LMFDB - Embedded newform 3549.2.a.v.1.4

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:	$1$
Dimension:	$4$
Coefficient field:	4.4.64436.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 7x^{2} + 7x + 2 $ x^4 - x^3 - 7x^2 + 7x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-2.60520$ 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)

$f(q)$	$=$	$q+2.60520 q^{2} -1.00000 q^{3} +4.78706 q^{4} -3.78706 q^{5} -2.60520 q^{6} +1.00000 q^{7} +7.26084 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.60520 q^{2} -1.00000 q^{3} +4.78706 q^{4} -3.78706 q^{5} -2.60520 q^{6} +1.00000 q^{7} +7.26084 q^{8} +1.00000 q^{9} -9.86604 q^{10} -2.55475 q^{11} -4.78706 q^{12} +2.60520 q^{14} +3.78706 q^{15} +9.34181 q^{16} +3.21040 q^{17} +2.60520 q^{18} -8.44270 q^{19} -18.1289 q^{20} -1.00000 q^{21} -6.65564 q^{22} -3.97809 q^{23} -7.26084 q^{24} +9.34181 q^{25} -1.00000 q^{27} +4.78706 q^{28} -2.86858 q^{29} +9.86604 q^{30} +0.868584 q^{31} +9.81560 q^{32} +2.55475 q^{33} +8.36372 q^{34} -3.78706 q^{35} +4.78706 q^{36} +5.10951 q^{37} -21.9949 q^{38} -27.4972 q^{40} -3.34436 q^{41} -2.60520 q^{42} -4.86858 q^{43} -12.2298 q^{44} -3.78706 q^{45} -10.3637 q^{46} -11.0983 q^{47} -9.34181 q^{48} +1.00000 q^{49} +24.3373 q^{50} -3.21040 q^{51} +1.33319 q^{53} -2.60520 q^{54} +9.67501 q^{55} +7.26084 q^{56} +8.44270 q^{57} -7.47323 q^{58} -10.6556 q^{59} +18.1289 q^{60} -4.10089 q^{61} +2.26283 q^{62} +1.00000 q^{63} +6.88795 q^{64} +6.65564 q^{66} -10.8467 q^{67} +15.3684 q^{68} +3.97809 q^{69} -9.86604 q^{70} -2.55475 q^{71} +7.26084 q^{72} +6.76770 q^{73} +13.3113 q^{74} -9.34181 q^{75} -40.4157 q^{76} -2.55475 q^{77} -1.23230 q^{79} -35.3780 q^{80} +1.00000 q^{81} -8.71272 q^{82} -11.0983 q^{83} -4.78706 q^{84} -12.1580 q^{85} -12.6836 q^{86} +2.86858 q^{87} -18.5497 q^{88} -5.52423 q^{89} -9.86604 q^{90} -19.0434 q^{92} -0.868584 q^{93} -28.9134 q^{94} +31.9730 q^{95} -9.81560 q^{96} +5.65819 q^{97} +2.60520 q^{98} -2.55475 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 2 q^{10} - 2 q^{11} - 7 q^{12} - q^{14} + 3 q^{15} + 17 q^{16} - 10 q^{17} - q^{18} - 7 q^{19} - 40 q^{20} - 4 q^{21} - 12 q^{22} + 3 q^{23} - 3 q^{24} + 17 q^{25} - 4 q^{27} + 7 q^{28} - 9 q^{29} + 2 q^{30} + q^{31} + 5 q^{32} + 2 q^{33} + 32 q^{34} - 3 q^{35} + 7 q^{36} + 4 q^{37} - 18 q^{38} - 4 q^{40} - 28 q^{41} + q^{42} - 17 q^{43} - 10 q^{44} - 3 q^{45} - 40 q^{46} - 3 q^{47} - 17 q^{48} + 4 q^{49} + 11 q^{50} + 10 q^{51} - 5 q^{53} + q^{54} + 8 q^{55} + 3 q^{56} + 7 q^{57} - 12 q^{58} - 28 q^{59} + 40 q^{60} - 10 q^{61} + 14 q^{62} + 4 q^{63} + 9 q^{64} + 12 q^{66} - 22 q^{67} - 12 q^{68} - 3 q^{69} - 2 q^{70} - 2 q^{71} + 3 q^{72} + 31 q^{73} + 24 q^{74} - 17 q^{75} - 46 q^{76} - 2 q^{77} - q^{79} - 54 q^{80} + 4 q^{81} + 24 q^{82} - 3 q^{83} - 7 q^{84} + 2 q^{85} - 10 q^{86} + 9 q^{87} + 4 q^{88} - 5 q^{89} - 2 q^{90} + 28 q^{92} - q^{93} - 36 q^{94} + 39 q^{95} - 5 q^{96} + 43 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 - 2 * q^10 - 2 * q^11 - 7 * q^12 - q^14 + 3 * q^15 + 17 * q^16 - 10 * q^17 - q^18 - 7 * q^19 - 40 * q^20 - 4 * q^21 - 12 * q^22 + 3 * q^23 - 3 * q^24 + 17 * q^25 - 4 * q^27 + 7 * q^28 - 9 * q^29 + 2 * q^30 + q^31 + 5 * q^32 + 2 * q^33 + 32 * q^34 - 3 * q^35 + 7 * q^36 + 4 * q^37 - 18 * q^38 - 4 * q^40 - 28 * q^41 + q^42 - 17 * q^43 - 10 * q^44 - 3 * q^45 - 40 * q^46 - 3 * q^47 - 17 * q^48 + 4 * q^49 + 11 * q^50 + 10 * q^51 - 5 * q^53 + q^54 + 8 * q^55 + 3 * q^56 + 7 * q^57 - 12 * q^58 - 28 * q^59 + 40 * q^60 - 10 * q^61 + 14 * q^62 + 4 * q^63 + 9 * q^64 + 12 * q^66 - 22 * q^67 - 12 * q^68 - 3 * q^69 - 2 * q^70 - 2 * q^71 + 3 * q^72 + 31 * q^73 + 24 * q^74 - 17 * q^75 - 46 * q^76 - 2 * q^77 - q^79 - 54 * q^80 + 4 * q^81 + 24 * q^82 - 3 * q^83 - 7 * q^84 + 2 * q^85 - 10 * q^86 + 9 * q^87 + 4 * q^88 - 5 * q^89 - 2 * q^90 + 28 * q^92 - q^93 - 36 * q^94 + 39 * q^95 - 5 * q^96 + 43 * 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 $

$2$	2.60520	1.84215	0.921077	−	0.389381i	$-0.127311\pi$
$2$	2.60520	1.84215	0.921077	+	0.389381i	$0.127311\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.78706	2.39353
$5$	−3.78706	−1.69362	−0.846812	−	0.531892i	$-0.821481\pi$
$5$	−3.78706	−1.69362	−0.846812	+	0.531892i	$0.821481\pi$
$6$	−2.60520	−1.06357
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	7.26084	2.56709
$9$	1.00000	0.333333
$10$	−9.86604	−3.11992
$11$	−2.55475	−0.770287	−0.385144	−	0.922857i	$-0.625848\pi$
$11$	−2.55475	−0.770287	−0.385144	+	0.922857i	$0.625848\pi$
$12$	−4.78706	−1.38190
$13$	0	0
$13$	0	0
$14$	2.60520	0.696269
$15$	3.78706	0.977814
$16$	9.34181	2.33545
$17$	3.21040	0.778636	0.389318	−	0.921103i	$-0.372711\pi$
$17$	3.21040	0.778636	0.389318	+	0.921103i	$0.372711\pi$
$18$	2.60520	0.614051
$19$	−8.44270	−1.93689	−0.968444	−	0.249230i	$-0.919822\pi$
$19$	−8.44270	−1.93689	−0.968444	+	0.249230i	$0.919822\pi$
$20$	−18.1289	−4.05374
$21$	−1.00000	−0.218218
$22$	−6.65564	−1.41899
$23$	−3.97809	−0.829490	−0.414745	−	0.909938i	$-0.636129\pi$
$23$	−3.97809	−0.829490	−0.414745	+	0.909938i	$0.636129\pi$
$24$	−7.26084	−1.48211
