LMFDB - Embedded newform 9251.2.a.t.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9251,2,Mod(1,9251)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9251, 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("9251.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9251 = 11 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9251.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:	$73.8696069099$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 24 x^{16} - x^{15} + 233 x^{14} + 24 x^{13} - 1184 x^{12} - 207 x^{11} + 3413 x^{10} + \cdots - 41 $ x^18 - 24x^16 - x^15 + 233x^14 + 24x^13 - 1184x^12 - 207x^11 + 3413x^10 + 820x^9 - 5661x^8 - 1595x^7 + 5262x^6 + 1498x^5 - 2567x^4 - 605x^3 + 583x^2 + 80*x - 41
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.667395$ of defining polynomial
Character	$\chi$	$=$	9251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.667395 q^{2} -2.28148 q^{3} -1.55458 q^{4} -0.818040 q^{5} +1.52265 q^{6} +0.455915 q^{7} +2.37231 q^{8} +2.20514 q^{9} +O(q^{10})$	\(q-0.667395 q^{2} -2.28148 q^{3} -1.55458 q^{4} -0.818040 q^{5} +1.52265 q^{6} +0.455915 q^{7} +2.37231 q^{8} +2.20514 q^{9} +0.545956 q^{10} -1.00000 q^{11} +3.54675 q^{12} +2.90357 q^{13} -0.304275 q^{14} +1.86634 q^{15} +1.52590 q^{16} +1.97420 q^{17} -1.47170 q^{18} +1.29640 q^{19} +1.27171 q^{20} -1.04016 q^{21} +0.667395 q^{22} -2.60035 q^{23} -5.41238 q^{24} -4.33081 q^{25} -1.93783 q^{26} +1.81345 q^{27} -0.708757 q^{28} -1.24559 q^{30} -0.242131 q^{31} -5.76300 q^{32} +2.28148 q^{33} -1.31757 q^{34} -0.372956 q^{35} -3.42808 q^{36} +1.90079 q^{37} -0.865213 q^{38} -6.62444 q^{39} -1.94065 q^{40} +2.00453 q^{41} +0.694197 q^{42} -2.99700 q^{43} +1.55458 q^{44} -1.80390 q^{45} +1.73546 q^{46} -4.26415 q^{47} -3.48130 q^{48} -6.79214 q^{49} +2.89036 q^{50} -4.50409 q^{51} -4.51385 q^{52} -7.59723 q^{53} -1.21029 q^{54} +0.818040 q^{55} +1.08157 q^{56} -2.95772 q^{57} +5.58772 q^{59} -2.90138 q^{60} -8.11582 q^{61} +0.161597 q^{62} +1.00536 q^{63} +0.794407 q^{64} -2.37524 q^{65} -1.52265 q^{66} +3.98939 q^{67} -3.06905 q^{68} +5.93264 q^{69} +0.248909 q^{70} +4.45363 q^{71} +5.23129 q^{72} +13.6947 q^{73} -1.26858 q^{74} +9.88065 q^{75} -2.01537 q^{76} -0.455915 q^{77} +4.42112 q^{78} +7.18318 q^{79} -1.24824 q^{80} -10.7528 q^{81} -1.33782 q^{82} -8.96069 q^{83} +1.61701 q^{84} -1.61497 q^{85} +2.00018 q^{86} -2.37231 q^{88} -2.17689 q^{89} +1.20391 q^{90} +1.32378 q^{91} +4.04246 q^{92} +0.552416 q^{93} +2.84587 q^{94} -1.06051 q^{95} +13.1482 q^{96} -8.13111 q^{97} +4.53304 q^{98} -2.20514 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9}+O(q^{10}) $ 18 * q + 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 9 * q^9	\( 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9} + 5 q^{10} - 18 q^{11} + 3 q^{12} - 15 q^{13} - 12 q^{14} + 27 q^{15} + 4 q^{16} - 6 q^{17} + 12 q^{18} - 11 q^{19} - 18 q^{20} - 6 q^{21} - 20 q^{23} - 3 q^{24} - 4 q^{25} + 10 q^{26} - 6 q^{27} - 6 q^{28} - 19 q^{30} + 8 q^{31} + 24 q^{32} - 3 q^{33} - 22 q^{34} + 22 q^{35} + 17 q^{36} - 9 q^{37} - 3 q^{38} + 8 q^{39} + 36 q^{40} - 3 q^{41} + 28 q^{42} - 13 q^{43} - 12 q^{44} - q^{45} - 37 q^{46} + q^{47} - 46 q^{48} - 23 q^{49} - 34 q^{50} + 4 q^{51} - 33 q^{52} - 6 q^{53} - 56 q^{54} + 6 q^{55} - 10 q^{56} + 14 q^{57} - 16 q^{59} - 3 q^{60} + 2 q^{61} - 24 q^{62} - 67 q^{63} + 11 q^{64} - 35 q^{65} + q^{66} + 9 q^{67} - 5 q^{68} + 47 q^{69} + 69 q^{70} - 13 q^{71} - 22 q^{72} + 57 q^{73} + 33 q^{74} + q^{75} + 26 q^{76} + 5 q^{77} + 5 q^{78} - 27 q^{79} - 10 q^{80} - 34 q^{81} - 55 q^{82} + 10 q^{83} - 35 q^{84} - 40 q^{85} + 4 q^{86} + 3 q^{88} + 80 q^{89} - 64 q^{90} - 38 q^{91} - 58 q^{92} + 17 q^{93} + 8 q^{94} - 7 q^{95} + 8 q^{96} - 20 q^{97} + 78 q^{98} - 9 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 9 * q^9 + 5 * q^10 - 18 * q^11 + 3 * q^12 - 15 * q^13 - 12 * q^14 + 27 * q^15 + 4 * q^16 - 6 * q^17 + 12 * q^18 - 11 * q^19 - 18 * q^20 - 6 * q^21 - 20 * q^23 - 3 * q^24 - 4 * q^25 + 10 * q^26 - 6 * q^27 - 6 * q^28 - 19 * q^30 + 8 * q^31 + 24 * q^32 - 3 * q^33 - 22 * q^34 + 22 * q^35 + 17 * q^36 - 9 * q^37 - 3 * q^38 + 8 * q^39 + 36 * q^40 - 3 * q^41 + 28 * q^42 - 13 * q^43 - 12 * q^44 - q^45 - 37 * q^46 + q^47 - 46 * q^48 - 23 * q^49 - 34 * q^50 + 4 * q^51 - 33 * q^52 - 6 * q^53 - 56 * q^54 + 6 * q^55 - 10 * q^56 + 14 * q^57 - 16 * q^59 - 3 * q^60 + 2 * q^61 - 24 * q^62 - 67 * q^63 + 11 * q^64 - 35 * q^65 + q^66 + 9 * q^67 - 5 * q^68 + 47 * q^69 + 69 * q^70 - 13 * q^71 - 22 * q^72 + 57 * q^73 + 33 * q^74 + q^75 + 26 * q^76 + 5 * q^77 + 5 * q^78 - 27 * q^79 - 10 * q^80 - 34 * q^81 - 55 * q^82 + 10 * q^83 - 35 * q^84 - 40 * q^85 + 4 * q^86 + 3 * q^88 + 80 * q^89 - 64 * q^90 - 38 * q^91 - 58 * q^92 + 17 * q^93 + 8 * q^94 - 7 * q^95 + 8 * q^96 - 20 * q^97 + 78 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.667395	−0.471920	−0.235960	−	0.971763i	$-0.575823\pi$
$2$	−0.667395	−0.471920	−0.235960	+	0.971763i	$0.575823\pi$
$3$	−2.28148	−1.31721	−0.658606	−	0.752488i	$-0.728854\pi$
$3$	−2.28148	−1.31721	−0.658606	+	0.752488i	$0.728854\pi$
$4$	−1.55458	−0.777292
$5$	−0.818040	−0.365838	−0.182919	−	0.983128i	$-0.558555\pi$
$5$	−0.818040	−0.365838	−0.182919	+	0.983128i	$0.558555\pi$
$6$	1.52265	0.621619
$7$	0.455915	0.172320	0.0861598	−	0.996281i	$-0.472540\pi$
$7$	0.455915	0.172320	0.0861598	+	0.996281i	$0.472540\pi$
$8$	2.37231	0.838739
$9$	2.20514	0.735048
$10$	0.545956	0.172646
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	3.54675	1.02386
$13$	2.90357	0.805306	0.402653	−	0.915353i	$-0.368088\pi$
$13$	2.90357	0.805306	0.402653	+	0.915353i	$0.368088\pi$
$14$	−0.304275	−0.0813210
$15$	1.86634	0.481887
$16$	1.52590	0.381474
$17$	1.97420	0.478813	0.239407	−	0.970919i	$-0.423047\pi$
$17$	1.97420	0.478813	0.239407	+	0.970919i	$0.423047\pi$
$18$	−1.47170	−0.346884
$19$	1.29640	0.297415	0.148708	−	0.988881i	$-0.452489\pi$
$19$	1.29640	0.297415	0.148708	+	0.988881i	$0.452489\pi$
$20$	1.27171	0.284363
$21$	−1.04016	−0.226981
$22$	0.667395	0.142289
$23$	−2.60035	−0.542210	−0.271105	−	0.962550i	$-0.587389\pi$
$23$	−2.60035	−0.542210	−0.271105	+	0.962550i	$0.587389\pi$
