5.87739	−0.229124
$659$	−34.5124	−1.34441	−0.672205	−	0.740365i	$-0.734653\pi$
$659$	−34.5124	−1.34441	−0.672205	+	0.740365i	$0.734653\pi$
$660$	0	0
$661$	−2.56237	−0.0996647	−0.0498324	−	0.998758i	$-0.515869\pi$
$661$	−2.56237	−0.0996647	−0.0498324	+	0.998758i	$0.515869\pi$
$662$	4.04380	0.157167
$663$	6.72285	0.261094
$664$	−21.2845	−0.826000
$665$	6.55786	0.254303
$666$	3.62538	0.140480
$667$	22.0332	0.853128
$668$	30.9869	1.19892
$669$	4.01918	0.155390
$670$	21.7305	0.839523
$671$	0	0
$672$	−4.85799	−0.187401
$673$	−36.6670	−1.41341	−0.706704	−	0.707509i	$-0.749819\pi$
$673$	−36.6670	−1.41341	−0.706704	+	0.707509i	$0.749819\pi$
$674$	−8.17462	−0.314874
$675$	9.12868	0.351363
$676$	10.0643	0.387089
$677$	−31.9812	−1.22914	−0.614568	−	0.788864i	$-0.710670\pi$
$677$	−31.9812	−1.22914	−0.614568	+	0.788864i	$0.710670\pi$
$678$	2.42375	0.0930837
$679$	6.99638	0.268497
$680$	−16.6916	−0.640093
$681$	11.7020	0.448422
$682$	0	0
$683$	6.96871	0.266650	0.133325	−	0.991072i	$-0.457435\pi$
$683$	6.96871	0.266650	0.133325	+	0.991072i	$0.457435\pi$
$684$	−3.09781	−0.118448
$685$	−64.3119	−2.45723
$686$	−0.473713	−0.0180864
$687$	−6.54504	−0.249709
$688$	−20.9599	−0.799087
$689$	−23.9352	−0.911860
$690$	−6.76349	−0.257482
$691$	−5.07203	−0.192949	−0.0964746	−	0.995335i	$-0.530757\pi$
$691$	−5.07203	−0.192949	−0.0964746	+	0.995335i	$0.530757\pi$
$692$	−16.6186	−0.631744
$693$	0	0
$694$	1.96922	0.0747505
$695$	−73.3003	−2.78044
$696$	10.3746	0.393250
$697$	−10.3906	−0.393573
$698$	3.65131	0.138204
$699$	−0.172567	−0.00652709
$700$	−16.2088	−0.612637
$701$	−0.418223	−0.0157961	−0.00789803	−	0.999969i	$-0.502514\pi$
$701$	−0.418223	−0.0157961	−0.00789803	+	0.999969i	$0.502514\pi$
$702$	1.28269	0.0484121
$703$	−13.3521	−0.503583
$704$	0	0
$705$	46.6358	1.75641
$706$	2.29392	0.0863328
$707$	−2.71683	−0.102177
$708$	−8.06415	−0.303069
$709$	−3.60664	−0.135450	−0.0677251	−	0.997704i	$-0.521574\pi$
$709$	−3.60664	−0.135450	−0.0677251	+	0.997704i	$0.521574\pi$
$710$	−13.8172	−0.518551
$711$	7.05380	0.264538
$712$	−3.02585	−0.113398
$713$	8.53748	0.319731
$714$	1.17615	0.0440162
$715$	0	0
$716$	−9.75419	−0.364531
$717$	10.4504	0.390279
$718$	2.09303	0.0781110
$719$	−17.9697	−0.670155	−0.335078	−	0.942190i	$-0.608763\pi$
$719$	−17.9697	−0.670155	−0.335078	+	0.942190i	$0.608763\pi$
$720$	10.1636	0.378774
$721$	−0.255788	−0.00952606
$722$	7.55864	0.281303
$723$	3.41821	0.127124
$724$	19.8590	0.738055
