LMFDB - Embedded newform 3549.2.a.w.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3549,2,Mod(1,3549)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3549, 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("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3549 = 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3549.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:	$28.3389076774$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.17428.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 6x^{2} + 4x + 6 $ x^4 - x^3 - 6x^2 + 4x + 6
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.36865$ of defining polynomial
Character	$\chi$	$=$	3549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61050 q^{2} +1.00000 q^{3} +4.81471 q^{4} +3.81471 q^{5} -2.61050 q^{6} -1.00000 q^{7} -7.34780 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.61050 q^{2} +1.00000 q^{3} +4.81471 q^{4} +3.81471 q^{5} -2.61050 q^{6} -1.00000 q^{7} -7.34780 q^{8} +1.00000 q^{9} -9.95830 q^{10} +4.73730 q^{11} +4.81471 q^{12} +2.61050 q^{14} +3.81471 q^{15} +9.55201 q^{16} -5.22100 q^{17} -2.61050 q^{18} -2.92259 q^{19} +18.3667 q^{20} -1.00000 q^{21} -12.3667 q^{22} +3.33101 q^{23} -7.34780 q^{24} +9.55201 q^{25} +1.00000 q^{27} -4.81471 q^{28} -0.922589 q^{29} -9.95830 q^{30} +7.51941 q^{31} -10.2399 q^{32} +4.73730 q^{33} +13.6294 q^{34} -3.81471 q^{35} +4.81471 q^{36} -0.154821 q^{37} +7.62942 q^{38} -28.0297 q^{40} -6.36672 q^{41} +2.61050 q^{42} -6.55201 q^{43} +22.8087 q^{44} +3.81471 q^{45} -8.69560 q^{46} -9.03571 q^{47} +9.55201 q^{48} +1.00000 q^{49} -24.9355 q^{50} -5.22100 q^{51} +8.55201 q^{53} -2.61050 q^{54} +18.0714 q^{55} +7.34780 q^{56} -2.92259 q^{57} +2.40842 q^{58} -3.95830 q^{59} +18.3667 q^{60} +12.4420 q^{61} -19.6294 q^{62} -1.00000 q^{63} +7.62729 q^{64} -12.3667 q^{66} +10.6620 q^{67} -25.1376 q^{68} +3.33101 q^{69} +9.95830 q^{70} +6.58248 q^{71} -7.34780 q^{72} +7.73517 q^{73} +0.404161 q^{74} +9.55201 q^{75} -14.0714 q^{76} -4.73730 q^{77} +13.3646 q^{79} +36.4381 q^{80} +1.00000 q^{81} +16.6203 q^{82} +1.40629 q^{83} -4.81471 q^{84} -19.9166 q^{85} +17.1040 q^{86} -0.922589 q^{87} -34.8087 q^{88} +1.96953 q^{89} -9.95830 q^{90} +16.0378 q^{92} +7.51941 q^{93} +23.5877 q^{94} -11.1488 q^{95} -10.2399 q^{96} +2.11001 q^{97} -2.61050 q^{98} +4.73730 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + 4 q^{3} + 7 q^{4} + 3 q^{5} - q^{6} - 4 q^{7} - 3 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - q^2 + 4 * q^3 + 7 * q^4 + 3 * q^5 - q^6 - 4 * q^7 - 3 * q^8 + 4 * q^9	$ 4 q - q^{2} + 4 q^{3} + 7 q^{4} + 3 q^{5} - q^{6} - 4 q^{7} - 3 q^{8} + 4 q^{9} - 4 q^{10} + 2 q^{11} + 7 q^{12} + q^{14} + 3 q^{15} + 9 q^{16} - 2 q^{17} - q^{18} - 7 q^{19} + 32 q^{20} - 4 q^{21} - 8 q^{22} + 3 q^{23} - 3 q^{24} + 9 q^{25} + 4 q^{27} - 7 q^{28} + q^{29} - 4 q^{30} - 3 q^{31} - 7 q^{32} + 2 q^{33} + 30 q^{34} - 3 q^{35} + 7 q^{36} - 10 q^{37} + 6 q^{38} - 14 q^{40} + 16 q^{41} + q^{42} + 3 q^{43} + 12 q^{44} + 3 q^{45} + 18 q^{46} - 5 q^{47} + 9 q^{48} + 4 q^{49} - 13 q^{50} - 2 q^{51} + 5 q^{53} - q^{54} + 10 q^{55} + 3 q^{56} - 7 q^{57} + 4 q^{58} + 20 q^{59} + 32 q^{60} + 12 q^{61} - 54 q^{62} - 4 q^{63} + 5 q^{64} - 8 q^{66} + 22 q^{67} - 10 q^{68} + 3 q^{69} + 4 q^{70} - 3 q^{72} + 13 q^{73} - 6 q^{74} + 9 q^{75} + 6 q^{76} - 2 q^{77} + 11 q^{79} + 42 q^{80} + 4 q^{81} + 10 q^{82} - q^{83} - 7 q^{84} - 8 q^{85} + 10 q^{86} + q^{87} - 60 q^{88} + 5 q^{89} - 4 q^{90} + 34 q^{92} - 3 q^{93} + 34 q^{94} + 13 q^{95} - 7 q^{96} + 17 q^{97} - q^{98} + 2 q^{99}+O(q^{100}) $ 4 * q - q^2 + 4 * q^3 + 7 * q^4 + 3 * q^5 - q^6 - 4 * q^7 - 3 * q^8 + 4 * q^9 - 4 * q^10 + 2 * q^11 + 7 * q^12 + q^14 + 3 * q^15 + 9 * q^16 - 2 * q^17 - q^18 - 7 * q^19 + 32 * q^20 - 4 * q^21 - 8 * q^22 + 3 * q^23 - 3 * q^24 + 9 * q^25 + 4 * q^27 - 7 * q^28 + q^29 - 4 * q^30 - 3 * q^31 - 7 * q^32 + 2 * q^33 + 30 * q^34 - 3 * q^35 + 7 * q^36 - 10 * q^37 + 6 * q^38 - 14 * q^40 + 16 * q^41 + q^42 + 3 * q^43 + 12 * q^44 + 3 * q^45 + 18 * q^46 - 5 * q^47 + 9 * q^48 + 4 * q^49 - 13 * q^50 - 2 * q^51 + 5 * q^53 - q^54 + 10 * q^55 + 3 * q^56 - 7 * q^57 + 4 * q^58 + 20 * q^59 + 32 * q^60 + 12 * q^61 - 54 * q^62 - 4 * q^63 + 5 * q^64 - 8 * q^66 + 22 * q^67 - 10 * q^68 + 3 * q^69 + 4 * q^70 - 3 * q^72 + 13 * q^73 - 6 * q^74 + 9 * q^75 + 6 * q^76 - 2 * q^77 + 11 * q^79 + 42 * q^80 + 4 * q^81 + 10 * q^82 - q^83 - 7 * q^84 - 8 * q^85 + 10 * q^86 + q^87 - 60 * q^88 + 5 * q^89 - 4 * q^90 + 34 * q^92 - 3 * q^93 + 34 * q^94 + 13 * q^95 - 7 * q^96 + 17 * q^97 - q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.61050	−1.84590	−0.922951	−	0.384917i	$-0.874230\pi$
$2$	−2.61050	−1.84590	−0.922951	+	0.384917i	$0.874230\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.81471	2.40735
$5$	3.81471	1.70599	0.852995	−	0.521919i	$-0.174784\pi$
$5$	3.81471	1.70599	0.852995	+	0.521919i	$0.174784\pi$
$6$	−2.61050	−1.06573
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−7.34780	−2.59784
$9$	1.00000	0.333333
$10$	−9.95830	−3.14909
$11$	4.73730	1.42835	0.714175	−	0.699968i	$-0.246802\pi$
$11$	4.73730	1.42835	0.714175	+	0.699968i	$0.246802\pi$
$12$	4.81471	1.38989
$13$	0	0
$13$	0	0
$14$	2.61050	0.697685
$15$	3.81471	0.984954
$16$	9.55201	2.38800
$17$	−5.22100	−1.26628	−0.633139	−	0.774038i	$-0.718234\pi$
$17$	−5.22100	−1.26628	−0.633139	+	0.774038i	$0.718234\pi$
$18$	−2.61050	−0.615301
$19$	−2.92259	−0.670488	−0.335244	−	0.942131i	$-0.608819\pi$
$19$	−2.92259	−0.670488	−0.335244	+	0.942131i	$0.608819\pi$
$20$	18.3667	4.10692
$21$	−1.00000	−0.218218
$22$	−12.3667	−2.63659
$23$	3.33101	0.694563	0.347282	−	0.937761i	$-0.387105\pi$
$23$	3.33101	0.694563	0.347282	+	0.937761i	$0.387105\pi$
$24$	−7.34780	−1.49986
$25$	9.55201	1.91040
$26$	0	0
$27$	1.00000	0.192450
$28$	−4.81471	−0.909895
$29$	−0.922589	−0.171321	−0.0856603	−	0.996324i	$-0.527300\pi$
$29$	−0.922589	−0.171321	−0.0856603	+	0.996324i	$0.527300\pi$
$30$	−9.95830	−1.81813
$31$	7.51941	1.35053	0.675263	−	0.737577i	$-0.264030\pi$