$24$	−5.41238	−1.10480
$25$	−4.33081	−0.866162
$26$	−1.93783	−0.380040
$27$	1.81345	0.348998
$28$	−0.708757	−0.133943
$29$	0	0
$29$	0	0
$30$	−1.24559	−0.227412
$31$	−0.242131	−0.0434880	−0.0217440	−	0.999764i	$-0.506922\pi$
$31$	−0.242131	−0.0434880	−0.0217440	+	0.999764i	$0.506922\pi$
$32$	−5.76300	−1.01876
$33$	2.28148	0.397154
$34$	−1.31757	−0.225961
$35$	−0.372956	−0.0630411
$36$	−3.42808	−0.571347
$37$	1.90079	0.312487	0.156244	−	0.987719i	$-0.450062\pi$
$37$	1.90079	0.312487	0.156244	+	0.987719i	$0.450062\pi$
$38$	−0.865213	−0.140356
$39$	−6.62444	−1.06076
$40$	−1.94065	−0.306843
$41$	2.00453	0.313056	0.156528	−	0.987674i	$-0.449970\pi$
$41$	2.00453	0.313056	0.156528	+	0.987674i	$0.449970\pi$
$42$	0.694197	0.107117
$43$	−2.99700	−0.457038	−0.228519	−	0.973539i	$-0.573388\pi$
$43$	−2.99700	−0.457038	−0.228519	+	0.973539i	$0.573388\pi$
$44$	1.55458	0.234362
$45$	−1.80390	−0.268909
$46$	1.73546	0.255880
$47$	−4.26415	−0.621990	−0.310995	−	0.950412i	$-0.600662\pi$
$47$	−4.26415	−0.621990	−0.310995	+	0.950412i	$0.600662\pi$
$48$	−3.48130	−0.502482
$49$	−6.79214	−0.970306
$50$	2.89036	0.408759
$51$	−4.50409	−0.630699
$52$	−4.51385	−0.625958
$53$	−7.59723	−1.04356	−0.521780	−	0.853080i	$-0.674732\pi$
$53$	−7.59723	−1.04356	−0.521780	+	0.853080i	$0.674732\pi$
$54$	−1.21029	−0.164699
$55$	0.818040	0.110304
$56$	1.08157	0.144531
$57$	−2.95772	−0.391759
$58$	0	0
$59$	5.58772	0.727459	0.363730	−	0.931505i	$-0.381503\pi$
$59$	5.58772	0.727459	0.363730	+	0.931505i	$0.381503\pi$
$60$	−2.90138	−0.374567
$61$	−8.11582	−1.03912	−0.519562	−	0.854433i	$-0.673905\pi$
$61$	−8.11582	−1.03912	−0.519562	+	0.854433i	$0.673905\pi$
$62$	0.161597	0.0205228
$63$	1.00536	0.126663
$64$	0.794407	0.0993009
$65$	−2.37524	−0.294612
$66$	−1.52265	−0.187425
$67$	3.98939	0.487382	0.243691	−	0.969853i	$-0.421642\pi$
$67$	3.98939	0.487382	0.243691	+	0.969853i	$0.421642\pi$
$68$	−3.06905	−0.372178
$69$	5.93264	0.714206
$70$	0.248909	0.0297503
$71$	4.45363	0.528548	0.264274	−	0.964448i	$-0.414868\pi$
$71$	4.45363	0.528548	0.264274	+	0.964448i	$0.414868\pi$
$72$	5.23129	0.616514
$73$	13.6947	1.60285	0.801423	−	0.598098i	$-0.204077\pi$
$73$	13.6947	1.60285	0.801423	+	0.598098i	$0.204077\pi$
$74$	−1.26858	−0.147469
$75$	9.88065	1.14092
$76$	−2.01537	−0.231178
$77$	−0.455915	−0.0519563
$78$	4.42112	0.500593
$79$	7.18318	0.808171	0.404085	−	0.914721i	$-0.367590\pi$
$79$	7.18318	0.808171	0.404085	+	0.914721i	$0.367590\pi$
$80$	−1.24824	−0.139558
$81$	−10.7528	−1.19475
$82$	−1.33782	−0.147737
$83$	−8.96069	−0.983563	−0.491782	−	0.870719i	$-0.663654\pi$
$83$	−8.96069	−0.983563	−0.491782	+	0.870719i	$0.663654\pi$
$84$	1.61701	0.176431
$85$	−1.61497	−0.175168
$86$	2.00018	0.215685
$87$	0	0
$88$	−2.37231	−0.252889
$89$	−2.17689	−0.230749	−0.115375	−	0.993322i	$-0.536807\pi$
$89$	−2.17689	−0.230749	−0.115375	+	0.993322i	$0.536807\pi$
$90$	1.20391	0.126903
$91$	1.32378	0.138770
$92$	4.04246	0.421455
$93$	0.552416	0.0572829
$94$	2.84587	0.293529
$95$	−1.06051	−0.108806
$96$	13.1482	1.34193
$97$	−8.13111	−0.825589	−0.412795	−	0.910824i	$-0.635447\pi$
$97$	−8.13111	−0.825589	−0.412795	+	0.910824i	$0.635447\pi$
$98$	4.53304	0.457907
$99$	−2.20514	−0.221625
$100$	6.73261	0.673261
$101$	1.77174	0.176295	0.0881473	−	0.996107i	$-0.471905\pi$
$101$	1.77174	0.176295	0.0881473	+	0.996107i	$0.471905\pi$
$102$	3.00601	0.297639
$103$	−8.40002	−0.827679	−0.413839	−	0.910350i	$-0.635812\pi$
$103$	−8.40002	−0.827679	−0.413839	+	0.910350i	$0.635812\pi$
$104$	6.88818	0.675442
$105$	0.850891	0.0830385
$106$	5.07036	0.492477
$107$	1.10683	0.107001	0.0535005	−	0.998568i	$-0.482962\pi$
$107$	1.10683	0.107001	0.0535005	+	0.998568i	$0.482962\pi$
$108$	−2.81915	−0.271273
$109$	−2.26829	−0.217263	−0.108631	−	0.994082i	$-0.534647\pi$
$109$	−2.26829	−0.217263	−0.108631	+	0.994082i	$0.534647\pi$
$110$	−0.545956	−0.0520548
$111$	−4.33660	−0.411612
$112$	0.695678	0.0657354
$113$	19.2468	1.81059	0.905294	−	0.424786i	$-0.139651\pi$
$113$	19.2468	1.81059	0.905294	+	0.424786i	$0.139651\pi$
$114$	1.97397	0.184879
$115$	2.12719	0.198361
$116$	0	0
$117$	6.40280	0.591939
$118$	−3.72922	−0.343302
$119$	0.900065	0.0825089
$120$	4.42754	0.404177
$121$	1.00000	0.0909091
$122$	5.41646	0.490384
$123$	−4.57330	−0.412361
$124$	0.376412	0.0338028
$125$	7.63297	0.682714
$126$	−0.670971	−0.0597748
$127$	14.1852	1.25873	0.629365	−	0.777110i	$-0.283315\pi$
$127$	14.1852	1.25873	0.629365	+	0.777110i	$0.283315\pi$
$128$	10.9958	0.971902
$129$	6.83759	0.602016
$130$	1.58522	0.139033
$131$	19.5150	1.70503	0.852515	−	0.522703i	$-0.175076\pi$
$131$	19.5150	1.70503	0.852515	+	0.522703i	$0.175076\pi$
$132$	−3.54675	−0.308705
$133$	0.591049	0.0512505
$134$	−2.66250	−0.230005
$135$	−1.48347	−0.127677
$136$	4.68341	0.401599
$137$	1.51892	0.129770	0.0648850	−	0.997893i	$-0.479332\pi$
$137$	1.51892	0.129770	0.0648850	+	0.997893i	$0.479332\pi$
$138$	−3.95942	−0.337048
$139$	−9.98760	−0.847138	−0.423569	−	0.905864i	$-0.639223\pi$
$139$	−9.98760	−0.847138	−0.423569	+	0.905864i	$0.639223\pi$
$140$	0.579791	0.0490013
$141$	9.72856	0.819293
$142$	−2.97233	−0.249432
$143$	−2.90357	−0.242809
$144$	3.36482	0.280402
$145$	0	0
$146$	−9.13980	−0.756415
$147$	15.4961	1.27810
$148$	−2.95493	−0.242894
$149$	−8.27875	−0.678222	−0.339111	−	0.940746i	$-0.610126\pi$
$149$	−8.27875	−0.678222	−0.339111	+	0.940746i	$0.610126\pi$
$150$	−6.59430	−0.538422
$151$	−10.2530	−0.834381	−0.417191	−	0.908819i	$-0.636985\pi$
$151$	−10.2530	−0.834381	−0.417191	+	0.908819i	$0.636985\pi$
$152$	3.07547	0.249454
$153$	4.35339	0.351951
$154$	0.304275	0.0245192
$155$	0.198072	0.0159096
$156$	10.2982	0.824519
$157$	−7.91281	−0.631511	−0.315755	−	0.948841i	$-0.602258\pi$
$157$	−7.91281	−0.631511	−0.315755	+	0.948841i	$0.602258\pi$
$158$	−4.79402	−0.381392
$159$	17.3329	1.37459
$160$	4.71436	0.372703
$161$	−1.18554	−0.0934334
$162$	7.17635	0.563827
$163$	−2.12685	−0.166587	−0.0832937	−	0.996525i	$-0.526544\pi$
$163$	−2.12685	−0.166587	−0.0832937	+	0.996525i	$0.526544\pi$
$164$	−3.11622	−0.243336
$165$	−1.86634	−0.145294
$166$	5.98032	0.464163
$167$	−0.913949	−0.0707235	−0.0353618	−	0.999375i	$-0.511258\pi$