$725$	52.9518	1.96658
$726$	0	0
$727$	10.0774	0.373752	0.186876	−	0.982384i	$-0.440164\pi$
$727$	10.0774	0.373752	0.186876	+	0.982384i	$0.440164\pi$
$728$	−4.84293	−0.179491
$729$	1.00000	0.0370370
$730$	27.9191	1.03333
$731$	19.2459	0.711836
$732$	−20.3883	−0.753574
$733$	12.2275	0.451631	0.225816	−	0.974170i	$-0.427495\pi$
$733$	12.2275	0.451631	0.225816	+	0.974170i	$0.427495\pi$
$734$	13.9895	0.516360
$735$	3.75881	0.138646
$736$	−18.4527	−0.680177
$737$	0	0
$738$	−1.98249	−0.0729764
$739$	−3.49821	−0.128684	−0.0643419	−	0.997928i	$-0.520495\pi$
$739$	−3.49821	−0.128684	−0.0643419	+	0.997928i	$0.520495\pi$
$740$	51.0779	1.87766
$741$	−4.72409	−0.173544
$742$	−4.18741	−0.153725
$743$	−2.73642	−0.100389	−0.0501947	−	0.998739i	$-0.515984\pi$
$743$	−2.73642	−0.100389	−0.0501947	+	0.998739i	$0.515984\pi$
$744$	4.02000	0.147380
$745$	37.1761	1.36203
$746$	3.62374	0.132674
$747$	−11.9004	−0.435414
$748$	0	0
$749$	−11.8608	−0.433382
$750$	−7.35151	−0.268439
$751$	−10.0480	−0.366655	−0.183327	−	0.983052i	$-0.558687\pi$
$751$	−10.0480	−0.366655	−0.183327	+	0.983052i	$0.558687\pi$
$752$	33.5479	1.22337
$753$	12.6751	0.461908
$754$	7.44038	0.270963
$755$	58.2667	2.12054
$756$	−1.77560	−0.0645778
$757$	15.1490	0.550600	0.275300	−	0.961358i	$-0.411223\pi$
$757$	15.1490	0.550600	0.275300	+	0.961358i	$0.411223\pi$
$758$	5.31004	0.192869
$759$	0	0
$760$	11.7290	0.425457
$761$	−35.4413	−1.28475	−0.642373	−	0.766392i	$-0.722050\pi$
$761$	−35.4413	−1.28475	−0.642373	+	0.766392i	$0.722050\pi$
$762$	0.0963238	0.00348944
$763$	15.8720	0.574604
$764$	10.2243	0.369901
$765$	−9.33248	−0.337416
$766$	11.7219	0.423530
$767$	−12.2976	−0.444042
$768$	0.913441	0.0329610
$769$	−38.7592	−1.39769	−0.698845	−	0.715273i	$-0.746302\pi$
$769$	−38.7592	−1.39769	−0.698845	+	0.715273i	$0.746302\pi$
$770$	0	0
$771$	−18.1852	−0.654925
$772$	−26.4290	−0.951200
$773$	26.5419	0.954646	0.477323	−	0.878728i	$-0.341607\pi$
$773$	26.5419	0.954646	0.477323	+	0.878728i	$0.341607\pi$
$774$	3.67204	0.131989
$775$	20.5179	0.737025
$776$	12.5134	0.449204
$777$	−7.65311	−0.274554
$778$	13.7541	0.493109
$779$	7.30140	0.261600
$780$	18.0718	0.647075
$781$	0	0
$782$	4.46752	0.159758
$783$	5.80060	0.207296
$784$	2.70393	0.0965690
$785$	63.7255	2.27446
$786$	−4.86922	−0.173679
$787$	−19.6802	−0.701524	−0.350762	−	0.936465i	$-0.614077\pi$
$787$	−19.6802	−0.701524	−0.350762	+	0.936465i	$0.614077\pi$
$788$	22.2794	0.793672