$25$	9.34181	1.86836
$26$	0	0
$27$	−1.00000	−0.192450
$28$	4.78706	0.904669
$29$	−2.86858	−0.532683	−0.266341	−	0.963879i	$-0.585815\pi$
$29$	−2.86858	−0.532683	−0.266341	+	0.963879i	$0.585815\pi$
$30$	9.86604	1.80128
$31$	0.868584	0.156002	0.0780011	−	0.996953i	$-0.475146\pi$
$31$	0.868584	0.156002	0.0780011	+	0.996953i	$0.475146\pi$
$32$	9.81560	1.73517
$33$	2.55475	0.444726
$34$	8.36372	1.43437
$35$	−3.78706	−0.640130
$36$	4.78706	0.797843
$37$	5.10951	0.839998	0.419999	−	0.907525i	$-0.362030\pi$
$37$	5.10951	0.839998	0.419999	+	0.907525i	$0.362030\pi$
$38$	−21.9949	−3.56805
$39$	0	0
$40$	−27.4972	−4.34769
$41$	−3.34436	−0.522301	−0.261150	−	0.965298i	$-0.584102\pi$
$41$	−3.34436	−0.522301	−0.261150	+	0.965298i	$0.584102\pi$
$42$	−2.60520	−0.401991
$43$	−4.86858	−0.742452	−0.371226	−	0.928543i	$-0.621062\pi$
$43$	−4.86858	−0.742452	−0.371226	+	0.928543i	$0.621062\pi$
$44$	−12.2298	−1.84371
$45$	−3.78706	−0.564541
$46$	−10.3637	−1.52805
$47$	−11.0983	−1.61886	−0.809430	−	0.587217i	$-0.800224\pi$
$47$	−11.0983	−1.61886	−0.809430	+	0.587217i	$0.800224\pi$
$48$	−9.34181	−1.34837
$49$	1.00000	0.142857
$50$	24.3373	3.44181
$51$	−3.21040	−0.449545
$52$	0	0
$53$	1.33319	0.183128	0.0915640	−	0.995799i	$-0.470813\pi$
$53$	1.33319	0.183128	0.0915640	+	0.995799i	$0.470813\pi$
$54$	−2.60520	−0.354523
$55$	9.67501	1.30458
$56$	7.26084	0.970271
$57$	8.44270	1.11826
$58$	−7.47323	−0.981283
$59$	−10.6556	−1.38725	−0.693623	−	0.720338i	$-0.743987\pi$
$59$	−10.6556	−1.38725	−0.693623	+	0.720338i	$0.743987\pi$
$60$	18.1289	2.34043
$61$	−4.10089	−0.525065	−0.262532	−	0.964923i	$-0.584558\pi$
$61$	−4.10089	−0.525065	−0.262532	+	0.964923i	$0.584558\pi$
$62$	2.26283	0.287380
$63$	1.00000	0.125988
$64$	6.88795	0.860993
$65$	0	0
$66$	6.65564	0.819253
$67$	−10.8467	−1.32513	−0.662566	−	0.749003i	$-0.730533\pi$
$67$	−10.8467	−1.32513	−0.662566	+	0.749003i	$0.730533\pi$
$68$	15.3684	1.86369
$69$	3.97809	0.478906
$70$	−9.86604	−1.17922
$71$	−2.55475	−0.303194	−0.151597	−	0.988442i	$-0.548442\pi$
$71$	−2.55475	−0.303194	−0.151597	+	0.988442i	$0.548442\pi$
$72$	7.26084	0.855698
$73$	6.76770	0.792099	0.396049	−	0.918229i	$-0.370381\pi$
$73$	6.76770	0.792099	0.396049	+	0.918229i	$0.370381\pi$
$74$	13.3113	1.54741
$75$	−9.34181	−1.07870
$76$	−40.4157	−4.63600
$77$	−2.55475	−0.291141
$78$	0	0
$79$	−1.23230	−0.138645	−0.0693225	−	0.997594i	$-0.522084\pi$
$79$	−1.23230	−0.138645	−0.0693225	+	0.997594i	$0.522084\pi$
$80$	−35.3780	−3.95538
$81$	1.00000	0.111111
$82$	−8.71272	−0.962158
$83$	−11.0983	−1.21820	−0.609101	−	0.793093i	$-0.708469\pi$
$83$	−11.0983	−1.21820	−0.609101	+	0.793093i	$0.708469\pi$
$84$	−4.78706	−0.522311
$85$	−12.1580	−1.31872
$86$	−12.6836	−1.36771
$87$	2.86858	0.307544
$88$	−18.5497	−1.97740
$89$	−5.52423	−0.585567	−0.292783	−	0.956179i	$-0.594581\pi$
$89$	−5.52423	−0.585567	−0.292783	+	0.956179i	$0.594581\pi$
$90$	−9.86604	−1.03997
$91$	0	0
$92$	−19.0434	−1.98541
$93$	−0.868584	−0.0900679
$94$	−28.9134	−2.98219
$95$	31.9730	3.28036
$96$	−9.81560	−1.00180
$97$	5.65819	0.574502	0.287251	−	0.957855i	$-0.407259\pi$
$97$	5.65819	0.574502	0.287251	+	0.957855i	$0.407259\pi$
$98$	2.60520	0.263165
$99$	−2.55475	−0.256762
$100$	44.7198	4.47198
$101$	8.94756	0.890316	0.445158	−	0.895452i	$-0.353148\pi$
$101$	8.94756	0.890316	0.445158	+	0.895452i	$0.353148\pi$
$102$	−8.36372	−0.828132
$103$	1.67501	0.165043	0.0825216	−	0.996589i	$-0.473703\pi$
$103$	1.67501	0.165043	0.0825216	+	0.996589i	$0.473703\pi$
$104$	0	0
$105$	3.78706	0.369579
$106$	3.47323	0.337350
$107$	−0.846676	−0.0818513	−0.0409256	−	0.999162i	$-0.513031\pi$
$107$	−0.846676	−0.0818513	−0.0409256	+	0.999162i	$0.513031\pi$
$108$	−4.78706	−0.460635
$109$	17.9949	1.72360	0.861800	−	0.507248i	$-0.169337\pi$
$109$	17.9949	1.72360	0.861800	+	0.507248i	$0.169337\pi$
$110$	25.2053	2.40323
$111$	−5.10951	−0.484973
$112$	9.34181	0.882718
$113$	2.86858	0.269854	0.134927	−	0.990856i	$-0.456920\pi$
$113$	2.86858	0.269854	0.134927	+	0.990856i	$0.456920\pi$
$114$	21.9949	2.06001
$115$	15.0653	1.40484
$116$	−13.7321	−1.27499
$117$	0	0
$118$	−27.7601	−2.55552
$119$	3.21040	0.294297
$120$	27.4972	2.51014
$121$	−4.47323	−0.406657
$122$	−10.6836	−0.967250
$123$	3.34436	0.301551
$124$	4.15796	0.373396
$125$	−16.4427	−1.47068
$126$	2.60520	0.232090
$127$	−17.2053	−1.52672	−0.763362	−	0.645971i	$-0.776453\pi$
$127$	−17.2053	−1.52672	−0.763362	+	0.645971i	$0.776453\pi$
$128$	−1.68672	−0.149087
$129$	4.86858	0.428655
$130$	0	0
$131$	16.6836	1.45766	0.728828	−	0.684697i	$-0.240066\pi$
$131$	16.6836	1.45766	0.728828	+	0.684697i	$0.240066\pi$
$132$	12.2298	1.06446
$133$	−8.44270	−0.732075
$134$	−28.2577	−2.44110
$135$	3.78706	0.325938
$136$	23.3102	1.99883
$137$	18.9134	1.61588	0.807940	−	0.589265i	$-0.200583\pi$
$137$	18.9134	1.61588	0.807940	+	0.589265i	$0.200583\pi$
$138$	10.3637	0.882218
$139$	5.67501	0.481348	0.240674	−	0.970606i	$-0.422632\pi$
$139$	5.67501	0.481348	0.240674	+	0.970606i	$0.422632\pi$
$140$	−18.1289	−1.53217
$141$	11.0983	0.934649
$142$	−6.65564	−0.558529
$143$	0	0
$144$	9.34181	0.778484
$145$	10.8635	0.902164
$146$	17.6312	1.45917