$167$	−0.913949	−0.0707235	−0.0353618	+	0.999375i	$0.511258\pi$
$168$	−2.46758	−0.190378
$169$	−4.56926	−0.351482
$170$	1.07782	0.0826654
$171$	2.85876	0.218615
$172$	4.65908	0.355252
$173$	20.7269	1.57584	0.787918	−	0.615781i	$-0.211159\pi$
$173$	20.7269	1.57584	0.787918	+	0.615781i	$0.211159\pi$
$174$	0	0
$175$	−1.97448	−0.149257
$176$	−1.52590	−0.115019
$177$	−12.7483	−0.958218
$178$	1.45284	0.108895
$179$	−7.52316	−0.562307	−0.281154	−	0.959663i	$-0.590717\pi$
$179$	−7.52316	−0.562307	−0.281154	+	0.959663i	$0.590717\pi$
$180$	2.80431	0.209021
$181$	26.4252	1.96417	0.982085	−	0.188438i	$-0.0603425\pi$
$181$	26.4252	1.96417	0.982085	+	0.188438i	$0.0603425\pi$
$182$	−0.883485	−0.0654883
$183$	18.5161	1.36875
$184$	−6.16884	−0.454773
$185$	−1.55492	−0.114320
$186$	−0.368680	−0.0270329
$187$	−1.97420	−0.144368
$188$	6.62897	0.483468
$189$	0.826777	0.0601392
$190$	0.707779	0.0513477
$191$	7.26026	0.525334	0.262667	−	0.964887i	$-0.415398\pi$
$191$	7.26026	0.525334	0.262667	+	0.964887i	$0.415398\pi$
$192$	−1.81242	−0.130800
$193$	−2.57307	−0.185214	−0.0926069	−	0.995703i	$-0.529520\pi$
$193$	−2.57307	−0.185214	−0.0926069	+	0.995703i	$0.529520\pi$
$194$	5.42667	0.389612
$195$	5.41905	0.388067
$196$	10.5590	0.754211
$197$	−8.55042	−0.609192	−0.304596	−	0.952482i	$-0.598521\pi$
$197$	−8.55042	−0.609192	−0.304596	+	0.952482i	$0.598521\pi$
$198$	1.47170	0.104589
$199$	13.5010	0.957058	0.478529	−	0.878072i	$-0.341170\pi$
$199$	13.5010	0.957058	0.478529	+	0.878072i	$0.341170\pi$
$200$	−10.2740	−0.726484
$201$	−9.10172	−0.641985
$202$	−1.18245	−0.0831969
$203$	0	0
$204$	7.00198	0.490237
$205$	−1.63979	−0.114528
$206$	5.60613	0.390598
$207$	−5.73414	−0.398551
$208$	4.43055	0.307204
$209$	−1.29640	−0.0896741
$210$	−0.567881	−0.0391875
$211$	6.24162	0.429691	0.214845	−	0.976648i	$-0.431075\pi$
$211$	6.24162	0.429691	0.214845	+	0.976648i	$0.431075\pi$
$212$	11.8105	0.811151
$213$	−10.1609	−0.696210
$214$	−0.738691	−0.0504959
$215$	2.45166	0.167202
$216$	4.30206	0.292718
$217$	−0.110391	−0.00749382
$218$	1.51385	0.102531
$219$	−31.2442	−2.11129
$220$	−1.27171	−0.0857387
$221$	5.73223	0.385591
$222$	2.89423	0.194248
$223$	−28.1633	−1.88596	−0.942979	−	0.332853i	$-0.891989\pi$
$223$	−28.1633	−1.88596	−0.942979	+	0.332853i	$0.891989\pi$
$224$	−2.62744	−0.175553
$225$	−9.55006	−0.636671
$226$	−12.8452	−0.854452
$227$	−12.5449	−0.832635	−0.416318	−	0.909219i	$-0.636680\pi$
$227$	−12.5449	−0.832635	−0.416318	+	0.909219i	$0.636680\pi$
$228$	4.59802	0.304511
$229$	13.6050	0.899046	0.449523	−	0.893269i	$-0.351594\pi$
$229$	13.6050	0.899046	0.449523	+	0.893269i	$0.351594\pi$
$230$	−1.41968	−0.0936106
$231$	1.04016	0.0684375
$232$	0	0
$233$	6.51044	0.426513	0.213256	−	0.976996i	$-0.431593\pi$
$233$	6.51044	0.426513	0.213256	+	0.976996i	$0.431593\pi$
$234$	−4.27320	−0.279348
$235$	3.48824	0.227548
$236$	−8.68658	−0.565448
$237$	−16.3883	−1.06453
$238$	−0.600699	−0.0389376
$239$	24.4409	1.58095	0.790477	−	0.612492i	$-0.209833\pi$
$239$	24.4409	1.58095	0.790477	+	0.612492i	$0.209833\pi$
$240$	2.84784	0.183827
$241$	−0.591204	−0.0380828	−0.0190414	−	0.999819i	$-0.506061\pi$
$241$	−0.591204	−0.0380828	−0.0190414	+	0.999819i	$0.506061\pi$
$242$	−0.667395	−0.0429018
$243$	19.0919	1.22474
$244$	12.6167	0.807703
$245$	5.55624	0.354975
$246$	3.05220	0.194601
$247$	3.76420	0.239510
$248$	−0.574410	−0.0364750
$249$	20.4436	1.29556
$250$	−5.09421	−0.322186
$251$	−4.09850	−0.258695	−0.129347	−	0.991599i	$-0.541288\pi$
$251$	−4.09850	−0.258695	−0.129347	+	0.991599i	$0.541288\pi$
$252$	−1.56291	−0.0984542
$253$	2.60035	0.163483
$254$	−9.46711	−0.594019
$255$	3.68452	0.230734
$256$	−8.92737	−0.557961
$257$	15.0245	0.937202	0.468601	−	0.883410i	$-0.344758\pi$
$257$	15.0245	0.937202	0.468601	+	0.883410i	$0.344758\pi$
$258$	−4.56337	−0.284103
$259$	0.866596	0.0538476
$260$	3.69251	0.228999
$261$	0	0
$262$	−13.0242	−0.804637
$263$	−3.63240	−0.223983	−0.111992	−	0.993709i	$-0.535723\pi$
$263$	−3.63240	−0.223983	−0.111992	+	0.993709i	$0.535723\pi$
$264$	5.41238	0.333109
$265$	6.21484	0.381774
$266$	−0.394463	−0.0241861
$267$	4.96652	0.303946
$268$	−6.20184	−0.378838
$269$	−18.6180	−1.13516	−0.567579	−	0.823319i	$-0.692120\pi$
$269$	−18.6180	−1.13516	−0.567579	+	0.823319i	$0.692120\pi$
$270$	0.990062	0.0602532
$271$	21.8484	1.32720	0.663599	−	0.748088i	$-0.269028\pi$
$271$	21.8484	1.32720	0.663599	+	0.748088i	$0.269028\pi$
$272$	3.01242	0.182655
$273$	−3.02018	−0.182790
$274$	−1.01372	−0.0612410
$275$	4.33081	0.261158
$276$	−9.22278	−0.555146
$277$	−13.2372	−0.795345	−0.397672	−	0.917527i	$-0.630182\pi$
$277$	−13.2372	−0.795345	−0.397672	+	0.917527i	$0.630182\pi$
$278$	6.66568	0.399781
$279$	−0.533933	−0.0319657
$280$	−0.884769	−0.0528750
$281$	−6.57989	−0.392524	−0.196262	−	0.980552i	$-0.562880\pi$
$281$	−6.57989	−0.392524	−0.196262	+	0.980552i	$0.562880\pi$
$282$	−6.49280	−0.386640
$283$	28.6668	1.70406	0.852032	−	0.523489i	$-0.175370\pi$
$283$	28.6668	1.70406	0.852032	+	0.523489i	$0.175370\pi$
$284$	−6.92353	−0.410836
$285$	2.41953	0.143321
$286$	1.93783	0.114586
$287$	0.913896	0.0539456
$288$	−12.7082	−0.748841
$289$	−13.1025	−0.770738
$290$	0	0
$291$	18.5510	1.08748
$292$	−21.2896	−1.24588
$293$	13.2559	0.774417	0.387209	−	0.921992i	$-0.373439\pi$
$293$	13.2559	0.774417	0.387209	+	0.921992i	$0.373439\pi$
$294$	−10.3420	−0.603160
$295$	−4.57098	−0.266132
$296$	4.50926	0.262095
$297$	−1.81345	−0.105227
$298$	5.52520	0.320066
$299$	−7.55030	−0.436645
$300$	−15.3603	−0.886827
$301$	−1.36637	−0.0787565
$302$	6.84284	0.393761
$303$	−4.04218	−0.232217
$304$	1.97818	0.113456
$305$	6.63906	0.380152
$306$	−2.90543	−0.166092
$307$	−12.8223	−0.731808	−0.365904	−	0.930653i	$-0.619240\pi$
$307$	−12.8223	−0.731808	−0.365904	+	0.930653i	$0.619240\pi$
$308$	0.708757	0.0403852
$309$	19.1645	1.09023
$310$	−0.132193	−0.00750804
$311$	19.4438	1.10256	0.551278	−	0.834321i	$-0.314140\pi$
$311$	19.4438	1.10256	0.551278	+	0.834321i	$0.314140\pi$
$312$	−15.7152	−0.889700
$313$	20.5876	1.16368	0.581839	−	0.813304i	$-0.302333\pi$
$313$	20.5876	1.16368	0.581839	+	0.813304i	$0.302333\pi$
$314$	5.28097	0.298022
$315$	−0.822422	−0.0463382