$31$	7.51941	1.35053	0.675263	+	0.737577i	$0.264030\pi$
$32$	−10.2399	−1.81018
$33$	4.73730	0.824658
$34$	13.6294	2.33743
$35$	−3.81471	−0.644804
$36$	4.81471	0.802452
$37$	−0.154821	−0.0254525	−0.0127262	−	0.999919i	$-0.504051\pi$
$37$	−0.154821	−0.0254525	−0.0127262	+	0.999919i	$0.504051\pi$
$38$	7.62942	1.23766
$39$	0	0
$40$	−28.0297	−4.43189
$41$	−6.36672	−0.994314	−0.497157	−	0.867661i	$-0.665623\pi$
$41$	−6.36672	−0.994314	−0.497157	+	0.867661i	$0.665623\pi$
$42$	2.61050	0.402809
$43$	−6.55201	−0.999172	−0.499586	−	0.866264i	$-0.666514\pi$
$43$	−6.55201	−0.999172	−0.499586	+	0.866264i	$0.666514\pi$
$44$	22.8087	3.43854
$45$	3.81471	0.568663
$46$	−8.69560	−1.28210
$47$	−9.03571	−1.31799	−0.658997	−	0.752146i	$-0.729019\pi$
$47$	−9.03571	−1.31799	−0.658997	+	0.752146i	$0.729019\pi$
$48$	9.55201	1.37871
$49$	1.00000	0.142857
$50$	−24.9355	−3.52641
$51$	−5.22100	−0.731086
$52$	0	0
$53$	8.55201	1.17471	0.587354	−	0.809330i	$-0.300170\pi$
$53$	8.55201	1.17471	0.587354	+	0.809330i	$0.300170\pi$
$54$	−2.61050	−0.355244
$55$	18.0714	2.43675
$56$	7.34780	0.981891
$57$	−2.92259	−0.387106
$58$	2.40842	0.316241
$59$	−3.95830	−0.515327	−0.257663	−	0.966235i	$-0.582953\pi$
$59$	−3.95830	−0.515327	−0.257663	+	0.966235i	$0.582953\pi$
$60$	18.3667	2.37113
$61$	12.4420	1.59303	0.796517	−	0.604616i	$-0.206673\pi$
$61$	12.4420	1.59303	0.796517	+	0.604616i	$0.206673\pi$
$62$	−19.6294	−2.49294
$63$	−1.00000	−0.125988
$64$	7.62729	0.953411
$65$	0	0
$66$	−12.3667	−1.52224
$67$	10.6620	1.30257	0.651286	−	0.758832i	$-0.274230\pi$
$67$	10.6620	1.30257	0.651286	+	0.758832i	$0.274230\pi$
$68$	−25.1376	−3.04838
$69$	3.33101	0.401006
$70$	9.95830	1.19024
$71$	6.58248	0.781196	0.390598	−	0.920561i	$-0.372268\pi$
$71$	6.58248	0.781196	0.390598	+	0.920561i	$0.372268\pi$
$72$	−7.34780	−0.865946
$73$	7.73517	0.905333	0.452667	−	0.891680i	$-0.350473\pi$
$73$	7.73517	0.905333	0.452667	+	0.891680i	$0.350473\pi$
$74$	0.404161	0.0469828
$75$	9.55201	1.10297
$76$	−14.0714	−1.61410
$77$	−4.73730	−0.539865
$78$	0	0
$79$	13.3646	1.50363	0.751817	−	0.659372i	$-0.229178\pi$
$79$	13.3646	1.50363	0.751817	+	0.659372i	$0.229178\pi$
$80$	36.4381	4.07391
$81$	1.00000	0.111111
$82$	16.6203	1.83541
$83$	1.40629	0.154360	0.0771802	−	0.997017i	$-0.475408\pi$
$83$	1.40629	0.154360	0.0771802	+	0.997017i	$0.475408\pi$
$84$	−4.81471	−0.525328
$85$	−19.9166	−2.16026
$86$	17.1040	1.84437
$87$	−0.922589	−0.0989120
$88$	−34.8087	−3.71062
$89$	1.96953	0.208770	0.104385	−	0.994537i	$-0.466713\pi$
$89$	1.96953	0.208770	0.104385	+	0.994537i	$0.466713\pi$
$90$	−9.95830	−1.04970
$91$	0	0
$92$	16.0378	1.67206
$93$	7.51941	0.779727
$94$	23.5877	2.43289
$95$	−11.1488	−1.14385
$96$	−10.2399	−1.04511
$97$	2.11001	0.214239	0.107119	−	0.994246i	$-0.465837\pi$
$97$	2.11001	0.214239	0.107119	+	0.994246i	$0.465837\pi$
$98$	−2.61050	−0.263700
$99$	4.73730	0.476116
$100$	45.9901	4.59901
$101$	0.850419	0.0846198	0.0423099	−	0.999105i	$-0.486528\pi$
$101$	0.850419	0.0846198	0.0423099	+	0.999105i	$0.486528\pi$
$102$	13.6294	1.34951
$103$	−1.47460	−0.145296	−0.0726482	−	0.997358i	$-0.523145\pi$
$103$	−1.47460	−0.145296	−0.0726482	+	0.997358i	$0.523145\pi$
$104$	0	0
$105$	−3.81471	−0.372278
$106$	−22.3250	−2.16840
$107$	2.62418	0.253689	0.126844	−	0.991923i	$-0.459515\pi$
$107$	2.62418	0.253689	0.126844	+	0.991923i	$0.459515\pi$
$108$	4.81471	0.463296
$109$	17.9166	1.71610	0.858049	−	0.513567i	$-0.171676\pi$
$109$	17.9166	1.71610	0.858049	+	0.513567i	$0.171676\pi$
$110$	−47.1754	−4.49800
$111$	−0.154821	−0.0146950
$112$	−9.55201	−0.902580
$113$	0.922589	0.0867899	0.0433950	−	0.999058i	$-0.486183\pi$
$113$	0.922589	0.0867899	0.0433950	+	0.999058i	$0.486183\pi$
$114$	7.62942	0.714561
$115$	12.7068	1.18492
$116$	−4.44200	−0.412429
$117$	0	0
$118$	10.3331	0.951242
$119$	5.22100	0.478608
$120$	−28.0297	−2.55875
$121$	11.4420	1.04018
$122$	−32.4798	−2.94059
$123$	−6.36672	−0.574068
$124$	36.2038	3.25119
$125$	17.3646	1.55314
$126$	2.61050	0.232562
$127$	17.4746	1.55062	0.775310	−	0.631581i	$-0.217594\pi$
$127$	17.4746	1.55062	0.775310	+	0.631581i	$0.217594\pi$
$128$	0.568798	0.0502751
$129$	−6.55201	−0.576872
$130$	0	0
$131$	0.967402	0.0845223	0.0422611	−	0.999107i	$-0.486544\pi$
$131$	0.967402	0.0845223	0.0422611	+	0.999107i	$0.486544\pi$
$132$	22.8087	1.98524
$133$	2.92259	0.253421
$134$	−27.8332	−2.40442
$135$	3.81471	0.328318
$136$	38.3629	3.28959
$137$	−3.29628	−0.281620	−0.140810	−	0.990037i	$-0.544971\pi$
$137$	−3.29628	−0.281620	−0.140810	+	0.990037i	$0.544971\pi$
$138$	−8.69560	−0.740218
$139$	0.370581	0.0314323	0.0157161	−	0.999876i	$-0.494997\pi$
$139$	0.370581	0.0314323	0.0157161	+	0.999876i	$0.494997\pi$
$140$	−18.3667	−1.55227
$141$	−9.03571	−0.760944
$142$	−17.1836	−1.44201
$143$	0	0
$144$	9.55201	0.796001
$145$	−3.51941	−0.292271
$146$	−20.1927	−1.67116
$147$	1.00000	0.0824786
$148$	−0.745420	−0.0612732
$149$	15.7425	1.28968	0.644840	−	0.764318i	$-0.276924\pi$
$149$	15.7425	1.28968	0.644840	+	0.764318i	$0.276924\pi$
$150$	−24.9355	−2.03598
$151$	−10.2914	−0.837505	−0.418753	−	0.908100i	$-0.637533\pi$
$151$	−10.2914	−0.837505	−0.418753	+	0.908100i	$0.637533\pi$
$152$	21.4746	1.74182
$153$	−5.22100	−0.422093
$154$	12.3667	0.996539
$155$	28.6844	2.30398
$156$	0	0
$157$	−11.4137	−0.910909	−0.455455	−	0.890259i	$-0.650523\pi$
$157$	−11.4137	−0.910909	−0.455455	+	0.890259i	$0.650523\pi$
$158$	−34.8883	−2.77556
$159$	8.55201	0.678218
$160$	−39.0623	−3.08815
$161$	−3.33101	−0.262520
$162$	−2.61050	−0.205100
$163$	13.4746	1.05541	0.527706	−	0.849427i	$-0.323052\pi$
$163$	13.4746	1.05541	0.527706	+	0.849427i	$0.323052\pi$
$164$	−30.6539	−2.39367
$165$	18.0714	1.40686
$166$	−3.67112	−0.284934
$167$	−19.1905	−1.48501	−0.742504	−	0.669842i	$-0.766362\pi$
$167$	−19.1905	−1.48501	−0.742504	+	0.669842i	$0.766362\pi$
$168$	7.34780	0.566895
$169$	0	0
$170$	51.9923	3.98763
$171$	−2.92259	−0.223496
$172$	−31.5460	−2.40536
$173$	−19.5124	−1.48350	−0.741752	−	0.670675i	$-0.766005\pi$