$147$	−1.00000	−0.0824786
$148$	24.4595	2.01056
$149$	8.49259	0.695740	0.347870	−	0.937543i	$-0.386905\pi$
$149$	8.49259	0.695740	0.347870	+	0.937543i	$0.386905\pi$
$150$	−24.3373	−1.98713
$151$	−14.2190	−1.15713	−0.578564	−	0.815637i	$-0.696387\pi$
$151$	−14.2190	−1.15713	−0.578564	+	0.815637i	$0.696387\pi$
$152$	−61.3011	−4.97218
$153$	3.21040	0.259545
$154$	−6.65564	−0.536327
$155$	−3.28938	−0.264209
$156$	0	0
$157$	8.42079	0.672052	0.336026	−	0.941853i	$-0.390917\pi$
$157$	8.42079	0.672052	0.336026	+	0.941853i	$0.390917\pi$
$158$	−3.21040	−0.255405
$159$	−1.33319	−0.105729
$160$	−37.1722	−2.93872
$161$	−3.97809	−0.313518
$162$	2.60520	0.204684
$163$	3.77589	0.295751	0.147875	−	0.989006i	$-0.452757\pi$
$163$	3.77589	0.295751	0.147875	+	0.989006i	$0.452757\pi$
$164$	−16.0096	−1.25014
$165$	−9.67501	−0.753198
$166$	−28.9134	−2.24411
$167$	−8.83551	−0.683712	−0.341856	−	0.939752i	$-0.611056\pi$
$167$	−8.83551	−0.683712	−0.341856	+	0.939752i	$0.611056\pi$
$168$	−7.26084	−0.560186
$169$	0	0
$170$	−31.6739	−2.42928
$171$	−8.44270	−0.645629
$172$	−23.3062	−1.77708
$173$	−17.6750	−1.34381	−0.671903	−	0.740639i	$-0.734523\pi$
$173$	−17.6750	−1.34381	−0.671903	+	0.740639i	$0.734523\pi$
$174$	7.47323	0.566544
$175$	9.34181	0.706175
$176$	−23.8660	−1.79897
$177$	10.6556	0.800927
$178$	−14.3917	−1.07870
$179$	−16.9073	−1.26371	−0.631856	−	0.775086i	$-0.717707\pi$
$179$	−16.9073	−1.26371	−0.631856	+	0.775086i	$0.717707\pi$
$180$	−18.1289	−1.35125
$181$	−7.73717	−0.575099	−0.287550	−	0.957766i	$-0.592841\pi$
$181$	−7.73717	−0.575099	−0.287550	+	0.957766i	$0.592841\pi$
$182$	0	0
$183$	4.10089	0.303146
$184$	−28.8843	−2.12938
$185$	−19.3500	−1.42264
$186$	−2.26283	−0.165919
$187$	−8.20178	−0.599773
$188$	−53.1284	−3.87479
$189$	−1.00000	−0.0727393
$190$	83.2960	6.04293
$191$	5.57412	0.403329	0.201664	−	0.979455i	$-0.435365\pi$
$191$	5.57412	0.403329	0.201664	+	0.979455i	$0.435365\pi$
$192$	−6.88795	−0.497095
$193$	7.57412	0.545197	0.272598	−	0.962128i	$-0.412117\pi$
$193$	7.57412	0.545197	0.272598	+	0.962128i	$0.412117\pi$
$194$	14.7407	1.05832
$195$	0	0
$196$	4.78706	0.341933
$197$	−13.3444	−0.950746	−0.475373	−	0.879784i	$-0.657687\pi$
$197$	−13.3444	−0.950746	−0.475373	+	0.879784i	$0.657687\pi$
$198$	−6.65564	−0.472996
$199$	16.8854	1.19697	0.598487	−	0.801132i	$-0.295769\pi$
$199$	16.8854	1.19697	0.598487	+	0.801132i	$0.295769\pi$
$200$	67.8294	4.79626
$201$	10.8467	0.765066
$202$	23.3102	1.64010
$203$	−2.86858	−0.201335
$204$	−15.3684	−1.07600
$205$	12.6653	0.884581
$206$	4.36372	0.304035
$207$	−3.97809	−0.276497
$208$	0	0
$209$	21.5690	1.49196
$210$	9.86604	0.680821
$211$	11.6969	0.805249	0.402624	−	0.915365i	$-0.368098\pi$
$211$	11.6969	0.805249	0.402624	+	0.915365i	$0.368098\pi$
$212$	6.38207	0.438322
$213$	2.55475	0.175049
$214$	−2.20576	−0.150783
$215$	18.4376	1.25743
$216$	−7.26084	−0.494038
$217$	0.868584	0.0589633
$218$	46.8803	3.17514
$219$	−6.76770	−0.457319
$220$	46.3148	3.12254
$221$	0	0
$222$	−13.3113	−0.893395
$223$	4.24093	0.283993	0.141997	−	0.989867i	$-0.454648\pi$
$223$	4.24093	0.283993	0.141997	+	0.989867i	$0.454648\pi$
$224$	9.81560	0.655832
$225$	9.34181	0.622788
$226$	7.47323	0.497112
$227$	−1.72643	−0.114587	−0.0572934	−	0.998357i	$-0.518247\pi$
$227$	−1.72643	−0.114587	−0.0572934	+	0.998357i	$0.518247\pi$
$228$	40.4157	2.67660
$229$	−6.82833	−0.451229	−0.225614	−	0.974217i	$-0.572439\pi$
$229$	−6.82833	−0.451229	−0.225614	+	0.974217i	$0.572439\pi$
$230$	39.2480	2.58794
$231$	2.55475	0.168091
$232$	−20.8283	−1.36745
$233$	1.33319	0.0873403	0.0436702	−	0.999046i	$-0.486095\pi$
$233$	1.33319	0.0873403	0.0436702	+	0.999046i	$0.486095\pi$
$234$	0	0
$235$	42.0301	2.74174
$236$	−51.0092	−3.32042
$237$	1.23230	0.0800468
$238$	8.36372	0.542139
$239$	3.90985	0.252907	0.126454	−	0.991973i	$-0.459640\pi$
$239$	3.90985	0.252907	0.126454	+	0.991973i	$0.459640\pi$
$240$	35.3780	2.28364
$241$	25.3903	1.63553	0.817765	−	0.575552i	$-0.195213\pi$
$241$	25.3903	1.63553	0.817765	+	0.575552i	$0.195213\pi$
$242$	−11.6537	−0.749125
$243$	−1.00000	−0.0641500
$244$	−19.6312	−1.25676
$245$	−3.78706	−0.241946
$246$	8.71272	0.555502
$247$	0	0
$248$	6.30665	0.400473
$249$	11.0983	0.703329
$250$	−42.8365	−2.70922
$251$	25.7708	1.62664	0.813319	−	0.581818i	$-0.197658\pi$
$251$	25.7708	1.62664	0.813319	+	0.581818i	$0.197658\pi$
$252$	4.78706	0.301556
$253$	10.1631	0.638945
$254$	−44.8232	−2.81246
$255$	12.1580	0.761361
$256$	−18.1701	−1.13563
$257$	−5.87678	−0.366584	−0.183292	−	0.983059i	$-0.558675\pi$
$257$	−5.87678	−0.366584	−0.183292	+	0.983059i	$0.558675\pi$
$258$	12.6836	0.789648
$259$	5.10951	0.317489
$260$	0	0
$261$	−2.86858	−0.177561
$262$	43.4642	2.68522
$263$	−10.2409	−0.631483	−0.315741	−	0.948845i	$-0.602253\pi$
$263$	−10.2409	−0.631483	−0.315741	+	0.948845i	$0.602253\pi$
$264$	18.5497	1.14165
$265$	−5.04888	−0.310150
$266$	−21.9949	−1.34859
$267$	5.52423	0.338077
$268$	−51.9237	−3.17174
$269$	−16.1396	−0.984050	−0.492025	−	0.870581i	$-0.663743\pi$
$269$	−16.1396	−0.984050	−0.492025	+	0.870581i	$0.663743\pi$
$270$	9.86604	0.600428