$789$	−15.7837	−0.561914
$790$	−12.5600	−0.446864
$791$	−5.11650	−0.181922
$792$	0	0
$793$	−31.0917	−1.10410
$794$	3.91979	0.139108
$795$	33.2262	1.17841
$796$	−1.48159	−0.0525135
$797$	−25.2797	−0.895451	−0.447726	−	0.894171i	$-0.647766\pi$
$797$	−25.2797	−0.895451	−0.447726	+	0.894171i	$0.647766\pi$
$798$	−0.826469	−0.0292567
$799$	−30.8046	−1.08979
$800$	−44.3470	−1.56790
$801$	−1.69179	−0.0597764
$802$	12.6666	0.447274
$803$	0	0
$804$	21.6695	0.764223
$805$	14.2776	0.503219
$806$	2.88302	0.101550
$807$	22.9896	0.809273
$808$	−4.85918	−0.170945
$809$	35.7891	1.25828	0.629138	−	0.777293i	$-0.283408\pi$
$809$	35.7891	1.25828	0.629138	+	0.777293i	$0.283408\pi$
$810$	−1.78060	−0.0625639
$811$	−20.9415	−0.735355	−0.367677	−	0.929953i	$-0.619847\pi$
$811$	−20.9415	−0.735355	−0.367677	+	0.929953i	$0.619847\pi$
$812$	−10.2995	−0.361442
$813$	−9.34021	−0.327575
$814$	0	0
$815$	75.0780	2.62987
$816$	−6.71339	−0.235016
$817$	−13.5240	−0.473143
$818$	16.4297	0.574452
$819$	−2.70774	−0.0946162
$820$	−27.9312	−0.975401
$821$	8.06663	0.281527	0.140764	−	0.990043i	$-0.455044\pi$
$821$	8.06663	0.281527	0.140764	+	0.990043i	$0.455044\pi$
$822$	8.10505	0.282696
$823$	−20.1359	−0.701895	−0.350948	−	0.936395i	$-0.614140\pi$
$823$	−20.1359	−0.701895	−0.350948	+	0.936395i	$0.614140\pi$
$824$	−0.457490	−0.0159374
$825$	0	0
$826$	−2.15144	−0.0748583
$827$	21.4181	0.744780	0.372390	−	0.928076i	$-0.378538\pi$
$827$	21.4181	0.744780	0.372390	+	0.928076i	$0.378538\pi$
$828$	−6.74448	−0.234387
$829$	−27.3960	−0.951504	−0.475752	−	0.879580i	$-0.657824\pi$
$829$	−27.3960	−0.951504	−0.475752	+	0.879580i	$0.657824\pi$
$830$	21.1899	0.735512
$831$	−19.4367	−0.674251
$832$	8.41181	0.291627
$833$	−2.48283	−0.0860248
$834$	9.23784	0.319880
$835$	−65.5972	−2.27008
$836$	0	0
$837$	2.24763	0.0776895
$838$	2.05850	0.0711097
$839$	−20.3757	−0.703446	−0.351723	−	0.936104i	$-0.614404\pi$
$839$	−20.3757	−0.703446	−0.351723	+	0.936104i	$0.614404\pi$
$840$	6.72282	0.231959
$841$	4.64691	0.160238
$842$	2.24465	0.0773556
$843$	4.44358	0.153045
$844$	−47.7108	−1.64227
$845$	−21.3055	−0.732930
$846$	−5.87739	−0.202069
$847$	0	0
$848$	23.9016	0.820783
$849$	−13.8486	−0.475284
$850$	10.7367	0.368264
$851$	−29.0698	−0.996501
$852$	−13.7784	−0.472041
$853$	8.28686	0.283737	0.141868	−	0.989886i	$-0.454689\pi$
$853$	8.28686	0.283737	0.141868	+	0.989886i	$0.454689\pi$
$854$	−5.43942	−0.186133
$855$	6.55786	0.224274