$173$	−19.5124	−1.48350	−0.741752	+	0.670675i	$0.766005\pi$
$174$	2.40842	0.182582
$175$	−9.55201	−0.722064
$176$	45.2507	3.41090
$177$	−3.95830	−0.297524
$178$	−5.14146	−0.385369
$179$	−16.5856	−1.23967	−0.619833	−	0.784734i	$-0.712799\pi$
$179$	−16.5856	−1.23967	−0.619833	+	0.784734i	$0.712799\pi$
$180$	18.3667	1.36897
$181$	−2.81684	−0.209374	−0.104687	−	0.994505i	$-0.533384\pi$
$181$	−2.81684	−0.209374	−0.104687	+	0.994505i	$0.533384\pi$
$182$	0	0
$183$	12.4420	0.919739
$184$	−24.4756	−1.80436
$185$	−0.590599	−0.0434217
$186$	−19.6294	−1.43930
$187$	−24.7334	−1.80869
$188$	−43.5043	−3.17288
$189$	−1.00000	−0.0727393
$190$	29.1040	2.11143
$191$	15.1601	1.09694	0.548472	−	0.836169i	$-0.315210\pi$
$191$	15.1601	1.09694	0.548472	+	0.836169i	$0.315210\pi$
$192$	7.62729	0.550452
$193$	−0.0651962	−0.00469293	−0.00234646	−	0.999997i	$-0.500747\pi$
$193$	−0.0651962	−0.00469293	−0.00234646	+	0.999997i	$0.500747\pi$
$194$	−5.50818	−0.395464
$195$	0	0
$196$	4.81471	0.343908
$197$	17.1415	1.22128	0.610639	−	0.791909i	$-0.290913\pi$
$197$	17.1415	1.22128	0.610639	+	0.791909i	$0.290913\pi$
$198$	−12.3667	−0.878864
$199$	6.44200	0.456661	0.228331	−	0.973584i	$-0.426673\pi$
$199$	6.44200	0.456661	0.228331	+	0.973584i	$0.426673\pi$
$200$	−70.1862	−4.96292
$201$	10.6620	0.752041
$202$	−2.22002	−0.156200
$203$	0.922589	0.0647531
$204$	−25.1376	−1.75998
$205$	−24.2872	−1.69629
$206$	3.84944	0.268203
$207$	3.33101	0.231521
$208$	0	0
$209$	−13.8452	−0.957691
$210$	9.95830	0.687188
$211$	−16.0266	−1.10332	−0.551659	−	0.834070i	$-0.686005\pi$
$211$	−16.0266	−1.10332	−0.551659	+	0.834070i	$0.686005\pi$
$212$	41.1754	2.82794
$213$	6.58248	0.451024
$214$	−6.85042	−0.468285
$215$	−24.9940	−1.70458
$216$	−7.34780	−0.499954
$217$	−7.51941	−0.510451
$218$	−46.7713	−3.16775
$219$	7.73517	0.522694
$220$	87.0086	5.86612
$221$	0	0
$222$	0.404161	0.0271255
$223$	−20.0266	−1.34108	−0.670540	−	0.741873i	$-0.733938\pi$
$223$	−20.0266	−1.34108	−0.670540	+	0.741873i	$0.733938\pi$
$224$	10.2399	0.684183
$225$	9.55201	0.636801
$226$	−2.40842	−0.160206
$227$	−19.2171	−1.27549	−0.637743	−	0.770249i	$-0.720132\pi$
$227$	−19.2171	−1.27549	−0.637743	+	0.770249i	$0.720132\pi$
$228$	−14.0714	−0.931902
$229$	−5.25884	−0.347514	−0.173757	−	0.984789i	$-0.555591\pi$
$229$	−5.25884	−0.347514	−0.173757	+	0.984789i	$0.555591\pi$
$230$	−33.1712	−2.18724
$231$	−4.73730	−0.311691
$232$	6.77900	0.445063
$233$	−26.6234	−1.74416	−0.872079	−	0.489365i	$-0.837229\pi$
$233$	−26.6234	−1.74416	−0.872079	+	0.489365i	$0.837229\pi$
$234$	0	0
$235$	−34.4686	−2.24848
$236$	−19.0581	−1.24057
$237$	13.3646	0.868123
$238$	−13.6294	−0.883464
$239$	−4.29104	−0.277564	−0.138782	−	0.990323i	$-0.544319\pi$
$239$	−4.29104	−0.277564	−0.138782	+	0.990323i	$0.544319\pi$
$240$	36.4381	2.35207
$241$	−7.52367	−0.484642	−0.242321	−	0.970196i	$-0.577909\pi$
$241$	−7.52367	−0.484642	−0.242321	+	0.970196i	$0.577909\pi$
$242$	−29.8693	−1.92007
$243$	1.00000	0.0641500
$244$	59.9046	3.83500
$245$	3.81471	0.243713
$246$	16.6203	1.05967
$247$	0	0
$248$	−55.2511	−3.50845
$249$	1.40629	0.0891200
$250$	−45.3303	−2.86694
$251$	11.3198	0.714498	0.357249	−	0.934009i	$-0.383715\pi$
$251$	11.3198	0.714498	0.357249	+	0.934009i	$0.383715\pi$
$252$	−4.81471	−0.303298
$253$	15.7800	0.992079
$254$	−45.6174	−2.86229
$255$	−19.9166	−1.24723
$256$	−16.7394	−1.04621
$257$	−24.8504	−1.55013	−0.775063	−	0.631884i	$-0.782282\pi$
$257$	−24.8504	−1.55013	−0.775063	+	0.631884i	$0.782282\pi$
$258$	17.1040	1.06485
$259$	0.154821	0.00962013
$260$	0	0
$261$	−0.922589	−0.0571068
$262$	−2.52540	−0.156020
$263$	17.1762	1.05913	0.529565	−	0.848270i	$-0.322355\pi$
$263$	17.1762	1.05913	0.529565	+	0.848270i	$0.322355\pi$
$264$	−34.8087	−2.14233
$265$	32.6234	2.00404
$266$	−7.62942	−0.467790
$267$	1.96953	0.120533
$268$	51.3345	3.13575
$269$	−7.74640	−0.472306	−0.236153	−	0.971716i	$-0.575887\pi$
$269$	−7.74640	−0.472306	−0.236153	+	0.971716i	$0.575887\pi$
$270$	−9.95830	−0.606043
$271$	29.7008	1.80420	0.902099	−	0.431530i	$-0.142026\pi$
$271$	29.7008	1.80420	0.902099	+	0.431530i	$0.142026\pi$
$272$	−49.8710	−3.02388
$273$	0	0
$274$	8.60494	0.519844
$275$	45.2507	2.72872
$276$	16.0378	0.965364
$277$	25.1488	1.51105	0.755523	−	0.655122i	$-0.227383\pi$
$277$	25.1488	1.51105	0.755523	+	0.655122i	$0.227383\pi$
$278$	−0.967402	−0.0580209
$279$	7.51941	0.450175
$280$	28.0297	1.67510
$281$	−8.40030	−0.501120	−0.250560	−	0.968101i	$-0.580615\pi$
$281$	−8.40030	−0.501120	−0.250560	+	0.968101i	$0.580615\pi$
$282$	23.5877	1.40463
$283$	−21.3912	−1.27157	−0.635787	−	0.771864i	$-0.719324\pi$
$283$	−21.3912	−1.27157	−0.635787	+	0.771864i	$0.719324\pi$
$284$	31.6927	1.88062
$285$	−11.1488	−0.660400
$286$	0	0
$287$	6.36672	0.375815
$288$	−10.2399	−0.603393
$289$	10.2588	0.603461
$290$	9.18742	0.539504
$291$	2.11001	0.123691
$292$	37.2426	2.17946
$293$	9.59895	0.560777	0.280388	−	0.959887i	$-0.409537\pi$
$293$	9.59895	0.560777	0.280388	+	0.959887i	$0.409537\pi$
$294$	−2.61050	−0.152247
$295$	−15.0998	−0.879142
$296$	1.13760	0.0661215
$297$	4.73730	0.274886
$298$	−41.0959	−2.38062
$299$	0	0
$300$	45.9901	2.65524
$301$	6.55201	0.377651
$302$	26.8658	1.54595
$303$	0.850419	0.0488553
$304$	−27.9166	−1.60113
$305$	47.4626	2.71770
$306$	13.6294	0.779142
$307$	15.1488	0.864589	0.432295	−	0.901732i	$-0.357704\pi$
$307$	15.1488	0.864589	0.432295	+	0.901732i	$0.357704\pi$
$308$	−22.8087	−1.29965
$309$	−1.47460	−0.0838869
$310$	−74.8805	−4.25293
$311$	−4.37058	−0.247833	−0.123916	−	0.992293i	$-0.539545\pi$
$311$	−4.37058	−0.247833	−0.123916	+	0.992293i	$0.539545\pi$
$312$	0	0
$313$	−1.49280	−0.0843783	−0.0421891	−	0.999110i	$-0.513433\pi$
$313$	−1.49280	−0.0843783	−0.0421891	+	0.999110i	$0.513433\pi$
$314$	29.7954	1.68145
$315$	−3.81471	−0.214935
$316$	64.3466	3.61978
$317$	−23.2129	−1.30377	−0.651883	−	0.758320i	$-0.726021\pi$
$317$	−23.2129	−1.30377	−0.651883	+	0.758320i	$0.726021\pi$
$318$	−22.3250	−1.25192
$319$	−4.37058	−0.244706
$320$	29.0959	1.62651
$321$	2.62418	0.146467