$316$	−11.1669	−0.628184
$317$	−26.9821	−1.51546	−0.757732	−	0.652565i	$-0.773693\pi$
$317$	−26.9821	−1.51546	−0.757732	+	0.652565i	$0.773693\pi$
$318$	−11.5679	−0.648696
$319$	0	0
$320$	−0.649857	−0.0363281
$321$	−2.52520	−0.140943
$322$	0.791222	0.0440931
$323$	2.55936	0.142406
$324$	16.7161	0.928671
$325$	−12.5748	−0.697526
$326$	1.41945	0.0786159
$327$	5.17506	0.286181
$328$	4.75538	0.262572
$329$	−1.94409	−0.107181
$330$	1.24559	0.0685673
$331$	7.50796	0.412675	0.206337	−	0.978481i	$-0.433846\pi$
$331$	7.50796	0.412675	0.206337	+	0.978481i	$0.433846\pi$
$332$	13.9301	0.764515
$333$	4.19151	0.229693
$334$	0.609965	0.0333758
$335$	−3.26348	−0.178303
$336$	−1.58718	−0.0865875
$337$	28.1314	1.53242	0.766208	−	0.642593i	$-0.222141\pi$
$337$	28.1314	1.53242	0.766208	+	0.642593i	$0.222141\pi$
$338$	3.04951	0.165871
$339$	−43.9112	−2.38493
$340$	2.51061	0.136157
$341$	0.242131	0.0131121
$342$	−1.90792	−0.103169
$343$	−6.28804	−0.339522
$344$	−7.10981	−0.383336
$345$	−4.85313	−0.261284
$346$	−13.8330	−0.743668
$347$	11.2789	0.605481	0.302740	−	0.953073i	$-0.402098\pi$
$347$	11.2789	0.605481	0.302740	+	0.953073i	$0.402098\pi$
$348$	0	0
$349$	−6.18589	−0.331123	−0.165562	−	0.986199i	$-0.552944\pi$
$349$	−6.18589	−0.331123	−0.165562	+	0.986199i	$0.552944\pi$
$350$	1.31776	0.0704372
$351$	5.26547	0.281050
$352$	5.76300	0.307169
$353$	−34.5564	−1.83925	−0.919626	−	0.392795i	$-0.871508\pi$
$353$	−34.5564	−1.83925	−0.919626	+	0.392795i	$0.871508\pi$
$354$	8.50813	0.452202
$355$	−3.64324	−0.193363
$356$	3.38415	0.179360
$357$	−2.05348	−0.108682
$358$	5.02092	0.265364
$359$	−16.1081	−0.850152	−0.425076	−	0.905158i	$-0.639753\pi$
$359$	−16.1081	−0.850152	−0.425076	+	0.905158i	$0.639753\pi$
$360$	−4.27940	−0.225544
$361$	−17.3193	−0.911544
$362$	−17.6361	−0.926931
$363$	−2.28148	−0.119747
$364$	−2.05793	−0.107865
$365$	−11.2028	−0.586383
$366$	−12.3575	−0.645939
$367$	−7.49049	−0.391000	−0.195500	−	0.980704i	$-0.562633\pi$
$367$	−7.49049	−0.391000	−0.195500	+	0.980704i	$0.562633\pi$
$368$	−3.96786	−0.206839
$369$	4.42029	0.230111
$370$	1.03774	0.0539498
$371$	−3.46369	−0.179826
$372$	−0.858777	−0.0445255
$373$	−30.4654	−1.57744	−0.788720	−	0.614753i	$-0.789256\pi$
$373$	−30.4654	−1.57744	−0.788720	+	0.614753i	$0.789256\pi$
$374$	1.31757	0.0681299
$375$	−17.4145	−0.899279
$376$	−10.1159	−0.521687
$377$	0	0
$378$	−0.551787	−0.0283809
$379$	−23.1479	−1.18903	−0.594514	−	0.804085i	$-0.702656\pi$
$379$	−23.1479	−1.18903	−0.594514	+	0.804085i	$0.702656\pi$
$380$	1.64865	0.0845740
$381$	−32.3631	−1.65801
$382$	−4.84546	−0.247915
$383$	−23.7484	−1.21349	−0.606743	−	0.794898i	$-0.707524\pi$
$383$	−23.7484	−1.21349	−0.606743	+	0.794898i	$0.707524\pi$
$384$	−25.0867	−1.28020
$385$	0.372956	0.0190076
$386$	1.71726	0.0874061
$387$	−6.60881	−0.335945
$388$	12.6405	0.641724
$389$	11.4719	0.581647	0.290824	−	0.956777i	$-0.406071\pi$
$389$	11.4719	0.581647	0.290824	+	0.956777i	$0.406071\pi$
$390$	−3.61665	−0.183136
$391$	−5.13360	−0.259617
$392$	−16.1131	−0.813834
$393$	−44.5229	−2.24589
$394$	5.70651	0.287490
$395$	−5.87612	−0.295660
$396$	3.42808	0.172268
$397$	−19.0131	−0.954241	−0.477120	−	0.878838i	$-0.658319\pi$
$397$	−19.0131	−0.954241	−0.477120	+	0.878838i	$0.658319\pi$
$398$	−9.01048	−0.451655
$399$	−1.34847	−0.0675077
$400$	−6.60837	−0.330418
$401$	−6.82045	−0.340597	−0.170298	−	0.985393i	$-0.554473\pi$
$401$	−6.82045	−0.340597	−0.170298	+	0.985393i	$0.554473\pi$
$402$	6.07444	0.302966
$403$	−0.703044	−0.0350211
$404$	−2.75432	−0.137032
$405$	8.79619	0.437086
$406$	0	0
$407$	−1.90079	−0.0942184
$408$	−10.6851	−0.528992
$409$	−8.06438	−0.398758	−0.199379	−	0.979922i	$-0.563892\pi$
$409$	−8.06438	−0.398758	−0.199379	+	0.979922i	$0.563892\pi$
$410$	1.09439	0.0540479
$411$	−3.46538	−0.170935
$412$	13.0585	0.643348
$413$	2.54752	0.125355
$414$	3.82694	0.188084
$415$	7.33020	0.359825
$416$	−16.7333	−0.820417
$417$	22.7865	1.11586
$418$	0.865213	0.0423190
$419$	20.1358	0.983700	0.491850	−	0.870680i	$-0.336321\pi$
$419$	20.1358	0.983700	0.491850	+	0.870680i	$0.336321\pi$
$420$	−1.32278	−0.0645451
$421$	19.4791	0.949354	0.474677	−	0.880160i	$-0.342565\pi$
$421$	19.4791	0.949354	0.474677	+	0.880160i	$0.342565\pi$
$422$	−4.16563	−0.202780
$423$	−9.40306	−0.457192
$424$	−18.0230	−0.875275
$425$	−8.54988	−0.414730
$426$	6.78131	0.328555
$427$	−3.70012	−0.179061
$428$	−1.72065	−0.0831710
$429$	6.62444	0.319831
$430$	−1.63623	−0.0789059
$431$	15.7725	0.759733	0.379867	−	0.925041i	$-0.375970\pi$
$431$	15.7725	0.759733	0.379867	+	0.925041i	$0.375970\pi$
$432$	2.76713	0.133134
$433$	5.01820	0.241160	0.120580	−	0.992704i	$-0.461525\pi$
$433$	5.01820	0.241160	0.120580	+	0.992704i	$0.461525\pi$
$434$	0.0736744	0.00353648
$435$	0	0
$436$	3.52625	0.168877
$437$	−3.37110	−0.161262
$438$	20.8522	0.996359
$439$	22.9934	1.09742	0.548708	−	0.836014i	$-0.315120\pi$
$439$	22.9934	1.09742	0.548708	+	0.836014i	$0.315120\pi$
$440$	1.94065	0.0925166
$441$	−14.9777	−0.713222
$442$	−3.82566	−0.181968
$443$	−14.8021	−0.703269	−0.351634	−	0.936137i	$-0.614374\pi$
$443$	−14.8021	−0.703269	−0.351634	+	0.936137i	$0.614374\pi$
$444$	6.74161	0.319943
$445$	1.78078	0.0844170
$446$	18.7961	0.890021
$447$	18.8878	0.893362
$448$	0.362182	0.0171115
$449$	−14.0147	−0.661396	−0.330698	−	0.943737i	$-0.607284\pi$
$449$	−14.0147	−0.661396	−0.330698	+	0.943737i	$0.607284\pi$
$450$	6.37367	0.300458
$451$	−2.00453	−0.0943898
$452$	−29.9208	−1.40735
$453$	23.3921	1.09906
$454$	8.37242	0.392937
$455$	−1.08291	−0.0507674
$456$	−7.01663	−0.328584
$457$	−10.6823	−0.499695	−0.249848	−	0.968285i	$-0.580380\pi$
$457$	−10.6823	−0.499695	−0.249848	+	0.968285i	$0.580380\pi$
$458$	−9.07993	−0.424277
$459$	3.58010	0.167105
$460$	−3.30689	−0.154185
$461$	−32.5949	−1.51809	−0.759047	−	0.651035i	$-0.774335\pi$
$461$	−32.5949	−1.51809	−0.759047	+	0.651035i	$0.774335\pi$
$462$	−0.694197	−0.0322970
$463$	−26.4768	−1.23048	−0.615241	−	0.788339i	$-0.710941\pi$
$463$	−26.4768	−1.23048	−0.615241	+	0.788339i	$0.710941\pi$
$464$	0	0
$465$	−0.451898	−0.0209563
$466$	−4.34504	−0.201280
$467$	29.1934	1.35091	0.675454	−	0.737402i	$-0.263948\pi$
$467$	29.1934	1.35091	0.675454	+	0.737402i	$0.263948\pi$