$271$	12.2577	0.744605	0.372302	−	0.928111i	$-0.378568\pi$
$271$	12.2577	0.744605	0.372302	+	0.928111i	$0.378568\pi$
$272$	29.9909	1.81847
$273$	0	0
$274$	49.2731	2.97670
$275$	−23.8660	−1.43918
$276$	19.0434	1.14628
$277$	−9.81504	−0.589729	−0.294864	−	0.955539i	$-0.595274\pi$
$277$	−9.81504	−0.589729	−0.294864	+	0.955539i	$0.595274\pi$
$278$	14.7845	0.886716
$279$	0.868584	0.0520007
$280$	−27.4972	−1.64327
$281$	−16.1910	−0.965876	−0.482938	−	0.875655i	$-0.660430\pi$
$281$	−16.1910	−0.965876	−0.482938	+	0.875655i	$0.660430\pi$
$282$	28.9134	1.72177
$283$	−19.1482	−1.13824	−0.569122	−	0.822253i	$-0.692717\pi$
$283$	−19.1482	−1.13824	−0.569122	+	0.822253i	$0.692717\pi$
$284$	−12.2298	−0.725703
$285$	−31.9730	−1.89392
$286$	0	0
$287$	−3.34436	−0.197411
$288$	9.81560	0.578389
$289$	−6.69335	−0.393727
$290$	28.3016	1.66192
$291$	−5.65819	−0.331689
$292$	32.3974	1.89591
$293$	24.6725	1.44138	0.720690	−	0.693257i	$-0.243825\pi$
$293$	24.6725	1.44138	0.720690	+	0.693257i	$0.243825\pi$
$294$	−2.60520	−0.151938
$295$	40.3535	2.34947
$296$	37.0993	2.15635
$297$	2.55475	0.148242
$298$	22.1249	1.28166
$299$	0	0
$300$	−44.7198	−2.58190
$301$	−4.86858	−0.280620
$302$	−37.0434	−2.13161
$303$	−8.94756	−0.514024
$304$	−78.8701	−4.52351
$305$	15.5303	0.889263
$306$	8.36372	0.478122
$307$	13.7540	0.784981	0.392491	−	0.919756i	$-0.371614\pi$
$307$	13.7540	0.784981	0.392491	+	0.919756i	$0.371614\pi$
$308$	−12.2298	−0.696855
$309$	−1.67501	−0.0952877
$310$	−8.56948	−0.486714
$311$	−12.1580	−0.689415	−0.344707	−	0.938710i	$-0.612022\pi$
$311$	−12.1580	−0.689415	−0.344707	+	0.938710i	$0.612022\pi$
$312$	0	0
$313$	21.6699	1.22486	0.612428	−	0.790526i	$-0.290193\pi$
$313$	21.6699	1.22486	0.612428	+	0.790526i	$0.290193\pi$
$314$	21.9378	1.23802
$315$	−3.78706	−0.213377
$316$	−5.89911	−0.331851
$317$	−29.3780	−1.65003	−0.825016	−	0.565109i	$-0.808834\pi$
$317$	−29.3780	−1.65003	−0.825016	+	0.565109i	$0.808834\pi$
$318$	−3.47323	−0.194769
$319$	7.32853	0.410319
$320$	−26.0851	−1.45820
$321$	0.846676	0.0472569
$322$	−10.3637	−0.577548
$323$	−27.1044	−1.50813
$324$	4.78706	0.265948
$325$	0	0
$326$	9.83695	0.544818
$327$	−17.9949	−0.995121
$328$	−24.2828	−1.34080
$329$	−11.0983	−0.611871
$330$	−25.2053	−1.38751
$331$	23.9124	1.31434	0.657171	−	0.753741i	$-0.271753\pi$
$331$	23.9124	1.31434	0.657171	+	0.753741i	$0.271753\pi$
$332$	−53.1284	−2.91580
$333$	5.10951	0.279999
$334$	−23.0183	−1.25950
$335$	41.0770	2.24428
$336$	−9.34181	−0.509638
$337$	15.5706	0.848182	0.424091	−	0.905620i	$-0.360594\pi$
$337$	15.5706	0.848182	0.424091	+	0.905620i	$0.360594\pi$
$338$	0	0
$339$	−2.86858	−0.155800
$340$	−58.2009	−3.15639
$341$	−2.21902	−0.120167
$342$	−21.9949	−1.18935
$343$	1.00000	0.0539949
$344$	−35.3500	−1.90594
$345$	−15.0653	−0.811087
$346$	−46.0469	−2.47550
$347$	1.04845	0.0562838	0.0281419	−	0.999604i	$-0.491041\pi$
$347$	1.04845	0.0562838	0.0281419	+	0.999604i	$0.491041\pi$
$348$	13.7321	0.736117
$349$	−13.8721	−0.742557	−0.371279	−	0.928521i	$-0.621081\pi$
$349$	−13.8721	−0.742557	−0.371279	+	0.928521i	$0.621081\pi$
$350$	24.3373	1.30088
$351$	0	0
$352$	−25.0764	−1.33658
$353$	−9.96693	−0.530486	−0.265243	−	0.964182i	$-0.585452\pi$
$353$	−9.96693	−0.530486	−0.265243	+	0.964182i	$0.585452\pi$
$354$	27.7601	1.47543
$355$	9.67501	0.513496
$356$	−26.4448	−1.40157
$357$	−3.21040	−0.169912
$358$	−44.0469	−2.32795
$359$	18.9705	1.00122	0.500611	−	0.865672i	$-0.333109\pi$
$359$	18.9705	1.00122	0.500611	+	0.865672i	$0.333109\pi$
$360$	−27.4972	−1.44923
$361$	52.2792	2.75154
$362$	−20.1569	−1.05942
$363$	4.47323	0.234784
$364$	0	0
$365$	−25.6297	−1.34152
$366$	10.6836	0.558442
$367$	22.3586	1.16711	0.583556	−	0.812073i	$-0.301661\pi$
$367$	22.3586	1.16711	0.583556	+	0.812073i	$0.301661\pi$
$368$	−37.1626	−1.93723
$369$	−3.34436	−0.174100
$370$	−50.4106	−2.62072
$371$	1.33319	0.0692159
$372$	−4.15796	−0.215580
$373$	26.0958	1.35119	0.675595	−	0.737273i	$-0.263887\pi$
$373$	26.0958	1.35119	0.675595	+	0.737273i	$0.263887\pi$
$374$	−21.3673	−1.10487
$375$	16.4427	0.849097
$376$	−80.5833	−4.15577
$377$	0	0
$378$	−2.60520	−0.133997
$379$	−12.0000	−0.616399	−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000	−0.616399	−0.308199	+	0.951322i	$0.599726\pi$
$380$	153.057	7.85164
$381$	17.2053	0.881455
$382$	14.5217	0.742994
$383$	−4.96229	−0.253561	−0.126781	−	0.991931i	$-0.540464\pi$
$383$	−4.96229	−0.253561	−0.126781	+	0.991931i	$0.540464\pi$
$384$	1.68672	0.0860752
$385$	9.67501	0.493084
$386$	19.7321	1.00434
$387$	−4.86858	−0.247484
$388$	27.0861	1.37509
$389$	−17.8757	−0.906333	−0.453166	−	0.891426i	$-0.649706\pi$
$389$	−17.8757	−0.906333	−0.453166	+	0.891426i	$0.649706\pi$
$390$	0	0
$391$	−12.7713	−0.645870
$392$	7.26084	0.366728
$393$	−16.6836	−0.841578
$394$	−34.7647	−1.75142
$395$	4.66681	0.234813
$396$	−12.2298	−0.614569
$397$	−7.06925	−0.354796	−0.177398	−	0.984139i	$-0.556768\pi$
$397$	−7.06925	−0.354796	−0.177398	+	0.984139i	$0.556768\pi$
$398$	43.9898	2.20501
$399$	8.44270	0.422664
$400$	87.2695	4.36347
$401$	9.12025	0.455444	0.227722	−	0.973726i	$-0.426872\pi$
$401$	9.12025	0.455444	0.227722	+	0.973726i	$0.426872\pi$