$322$	8.69560	0.484587
$323$	15.2588	0.849024
$324$	4.81471	0.267484
$325$	0	0
$326$	−35.1754	−1.94819
$327$	17.9166	0.990790
$328$	46.7814	2.58307
$329$	9.03571	0.498155
$330$	−47.1754	−2.59692
$331$	−1.10402	−0.0606822	−0.0303411	−	0.999540i	$-0.509659\pi$
$331$	−1.10402	−0.0606822	−0.0303411	+	0.999540i	$0.509659\pi$
$332$	6.77088	0.371600
$333$	−0.154821	−0.00848416
$334$	50.0969	2.74118
$335$	40.6725	2.22218
$336$	−9.55201	−0.521105
$337$	−4.24237	−0.231096	−0.115548	−	0.993302i	$-0.536862\pi$
$337$	−4.24237	−0.231096	−0.115548	+	0.993302i	$0.536862\pi$
$338$	0	0
$339$	0.922589	0.0501082
$340$	−95.8926	−5.20051
$341$	35.6217	1.92902
$342$	7.62942	0.412552
$343$	−1.00000	−0.0539949
$344$	48.1428	2.59569
$345$	12.7068	0.684113
$346$	50.9372	2.73840
$347$	14.0336	0.753362	0.376681	−	0.926343i	$-0.377065\pi$
$347$	14.0336	0.753362	0.376681	+	0.926343i	$0.377065\pi$
$348$	−4.44200	−0.238116
$349$	−4.10575	−0.219776	−0.109888	−	0.993944i	$-0.535049\pi$
$349$	−4.10575	−0.219776	−0.109888	+	0.993944i	$0.535049\pi$
$350$	24.9355	1.33286
$351$	0	0
$352$	−48.5096	−2.58557
$353$	16.0753	0.855601	0.427800	−	0.903873i	$-0.359289\pi$
$353$	16.0753	0.855601	0.427800	+	0.903873i	$0.359289\pi$
$354$	10.3331	0.549200
$355$	25.1102	1.33271
$356$	9.48272	0.502583
$357$	5.22100	0.276325
$358$	43.2967	2.28830
$359$	18.1510	0.957971	0.478985	−	0.877823i	$-0.341005\pi$
$359$	18.1510	0.957971	0.478985	+	0.877823i	$0.341005\pi$
$360$	−28.0297	−1.47730
$361$	−10.4585	−0.550446
$362$	7.35336	0.386484
$363$	11.4420	0.600549
$364$	0	0
$365$	29.5074	1.54449
$366$	−32.4798	−1.69775
$367$	−23.3955	−1.22123	−0.610616	−	0.791927i	$-0.709078\pi$
$367$	−23.3955	−1.22123	−0.610616	+	0.791927i	$0.709078\pi$
$368$	31.8178	1.65862
$369$	−6.36672	−0.331438
$370$	1.54176	0.0801522
$371$	−8.55201	−0.443998
$372$	36.2038	1.87708
$373$	−4.75164	−0.246031	−0.123015	−	0.992405i	$-0.539256\pi$
$373$	−4.75164	−0.246031	−0.123015	+	0.992405i	$0.539256\pi$
$374$	64.5666	3.33866
$375$	17.3646	0.896704
$376$	66.3926	3.42394
$377$	0	0
$378$	2.61050	0.134270
$379$	6.81258	0.349939	0.174969	−	0.984574i	$-0.444017\pi$
$379$	6.81258	0.349939	0.174969	+	0.984574i	$0.444017\pi$
$380$	−53.6784	−2.75364
$381$	17.4746	0.895251
$382$	−39.5753	−2.02485
$383$	−2.25746	−0.115351	−0.0576754	−	0.998335i	$-0.518369\pi$
$383$	−2.25746	−0.115351	−0.0576754	+	0.998335i	$0.518369\pi$
$384$	0.568798	0.0290264
$385$	−18.0714	−0.921005
$386$	0.170195	0.00866268
$387$	−6.55201	−0.333057
$388$	10.1591	0.515749
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	0	0
$391$	−17.3912	−0.879511
$392$	−7.34780	−0.371120
$393$	0.967402	0.0487990
$394$	−44.7478	−2.25436
$395$	50.9820	2.56518
$396$	22.8087	1.14618
$397$	−24.9897	−1.25420	−0.627100	−	0.778939i	$-0.715758\pi$
$397$	−24.9897	−1.25420	−0.627100	+	0.778939i	$0.715758\pi$
$398$	−16.8168	−0.842952
$399$	2.92259	0.146312
$400$	91.2409	4.56204
$401$	−27.6529	−1.38092	−0.690460	−	0.723370i	$-0.742592\pi$
$401$	−27.6529	−1.38092	−0.690460	+	0.723370i	$0.742592\pi$
$402$	−27.8332	−1.38819
$403$	0	0
$404$	4.09452	0.203710
$405$	3.81471	0.189554
$406$	−2.40842	−0.119528
$407$	−0.733435	−0.0363550
$408$	38.3629	1.89924
$409$	−13.1488	−0.650168	−0.325084	−	0.945685i	$-0.605393\pi$
$409$	−13.1488	−0.650168	−0.325084	+	0.945685i	$0.605393\pi$
$410$	63.4017	3.13119
$411$	−3.29628	−0.162594
$412$	−7.09976	−0.349780
$413$	3.95830	0.194775
$414$	−8.69560	−0.427365
$415$	5.36459	0.263337
$416$	0	0
$417$	0.370581	0.0181474
$418$	36.1428	1.76780
$419$	−5.69462	−0.278200	−0.139100	−	0.990278i	$-0.544421\pi$
$419$	−5.69462	−0.278200	−0.139100	+	0.990278i	$0.544421\pi$
$420$	−18.3667	−0.896204
$421$	23.0206	1.12196	0.560978	−	0.827831i	$-0.310425\pi$
$421$	23.0206	1.12196	0.560978	+	0.827831i	$0.310425\pi$
$422$	41.8375	2.03662
$423$	−9.03571	−0.439331
$424$	−62.8384	−3.05170
$425$	−49.8710	−2.41910
$426$	−17.1836	−0.832546
$427$	−12.4420	−0.602111
$428$	12.6347	0.610719
$429$	0	0
$430$	65.2469	3.14648
$431$	−20.8045	−1.00212	−0.501058	−	0.865414i	$-0.667056\pi$
$431$	−20.8045	−1.00212	−0.501058	+	0.865414i	$0.667056\pi$
$432$	9.55201	0.459571
$433$	31.4808	1.51287	0.756436	−	0.654068i	$-0.226939\pi$
$433$	31.4808	1.51287	0.756436	+	0.654068i	$0.226939\pi$
$434$	19.6294	0.942242
$435$	−3.51941	−0.168743
$436$	86.2632	4.13126
$437$	−9.73517	−0.465696
$438$	−20.1927	−0.964843
$439$	22.3811	1.06819	0.534095	−	0.845425i	$-0.320653\pi$
$439$	22.3811	1.06819	0.534095	+	0.845425i	$0.320653\pi$
$440$	−132.785	−6.33028
$441$	1.00000	0.0476190
$442$	0	0
$443$	8.52465	0.405018	0.202509	−	0.979280i	$-0.435090\pi$
$443$	8.52465	0.405018	0.202509	+	0.979280i	$0.435090\pi$
$444$	−0.745420	−0.0353761
$445$	7.51319	0.356159
$446$	52.2795	2.47550
$447$	15.7425	0.744597
$448$	−7.62729	−0.360356
$449$	−18.7142	−0.883178	−0.441589	−	0.897218i	$-0.645585\pi$
$449$	−18.7142	−0.883178	−0.441589	+	0.897218i	$0.645585\pi$
$450$	−24.9355	−1.17547
$451$	−30.1610	−1.42023
$452$	4.44200	0.208934
$453$	−10.2914	−0.483534
$454$	50.1663	2.35442
$455$	0	0
$456$	21.4746	1.00564
$457$	14.1366	0.661283	0.330641	−	0.943756i	$-0.392735\pi$
$457$	14.1366	0.661283	0.330641	+	0.943756i	$0.392735\pi$
$458$	13.7282	0.641476
$459$	−5.22100	−0.243695
$460$	61.1797	2.85252
$461$	2.67636	0.124651	0.0623253	−	0.998056i	$-0.480148\pi$
$461$	2.67636	0.124651	0.0623253	+	0.998056i	$0.480148\pi$
$462$	12.3667	0.575352
$463$	2.53162	0.117655	0.0588273	−	0.998268i	$-0.481264\pi$
$463$	2.53162	0.117655	0.0588273	+	0.998268i	$0.481264\pi$
$464$	−8.81258	−0.409114
$465$	28.6844	1.33021
$466$	69.5005	3.21955
$467$	2.00426	0.0927460	0.0463730	−	0.998924i	$-0.485234\pi$
$467$	2.00426	0.0927460	0.0463730	+	0.998924i	$0.485234\pi$
$468$	0	0
$469$	−10.6620	−0.492326
$470$	89.9803	4.15048
$471$	−11.4137	−0.525914
$472$	29.0848	1.33874
$473$	−31.0388	−1.42717
$474$	−34.8883	−1.60247
$475$	−27.9166	−1.28090
$476$	25.1376	1.15218
$477$	8.55201	0.391570
$478$	11.2018	0.512357
$479$	14.6609	0.669872	0.334936	−	0.942241i	$-0.391285\pi$