$468$	−9.95368	−0.460109
$469$	1.81882	0.0839854
$470$	−2.32804	−0.107384
$471$	18.0529	0.831834
$472$	13.2558	0.610148
$473$	2.99700	0.137802
$474$	10.9375	0.502374
$475$	−5.61448	−0.257610
$476$	−1.39923	−0.0641334
$477$	−16.7530	−0.767067
$478$	−16.3118	−0.746083
$479$	4.41171	0.201576	0.100788	−	0.994908i	$-0.467864\pi$
$479$	4.41171	0.201576	0.100788	+	0.994908i	$0.467864\pi$
$480$	−10.7557	−0.490929
$481$	5.51907	0.251648
$482$	0.394567	0.0179720
$483$	2.70478	0.123072
$484$	−1.55458	−0.0706629
$485$	6.65157	0.302032
$486$	−12.7418	−0.577981
$487$	−9.13554	−0.413971	−0.206986	−	0.978344i	$-0.566365\pi$
$487$	−9.13554	−0.413971	−0.206986	+	0.978344i	$0.566365\pi$
$488$	−19.2533	−0.871555
$489$	4.85235	0.219431
$490$	−3.70821	−0.167520
$491$	23.7205	1.07049	0.535245	−	0.844697i	$-0.320219\pi$
$491$	23.7205	1.07049	0.535245	+	0.844697i	$0.320219\pi$
$492$	7.10958	0.320525
$493$	0	0
$494$	−2.51221	−0.113030
$495$	1.80390	0.0810791
$496$	−0.369466	−0.0165895
$497$	2.03047	0.0910792
$498$	−13.6440	−0.611401
$499$	−2.00784	−0.0898833	−0.0449416	−	0.998990i	$-0.514310\pi$
$499$	−2.00784	−0.0898833	−0.0449416	+	0.998990i	$0.514310\pi$
$500$	−11.8661	−0.530668
$501$	2.08516	0.0931579
$502$	2.73532	0.122083
$503$	26.5126	1.18214	0.591069	−	0.806621i	$-0.298706\pi$
$503$	26.5126	1.18214	0.591069	+	0.806621i	$0.298706\pi$
$504$	2.38502	0.106237
$505$	−1.44935	−0.0644953
$506$	−1.73546	−0.0771506
$507$	10.4247	0.462976
$508$	−22.0520	−0.978400
$509$	19.8175	0.878394	0.439197	−	0.898391i	$-0.355263\pi$
$509$	19.8175	0.878394	0.439197	+	0.898391i	$0.355263\pi$
$510$	−2.45903	−0.108888
$511$	6.24362	0.276202
$512$	−16.0336	−0.708589
$513$	2.35096	0.103797
$514$	−10.0273	−0.442284
$515$	6.87155	0.302797
$516$	−10.6296	−0.467942
$517$	4.26415	0.187537
$518$	−0.578362	−0.0254118
$519$	−47.2879	−2.07571
$520$	−5.63481	−0.247103
$521$	−31.1996	−1.36688	−0.683440	−	0.730007i	$-0.739517\pi$
$521$	−31.1996	−1.36688	−0.683440	+	0.730007i	$0.739517\pi$
$522$	0	0
$523$	21.4242	0.936814	0.468407	−	0.883513i	$-0.344828\pi$
$523$	21.4242	0.936814	0.468407	+	0.883513i	$0.344828\pi$
$524$	−30.3376	−1.32531
$525$	4.50473	0.196603
$526$	2.42424	0.105702
$527$	−0.478014	−0.0208226
$528$	3.48130	0.151504
$529$	−16.2382	−0.706008
$530$	−4.14775	−0.180167
$531$	12.3217	0.534717
$532$	−0.918835	−0.0398366
$533$	5.82031	0.252106
$534$	−3.31463	−0.143438
$535$	−0.905428	−0.0391451
$536$	9.46409	0.408786
$537$	17.1639	0.740678
$538$	12.4256	0.535704
$539$	6.79214	0.292558
$540$	2.30618	0.0992422
$541$	−17.2892	−0.743321	−0.371660	−	0.928369i	$-0.621211\pi$
$541$	−17.2892	−0.743321	−0.371660	+	0.928369i	$0.621211\pi$
$542$	−14.5815	−0.626331
$543$	−60.2885	−2.58723
$544$	−11.3773	−0.487798
$545$	1.85555	0.0794831
$546$	2.01565	0.0862620
$547$	39.3230	1.68133	0.840666	−	0.541554i	$-0.182164\pi$
$547$	39.3230	1.68133	0.840666	+	0.541554i	$0.182164\pi$
$548$	−2.36129	−0.100869
$549$	−17.8966	−0.763807
$550$	−2.89036	−0.123246
$551$	0	0
$552$	14.0741	0.599032
$553$	3.27492	0.139264
$554$	8.83443	0.375339
$555$	3.54751	0.150583
$556$	15.5266	0.658473
$557$	38.5179	1.63206	0.816029	−	0.578012i	$-0.196171\pi$
$557$	38.5179	1.63206	0.816029	+	0.578012i	$0.196171\pi$
$558$	0.356344	0.0150853
$559$	−8.70200	−0.368055
$560$	−0.569093	−0.0240485
$561$	4.50409	0.190163
$562$	4.39139	0.185240
$563$	39.2214	1.65299	0.826493	−	0.562947i	$-0.190333\pi$
$563$	39.2214	1.65299	0.826493	+	0.562947i	$0.190333\pi$
$564$	−15.1239	−0.636829
$565$	−15.7446	−0.662382
$566$	−19.1321	−0.804182
$567$	−4.90235	−0.205879
$568$	10.5654	0.443314
$569$	19.3275	0.810250	0.405125	−	0.914261i	$-0.367228\pi$
$569$	19.3275	0.810250	0.405125	+	0.914261i	$0.367228\pi$
$570$	−1.61478	−0.0676358
$571$	−39.6102	−1.65763	−0.828817	−	0.559520i	$-0.810985\pi$
$571$	−39.6102	−1.65763	−0.828817	+	0.559520i	$0.810985\pi$
$572$	4.51385	0.188733
$573$	−16.5641	−0.691976
$574$	−0.609930	−0.0254580
$575$	11.2616	0.469642
$576$	1.75178	0.0729909
$577$	−18.8957	−0.786638	−0.393319	−	0.919402i	$-0.628673\pi$
$577$	−18.8957	−0.786638	−0.393319	+	0.919402i	$0.628673\pi$
$578$	8.74458	0.363726
$579$	5.87041	0.243966
$580$	0	0
$581$	−4.08531	−0.169487
$582$	−12.3808	−0.513202
$583$	7.59723	0.314645
$584$	32.4882	1.34437
$585$	−5.23774	−0.216554
$586$	−8.84692	−0.365463
$587$	34.0285	1.40451	0.702254	−	0.711926i	$-0.252177\pi$
$587$	34.0285	1.40451	0.702254	+	0.711926i	$0.252177\pi$
$588$	−24.0900	−0.993456
$589$	−0.313899	−0.0129340
$590$	3.05065	0.125593
$591$	19.5076	0.802435
$592$	2.90040	0.119206
$593$	−23.1938	−0.952456	−0.476228	−	0.879322i	$-0.657996\pi$
$593$	−23.1938	−0.952456	−0.476228	+	0.879322i	$0.657996\pi$
$594$	1.21029	0.0496586
$595$	−0.736289	−0.0301849
$596$	12.8700	0.527176
$597$	−30.8022	−1.26065
$598$	5.03904	0.206062
$599$	−27.3949	−1.11933	−0.559663	−	0.828720i	$-0.689070\pi$
$599$	−27.3949	−1.11933	−0.559663	+	0.828720i	$0.689070\pi$
$600$	23.4400	0.956934
$601$	−30.0110	−1.22418	−0.612088	−	0.790790i	$-0.709670\pi$
$601$	−30.0110	−1.22418	−0.612088	+	0.790790i	$0.709670\pi$
$602$	0.911912	0.0371668
$603$	8.79719	0.358249
$604$	15.9392	0.648557
$605$	−0.818040	−0.0332580
$606$	2.69773	0.109588
$607$	−4.37991	−0.177775	−0.0888875	−	0.996042i	$-0.528331\pi$
$607$	−4.37991	−0.177775	−0.0888875	+	0.996042i	$0.528331\pi$
$608$	−7.47117	−0.302996
$609$	0	0
$610$	−4.43088	−0.179401
$611$	−12.3813	−0.500892
$612$	−6.76771	−0.273568
$613$	−31.1538	−1.25829	−0.629145	−	0.777288i	$-0.716595\pi$
$613$	−31.1538	−1.25829	−0.629145	+	0.777288i	$0.716595\pi$
$614$	8.55755	0.345355
$615$	3.74114	0.150857
$616$	−1.08157	−0.0435778
$617$	−35.7072	−1.43752	−0.718758	−	0.695260i	$-0.755289\pi$
$617$	−35.7072	−1.43752	−0.718758	+	0.695260i	$0.755289\pi$
$618$	−12.7903	−0.514500
$619$	−6.67624	−0.268341	−0.134170	−	0.990958i	$-0.542837\pi$
$619$	−6.67624	−0.268341	−0.134170	+	0.990958i	$0.542837\pi$
$620$	−0.307920	−0.0123664
$621$	−4.71559	−0.189230
$622$	−12.9767	−0.520318
$623$	−0.992474	−0.0397626
$624$	−10.1082	−0.404652
$625$	15.4100	0.616399
$626$	−13.7401	−0.549163
$627$	2.95772	0.118120
$628$	12.3011	0.490868
$629$	3.75253	0.149623