$856$	−21.2135	−0.725064
$857$	31.0459	1.06051	0.530254	−	0.847839i	$-0.322097\pi$
$857$	31.0459	1.06051	0.530254	+	0.847839i	$0.322097\pi$
$858$	0	0
$859$	−1.63124	−0.0556573	−0.0278287	−	0.999613i	$-0.508859\pi$
$859$	−1.63124	−0.0556573	−0.0278287	+	0.999613i	$0.508859\pi$
$860$	51.7354	1.76416
$861$	4.18500	0.142624
$862$	−14.1461	−0.481819
$863$	5.32862	0.181388	0.0906942	−	0.995879i	$-0.471091\pi$
$863$	5.32862	0.181388	0.0906942	+	0.995879i	$0.471091\pi$
$864$	−4.85799	−0.165272
$865$	35.1804	1.19617
$866$	10.2909	0.349699
$867$	−10.8356	−0.367996
$868$	−3.99088	−0.135459
$869$	0	0
$870$	−10.3285	−0.350170
$871$	33.0454	1.11970
$872$	28.3878	0.961332
$873$	6.99638	0.236792
$874$	−3.13929	−0.106188
$875$	15.5189	0.524635
$876$	27.8406	0.940648
$877$	16.1267	0.544561	0.272281	−	0.962218i	$-0.412222\pi$
$877$	16.1267	0.544561	0.272281	+	0.962218i	$0.412222\pi$
$878$	−19.1118	−0.644992
$879$	19.2359	0.648811
$880$	0	0
$881$	−35.1173	−1.18313	−0.591565	−	0.806257i	$-0.701490\pi$
$881$	−35.1173	−1.18313	−0.591565	+	0.806257i	$0.701490\pi$
$882$	−0.473713	−0.0159507
$883$	0.480232	0.0161611	0.00808054	−	0.999967i	$-0.497428\pi$
$883$	0.480232	0.0161611	0.00808054	+	0.999967i	$0.497428\pi$
$884$	−11.9371	−0.401487
$885$	17.0713	0.573844
$886$	6.57463	0.220879
$887$	−36.7238	−1.23306	−0.616532	−	0.787330i	$-0.711463\pi$
$887$	−36.7238	−1.23306	−0.616532	+	0.787330i	$0.711463\pi$
$888$	−13.6880	−0.459338
$889$	−0.203338	−0.00681973
$890$	3.01240	0.100976
$891$	0	0
$892$	−7.13644	−0.238946
$893$	21.6461	0.724360
$894$	−4.68520	−0.156696
$895$	20.6489	0.690218
$896$	11.1876	0.373751
$897$	−10.2852	−0.343412
$898$	6.77517	0.226090
$899$	13.0376	0.434828
$900$	−16.2088	−0.540295
$901$	−21.9471	−0.731163
$902$	0	0
$903$	−7.75162	−0.257958
$904$	−9.15112	−0.304362
$905$	−42.0402	−1.39746
$906$	−7.34319	−0.243961
$907$	12.1917	0.404818	0.202409	−	0.979301i	$-0.435123\pi$
$907$	12.1917	0.404818	0.202409	+	0.979301i	$0.435123\pi$
$908$	−20.7781	−0.689544
$909$	−2.71683	−0.0901116
$910$	4.82140	0.159828
$911$	−8.11848	−0.268977	−0.134489	−	0.990915i	$-0.542939\pi$
$911$	−8.11848	−0.268977	−0.134489	+	0.990915i	$0.542939\pi$
$912$	4.71745	0.156210
$913$	0	0
$914$	−6.69251	−0.221369
$915$	43.1606	1.42685
$916$	11.6213	0.383980
$917$	10.2788	0.339438
$918$	1.17615	0.0388186
$919$	49.6539	1.63793	0.818965	−	0.573843i	$-0.194548\pi$
$919$	49.6539	1.63793	0.818965	+	0.573843i	$0.194548\pi$