$479$	14.6609	0.669872	0.334936	+	0.942241i	$0.391285\pi$
$480$	−39.0623	−1.78294
$481$	0	0
$482$	19.6405	0.894602
$483$	−3.33101	−0.151566
$484$	55.0899	2.50409
$485$	8.04907	0.365489
$486$	−2.61050	−0.118415
$487$	−38.2143	−1.73165	−0.865827	−	0.500344i	$-0.833207\pi$
$487$	−38.2143	−1.73165	−0.865827	+	0.500344i	$0.833207\pi$
$488$	−91.4213	−4.13845
$489$	13.4746	0.609342
$490$	−9.95830	−0.449870
$491$	21.3758	0.964677	0.482339	−	0.875985i	$-0.339787\pi$
$491$	21.3758	0.964677	0.482339	+	0.875985i	$0.339787\pi$
$492$	−30.6539	−1.38198
$493$	4.81684	0.216939
$494$	0	0
$495$	18.0714	0.812250
$496$	71.8255	3.22506
$497$	−6.58248	−0.295264
$498$	−3.67112	−0.164507
$499$	−27.0920	−1.21281	−0.606403	−	0.795158i	$-0.707388\pi$
$499$	−27.0920	−1.21281	−0.606403	+	0.795158i	$0.707388\pi$
$500$	83.6054	3.73895
$501$	−19.1905	−0.857370
$502$	−29.5503	−1.31889
$503$	24.8778	1.10925	0.554623	−	0.832102i	$-0.312863\pi$
$503$	24.8778	1.10925	0.554623	+	0.832102i	$0.312863\pi$
$504$	7.34780	0.327297
$505$	3.24410	0.144361
$506$	−41.1936	−1.83128
$507$	0	0
$508$	84.1351	3.73289
$509$	−2.70297	−0.119807	−0.0599034	−	0.998204i	$-0.519079\pi$
$509$	−2.70297	−0.119807	−0.0599034	+	0.998204i	$0.519079\pi$
$510$	51.9923	2.30226
$511$	−7.73517	−0.342184
$512$	42.5607	1.88093
$513$	−2.92259	−0.129035
$514$	64.8720	2.86138
$515$	−5.62516	−0.247874
$516$	−31.5460	−1.38874
$517$	−42.8049	−1.88256
$518$	−0.404161	−0.0177578
$519$	−19.5124	−0.856501
$520$	0	0
$521$	−33.4472	−1.46535	−0.732675	−	0.680579i	$-0.761728\pi$
$521$	−33.4472	−1.46535	−0.732675	+	0.680579i	$0.761728\pi$
$522$	2.40842	0.105414
$523$	19.3198	0.844795	0.422397	−	0.906411i	$-0.361189\pi$
$523$	19.3198	0.844795	0.422397	+	0.906411i	$0.361189\pi$
$524$	4.65776	0.203475
$525$	−9.55201	−0.416884
$526$	−44.8384	−1.95505
$527$	−39.2588	−1.71014
$528$	45.2507	1.96928
$529$	−11.9044	−0.517582
$530$	−85.1634	−3.69926
$531$	−3.95830	−0.171776
$532$	14.0714	0.610073
$533$	0	0
$534$	−5.14146	−0.222493
$535$	10.0105	0.432791
$536$	−78.3424	−3.38387
$537$	−16.5856	−0.715721
$538$	20.2220	0.871832
$539$	4.73730	0.204050
$540$	18.3667	0.790378
$541$	24.9554	1.07292	0.536459	−	0.843927i	$-0.319762\pi$
$541$	24.9554	1.07292	0.536459	+	0.843927i	$0.319762\pi$
$542$	−77.5340	−3.33037
$543$	−2.81684	−0.120882
$544$	53.4626	2.29219
$545$	68.3466	2.92765
$546$	0	0
$547$	3.80037	0.162492	0.0812460	−	0.996694i	$-0.474110\pi$
$547$	3.80037	0.162492	0.0812460	+	0.996694i	$0.474110\pi$
$548$	−15.8706	−0.677960
$549$	12.4420	0.531012
$550$	−118.127	−5.03695
$551$	2.69635	0.114868
$552$	−24.4756	−1.04175
$553$	−13.3646	−0.568320
$554$	−65.6510	−2.78924
$555$	−0.590599	−0.0250695
$556$	1.78424	0.0756686
$557$	−43.8792	−1.85922	−0.929610	−	0.368546i	$-0.879856\pi$
$557$	−43.8792	−1.85922	−0.929610	+	0.368546i	$0.879856\pi$
$558$	−19.6294	−0.830980
$559$	0	0
$560$	−36.4381	−1.53979
$561$	−24.7334	−1.04425
$562$	21.9290	0.925018
$563$	12.3768	0.521620	0.260810	−	0.965390i	$-0.416010\pi$
$563$	12.3768	0.521620	0.260810	+	0.965390i	$0.416010\pi$
$564$	−43.5043	−1.83186
$565$	3.51941	0.148063
$566$	55.8417	2.34720
$567$	−1.00000	−0.0419961
$568$	−48.3667	−2.02942
$569$	−26.6234	−1.11611	−0.558056	−	0.829803i	$-0.688453\pi$
$569$	−26.6234	−1.11611	−0.558056	+	0.829803i	$0.688453\pi$
$570$	29.1040	1.21903
$571$	10.9983	0.460263	0.230132	−	0.973160i	$-0.426084\pi$
$571$	10.9983	0.460263	0.230132	+	0.973160i	$0.426084\pi$
$572$	0	0
$573$	15.1601	0.633321
$574$	−16.6203	−0.693719
$575$	31.8178	1.32689
$576$	7.62729	0.317804
$577$	−30.4238	−1.26656	−0.633280	−	0.773923i	$-0.718292\pi$
$577$	−30.4238	−1.26656	−0.633280	+	0.773923i	$0.718292\pi$
$578$	−26.7807	−1.11393
$579$	−0.0651962	−0.00270946
$580$	−16.9449	−0.703600
$581$	−1.40629	−0.0583428
$582$	−5.50818	−0.228321
$583$	40.5134	1.67789
$584$	−56.8365	−2.35191
$585$	0	0
$586$	−25.0581	−1.03514
$587$	−3.84207	−0.158579	−0.0792895	−	0.996852i	$-0.525265\pi$
$587$	−3.84207	−0.158579	−0.0792895	+	0.996852i	$0.525265\pi$
$588$	4.81471	0.198555
$589$	−21.9761	−0.905511
$590$	39.4179	1.62281
$591$	17.1415	0.705105
$592$	−1.47886	−0.0607806
$593$	23.8904	0.981061	0.490530	−	0.871424i	$-0.336803\pi$
$593$	23.8904	0.981061	0.490530	+	0.871424i	$0.336803\pi$
$594$	−12.3667	−0.507413
$595$	19.9166	0.816501
$596$	75.7958	3.10471
$597$	6.44200	0.263653
$598$	0	0
$599$	−15.4206	−0.630070	−0.315035	−	0.949080i	$-0.602016\pi$
$599$	−15.4206	−0.630070	−0.315035	+	0.949080i	$0.602016\pi$
$600$	−70.1862	−2.86534
$601$	−1.49280	−0.0608928	−0.0304464	−	0.999536i	$-0.509693\pi$
$601$	−1.49280	−0.0608928	−0.0304464	+	0.999536i	$0.509693\pi$
$602$	−17.1040	−0.697108
$603$	10.6620	0.434191
$604$	−49.5503	−2.01617
$605$	43.6479	1.77454
$606$	−2.22002	−0.0901821
$607$	−4.44626	−0.180468	−0.0902340	−	0.995921i	$-0.528761\pi$
$607$	−4.44626	−0.180468	−0.0902340	+	0.995921i	$0.528761\pi$
$608$	29.9271	1.21370
$609$	0.922589	0.0373852
$610$	−123.901	−5.01661
$611$	0	0
$612$	−25.1376	−1.01613
$613$	−26.6640	−1.07695	−0.538474	−	0.842642i	$-0.680999\pi$
$613$	−26.6640	−1.07695	−0.538474	+	0.842642i	$0.680999\pi$
$614$	−39.5460	−1.59595
$615$	−24.2872	−0.979354
$616$	34.8087	1.40248
$617$	−27.3495	−1.10105	−0.550525	−	0.834819i	$-0.685572\pi$
$617$	−27.3495	−1.10105	−0.550525	+	0.834819i	$0.685572\pi$
$618$	3.84944	0.154847
$619$	9.24836	0.371723	0.185861	−	0.982576i	$-0.440492\pi$
$619$	9.24836	0.371723	0.185861	+	0.982576i	$0.440492\pi$
$620$	138.107	5.54651
$621$	3.33101	0.133669
$622$	11.4094	0.457475
$623$	−1.96953	−0.0789076
$624$	0	0
$625$	18.4808	0.739233
$626$	3.89697	0.155754
$627$	−13.8452	−0.552923
$628$	−54.9535	−2.19288
$629$	0.808323	0.0322299
$630$	9.95830	0.396748
$631$	−24.5134	−0.975864	−0.487932	−	0.872882i	$-0.662249\pi$
$631$	−24.5134	−0.975864	−0.487932	+	0.872882i	$0.662249\pi$
$632$	−98.2003	−3.90620
$633$	−16.0266	−0.637000
$634$	60.5972	2.40662
$635$	66.6605	2.64534
$636$	41.1754	1.63271
$637$	0	0
$638$	11.4094	0.451703
$639$	6.58248	0.260399
$640$	2.16980	0.0857689