$630$	0.548881	0.0218679
$631$	−32.2310	−1.28310	−0.641548	−	0.767083i	$-0.721707\pi$
$631$	−32.2310	−1.28310	−0.641548	+	0.767083i	$0.721707\pi$
$632$	17.0407	0.677844
$633$	−14.2401	−0.565994
$634$	18.0077	0.715178
$635$	−11.6040	−0.460492
$636$	−26.9455	−1.06846
$637$	−19.7215	−0.781394
$638$	0	0
$639$	9.82089	0.388508
$640$	−8.99502	−0.355559
$641$	28.0832	1.10922	0.554610	−	0.832110i	$-0.312868\pi$
$641$	28.0832	1.10922	0.554610	+	0.832110i	$0.312868\pi$
$642$	1.68531	0.0665138
$643$	6.20846	0.244838	0.122419	−	0.992479i	$-0.460935\pi$
$643$	6.20846	0.244838	0.122419	+	0.992479i	$0.460935\pi$
$644$	1.84302	0.0726250
$645$	−5.59342	−0.220241
$646$	−1.70810	−0.0672044
$647$	−29.1650	−1.14660	−0.573298	−	0.819347i	$-0.694336\pi$
$647$	−29.1650	−1.14660	−0.573298	+	0.819347i	$0.694336\pi$
$648$	−25.5089	−1.00209
$649$	−5.58772	−0.219337
$650$	8.39238	0.329176
$651$	0.251854	0.00987095
$652$	3.30636	0.129487
$653$	−40.0154	−1.56592	−0.782962	−	0.622070i	$-0.786292\pi$
$653$	−40.0154	−1.56592	−0.782962	+	0.622070i	$0.786292\pi$
$654$	−3.45381	−0.135055
$655$	−15.9640	−0.623765
$656$	3.05871	0.119423
$657$	30.1988	1.17817
$658$	1.29747	0.0505808
$659$	33.6595	1.31119	0.655594	−	0.755113i	$-0.272418\pi$
$659$	33.6595	1.31119	0.655594	+	0.755113i	$0.272418\pi$
$660$	2.90138	0.112936
$661$	−11.4103	−0.443811	−0.221905	−	0.975068i	$-0.571228\pi$
$661$	−11.4103	−0.443811	−0.221905	+	0.975068i	$0.571228\pi$
$662$	−5.01077	−0.194749
$663$	−13.0780	−0.507906
$664$	−21.2575	−0.824953
$665$	−0.483502	−0.0187494
$666$	−2.79739	−0.108397
$667$	0	0
$668$	1.42081	0.0549728
$669$	64.2541	2.48421
$670$	2.17803	0.0841447
$671$	8.11582	0.313308
$672$	5.99444	0.231241
$673$	10.1130	0.389826	0.194913	−	0.980821i	$-0.437558\pi$
$673$	10.1130	0.389826	0.194913	+	0.980821i	$0.437558\pi$
$674$	−18.7748	−0.723177
$675$	−7.85370	−0.302289
$676$	7.10330	0.273204
$677$	−29.8725	−1.14809	−0.574047	−	0.818823i	$-0.694627\pi$
$677$	−29.8725	−1.14809	−0.574047	+	0.818823i	$0.694627\pi$
$678$	29.3061	1.12549
$679$	−3.70709	−0.142265
$680$	−3.83122	−0.146920
$681$	28.6210	1.09676
$682$	−0.161597	−0.00618786
$683$	−8.09528	−0.309757	−0.154879	−	0.987933i	$-0.549499\pi$
$683$	−8.09528	−0.309757	−0.154879	+	0.987933i	$0.549499\pi$
$684$	−4.44417	−0.169927
$685$	−1.24254	−0.0474748
$686$	4.19661	0.160227
$687$	−31.0396	−1.18423
$688$	−4.57311	−0.174348
$689$	−22.0591	−0.840386
$690$	3.23896	0.123305
$691$	1.74699	0.0664586	0.0332293	−	0.999448i	$-0.489421\pi$
$691$	1.74699	0.0664586	0.0332293	+	0.999448i	$0.489421\pi$
$692$	−32.2217	−1.22488
$693$	−1.00536	−0.0381904
$694$	−7.52746	−0.285738
$695$	8.17026	0.309915
$696$	0	0
$697$	3.95735	0.149895
$698$	4.12843	0.156264
$699$	−14.8534	−0.561808
$700$	3.06949	0.116016
$701$	−27.3565	−1.03324	−0.516620	−	0.856215i	$-0.672810\pi$
$701$	−27.3565	−1.03324	−0.516620	+	0.856215i	$0.672810\pi$
$702$	−3.51415	−0.132633
$703$	2.46418	0.0929385
$704$	−0.794407	−0.0299404
$705$	−7.95835	−0.299729
$706$	23.0628	0.867980
$707$	0.807762	0.0303790
$708$	19.8182	0.744815
$709$	−47.6146	−1.78820	−0.894102	−	0.447864i	$-0.852185\pi$
$709$	−47.6146	−1.78820	−0.894102	+	0.447864i	$0.852185\pi$
$710$	2.43148	0.0912519
$711$	15.8399	0.594044
$712$	−5.16425	−0.193539
$713$	0.629624	0.0235796
$714$	1.37048	0.0512890
$715$	2.37524	0.0888289
$716$	11.6954	0.437077
$717$	−55.7615	−2.08245
$718$	10.7505	0.401203
$719$	−19.8884	−0.741712	−0.370856	−	0.928690i	$-0.620936\pi$
$719$	−19.8884	−0.741712	−0.370856	+	0.928690i	$0.620936\pi$
$720$	−2.75256	−0.102582
$721$	−3.82969	−0.142625
$722$	11.5588	0.430176
$723$	1.34882	0.0501631
$724$	−41.0802	−1.52673
$725$	0	0
$726$	1.52265	0.0565108
$727$	−5.06657	−0.187909	−0.0939544	−	0.995576i	$-0.529951\pi$
$727$	−5.06657	−0.187909	−0.0939544	+	0.995576i	$0.529951\pi$
$728$	3.14042	0.116392
$729$	−11.2994	−0.418496
$730$	7.47671	0.276726
$731$	−5.91666	−0.218836
$732$	−28.7848	−1.06392
$733$	−28.5615	−1.05494	−0.527471	−	0.849573i	$-0.676860\pi$
$733$	−28.5615	−1.05494	−0.527471	+	0.849573i	$0.676860\pi$
$734$	4.99912	0.184521
$735$	−12.6764	−0.467578
$736$	14.9858	0.552384
$737$	−3.98939	−0.146951
$738$	−2.95008	−0.108594
$739$	−41.4525	−1.52486	−0.762428	−	0.647073i	$-0.775993\pi$
$739$	−41.4525	−1.52486	−0.762428	+	0.647073i	$0.775993\pi$
$740$	2.41725	0.0888598
$741$	−8.58794	−0.315486
$742$	2.31165	0.0848633
$743$	0.216975	0.00796004	0.00398002	−	0.999992i	$-0.498733\pi$
$743$	0.216975	0.00796004	0.00398002	+	0.999992i	$0.498733\pi$
$744$	1.31050	0.0480454
$745$	6.77235	0.248120
$746$	20.3325	0.744425
$747$	−19.7596	−0.722966
$748$	3.06905	0.112216
$749$	0.504618	0.0184384
$750$	11.6223	0.424388
$751$	39.6340	1.44627	0.723133	−	0.690709i	$-0.242701\pi$
$751$	39.6340	1.44627	0.723133	+	0.690709i	$0.242701\pi$
$752$	−6.50665	−0.237273
$753$	9.35063	0.340756
$754$	0	0
$755$	8.38740	0.305249
$756$	−1.28529	−0.0467457
$757$	19.8967	0.723159	0.361580	−	0.932341i	$-0.382238\pi$
$757$	19.8967	0.723159	0.361580	+	0.932341i	$0.382238\pi$
$758$	15.4488	0.561126
$759$	−5.93264	−0.215341
$760$	−2.51586	−0.0912598
$761$	27.5418	0.998389	0.499194	−	0.866490i	$-0.333629\pi$
$761$	27.5418	0.998389	0.499194	+	0.866490i	$0.333629\pi$
$762$	21.5990	0.782449
$763$	−1.03415	−0.0374386
$764$	−11.2867	−0.408338
$765$	−3.56125	−0.128757
$766$	15.8496	0.572669
$767$	16.2244	0.585827
$768$	20.3676	0.734953
$769$	1.06381	0.0383619	0.0191810	−	0.999816i	$-0.493894\pi$
$769$	1.06381	0.0383619	0.0191810	+	0.999816i	$0.493894\pi$
$770$	−0.248909	−0.00897007
$771$	−34.2781	−1.23449
$772$	4.00006	0.143965
$773$	−27.3014	−0.981964	−0.490982	−	0.871170i	$-0.663362\pi$
$773$	−27.3014	−0.981964	−0.490982	+	0.871170i	$0.663362\pi$
$774$	4.41069	0.158539
$775$	1.04862	0.0376676
$776$	−19.2895	−0.692454
$777$	−1.97712	−0.0709288
$778$	−7.65628	−0.274491
$779$	2.59868	0.0931075
$780$	−8.42437	−0.301641
$781$	−4.45363	−0.159363
$782$	3.42614	0.122519
$783$	0	0
$784$	−10.3641	−0.370147
$785$	6.47299	0.231031
$786$	29.7144	1.05988
$787$	6.75000	0.240611	0.120306	−	0.992737i	$-0.461613\pi$
$787$	6.75000	0.240611	0.120306	+	0.992737i	$0.461613\pi$
$788$	13.2923	0.473520