$402$	28.2577	1.40937
$403$	0	0
$404$	42.8325	2.13100
$405$	−3.78706	−0.188180
$406$	−7.47323	−0.370890
$407$	−13.0535	−0.647040
$408$	−23.3102	−1.15403
$409$	−18.2542	−0.902611	−0.451306	−	0.892369i	$-0.649042\pi$
$409$	−18.2542	−0.902611	−0.451306	+	0.892369i	$0.649042\pi$
$410$	32.9956	1.62953
$411$	−18.9134	−0.932929
$412$	8.01835	0.395036
$413$	−10.6556	−0.524330
$414$	−10.3637	−0.509349
$415$	42.0301	2.06318
$416$	0	0
$417$	−5.67501	−0.277906
$418$	56.1916	2.74842
$419$	13.6934	0.668964	0.334482	−	0.942402i	$-0.391439\pi$
$419$	13.6934	0.668964	0.334482	+	0.942402i	$0.391439\pi$
$420$	18.1289	0.884598
$421$	−33.8146	−1.64802	−0.824012	−	0.566573i	$-0.808269\pi$
$421$	−33.8146	−1.64802	−0.824012	+	0.566573i	$0.808269\pi$
$422$	30.4728	1.48339
$423$	−11.0983	−0.539620
$424$	9.68009	0.470107
$425$	29.9909	1.45477
$426$	6.65564	0.322467
$427$	−4.10089	−0.198456
$428$	−4.05309	−0.195913
$429$	0	0
$430$	48.0336	2.31639
$431$	20.3256	0.979048	0.489524	−	0.871990i	$-0.337171\pi$
$431$	20.3256	0.979048	0.489524	+	0.871990i	$0.337171\pi$
$432$	−9.34181	−0.449458
$433$	17.1106	0.822284	0.411142	−	0.911571i	$-0.365130\pi$
$433$	17.1106	0.822284	0.411142	+	0.911571i	$0.365130\pi$
$434$	2.26283	0.108619
$435$	−10.8635	−0.520865
$436$	86.1427	4.12549
$437$	33.5858	1.60663
$438$	−17.6312	−0.842451
$439$	1.67501	0.0799436	0.0399718	−	0.999201i	$-0.487273\pi$
$439$	1.67501	0.0799436	0.0399718	+	0.999201i	$0.487273\pi$
$440$	70.2487	3.34897
$441$	1.00000	0.0476190
$442$	0	0
$443$	−12.9073	−0.613245	−0.306622	−	0.951831i	$-0.599199\pi$
$443$	−12.9073	−0.613245	−0.306622	+	0.951831i	$0.599199\pi$
$444$	−24.4595	−1.16080
$445$	20.9206	0.991730
$446$	11.0485	0.523159
$447$	−8.49259	−0.401686
$448$	6.88795	0.325425
$449$	−21.1762	−0.999368	−0.499684	−	0.866208i	$-0.666550\pi$
$449$	−21.1762	−0.999368	−0.499684	+	0.866208i	$0.666550\pi$
$450$	24.3373	1.14727
$451$	8.54401	0.402322
$452$	13.7321	0.645903
$453$	14.2190	0.668068
$454$	−4.49768	−0.211087
$455$	0	0
$456$	61.3011	2.87069
$457$	−8.41570	−0.393670	−0.196835	−	0.980437i	$-0.563066\pi$
$457$	−8.41570	−0.393670	−0.196835	+	0.980437i	$0.563066\pi$
$458$	−17.7892	−0.831232
$459$	−3.21040	−0.149848
$460$	72.1183	3.36253
$461$	1.76515	0.0822113	0.0411056	−	0.999155i	$-0.486912\pi$
$461$	1.76515	0.0822113	0.0411056	+	0.999155i	$0.486912\pi$
$462$	6.65564	0.309649
$463$	−38.9241	−1.80896	−0.904479	−	0.426519i	$-0.859740\pi$
$463$	−38.9241	−1.80896	−0.904479	+	0.426519i	$0.859740\pi$
$464$	−26.7978	−1.24406
$465$	3.28938	0.152541
$466$	3.47323	0.160894
$467$	30.4544	1.40926	0.704631	−	0.709573i	$-0.251112\pi$
$467$	30.4544	1.40926	0.704631	+	0.709573i	$0.251112\pi$
$468$	0	0
$469$	−10.8467	−0.500853
$470$	109.497	5.05071
$471$	−8.42079	−0.388010
$472$	−77.3689	−3.56119
$473$	12.4380	0.571902
$474$	3.21040	0.147458
$475$	−78.8701	−3.61881
$476$	15.3684	0.704408
$477$	1.33319	0.0610427
$478$	10.1859	0.465894
$479$	3.54656	0.162046	0.0810232	−	0.996712i	$-0.474181\pi$
$479$	3.54656	0.162046	0.0810232	+	0.996712i	$0.474181\pi$
$480$	37.1722	1.69667
$481$	0	0
$482$	66.1467	3.01290
$483$	3.97809	0.181009
$484$	−21.4136	−0.973346
$485$	−21.4279	−0.972990
$486$	−2.60520	−0.118174
$487$	39.9898	1.81211	0.906056	−	0.423158i	$-0.139078\pi$
$487$	39.9898	1.81211	0.906056	+	0.423158i	$0.139078\pi$
$488$	−29.7759	−1.34789
$489$	−3.77589	−0.170752
$490$	−9.86604	−0.445702
$491$	9.69844	0.437685	0.218842	−	0.975760i	$-0.429772\pi$
$491$	9.69844	0.437685	0.218842	+	0.975760i	$0.429772\pi$
$492$	16.0096	0.721770
$493$	−9.20929	−0.414766
$494$	0	0
$495$	9.67501	0.434859
$496$	8.11415	0.364336
$497$	−2.55475	−0.114596
$498$	28.9134	1.29564
$499$	24.0336	1.07589	0.537947	−	0.842979i	$-0.319200\pi$
$499$	24.0336	1.07589	0.537947	+	0.842979i	$0.319200\pi$
$500$	−78.7122	−3.52012
$501$	8.83551	0.394741
$502$	67.1381	2.99652
$503$	3.67390	0.163811	0.0819056	−	0.996640i	$-0.473899\pi$
$503$	3.67390	0.163811	0.0819056	+	0.996640i	$0.473899\pi$
$504$	7.26084	0.323424
$505$	−33.8849	−1.50786
$506$	26.4768	1.17704
$507$	0	0
$508$	−82.3628	−3.65426
$509$	19.3612	0.858169	0.429085	−	0.903264i	$-0.358836\pi$
$509$	19.3612	0.858169	0.429085	+	0.903264i	$0.358836\pi$
$510$	31.6739	1.40254
$511$	6.76770	0.299385
$512$	−43.9634	−1.94293
$513$	8.44270	0.372754
$514$	−15.3102	−0.675303
$515$	−6.34334	−0.279521
$516$	23.3062	1.02600
$517$	28.3535	1.24699
$518$	13.3113	0.584864
$519$	17.6750	0.775847
$520$	0	0
$521$	34.1130	1.49452	0.747260	−	0.664532i	$-0.231369\pi$
$521$	34.1130	1.49452	0.747260	+	0.664532i	$0.231369\pi$
$522$	−7.47323	−0.327094
$523$	−33.0250	−1.44408	−0.722042	−	0.691850i	$-0.756796\pi$
$523$	−33.0250	−1.44408	−0.722042	+	0.691850i	$0.756796\pi$
$524$	79.8655	3.48894
$525$	−9.34181	−0.407710
$526$	−26.6796	−1.16329
$527$	2.78850	0.121469
$528$	23.8660	1.03864
$529$	−7.17478	−0.311947
$530$	−13.1533	−0.571344
$531$	−10.6556	−0.462415
$532$	−40.4157	−1.75224
$533$	0	0
$534$	14.3917	0.622790
$535$	3.20641	0.138625
$536$	−78.7560	−3.40174
$537$	16.9073	0.729604
$538$	−42.0469	−1.81277
$539$	−2.55475	−0.110041
$540$	18.1289	0.780142