$641$	34.3972	1.35861	0.679304	−	0.733857i	$-0.262282\pi$
$641$	34.3972	1.35861	0.679304	+	0.733857i	$0.262282\pi$
$642$	−6.85042	−0.270364
$643$	7.69036	0.303278	0.151639	−	0.988436i	$-0.451545\pi$
$643$	7.69036	0.303278	0.151639	+	0.988436i	$0.451545\pi$
$644$	−16.0378	−0.631979
$645$	−24.9940	−0.984138
$646$	−39.8332	−1.56722
$647$	41.9123	1.64774	0.823872	−	0.566776i	$-0.191809\pi$
$647$	41.9123	1.64774	0.823872	+	0.566776i	$0.191809\pi$
$648$	−7.34780	−0.288649
$649$	−18.7516	−0.736066
$650$	0	0
$651$	−7.51941	−0.294709
$652$	64.8763	2.54075
$653$	34.2262	1.33938	0.669688	−	0.742642i	$-0.266428\pi$
$653$	34.2262	1.33938	0.669688	+	0.742642i	$0.266428\pi$
$654$	−46.7713	−1.82890
$655$	3.69036	0.144194
$656$	−60.8149	−2.37442
$657$	7.73517	0.301778
$658$	−23.5877	−0.919545
$659$	45.1685	1.75951	0.879757	−	0.475424i	$-0.157705\pi$
$659$	45.1685	1.75951	0.879757	+	0.475424i	$0.157705\pi$
$660$	87.0086	3.38681
$661$	−11.9839	−0.466119	−0.233059	−	0.972463i	$-0.574874\pi$
$661$	−11.9839	−0.466119	−0.233059	+	0.972463i	$0.574874\pi$
$662$	2.88203	0.112013
$663$	0	0
$664$	−10.3331	−0.401004
$665$	11.1488	0.432333
$666$	0.404161	0.0156609
$667$	−3.07315	−0.118993
$668$	−92.3968	−3.57494
$669$	−20.0266	−0.774273
$670$	−106.176	−4.10192
$671$	58.9415	2.27541
$672$	10.2399	0.395013
$673$	−29.5117	−1.13759	−0.568796	−	0.822479i	$-0.692591\pi$
$673$	−29.5117	−1.13759	−0.568796	+	0.822479i	$0.692591\pi$
$674$	11.0747	0.426581
$675$	9.55201	0.367657
$676$	0	0
$677$	−31.0662	−1.19397	−0.596985	−	0.802252i	$-0.703635\pi$
$677$	−31.0662	−1.19397	−0.596985	+	0.802252i	$0.703635\pi$
$678$	−2.40842	−0.0924948
$679$	−2.11001	−0.0809747
$680$	146.343	5.61200
$681$	−19.2171	−0.736402
$682$	−92.9904	−3.56079
$683$	−5.79433	−0.221714	−0.110857	−	0.993836i	$-0.535360\pi$
$683$	−5.79433	−0.221714	−0.110857	+	0.993836i	$0.535360\pi$
$684$	−14.0714	−0.538034
$685$	−12.5744	−0.480441
$686$	2.61050	0.0996693
$687$	−5.25884	−0.200637
$688$	−62.5848	−2.38602
$689$	0	0
$690$	−33.1712	−1.26281
$691$	−18.8617	−0.717531	−0.358766	−	0.933428i	$-0.616802\pi$
$691$	−18.8617	−0.717531	−0.358766	+	0.933428i	$0.616802\pi$
$692$	−93.9467	−3.57132
$693$	−4.73730	−0.179955
$694$	−36.6347	−1.39063
$695$	1.41366	0.0536232
$696$	6.77900	0.256957
$697$	33.2406	1.25908
$698$	10.7181	0.405685
$699$	−26.6234	−1.00699
$700$	−45.9901	−1.73826
$701$	−32.3180	−1.22064	−0.610318	−	0.792157i	$-0.708958\pi$
$701$	−32.3180	−1.22064	−0.610318	+	0.792157i	$0.708958\pi$
$702$	0	0
$703$	0.452479	0.0170656
$704$	36.1328	1.36180
$705$	−34.4686	−1.29816
$706$	−41.9645	−1.57936
$707$	−0.850419	−0.0319833
$708$	−19.0581	−0.716246
$709$	−4.72296	−0.177374	−0.0886872	−	0.996060i	$-0.528267\pi$
$709$	−4.72296	−0.177374	−0.0886872	+	0.996060i	$0.528267\pi$
$710$	−65.5503	−2.46006
$711$	13.3646	0.501211
$712$	−14.4717	−0.542350
$713$	25.0472	0.938026
$714$	−13.6294	−0.510068
$715$	0	0
$716$	−79.8548	−2.98431
$717$	−4.29104	−0.160252
$718$	−47.3831	−1.76832
$719$	−40.8902	−1.52495	−0.762474	−	0.647019i	$-0.776015\pi$
$719$	−40.8902	−1.52495	−0.762474	+	0.647019i	$0.776015\pi$
$720$	36.4381	1.35797
$721$	1.47460	0.0549169
$722$	27.3018	1.01607
$723$	−7.52367	−0.279808
$724$	−13.5623	−0.504037
$725$	−8.81258	−0.327291
$726$	−29.8693	−1.10856
$727$	18.7292	0.694627	0.347313	−	0.937749i	$-0.387094\pi$
$727$	18.7292	0.694627	0.347313	+	0.937749i	$0.387094\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−77.0291	−2.85098
$731$	34.2080	1.26523
$732$	59.9046	2.21414
$733$	14.1100	0.521165	0.260583	−	0.965452i	$-0.416085\pi$
$733$	14.1100	0.521165	0.260583	+	0.965452i	$0.416085\pi$
$734$	61.0738	2.25428
$735$	3.81471	0.140708
$736$	−34.1093	−1.25728
$737$	50.5092	1.86053
$738$	16.6203	0.611802
$739$	49.9209	1.83637	0.918184	−	0.396154i	$-0.129655\pi$
$739$	49.9209	1.83637	0.918184	+	0.396154i	$0.129655\pi$
$740$	−2.84356	−0.104531
$741$	0	0
$742$	22.3250	0.819577
$743$	−2.15868	−0.0791945	−0.0395972	−	0.999216i	$-0.512607\pi$
$743$	−2.15868	−0.0791945	−0.0395972	+	0.999216i	$0.512607\pi$
$744$	−55.2511	−2.02560
$745$	60.0532	2.20018
$746$	12.4042	0.454149
$747$	1.40629	0.0514535
$748$	−119.084	−4.35415
$749$	−2.62418	−0.0958854
$750$	−45.3303	−1.65523
$751$	16.8372	0.614399	0.307199	−	0.951645i	$-0.400608\pi$
$751$	16.8372	0.614399	0.307199	+	0.951645i	$0.400608\pi$
$752$	−86.3092	−3.14737
$753$	11.3198	0.412516
$754$	0	0
$755$	−39.2588	−1.42878
$756$	−4.81471	−0.175109
$757$	−17.6028	−0.639785	−0.319893	−	0.947454i	$-0.603647\pi$
$757$	−17.6028	−0.639785	−0.319893	+	0.947454i	$0.603647\pi$
$758$	−17.7842	−0.645953
$759$	15.7800	0.572777
$760$	81.9193	2.97153
$761$	−19.2179	−0.696648	−0.348324	−	0.937374i	$-0.613249\pi$
$761$	−19.2179	−0.696648	−0.348324	+	0.937374i	$0.613249\pi$
$762$	−45.6174	−1.65255
$763$	−17.9166	−0.648624
$764$	72.9913	2.64073
$765$	−19.9166	−0.720086
$766$	5.89310	0.212926
$767$	0	0
$768$	−16.7394	−0.604032
$769$	14.0406	0.506315	0.253158	−	0.967425i	$-0.418531\pi$
$769$	14.0406	0.506315	0.253158	+	0.967425i	$0.418531\pi$
$770$	47.1754	1.70008
$771$	−24.8504	−0.894966
$772$	−0.313901	−0.0112975
$773$	−22.4339	−0.806891	−0.403445	−	0.915004i	$-0.632187\pi$
$773$	−22.4339	−0.806891	−0.403445	+	0.915004i	$0.632187\pi$
$774$	17.1040	0.614791
$775$	71.8255	2.58005
$776$	−15.5039	−0.556558
$777$	0.154821	0.00555419
$778$	−15.6630	−0.561546
$779$	18.6073	0.666676
$780$	0	0
$781$	31.1832	1.11582
$782$	45.3997	1.62349
$783$	−0.922589	−0.0329707
$784$	9.55201	0.341143
$785$	−43.5398	−1.55400
$786$	−2.52540	−0.0900781
$787$	0.926847	0.0330385	0.0165193	−	0.999864i	$-0.494742\pi$
$787$	0.926847	0.0330385	0.0165193	+	0.999864i	$0.494742\pi$
$788$	82.5311	2.94005
$789$	17.1762	0.611488
$790$	−133.089	−4.73508
$791$	−0.922589	−0.0328035
$792$	−34.8087	−1.23687
$793$	0	0
$794$	65.2357	2.31513
$795$	32.6234	1.15703
$796$	31.0164	1.09935
$797$	−26.0154	−0.921512	−0.460756	−	0.887527i	$-0.652422\pi$
$797$	−26.0154	−0.921512	−0.460756	+	0.887527i	$0.652422\pi$
$798$	−7.62942	−0.270079