$920$	25.5362	0.841903
$921$	−2.24474	−0.0739668
$922$	−0.457955	−0.0150820
$923$	−21.0118	−0.691610
$924$	0	0
$925$	−69.8627	−2.29707
$926$	−15.0697	−0.495221
$927$	−0.255788	−0.00840119
$928$	−28.1792	−0.925028
$929$	−0.373776	−0.0122632	−0.00613160	−	0.999981i	$-0.501952\pi$
$929$	−0.373776	−0.0122632	−0.00613160	+	0.999981i	$0.501952\pi$
$930$	−4.00213	−0.131235
$931$	1.74466	0.0571790
$932$	0.306409	0.0100368
$933$	12.6291	0.413458
$934$	14.0282	0.459016
$935$	0	0
$936$	−4.84293	−0.158296
$937$	46.0667	1.50493	0.752467	−	0.658630i	$-0.228864\pi$
$937$	46.0667	1.50493	0.752467	+	0.658630i	$0.228864\pi$
$938$	5.78122	0.188763
$939$	1.06646	0.0348025
$940$	−82.8064	−2.70085
$941$	19.3374	0.630380	0.315190	−	0.949029i	$-0.397932\pi$
$941$	19.3374	0.630380	0.315190	+	0.949029i	$0.397932\pi$
$942$	−8.03115	−0.261669
$943$	15.8964	0.517659
$944$	12.2803	0.399691
$945$	3.75881	0.122274
$946$	0	0
$947$	−8.06969	−0.262230	−0.131115	−	0.991367i	$-0.541856\pi$
$947$	−8.06969	−0.262230	−0.131115	+	0.991367i	$0.541856\pi$
$948$	−12.5247	−0.406783
$949$	42.4563	1.37819
$950$	−7.54457	−0.244778
$951$	−25.1710	−0.816225
$952$	−4.44065	−0.143922
$953$	−34.6358	−1.12196	−0.560982	−	0.827828i	$-0.689576\pi$
$953$	−34.6358	−1.12196	−0.560982	+	0.827828i	$0.689576\pi$
$954$	−4.18741	−0.135572
$955$	−21.6441	−0.700385
$956$	−18.5557	−0.600136
$957$	0	0
$958$	−12.5938	−0.406887
$959$	−17.1096	−0.552498
$960$	−11.6770	−0.376875
$961$	−25.9482	−0.837037
$962$	−9.81659	−0.316499
$963$	−11.8608	−0.382207
$964$	−6.06935	−0.195481
$965$	55.9483	1.80104
$966$	−1.79937	−0.0578937
$967$	−8.15074	−0.262110	−0.131055	−	0.991375i	$-0.541836\pi$
$967$	−8.15074	−0.262110	−0.131055	+	0.991375i	$0.541836\pi$
$968$	0	0
$969$	−4.33169	−0.139154
$970$	−12.4578	−0.399994
$971$	33.4330	1.07292	0.536458	−	0.843927i	$-0.319762\pi$
$971$	33.4330	1.07292	0.536458	+	0.843927i	$0.319762\pi$
$972$	−1.77560	−0.0569523
$973$	−19.5009	−0.625171
$974$	−6.69560	−0.214541
$975$	−24.7181	−0.791613
$976$	31.0480	0.993821
$977$	−5.48798	−0.175576	−0.0877880	−	0.996139i	$-0.527980\pi$
$977$	−5.48798	−0.175576	−0.0877880	+	0.996139i	$0.527980\pi$
$978$	−9.46188	−0.302557
$979$	0	0
$980$	−6.67413	−0.213197
$981$	15.8720	0.506753
$982$	7.30398	0.233080
$983$	14.5404	0.463767	0.231884	−	0.972744i	$-0.425511\pi$
$983$	14.5404	0.463767	0.231884	+	0.972744i	$0.425511\pi$
$984$	7.48507	0.238615
$985$	−47.1640	−1.50277
$986$	6.82235	0.217268