$541$	24.8416	1.06802	0.534012	−	0.845477i	$-0.320684\pi$
$541$	24.8416	1.06802	0.534012	+	0.845477i	$0.320684\pi$
$542$	31.9339	1.37168
$543$	7.73717	0.332034
$544$	31.5120	1.35106
$545$	−68.1478	−2.91913
$546$	0	0
$547$	8.14114	0.348090	0.174045	−	0.984738i	$-0.444316\pi$
$547$	8.14114	0.348090	0.174045	+	0.984738i	$0.444316\pi$
$548$	90.5395	3.86766
$549$	−4.10089	−0.175022
$550$	−62.1758	−2.65118
$551$	24.2186	1.03175
$552$	28.8843	1.22940
$553$	−1.23230	−0.0524029
$554$	−25.5701	−1.08637
$555$	19.3500	0.821362
$556$	27.1666	1.15212
$557$	−8.11052	−0.343654	−0.171827	−	0.985127i	$-0.554967\pi$
$557$	−8.11052	−0.343654	−0.171827	+	0.985127i	$0.554967\pi$
$558$	2.26283	0.0957933
$559$	0	0
$560$	−35.3780	−1.49499
$561$	8.20178	0.346279
$562$	−42.1809	−1.77929
$563$	−11.1044	−0.467995	−0.233998	−	0.972237i	$-0.575181\pi$
$563$	−11.1044	−0.467995	−0.233998	+	0.972237i	$0.575181\pi$
$564$	53.1284	2.23711
$565$	−10.8635	−0.457031
$566$	−49.8849	−2.09682
$567$	1.00000	0.0419961
$568$	−18.5497	−0.778327
$569$	−2.86858	−0.120257	−0.0601286	−	0.998191i	$-0.519151\pi$
$569$	−2.86858	−0.120257	−0.0601286	+	0.998191i	$0.519151\pi$
$570$	−83.2960	−3.48889
$571$	−32.4947	−1.35986	−0.679930	−	0.733277i	$-0.737990\pi$
$571$	−32.4947	−1.35986	−0.679930	+	0.733277i	$0.737990\pi$
$572$	0	0
$573$	−5.57412	−0.232862
$574$	−8.71272	−0.363662
$575$	−37.1626	−1.54979
$576$	6.88795	0.286998
$577$	−24.3759	−1.01478	−0.507390	−	0.861716i	$-0.669390\pi$
$577$	−24.3759	−1.01478	−0.507390	+	0.861716i	$0.669390\pi$
$578$	−17.4375	−0.725305
$579$	−7.57412	−0.314770
$580$	52.0042	2.15936
$581$	−11.0983	−0.460437
$582$	−14.7407	−0.611022
$583$	−3.40598	−0.141061
$584$	49.1392	2.03339
$585$	0	0
$586$	64.2767	2.65524
$587$	−11.7483	−0.484906	−0.242453	−	0.970163i	$-0.577952\pi$
$587$	−11.7483	−0.484906	−0.242453	+	0.970163i	$0.577952\pi$
$588$	−4.78706	−0.197415
$589$	−7.33319	−0.302159
$590$	105.129	4.32809
$591$	13.3444	0.548914
$592$	47.7321	1.96178
$593$	−46.6459	−1.91552	−0.957759	−	0.287574i	$-0.907151\pi$
$593$	−46.6459	−1.91552	−0.957759	+	0.287574i	$0.907151\pi$
$594$	6.65564	0.273084
$595$	−12.1580	−0.498428
$596$	40.6545	1.66527
$597$	−16.8854	−0.691073
$598$	0	0
$599$	−20.8197	−0.850669	−0.425335	−	0.905036i	$-0.639844\pi$
$599$	−20.8197	−0.850669	−0.425335	+	0.905036i	$0.639844\pi$
$600$	−67.8294	−2.76912
$601$	24.2588	0.989539	0.494770	−	0.869024i	$-0.335252\pi$
$601$	24.2588	0.989539	0.494770	+	0.869024i	$0.335252\pi$
$602$	−12.6836	−0.516946
$603$	−10.8467	−0.441711
$604$	−68.0673	−2.76962
$605$	16.9404	0.688724
$606$	−23.3102	−0.946911
$607$	6.20067	0.251677	0.125839	−	0.992051i	$-0.459838\pi$
$607$	6.20067	0.251677	0.125839	+	0.992051i	$0.459838\pi$
$608$	−82.8701	−3.36083
$609$	2.86858	0.116241
$610$	40.4595	1.63816
$611$	0	0
$612$	15.3684	0.621229
$613$	−14.9026	−0.601912	−0.300956	−	0.953638i	$-0.597306\pi$
$613$	−14.9026	−0.601912	−0.300956	+	0.953638i	$0.597306\pi$
$614$	35.8319	1.44606
$615$	−12.6653	−0.510713
$616$	−18.5497	−0.747387
$617$	−24.1472	−0.972130	−0.486065	−	0.873923i	$-0.661568\pi$
$617$	−24.1472	−0.972130	−0.486065	+	0.873923i	$0.661568\pi$
$618$	−4.36372	−0.175535
$619$	−43.9339	−1.76585	−0.882925	−	0.469513i	$-0.844429\pi$
$619$	−43.9339	−1.76585	−0.882925	+	0.469513i	$0.844429\pi$
$620$	−15.7464	−0.632392
$621$	3.97809	0.159635
$622$	−31.6739	−1.27001
$623$	−5.52423	−0.221323
$624$	0	0
$625$	15.5604	0.622416
$626$	56.4544	2.25637
$627$	−21.5690	−0.861384
$628$	40.3108	1.60858
$629$	16.4036	0.654052
$630$	−9.86604	−0.393072
$631$	25.9511	1.03310	0.516548	−	0.856258i	$-0.327217\pi$
$631$	25.9511	1.03310	0.516548	+	0.856258i	$0.327217\pi$
$632$	−8.94756	−0.355915
$633$	−11.6969	−0.464911
$634$	−76.5355	−3.03961
$635$	65.1575	2.58570
$636$	−6.38207	−0.253065
$637$	0	0
$638$	19.0923	0.755870
$639$	−2.55475	−0.101065
$640$	6.38772	0.252497
$641$	39.5858	1.56355	0.781773	−	0.623563i	$-0.214315\pi$
$641$	39.5858	1.56355	0.781773	+	0.623563i	$0.214315\pi$
$642$	2.20576	0.0870544
$643$	−17.0434	−0.672125	−0.336062	−	0.941840i	$-0.609095\pi$
$643$	−17.0434	−0.672125	−0.336062	+	0.941840i	$0.609095\pi$
$644$	−19.0434	−0.750414
$645$	−18.4376	−0.725980
$646$	−70.6124	−2.77821
$647$	27.7544	1.09114	0.545569	−	0.838066i	$-0.316313\pi$
$647$	27.7544	1.09114	0.545569	+	0.838066i	$0.316313\pi$
$648$	7.26084	0.285233
$649$	27.2225	1.06858
$650$	0	0
$651$	−0.868584	−0.0340425
$652$	18.0754	0.707888
$653$	−7.77080	−0.304095	−0.152048	−	0.988373i	$-0.548587\pi$
$653$	−7.77080	−0.304095	−0.152048	+	0.988373i	$0.548587\pi$
$654$	−46.8803	−1.83317
$655$	−63.1819	−2.46872
$656$	−31.2424	−1.21981
$657$	6.76770	0.264033
$658$	−28.9134	−1.12716
$659$	−4.74935	−0.185008	−0.0925042	−	0.995712i	$-0.529487\pi$
$659$	−4.74935	−0.185008	−0.0925042	+	0.995712i	$0.529487\pi$
$660$	−46.3148	−1.80280
$661$	38.0301	1.47920	0.739599	−	0.673047i	$-0.235015\pi$
$661$	38.0301	1.47920	0.739599	+	0.673047i	$0.235015\pi$
$662$	62.2965	2.42122
$663$	0	0
$664$	−80.5833	−3.12724
$665$	31.9730	1.23986
$666$	13.3113	0.515802
$667$	11.4115	0.441855
$668$	−42.2961	−1.63649
$669$	−4.24093	−0.163964