$799$	47.1754	1.66895
$800$	−97.8118	−3.45817
$801$	1.96953	0.0695900
$802$	72.1879	2.54904
$803$	36.6438	1.29313
$804$	51.3345	1.81043
$805$	−12.7068	−0.447857
$806$	0	0
$807$	−7.74640	−0.272686
$808$	−6.24870	−0.219829
$809$	−44.8539	−1.57698	−0.788490	−	0.615048i	$-0.789137\pi$
$809$	−44.8539	−1.57698	−0.788490	+	0.615048i	$0.789137\pi$
$810$	−9.95830	−0.349899
$811$	−27.2511	−0.956916	−0.478458	−	0.878110i	$-0.658804\pi$
$811$	−27.2511	−0.956916	−0.478458	+	0.878110i	$0.658804\pi$
$812$	4.44200	0.155884
$813$	29.7008	1.04165
$814$	1.91463	0.0671078
$815$	51.4017	1.80052
$816$	−49.8710	−1.74584
$817$	19.1488	0.669933
$818$	34.3250	1.20015
$819$	0	0
$820$	−116.936	−4.08357
$821$	−20.4003	−0.711975	−0.355988	−	0.934491i	$-0.615855\pi$
$821$	−20.4003	−0.711975	−0.355988	+	0.934491i	$0.615855\pi$
$822$	8.60494	0.300132
$823$	54.3509	1.89455	0.947276	−	0.320418i	$-0.103824\pi$
$823$	54.3509	1.89455	0.947276	+	0.320418i	$0.103824\pi$
$824$	10.8350	0.377457
$825$	45.2507	1.57543
$826$	−10.3331	−0.359536
$827$	−3.48272	−0.121106	−0.0605530	−	0.998165i	$-0.519286\pi$
$827$	−3.48272	−0.121106	−0.0605530	+	0.998165i	$0.519286\pi$
$828$	16.0378	0.557353
$829$	−29.8417	−1.03645	−0.518223	−	0.855246i	$-0.673406\pi$
$829$	−29.8417	−1.03645	−0.518223	+	0.855246i	$0.673406\pi$
$830$	−14.0043	−0.486095
$831$	25.1488	0.872403
$832$	0	0
$833$	−5.22100	−0.180897
$834$	−0.967402	−0.0334984
$835$	−73.2063	−2.53341
$836$	−66.6605	−2.30550
$837$	7.51941	0.259909
$838$	14.8658	0.513530
$839$	43.0033	1.48464	0.742320	−	0.670045i	$-0.233725\pi$
$839$	43.0033	1.48464	0.742320	+	0.670045i	$0.233725\pi$
$840$	28.0297	0.967117
$841$	−28.1488	−0.970649
$842$	−60.0953	−2.07102
$843$	−8.40030	−0.289322
$844$	−77.1634	−2.65608
$845$	0	0
$846$	23.5877	0.810962
$847$	−11.4420	−0.393152
$848$	81.6889	2.80521
$849$	−21.3912	−0.734144
$850$	130.188	4.46542
$851$	−0.515711	−0.0176784
$852$	31.6927	1.08577
$853$	−34.1023	−1.16764	−0.583820	−	0.811883i	$-0.698443\pi$
$853$	−34.1023	−1.16764	−0.583820	+	0.811883i	$0.698443\pi$
$854$	32.4798	1.11144
$855$	−11.1488	−0.381282
$856$	−19.2819	−0.659043
$857$	−45.7344	−1.56226	−0.781129	−	0.624370i	$-0.785356\pi$
$857$	−45.7344	−1.56226	−0.781129	+	0.624370i	$0.785356\pi$
$858$	0	0
$859$	15.9861	0.545437	0.272719	−	0.962094i	$-0.412077\pi$
$859$	15.9861	0.545437	0.272719	+	0.962094i	$0.412077\pi$
$860$	−120.339	−4.10352
$861$	6.36672	0.216977
$862$	54.3100	1.84981
$863$	24.5096	0.834315	0.417157	−	0.908834i	$-0.363026\pi$
$863$	24.5096	0.834315	0.417157	+	0.908834i	$0.363026\pi$
$864$	−10.2399	−0.348369
$865$	−74.4343	−2.53084
$866$	−82.1807	−2.79261
$867$	10.2588	0.348408
$868$	−36.2038	−1.22884
$869$	63.3120	2.14771
$870$	9.18742	0.311483
$871$	0	0
$872$	−131.648	−4.45815
$873$	2.11001	0.0714130
$874$	25.4137	0.859630
$875$	−17.3646	−0.587030
$876$	37.2426	1.25831
$877$	−53.4913	−1.80627	−0.903136	−	0.429354i	$-0.858741\pi$
$877$	−53.4913	−1.80627	−0.903136	+	0.429354i	$0.858741\pi$
$878$	−58.4258	−1.97177
$879$	9.59895	0.323765
$880$	172.618	5.81896
$881$	26.1745	0.881840	0.440920	−	0.897546i	$-0.354652\pi$
$881$	26.1745	0.881840	0.440920	+	0.897546i	$0.354652\pi$
$882$	−2.61050	−0.0879001
$883$	23.1840	0.780202	0.390101	−	0.920772i	$-0.372440\pi$
$883$	23.1840	0.780202	0.390101	+	0.920772i	$0.372440\pi$
$884$	0	0
$885$	−15.0998	−0.507573
$886$	−22.2536	−0.747624
$887$	−13.7008	−0.460029	−0.230015	−	0.973187i	$-0.573877\pi$
$887$	−13.7008	−0.460029	−0.230015	+	0.973187i	$0.573877\pi$
$888$	1.13760	0.0381752
$889$	−17.4746	−0.586079
$890$	−19.6132	−0.657435
$891$	4.73730	0.158705
$892$	−96.4223	−3.22846
$893$	26.4077	0.883699
$894$	−41.0959	−1.37445
$895$	−63.2692	−2.11486
$896$	−0.568798	−0.0190022
$897$	0	0
$898$	48.8534	1.63026
$899$	−6.93733	−0.231373
$900$	45.9901	1.53300
$901$	−44.6500	−1.48751
$902$	78.7354	2.62160
$903$	6.55201	0.218037
$904$	−6.77900	−0.225466
$905$	−10.7454	−0.357190
$906$	26.8658	0.892556
$907$	25.5621	0.848777	0.424388	−	0.905480i	$-0.360489\pi$
$907$	25.5621	0.848777	0.424388	+	0.905480i	$0.360489\pi$
$908$	−92.5249	−3.07055
$909$	0.850419	0.0282066
$910$	0	0
$911$	2.07643	0.0687951	0.0343976	−	0.999408i	$-0.489049\pi$
$911$	2.07643	0.0687951	0.0343976	+	0.999408i	$0.489049\pi$
$912$	−27.9166	−0.924411
$913$	6.66202	0.220481
$914$	−36.9036	−1.22066
$915$	47.4626	1.56907
$916$	−25.3198	−0.836589
$917$	−0.967402	−0.0319464
$918$	13.6294	0.449838
$919$	17.8514	0.588863	0.294432	−	0.955673i	$-0.404870\pi$
$919$	17.8514	0.588863	0.294432	+	0.955673i	$0.404870\pi$
$920$	−93.3672	−3.07823
$921$	15.1488	0.499171
$922$	−6.98664	−0.230093
$923$	0	0
$924$	−22.8087	−0.750352
$925$	−1.47886	−0.0486245
$926$	−6.60881	−0.217179
$927$	−1.47460	−0.0484321
$928$	9.44724	0.310121
$929$	37.0553	1.21575	0.607873	−	0.794034i	$-0.292023\pi$
$929$	37.0553	1.21575	0.607873	+	0.794034i	$0.292023\pi$
$930$	−74.8805	−2.45543
$931$	−2.92259	−0.0957840
$932$	−128.184	−4.19881
$933$	−4.37058	−0.143086
$934$	−5.23212	−0.171200
$935$	−94.3509	−3.08560
$936$	0	0
$937$	39.7540	1.29871	0.649354	−	0.760486i	$-0.275039\pi$
$937$	39.7540	1.29871	0.649354	+	0.760486i	$0.275039\pi$
$938$	27.8332	0.908786
$939$	−1.49280	−0.0487158
$940$	−165.956	−5.41290
$941$	47.3530	1.54366	0.771832	−	0.635827i	$-0.219341\pi$
$941$	47.3530	1.54366	0.771832	+	0.635827i	$0.219341\pi$
$942$	29.7954	0.970785
$943$	−21.2076	−0.690614
$944$	−37.8097	−1.23060
$945$	−3.81471	−0.124093
$946$	81.0268	2.63441
$947$	−8.80446	−0.286106	−0.143053	−	0.989715i	$-0.545692\pi$
$947$	−8.80446	−0.286106	−0.143053	+	0.989715i	$0.545692\pi$
$948$	64.3466	2.08988
$949$	0	0
$950$	72.8763	2.36442
$951$	−23.2129	−0.752729
$952$	−38.3629	−1.24335
$953$	7.72895	0.250365	0.125183	−	0.992134i	$-0.460048\pi$
$953$	7.72895	0.250365	0.125183	+	0.992134i	$0.460048\pi$
$954$	−22.3250	−0.722799
$955$	57.8312	1.87137
$956$	−20.6601	−0.668196
$957$	−4.37058	−0.141281
$958$	−38.2722	−1.23652
$959$	3.29628	0.106442
$960$	29.0959	0.939066
$961$	25.5415	0.823920
$962$	0	0
$963$	2.62418	0.0845630