$789$	8.28723	0.295033
$790$	3.92170	0.139528
$791$	8.77490	0.311999
$792$	−5.23129	−0.185886
$793$	−23.5649	−0.836814
$794$	12.6893	0.450325
$795$	−14.1790	−0.502878
$796$	−20.9884	−0.743913
$797$	−3.41540	−0.120980	−0.0604899	−	0.998169i	$-0.519266\pi$
$797$	−3.41540	−0.120980	−0.0604899	+	0.998169i	$0.519266\pi$
$798$	0.899960	0.0318582
$799$	−8.41827	−0.297817
$800$	24.9585	0.882415
$801$	−4.80035	−0.169612
$802$	4.55194	0.160734
$803$	−13.6947	−0.483276
$804$	14.1494	0.499010
$805$	0.969816	0.0341815
$806$	0.469208	0.0165272
$807$	42.4765	1.49525
$808$	4.20312	0.147865
$809$	−29.6941	−1.04399	−0.521995	−	0.852948i	$-0.674812\pi$
$809$	−29.6941	−1.04399	−0.521995	+	0.852948i	$0.674812\pi$
$810$	−5.87054	−0.206270
$811$	13.5544	0.475960	0.237980	−	0.971270i	$-0.423515\pi$
$811$	13.5544	0.475960	0.237980	+	0.971270i	$0.423515\pi$
$812$	0	0
$813$	−49.8468	−1.74820
$814$	1.26858	0.0444635
$815$	1.73984	0.0609441
$816$	−6.87277	−0.240595
$817$	−3.88532	−0.135930
$818$	5.38213	0.188182
$819$	2.91913	0.102003
$820$	2.54919	0.0890215
$821$	34.6185	1.20819	0.604096	−	0.796911i	$-0.293534\pi$
$821$	34.6185	1.20819	0.604096	+	0.796911i	$0.293534\pi$
$822$	2.31278	0.0806674
$823$	−11.9458	−0.416405	−0.208202	−	0.978086i	$-0.566761\pi$
$823$	−11.9458	−0.416405	−0.208202	+	0.978086i	$0.566761\pi$
$824$	−19.9275	−0.694206
$825$	−9.88065	−0.344000
$826$	−1.70020	−0.0591577
$827$	−40.9944	−1.42551	−0.712757	−	0.701411i	$-0.752554\pi$
$827$	−40.9944	−1.42551	−0.712757	+	0.701411i	$0.752554\pi$
$828$	8.91420	0.309790
$829$	49.1119	1.70573	0.852864	−	0.522133i	$-0.174864\pi$
$829$	49.1119	1.70573	0.852864	+	0.522133i	$0.174864\pi$
$830$	−4.89214	−0.169809
$831$	30.2003	1.04764
$832$	2.30662	0.0799677
$833$	−13.4090	−0.464595
$834$	−15.2076	−0.526596
$835$	0.747647	0.0258734
$836$	2.01537	0.0697029
$837$	−0.439091	−0.0151772
$838$	−13.4386	−0.464227
$839$	−37.4010	−1.29122	−0.645612	−	0.763665i	$-0.723398\pi$
$839$	−37.4010	−1.29122	−0.645612	+	0.763665i	$0.723398\pi$
$840$	2.01858	0.0696476
$841$	0	0
$842$	−13.0003	−0.448019
$843$	15.0119	0.517037
$844$	−9.70312	−0.333995
$845$	3.73784	0.128586
$846$	6.27556	0.215758
$847$	0.455915	0.0156654
$848$	−11.5926	−0.398091
$849$	−65.4027	−2.24461
$850$	5.70615	0.195719
$851$	−4.94270	−0.169434
$852$	15.7959	0.541158
$853$	4.56333	0.156245	0.0781227	−	0.996944i	$-0.475107\pi$
$853$	4.56333	0.156245	0.0781227	+	0.996944i	$0.475107\pi$
$854$	2.46944	0.0845026
$855$	−2.33858	−0.0799776
$856$	2.62574	0.0897459
$857$	41.5192	1.41827	0.709134	−	0.705073i	$-0.249086\pi$
$857$	41.5192	1.41827	0.709134	+	0.705073i	$0.249086\pi$
$858$	−4.42112	−0.150935
$859$	−15.5093	−0.529169	−0.264585	−	0.964362i	$-0.585235\pi$
$859$	−15.5093	−0.529169	−0.264585	+	0.964362i	$0.585235\pi$
$860$	−3.81131	−0.129965
$861$	−2.08503	−0.0710578
$862$	−10.5265	−0.358533
$863$	12.4775	0.424741	0.212370	−	0.977189i	$-0.431882\pi$
$863$	12.4775	0.424741	0.212370	+	0.977189i	$0.431882\pi$
$864$	−10.4509	−0.355547
$865$	−16.9554	−0.576501
$866$	−3.34913	−0.113808
$867$	29.8932	1.01523
$868$	0.171612	0.00582489
$869$	−7.18318	−0.243673
$870$	0	0
$871$	11.5835	0.392492
$872$	−5.38109	−0.182227
$873$	−17.9303	−0.606848
$874$	2.24986	0.0761025
$875$	3.47998	0.117645
$876$	48.5717	1.64109
$877$	54.8431	1.85192	0.925960	−	0.377622i	$-0.123258\pi$
$877$	54.8431	1.85192	0.925960	+	0.377622i	$0.123258\pi$
$878$	−15.3457	−0.517892
$879$	−30.2430	−1.02007
$880$	1.24824	0.0420783
$881$	−33.9667	−1.14437	−0.572184	−	0.820125i	$-0.693904\pi$
$881$	−33.9667	−1.14437	−0.572184	+	0.820125i	$0.693904\pi$
$882$	9.99602	0.336583
$883$	−27.1408	−0.913361	−0.456680	−	0.889631i	$-0.650962\pi$
$883$	−27.1408	−0.913361	−0.456680	+	0.889631i	$0.650962\pi$
$884$	−8.91122	−0.299717
$885$	10.4286	0.350553
$886$	9.87885	0.331886
$887$	22.6079	0.759099	0.379550	−	0.925171i	$-0.376079\pi$
$887$	22.6079	0.759099	0.379550	+	0.925171i	$0.376079\pi$
$888$	−10.2878	−0.345235
$889$	6.46722	0.216904
$890$	−1.18848	−0.0398380
$891$	10.7528	0.360231
$892$	43.7823	1.46594
$893$	−5.52806	−0.184989
$894$	−12.6056	−0.421595
$895$	6.15424	0.205714
$896$	5.01315	0.167478
$897$	17.2259	0.575154
$898$	9.35337	0.312126
$899$	0	0
$900$	14.8464	0.494879
$901$	−14.9984	−0.499670
$902$	1.33782	0.0445444
$903$	3.11735	0.103739
$904$	45.6594	1.51861
$905$	−21.6169	−0.718569
$906$	−15.6118	−0.518667
$907$	−31.8143	−1.05638	−0.528188	−	0.849127i	$-0.677129\pi$
$907$	−31.8143	−1.05638	−0.528188	+	0.849127i	$0.677129\pi$
$908$	19.5021	0.647201
$909$	3.90694	0.129585
$910$	0.722726	0.0239581
$911$	−27.6326	−0.915508	−0.457754	−	0.889079i	$-0.651346\pi$
$911$	−27.6326	−0.915508	−0.457754	+	0.889079i	$0.651346\pi$
$912$	−4.51317	−0.149446
$913$	8.96069	0.296555
$914$	7.12929	0.235816
$915$	−15.1469	−0.500741
$916$	−21.1502	−0.698821
$917$	8.89715	0.293810
$918$	−2.38934	−0.0788601
$919$	−7.39780	−0.244031	−0.122015	−	0.992528i	$-0.538936\pi$
$919$	−7.39780	−0.244031	−0.122015	+	0.992528i	$0.538936\pi$
$920$	5.04636	0.166373
$921$	29.2538	0.963946
$922$	21.7537	0.716419
$923$	12.9314	0.425643
$924$	−1.61701	−0.0531959
$925$	−8.23194	−0.270665
$926$	17.6705	0.580689
$927$	−18.5233	−0.608383
$928$	0	0
$929$	27.3562	0.897527	0.448763	−	0.893651i	$-0.351865\pi$
$929$	27.3562	0.897527	0.448763	+	0.893651i	$0.351865\pi$
$930$	0.301595	0.00988968
$931$	−8.80535	−0.288584
$932$	−10.1210	−0.331525
$933$	−44.3606	−1.45230
$934$	−19.4835	−0.637520
$935$	1.61497	0.0528152
$936$	15.1894	0.496482
$937$	4.94100	0.161415	0.0807077	−	0.996738i	$-0.474282\pi$
$937$	4.94100	0.161415	0.0807077	+	0.996738i	$0.474282\pi$
$938$	−1.21387	−0.0396344
$939$	−46.9701	−1.53281
$940$	−5.42276	−0.176871
$941$	13.9335	0.454220	0.227110	−	0.973869i	$-0.427072\pi$
$941$	13.9335	0.454220	0.227110	+	0.973869i	$0.427072\pi$
$942$	−12.0484	−0.392559
$943$	−5.21249	−0.169742
$944$	8.52628	0.277507
$945$	−0.676336	−0.0220012
$946$	−2.00018	−0.0650315
$947$	−29.5274	−0.959511	−0.479755	−	0.877402i	$-0.659275\pi$
$947$	−29.5274	−0.959511	−0.479755	+	0.877402i	$0.659275\pi$
$948$	25.4769	0.827452
$949$	39.7636	1.29078
$950$	3.74708	0.121571
$951$	61.5590	1.99619
$952$	2.13524	0.0692034