$670$	107.014	4.13430
$671$	10.4768	0.404451
$672$	−9.81560	−0.378645
$673$	−23.0602	−0.888905	−0.444452	−	0.895803i	$-0.646602\pi$
$673$	−23.0602	−0.888905	−0.444452	+	0.895803i	$0.646602\pi$
$674$	40.5644	1.56248
$675$	−9.34181	−0.359567
$676$	0	0
$677$	−44.3759	−1.70550	−0.852752	−	0.522317i	$-0.825068\pi$
$677$	−44.3759	−1.70550	−0.852752	+	0.522317i	$0.825068\pi$
$678$	−7.47323	−0.287008
$679$	5.65819	0.217141
$680$	−88.2770	−3.38527
$681$	1.72643	0.0661568
$682$	−5.78098	−0.221365
$683$	−5.91494	−0.226329	−0.113165	−	0.993576i	$-0.536099\pi$
$683$	−5.91494	−0.226329	−0.113165	+	0.993576i	$0.536099\pi$
$684$	−40.4157	−1.54533
$685$	−71.6261	−2.73669
$686$	2.60520	0.0994669
$687$	6.82833	0.260517
$688$	−45.4814	−1.73396
$689$	0	0
$690$	−39.2480	−1.49415
$691$	−12.6883	−0.482685	−0.241343	−	0.970440i	$-0.577588\pi$
$691$	−12.6883	−0.482685	−0.241343	+	0.970440i	$0.577588\pi$
$692$	−84.6113	−3.21644
$693$	−2.55475	−0.0970471
$694$	2.73143	0.103683
$695$	−21.4916	−0.815222
$696$	20.8283	0.789496
$697$	−10.7367	−0.406682
$698$	−36.1396	−1.36790
$699$	−1.33319	−0.0504260
$700$	44.7198	1.69025
$701$	−25.8487	−0.976291	−0.488146	−	0.872762i	$-0.662326\pi$
$701$	−25.8487	−0.976291	−0.488146	+	0.872762i	$0.662326\pi$
$702$	0	0
$703$	−43.1381	−1.62698
$704$	−17.5970	−0.663212
$705$	−42.0301	−1.58294
$706$	−25.9658	−0.977237
$707$	8.94756	0.336508
$708$	51.0092	1.91704
$709$	−18.8803	−0.709065	−0.354533	−	0.935044i	$-0.615360\pi$
$709$	−18.8803	−0.709065	−0.354533	+	0.935044i	$0.615360\pi$
$710$	25.2053	0.945938
$711$	−1.23230	−0.0462150
$712$	−40.1105	−1.50321
$713$	−3.45531	−0.129402
$714$	−8.36372	−0.313004
$715$	0	0
$716$	−80.9363	−3.02473
$717$	−3.90985	−0.146016
$718$	49.4218	1.84441
$719$	40.1580	1.49764	0.748820	−	0.662774i	$-0.230621\pi$
$719$	40.1580	1.49764	0.748820	+	0.662774i	$0.230621\pi$
$720$	−35.3780	−1.31846
$721$	1.67501	0.0623804
$722$	136.198	5.06875
$723$	−25.3903	−0.944274
$724$	−37.0383	−1.37652
$725$	−26.7978	−0.995244
$726$	11.6537	0.432508
$727$	32.0336	1.18806	0.594031	−	0.804442i	$-0.297536\pi$
$727$	32.0336	1.18806	0.594031	+	0.804442i	$0.297536\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−66.7704	−2.47128
$731$	−15.6301	−0.578100
$732$	19.6312	0.725590
$733$	48.3265	1.78498	0.892491	−	0.451066i	$-0.148956\pi$
$733$	48.3265	1.78498	0.892491	+	0.451066i	$0.148956\pi$
$734$	58.2487	2.15000
$735$	3.78706	0.139688
$736$	−39.0473	−1.43930
$737$	27.7106	1.02073
$738$	−8.71272	−0.320719
$739$	−35.7321	−1.31443	−0.657213	−	0.753705i	$-0.728265\pi$
$739$	−35.7321	−1.31443	−0.657213	+	0.753705i	$0.728265\pi$
$740$	−92.6296	−3.40513
$741$	0	0
$742$	3.47323	0.127506
$743$	−45.0092	−1.65123	−0.825613	−	0.564236i	$-0.809171\pi$
$743$	−45.0092	−1.65123	−0.825613	+	0.564236i	$0.809171\pi$
$744$	−6.30665	−0.231213
$745$	−32.1619	−1.17832
$746$	67.9847	2.48910
$747$	−11.0983	−0.406067
$748$	−39.2624	−1.43557
$749$	−0.846676	−0.0309369
$750$	42.8365	1.56417
$751$	−5.39425	−0.196839	−0.0984195	−	0.995145i	$-0.531379\pi$
$751$	−5.39425	−0.196839	−0.0984195	+	0.995145i	$0.531379\pi$
$752$	−103.679	−3.78077
$753$	−25.7708	−0.939140
$754$	0	0
$755$	53.8483	1.95974
$756$	−4.78706	−0.174104
$757$	13.7896	0.501191	0.250595	−	0.968092i	$-0.419374\pi$
$757$	13.7896	0.501191	0.250595	+	0.968092i	$0.419374\pi$
$758$	−31.2624	−1.13550
$759$	−10.1631	−0.368895
$760$	232.151	8.42100
$761$	−30.6674	−1.11169	−0.555846	−	0.831286i	$-0.687605\pi$
$761$	−30.6674	−1.11169	−0.555846	+	0.831286i	$0.687605\pi$
$762$	44.8232	1.62377
$763$	17.9949	0.651460
$764$	26.6836	0.965380
$765$	−12.1580	−0.439572
$766$	−12.9277	−0.467099
$767$	0	0
$768$	18.1701	0.655659
$769$	−48.6160	−1.75314	−0.876568	−	0.481278i	$-0.840173\pi$
$769$	−48.6160	−1.75314	−0.876568	+	0.481278i	$0.840173\pi$
$770$	25.2053	0.908336
$771$	5.87678	0.211647
$772$	36.2577	1.30494
$773$	18.6729	0.671617	0.335808	−	0.941930i	$-0.390991\pi$
$773$	18.6729	0.671617	0.335808	+	0.941930i	$0.390991\pi$
$774$	−12.6836	−0.455904
$775$	8.11415	0.291469
$776$	41.0832	1.47480
$777$	−5.10951	−0.183303
$778$	−46.5697	−1.66960
$779$	28.2354	1.01164
$780$	0	0
$781$	6.52677	0.233546
$782$	−33.2717	−1.18979
$783$	2.86858	0.102515
$784$	9.34181	0.333636
$785$	−31.8900	−1.13820
$786$	−43.4642	−1.55032
$787$	9.61751	0.342827	0.171414	−	0.985199i	$-0.445167\pi$
$787$	9.61751	0.342827	0.171414	+	0.985199i	$0.445167\pi$
$788$	−63.8802	−2.27564
$789$	10.2409	0.364587
$790$	12.1580	0.432561
$791$	2.86858	0.101995
$792$	−18.5497	−0.659134
$793$	0	0
$794$	−18.4168	−0.653588
$795$	5.04888	0.179065
$796$	80.8314	2.86499
$797$	3.73606	0.132338	0.0661691	−	0.997808i	$-0.478922\pi$
$797$	3.73606	0.132338	0.0661691	+	0.997808i	$0.478922\pi$
$798$	21.9949	0.778611
$799$	−35.6301	−1.26050
$800$	91.6955	3.24192
$801$	−5.52423	−0.195189
$802$	23.7601	0.838997
$803$	−17.2898	−0.610144
$804$	51.9237	1.83121
$805$	15.0653	0.530981
$806$	0	0
$807$	16.1396	0.568141
$808$	64.9668	2.28553
$809$	−10.1850	−0.358084	−0.179042	−	0.983841i	$-0.557300\pi$
$809$	−10.1850	−0.358084	−0.179042	+	0.983841i	$0.557300\pi$
$810$	−9.86604	−0.346657