$987$	12.4071	0.394921
$988$	8.38808	0.266860
$989$	−29.4440	−0.936266
$990$	0	0
$991$	−9.68326	−0.307599	−0.153799	−	0.988102i	$-0.549151\pi$
$991$	−9.68326	−0.307599	−0.153799	+	0.988102i	$0.549151\pi$
$992$	−10.9190	−0.346677
$993$	−8.53640	−0.270894
$994$	−3.67596	−0.116594
$995$	3.13642	0.0994312
$996$	21.1304	0.669542
$997$	25.2216	0.798775	0.399388	−	0.916782i	$-0.369223\pi$
$997$	25.2216	0.798775	0.399388	+	0.916782i	$0.369223\pi$
$998$	−14.5441	−0.460387
$999$	−7.65311	−0.242134

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2541.2.a.br.1.5		10
3.2	odd	2		7623.2.a.cy.1.6		10
11.2	odd	10		231.2.j.g.169.3	✓	20
11.6	odd	10		231.2.j.g.190.3	yes	20
11.10	odd	2		2541.2.a.bq.1.6		10
33.2	even	10		693.2.m.j.631.3		20
33.17	even	10		693.2.m.j.190.3		20
33.32	even	2		7623.2.a.cx.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.g.169.3	✓	20	11.2	odd	10
231.2.j.g.190.3	yes	20	11.6	odd	10
693.2.m.j.190.3		20	33.17	even	10
693.2.m.j.631.3		20	33.2	even	10
2541.2.a.bq.1.6		10	11.10	odd	2
2541.2.a.br.1.5		10	1.1	even	1	trivial
7623.2.a.cx.1.5		10	33.32	even	2
7623.2.a.cy.1.6		10	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:	\( N \)	\(=\)	\( 2541 = 3 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2541.a (trivial)

\(f(q)\)	\(=\)	\(q-0.473713 q^{2} +1.00000 q^{3} -1.77560 q^{4} +3.75881 q^{5} -0.473713 q^{6} +1.00000 q^{7} +1.78855 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.473713 q^{2} +1.00000 q^{3} -1.77560 q^{4} +3.75881 q^{5} -0.473713 q^{6} +1.00000 q^{7} +1.78855 q^{8} +1.00000 q^{9} -1.78060 q^{10} -1.77560 q^{12} -2.70774 q^{13} -0.473713 q^{14} +3.75881 q^{15} +2.70393 q^{16} -2.48283 q^{17} -0.473713 q^{18} +1.74466 q^{19} -6.67413 q^{20} +1.00000 q^{21} +3.79843 q^{23} +1.78855 q^{24} +9.12868 q^{25} +1.28269 q^{26} +1.00000 q^{27} -1.77560 q^{28} +5.80060 q^{29} -1.78060 q^{30} +2.24763 q^{31} -4.85799 q^{32} +1.17615 q^{34} +3.75881 q^{35} -1.77560 q^{36} -7.65311 q^{37} -0.826469 q^{38} -2.70774 q^{39} +6.72282 q^{40} +4.18500 q^{41} -0.473713 q^{42} -7.75162 q^{43} +3.75881 q^{45} -1.79937 q^{46} +12.4071 q^{47} +2.70393 q^{48} +1.00000 q^{49} -4.32437 q^{50} -2.48283 q^{51} +4.80786 q^{52} +8.83956 q^{53} -0.473713 q^{54} +1.78855 q^{56} +1.74466 q^{57} -2.74782 q^{58} +4.54166 q^{59} -6.67413 q^{60} +11.4825 q^{61} -1.06473 q^{62} +1.00000 q^{63} -3.10658 q^{64} -10.1779 q^{65} -12.2041 q^{67} +4.40849 q^{68} +3.79843 