$953$	−4.70917	−0.152545	−0.0762725	−	0.997087i	$-0.524302\pi$
$953$	−4.70917	−0.152545	−0.0762725	+	0.997087i	$0.524302\pi$
$954$	11.1809	0.361994
$955$	−5.93918	−0.192187
$956$	−37.9955	−1.22886
$957$	0	0
$958$	−2.94436	−0.0951279
$959$	0.692497	0.0223619
$960$	1.48263	0.0478518
$961$	−30.9414	−0.998109
$962$	−3.68340	−0.118758
$963$	2.44071	0.0786509
$964$	0.919075	0.0296014
$965$	2.10488	0.0677583
$966$	−1.80516	−0.0580799
$967$	7.13518	0.229452	0.114726	−	0.993397i	$-0.463401\pi$
$967$	7.13518	0.229452	0.114726	+	0.993397i	$0.463401\pi$
$968$	2.37231	0.0762490
$969$	−5.83911	−0.187579
$970$	−4.43923	−0.142535
$971$	16.5204	0.530165	0.265082	−	0.964226i	$-0.414601\pi$
$971$	16.5204	0.530165	0.265082	+	0.964226i	$0.414601\pi$
$972$	−29.6799	−0.951984
$973$	−4.55349	−0.145978
$974$	6.09702	0.195361
$975$	28.6892	0.918790
$976$	−12.3839	−0.396399
$977$	−4.41093	−0.141118	−0.0705590	−	0.997508i	$-0.522478\pi$
$977$	−4.41093	−0.141118	−0.0705590	+	0.997508i	$0.522478\pi$
$978$	−3.23844	−0.103554
$979$	2.17689	0.0695736
$980$	−8.63764	−0.275919
$981$	−5.00191	−0.159699
$982$	−15.8309	−0.505186
$983$	8.29894	0.264695	0.132347	−	0.991203i	$-0.457749\pi$
$983$	8.29894	0.264695	0.132347	+	0.991203i	$0.457749\pi$
$984$	−10.8493	−0.345863
$985$	6.99458	0.222866
$986$	0	0
$987$	4.43539	0.141180
$988$	−5.85176	−0.186169
$989$	7.79324	0.247811
$990$	−1.20391	−0.0382628
$991$	21.9446	0.697093	0.348547	−	0.937291i	$-0.386675\pi$
$991$	21.9446	0.697093	0.348547	+	0.937291i	$0.386675\pi$
$992$	1.39540	0.0443040
$993$	−17.1292	−0.543580
$994$	−1.35513	−0.0429821
$995$	−11.0443	−0.350129
$996$	−31.7813	−1.00703
$997$	−61.6427	−1.95224	−0.976121	−	0.217225i	$-0.930299\pi$
$997$	−61.6427	−1.95224	−0.976121	+	0.217225i	$0.930299\pi$
$998$	1.34002	0.0424177
$999$	3.44697	0.109057

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9251.2.a.t.1.7	yes	18
29.28	even	2		9251.2.a.s.1.12	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9251.2.a.s.1.12	✓	18	29.28	even	2
9251.2.a.t.1.7	yes	18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9251 = 11 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9251.a (trivial)

\(f(q)\)	\(=\)	\(q-0.667395 q^{2} -2.28148 q^{3} -1.55458 q^{4} -0.818040 q^{5} +1.52265 q^{6} +0.455915 q^{7} +2.37231 q^{8} +2.20514 q^{9} +O(q^{10})\)	\(q-0.667395 q^{2} -2.28148 q^{3} -1.55458 q^{4} -0.818040 q^{5} +1.52265 q^{6} +0.455915 q^{7} +2.37231 q^{8} +2.20514 q^{9} +0.545956 q^{10} -1.00000 q^{11} +3.54675 q^{12} +2.90357 q^{13} -0.304275 q^{14} +1.86634 q^{15} +1.52590 q^{16} +1.97420 q^{17} -1.47170 q^{18} +1.29640 q^{19} +1.27171 q^{20} -1.04016 q^{21} +0.667395 q^{22} -2.60035 q^{23} -5.41238 q^{24} -4.33081 q^{25} -1.93783 q^{26} +1.81345 q^{27} -0.708757 q^{28} -1.24559 q^{30} -0.242131 q^{31} -5.76300 q^{32} +2.28148 q^{33} -1.31757 q^{34} -0.372956 q^{35} -3.42808 q^{36} +1.90079 q^{37} -0.865213 q^{38} -6.62444 q^{39} -1.94065 q^{40} +2.00453 q^{41} +0.694197 q^{42} -2.99700 q^{43} +1.55458 q^{44} -1.80390 q^{45} +1.73546 q^{46} -4.26415 q^{47} -3.48130 q^{48} -6.79214 q^{49} +2.89036 q^{50} -4.50409 q^{51} -4.51385 q^{52} -7.59723 q^{53} -1.21029 q^{54} +0.818040 q^{55} +1.08157 q^{56} -2.95772 q^{57} +5.58772 q^{59} -2.90138 q^{60} -8.11582 q^{61} +0.161597 q^{62} +1.00536 q^{63} +0.794407 q^{64} -2.37524 q^{65} -1.52265 q^{66} +3.98939 q^{67} -3.06905 q^{68} +5.93264 q^{69} +0.248909 q^{70} +4.45363 q^{71} +5.23129 q^{72} +13.6947 q^{73} -1.26858 q^{74} +9.88065 q^{75} -2.01537 q^{76} -0.455915 q^{77} +4.42112 q^{78} +7.18318 q^{79} -1.24824 q^{80} -10.7528 q^{81} -1.33782 q^{82} -8.96069 q^{83} +1.61701 q^{84} -1.61497 q^{85} +2.00018 q^{86} -2.37231 q^{88} -2.17689 q^{89} +1.20391 q^{90} +1.32378 q^{91} +4.04246 q^{92} +0.552416 q^{93} +2.84587 q^{94} -1.06051 q^{95} +13.1482 q^{96} -8.13111 q^{97} +4.53304 q^{98} -2.20514 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9}+O(q^{10}) \) 18 * q + 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 9 * q^9	\( 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9} + 5 q^{10} - 18 q^{11} + 3 q^{12} - 15 q^{13} - 12 q^{14} + 27 q^{15} + 4 q^{16} - 6 q^{17} + 12 q^{18} - 11 q^{19} - 18 q^{20} - 6 q^{21} - 20 q^{23} - 3 q^{24} - 4 q^{25} + 10 q^{26} - 6 q^{27} - 6 q^{28} - 19 q^{30} + 8 q^{31} + 24 q^{32} - 3 q^{33} - 22 q^{34} + 22 q^{35} + 17 q^{36} - 9 q^{37} - 3 q^{38} + 8 q^{39} + 36 q^{40} - 3 q^{41} + 28 q^{42} - 13 q^{43} - 12 q^{44} - q^{45} - 37 q^{46} + q^{47} - 46 q^{48} - 23 q^{49} - 34 q^{50} + 4 q^{51} - 33 q^{52} - 6 q^{53} - 56 q^{54} + 6 q^{55} - 10 q^{56} + 14 q^{57} - 16 q^{59} - 3 q^{60} + 2 q^{61} - 24 q^{62} - 67 q^{63} + 11 q^{64} - 35 q^{65} + q^{66} + 9 q^{67} - 5 q^{68} + 47 q^{69} + 69 q^{70} - 13 q^{71} - 22 q^{72} + 57 q^{73} + 33 q^{74} + q^{75} + 26 q^{76} + 5 q^{77} + 5 q^{78} - 27 q^{79} - 10 q^{80} - 34 q^{81} - 55 q^{82} + 10 q^{83} - 35 q^{84} - 40 q^{85} + 4 q^{86} + 3 q^{88} + 80 q^{89} - 64 q^{90} - 38 q^{91} - 58 q^{92} + 17 q^{93} + 8 q^{94} - 7 q^{95} + 8 q^{96} - 20 q^{97} + 78 q^{98} - 9 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 9 * q^9 + 5 * q^10 - 18 * q^11 + 3 * q^12 - 15 * q^13 - 12 * q^14 + 27 * q^15 + 4 * q^16 - 6 * q^17 + 12 * q^18 - 11 * q^19 - 18 * q^20 - 6 * q^21 - 20 * q^23 - 3 * q^24 - 4 * q^25 + 10 * q^26 - 6 * q^27 - 6 * q^28 - 19 * q^30 + 8 * q^31 + 24 * q^32 - 3 * q^33 - 22 * q^34 + 22 * q^35 + 17 * q^36 - 9 * q^37 - 3 * q^38 + 8 * q^39 + 36 * q^40 - 3 * q^41 + 28 * q^42 - 13 * q^43 - 12 * q^44 - q^45 - 37 * q^46 + q^47 - 46 * q^48 - 23 * q^49 - 34 * q^50 + 4 * q^51 - 33 * q^52 - 6 * q^53 - 56 * q^54 + 6 * q^55 - 10 * q^56 + 14 * q^57 - 16 * q^59 - 3 * q^60 + 2 * q^61 - 24 * q^62 - 67 * q^63 + 11 * q^64 - 35 * q^65 + q^66 + 9 * q^67 - 5 * q^68 + 47 * q^69 + 69 * q^70 - 13 * q^71 - 22 * q^72 + 57 * q^73 + 33 * q^74 + q^75 + 26 * q^76 + 5 * q^77 + 5 * q^78 - 27 * q^79 - 10 * q^80 - 34 * q^81 - 55 * q^82 + 10 * q^83 - 35 * q^84 - 40 * q^85 + 4 * q^86 + 3 * q^88 + 80 * q^89 - 64 * q^90 - 38 * q^91 - 58 * q^92 + 17 * q^93 + 8 * q^94 - 7 * q^95 + 8 * q^96 - 20 * q^97 + 78 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more