$964$	−36.2243	−1.16671
$965$	−0.248705	−0.00800608
$966$	8.69560	0.279776
$967$	−14.3054	−0.460030	−0.230015	−	0.973187i	$-0.573878\pi$
$967$	−14.3054	−0.460030	−0.230015	+	0.973187i	$0.573878\pi$
$968$	−84.0735	−2.70222
$969$	15.2588	0.490184
$970$	−21.0121	−0.674658
$971$	−15.1692	−0.486803	−0.243402	−	0.969926i	$-0.578263\pi$
$971$	−15.1692	−0.486803	−0.243402	+	0.969926i	$0.578263\pi$
$972$	4.81471	0.154432
$973$	−0.370581	−0.0118803
$974$	99.7583	3.19646
$975$	0	0
$976$	118.846	3.80417
$977$	8.25746	0.264180	0.132090	−	0.991238i	$-0.457831\pi$
$977$	8.25746	0.264180	0.132090	+	0.991238i	$0.457831\pi$
$978$	−35.1754	−1.12479
$979$	9.33026	0.298196
$980$	18.3667	0.586703
$981$	17.9166	0.572033
$982$	−55.8016	−1.78070
$983$	25.8525	0.824568	0.412284	−	0.911055i	$-0.364731\pi$
$983$	25.8525	0.824568	0.412284	+	0.911055i	$0.364731\pi$
$984$	46.7814	1.49134
$985$	65.3897	2.08349
$986$	−12.5744	−0.400449
$987$	9.03571	0.287610
$988$	0	0
$989$	−21.8248	−0.693988
$990$	−47.1754	−1.49933
$991$	−56.2100	−1.78557	−0.892785	−	0.450484i	$-0.851252\pi$
$991$	−56.2100	−1.78557	−0.892785	+	0.450484i	$0.851252\pi$
$992$	−76.9981	−2.44469
$993$	−1.10402	−0.0350349
$994$	17.1836	0.545029
$995$	24.5744	0.779059
$996$	6.77088	0.214544
$997$	37.4789	1.18697	0.593484	−	0.804846i	$-0.297752\pi$
$997$	37.4789	1.18697	0.593484	+	0.804846i	$0.297752\pi$
$998$	70.7237	2.23872
$999$	−0.154821	−0.00489833

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.w.1.1		4
13.12	even	2		273.2.a.e.1.4	✓	4
39.38	odd	2		819.2.a.k.1.1		4
52.51	odd	2		4368.2.a.br.1.1		4
65.64	even	2		6825.2.a.bg.1.1		4
91.90	odd	2		1911.2.a.s.1.4		4
273.272	even	2		5733.2.a.bf.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.a.e.1.4	✓	4	13.12	even	2
819.2.a.k.1.1		4	39.38	odd	2
1911.2.a.s.1.4		4	91.90	odd	2
3549.2.a.w.1.1		4	1.1	even	1	trivial
4368.2.a.br.1.1		4	52.51	odd	2
5733.2.a.bf.1.1		4	273.272	even	2
6825.2.a.bg.1.1		4	65.64	even	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:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.a (trivial)

\(f(q)\)	\(=\)	\(q-2.61050 q^{2} +1.00000 q^{3} +4.81471 q^{4} +3.81471 q^{5} -2.61050 q^{6} -1.00000 q^{7} -7.34780 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.61050 q^{2} +1.00000 q^{3} +4.81471 q^{4} +3.81471 q^{5} -2.61050 q^{6} -1.00000 q^{7} -7.34780 q^{8} +1.00000 q^{9} -9.95830 q^{10} +4.73730 q^{11} +4.81471 q^{12} +2.61050 q^{14} +3.81471 q^{15} +9.55201 q^{16} -5.22100 q^{17} -2.61050 q^{18} -2.92259 q^{19} +18.3667 q^{20} -1.00000 q^{21} -12.3667 q^{22} +3.33101 q^{23} -7.34780 q^{24} +9.55201 q^{25} +1.00000 q^{27} -4.81471 q^{28} -0.922589 q^{29} -9.95830 q^{30} +7.51941 q^{31} -10.2399 q^{32} +4.73730 q^{33} +13.6294 q^{34} -3.81471 q^{35} +4.81471 q^{36} -0.154821 q^{37} +7.62942 q^{38} -28.0297 q^{40} -6.36672 q^{41} +2.61050 q^{42} -6.55201 q^{43} +22.8087 q^{44} +3.81471 q^{45} -8.69560 q^{46} -9.03571 q^{47} +9.55201 q^{48} +1.00000 q^{49} -24.9355 q^{50} -5.22100 q^{51} +8.55201 q^{53} -2.61050 q^{54} +18.0714 q^{55} +7.34780 q^{56} -2.92259 q^{57} +2.40842 q^{58} -3.95830 q^{59} +18.3667 q^{60} +12.4420 q^{61} -19.6294 q^{62} -1.00000 q^{63} +7.62729 q^{64} -12.3667 q^{66} +10.6620 q^{67} -25.1376 q^{68} +3.33101 q^{69} +9.95830 q^{70} +6.58248 q^{71} -7.34780 q^{72} +7.73517 q^{73} +0.404161 q^{74} +9.55201 q^{75} -14.0714 q^{76} -4.73730 q^{77} +13.3646 q^{79} +36.4381 q^{80} +1.00000 q^{81} +16.6203 q^{82} +1.40629 q^{83} -4.81471 q^{84} -19.9166 q^{85} +17.1040 q^{86} -0.922589 q^{87} -34.8087 q^{88} +1.96953 q^{89} -9.95830 q^{90} +16.0378 q^{92} +7.51941 q^{93} +23.5877 q^{94} -11.1488 q^{95} -10.2399 q^{96} +2.11001 q^{97} -2.61050 q^{98} +4.73730 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + 4 q^{3} + 7 q^{4} + 3 q^{5} - q^{6} - 4 q^{7} - 3 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - q^2 + 4 * q^3 + 7 * q^4 + 3 * q^5 - q^6 - 4 * q^7 - 3 * q^8 + 4 * q^9	\( 4 q - q^{2} + 4 q^{3} + 7 q^{4} + 3 q^{5} - q^{6} - 4 q^{7} - 3 q^{8} + 4 q^{9} - 4 q^{10} + 2 q^{11} + 7 q^{12} + q^{14} + 3 q^{15} + 9 q^{16} - 2 q^{17} - q^{18} - 7 q^{19} + 32 q^{20} - 4 q^{21} - 8 q^{22} + 3 q^{23} - 3 q^{24} + 9 q^{25} + 4 q^{27} - 7 q^{28} + q^{29} - 4 q^{30} - 3 q^{31} - 7 q^{32} + 2 q^{33} + 30 q^{34} - 3 q^{35} + 7 q^{36} - 10 q^{37} + 6 q^{38} - 14 q^{40} + 16 q^{41} + q^{42} + 3 q^{43} + 12 q^{44} + 3 q^{45} + 18 q^{46} - 5 q^{47} + 9 q^{48} + 4 q^{49} - 13 q^{50} - 2 q^{51} + 5 q^{53} - q^{54} + 10 q^{55} + 3 q^{56} - 7 q^{57} + 4 q^{58} + 20 q^{59} + 32 q^{60} + 12 q^{61} - 54 q^{62} - 4 q^{63} + 5 q^{64} - 8 q^{66} + 22 q^{67} - 10 q^{68} + 3 q^{69} + 4 q^{70} - 3 q^{72} + 13 q^{73} - 6 q^{74} + 9 q^{75} + 6 q^{76} - 2 q^{77} + 11 q^{79} + 42 q^{80} + 4 q^{81} + 10 q^{82} - q^{83} - 7 q^{84} - 8 q^{85} + 10 q^{86} + q^{87} - 60 q^{88} + 5 q^{89} - 4 q^{90} + 34 q^{92} - 3 q^{93} + 34 q^{94} + 13 q^{95} - 7 q^{96} + 17 q^{97} - q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q - q^2 + 4 * q^3 + 7 * q^4 + 3 * q^5 - q^6 - 4 * q^7 - 3 * q^8 + 4 * q^9 - 4 * q^10 + 2 * q^11 + 7 * q^12 + q^14 + 3 * q^15 + 9 * q^16 - 2 * q^17 - q^18 - 7 * q^19 + 32 * q^20 - 4 * q^21 - 8 * q^22 + 3 * q^23 - 3 * q^24 + 9 * q^25 + 4 * q^27 - 7 * q^28 + q^29 - 4 * q^30 - 3 * q^31 - 7 * q^32 + 2 * q^33 + 30 * q^34 - 3 * q^35 + 7 * q^36 - 10 * q^37 + 6 * q^38 - 14 * q^40 + 16 * q^41 + q^42 + 3 * q^43 + 12 * q^44 + 3 * q^45 + 18 * q^46 - 5 * q^47 + 9 * q^48 + 4 * q^49 - 13 * q^50 - 2 * q^51 + 5 * q^53 - q^54 + 10 * q^55 + 3 * q^56 - 7 * q^57 + 4 * q^58 + 20 * q^59 + 32 * q^60 + 12 * q^61 - 54 * q^62 - 4 * q^63 + 5 * q^64 - 8 * q^66 + 22 * q^67 - 10 * q^68 + 3 * q^69 + 4 * q^70 - 3 * q^72 + 13 * q^73 - 6 * q^74 + 9 * q^75 + 6 * q^76 - 2 * q^77 + 11 * q^79 + 42 * q^80 + 4 * q^81 + 10 * q^82 - q^83 - 7 * q^84 - 8 * q^85 + 10 * q^86 + q^87 - 60 * q^88 + 5 * q^89 - 4 * q^90 + 34 * q^92 - 3 * q^93 + 34 * q^94 + 13 * q^95 - 7 * q^96 + 17 * q^97 - q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more