q^{69} -1.78060 q^{70} +7.75988 q^{71} +1.78855 q^{72} -15.6796 q^{73} +3.62538 q^{74} +9.12868 q^{75} -3.09781 q^{76} +1.28269 q^{78} +7.05380 q^{79} +10.1636 q^{80} +1.00000 q^{81} -1.98249 q^{82} -11.9004 q^{83} -1.77560 q^{84} -9.33248 q^{85} +3.67204 q^{86} +5.80060 q^{87} -1.69179 q^{89} -1.78060 q^{90} -2.70774 q^{91} -6.74448 q^{92} +2.24763 q^{93} -5.87739 q^{94} +6.55786 q^{95} -4.85799 q^{96} +6.99638 q^{97} -0.473713 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{3} + 18 q^{4} + 5 q^{5} + 10 q^{7} - 3 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 10 * q^3 + 18 * q^4 + 5 * q^5 + 10 * q^7 - 3 * q^8 + 10 * q^9	\( 10 q + 10 q^{3} + 18 q^{4} + 5 q^{5} + 10 q^{7} - 3 q^{8} + 10 q^{9} - 6 q^{10} + 18 q^{12} + 6 q^{13} + 5 q^{15} + 38 q^{16} + 8 q^{17} + 7 q^{20} + 10 q^{21} - 3 q^{24} + 31 q^{25} + q^{26} + 10 q^{27} + 18 q^{28} - 14 q^{29} - 6 q^{30} + 26 q^{31} - 41 q^{32} + 21 q^{34} + 5 q^{35} + 18 q^{36} + 24 q^{37} + 8 q^{38} + 6 q^{39} - 5 q^{40} + 19 q^{41} - 6 q^{43} + 5 q^{45} - q^{46} + 15 q^{47} + 38 q^{48} + 10 q^{49} - q^{50} + 8 q^{51} - 25 q^{52} - q^{53} - 3 q^{56} + 11 q^{58} + 23 q^{59} + 7 q^{60} + 11 q^{62} + 10 q^{63} + 53 q^{64} - 29 q^{65} + 38 q^{67} + 87 q^{68} - 6 q^{70} + 26 q^{71} - 3 q^{72} - q^{73} - 39 q^{74} + 31 q^{75} - 2 q^{76} + q^{78} + 5 q^{79} + 6 q^{80} + 10 q^{81} + 5 q^{82} + 6 q^{83} + 18 q^{84} - q^{85} - 41 q^{86} - 14 q^{87} - 9 q^{89} - 6 q^{90} + 6 q^{91} - 48 q^{92} + 26 q^{93} - 42 q^{95} - 41 q^{96} + 24 q^{97}+O(q^{100}) \) 10 * q + 10 * q^3 + 18 * q^4 + 5 * q^5 + 10 * q^7 - 3 * q^8 + 10 * q^9 - 6 * q^10 + 18 * q^12 + 6 * q^13 + 5 * q^15 + 38 * q^16 + 8 * q^17 + 7 * q^20 + 10 * q^21 - 3 * q^24 + 31 * q^25 + q^26 + 10 * q^27 + 18 * q^28 - 14 * q^29 - 6 * q^30 + 26 * q^31 - 41 * q^32 + 21 * q^34 + 5 * q^35 + 18 * q^36 + 24 * q^37 + 8 * q^38 + 6 * q^39 - 5 * q^40 + 19 * q^41 - 6 * q^43 + 5 * q^45 - q^46 + 15 * q^47 + 38 * q^48 + 10 * q^49 - q^50 + 8 * q^51 - 25 * q^52 - q^53 - 3 * q^56 + 11 * q^58 + 23 * q^59 + 7 * q^60 + 11 * q^62 + 10 * q^63 + 53 * q^64 - 29 * q^65 + 38 * q^67 + 87 * q^68 - 6 * q^70 + 26 * q^71 - 3 * q^72 - q^73 - 39 * q^74 + 31 * q^75 - 2 * q^76 + q^78 + 5 * q^79 + 6 * q^80 + 10 * q^81 + 5 * q^82 + 6 * q^83 + 18 * q^84 - q^85 - 41 * q^86 - 14 * q^87 - 9 * q^89 - 6 * q^90 + 6 * q^91 - 48 * q^92 + 26 * q^93 - 42 * q^95 - 41 * q^96 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more