$811$	6.21902	0.218379	0.109190	−	0.994021i	$-0.465174\pi$
$811$	6.21902	0.218379	0.109190	+	0.994021i	$0.465174\pi$
$812$	−13.7321	−0.481901
$813$	−12.2577	−0.429898
$814$	−34.0071	−1.19195
$815$	−14.2995	−0.500891
$816$	−29.9909	−1.04989
$817$	41.1040	1.43805
$818$	−47.5558	−1.66275
$819$	0	0
$820$	60.6294	2.11727
$821$	−55.4534	−1.93534	−0.967669	−	0.252224i	$-0.918838\pi$
$821$	−55.4534	−1.93534	−0.967669	+	0.252224i	$0.918838\pi$
$822$	−49.2731	−1.71860
$823$	20.4380	0.712425	0.356213	−	0.934405i	$-0.384068\pi$
$823$	20.4380	0.712425	0.356213	+	0.934405i	$0.384068\pi$
$824$	12.1619	0.423681
$825$	23.8660	0.830909
$826$	−27.7601	−0.965896
$827$	14.1289	0.491309	0.245655	−	0.969357i	$-0.420997\pi$
$827$	14.1289	0.491309	0.245655	+	0.969357i	$0.420997\pi$
$828$	−19.0434	−0.661803
$829$	−34.9159	−1.21268	−0.606340	−	0.795206i	$-0.707363\pi$
$829$	−34.9159	−1.21268	−0.606340	+	0.795206i	$0.707363\pi$
$830$	109.497	3.80069
$831$	9.81504	0.340480
$832$	0	0
$833$	3.21040	0.111234
$834$	−14.7845	−0.511946
$835$	33.4606	1.15795
$836$	103.252	3.57105
$837$	−0.868584	−0.0300226
$838$	35.6739	1.23233
$839$	−46.4437	−1.60341	−0.801707	−	0.597717i	$-0.796075\pi$
$839$	−46.4437	−1.60341	−0.801707	+	0.597717i	$0.796075\pi$
$840$	27.4972	0.948745
$841$	−20.7712	−0.716249
$842$	−88.0938	−3.03591
$843$	16.1910	0.557649
$844$	55.9938	1.92739
$845$	0	0
$846$	−28.9134	−0.994063
$847$	−4.47323	−0.153702
$848$	12.4544	0.427687
$849$	19.1482	0.657166
$850$	78.1323	2.67992
$851$	−20.3261	−0.696770
$852$	12.2298	0.418985
$853$	−41.4462	−1.41909	−0.709546	−	0.704659i	$-0.751100\pi$
$853$	−41.4462	−1.41909	−0.709546	+	0.704659i	$0.751100\pi$
$854$	−10.6836	−0.365586
$855$	31.9730	1.09345
$856$	−6.14758	−0.210120
$857$	−33.8666	−1.15686	−0.578431	−	0.815732i	$-0.696335\pi$
$857$	−33.8666	−1.15686	−0.578431	+	0.815732i	$0.696335\pi$
$858$	0	0
$859$	−37.2890	−1.27228	−0.636141	−	0.771573i	$-0.719470\pi$
$859$	−37.2890	−1.27228	−0.636141	+	0.771573i	$0.719470\pi$
$860$	88.2619	3.00971
$861$	3.34436	0.113975
$862$	52.9521	1.80356
$863$	38.7464	1.31894	0.659471	−	0.751730i	$-0.270781\pi$
$863$	38.7464	1.31894	0.659471	+	0.751730i	$0.270781\pi$
$864$	−9.81560	−0.333933
$865$	66.9363	2.27590
$866$	44.5765	1.51477
$867$	6.69335	0.227318
$868$	4.15796	0.141130
$869$	3.14823	0.106797
$870$	−28.3016	−0.959513
$871$	0	0
$872$	130.658	4.42464
$873$	5.65819	0.191501
$874$	87.4978	2.95966
$875$	−16.4427	−0.555865
$876$	−32.3974	−1.09461
$877$	51.8319	1.75024	0.875119	−	0.483908i	$-0.160783\pi$
$877$	51.8319	1.75024	0.875119	+	0.483908i	$0.160783\pi$
$878$	4.36372	0.147268
$879$	−24.6725	−0.832181
$880$	90.3821	3.04678
$881$	−20.7896	−0.700420	−0.350210	−	0.936671i	$-0.613890\pi$
$881$	−20.7896	−0.700420	−0.350210	+	0.936671i	$0.613890\pi$
$882$	2.60520	0.0877216
$883$	−17.5292	−0.589904	−0.294952	−	0.955512i	$-0.595304\pi$
$883$	−17.5292	−0.589904	−0.294952	+	0.955512i	$0.595304\pi$
$884$	0	0
$885$	−40.3535	−1.35647
$886$	−33.6261	−1.12969
$887$	9.53539	0.320167	0.160084	−	0.987103i	$-0.448824\pi$
$887$	9.53539	0.320167	0.160084	+	0.987103i	$0.448824\pi$
$888$	−37.0993	−1.24497
$889$	−17.2053	−0.577047
$890$	54.5022	1.82692
$891$	−2.55475	−0.0855875
$892$	20.3016	0.679746
$893$	93.7000	3.13555
$894$	−22.1249	−0.739967
$895$	64.0290	2.14025
$896$	−1.68672	−0.0563495
$897$	0	0
$898$	−55.1683	−1.84099
$899$	−2.49160	−0.0830997
$900$	44.7198	1.49066
$901$	4.28008	0.142590
$902$	22.2588	0.741139
$903$	4.86858	0.162016
$904$	20.8283	0.692740
$905$	29.3011	0.974002
$906$	37.0434	1.23068
$907$	−27.3270	−0.907378	−0.453689	−	0.891160i	$-0.649892\pi$
$907$	−27.3270	−0.907378	−0.453689	+	0.891160i	$0.649892\pi$
$908$	−8.26450	−0.274267
$909$	8.94756	0.296772
$910$	0	0
$911$	−38.9582	−1.29074	−0.645371	−	0.763869i	$-0.723297\pi$
$911$	−38.9582	−1.29074	−0.645371	+	0.763869i	$0.723297\pi$
$912$	78.8701	2.61165
$913$	28.3535	0.938365
$914$	−21.9246	−0.725201
$915$	−15.5303	−0.513416
$916$	−32.6876	−1.08003
$917$	16.6836	0.550942
$918$	−8.36372	−0.276044
$919$	9.94293	0.327987	0.163993	−	0.986461i	$-0.447562\pi$
$919$	9.94293	0.327987	0.163993	+	0.986461i	$0.447562\pi$
$920$	109.387	3.60637
$921$	−13.7540	−0.453209
$922$	4.59857	0.151446
$923$	0	0
$924$	12.2298	0.402330
$925$	47.7321	1.56942
$926$	−101.405	−3.33238
$927$	1.67501	0.0550144
$928$	−28.1569	−0.924294
$929$	−7.80854	−0.256190	−0.128095	−	0.991762i	$-0.540886\pi$
$929$	−7.80854	−0.256190	−0.128095	+	0.991762i	$0.540886\pi$
$930$	8.56948	0.281004
$931$	−8.44270	−0.276698
$932$	6.38207	0.209052
$933$	12.1580	0.398034
$934$	79.3398	2.59608
$935$	31.0606	1.01579
$936$	0	0
$937$	−9.59246	−0.313372	−0.156686	−	0.987648i	$-0.550081\pi$
$937$	−9.59246	−0.313372	−0.156686	+	0.987648i	$0.550081\pi$
$938$	−28.2577	−0.922648
$939$	−21.6699	−0.707171
$940$	201.200	6.56243
$941$	28.5043	0.929214	0.464607	−	0.885517i	$-0.346196\pi$
$941$	28.5043	0.929214	0.464607	+	0.885517i	$0.346196\pi$
$942$	−21.9378	−0.714773
$943$	13.3042	0.433243
$944$	−99.5430	−3.23985
$945$	3.78706	0.123193
$946$	32.4036	1.05353
$947$	−47.8997	−1.55653	−0.778265	−	0.627936i	$-0.783900\pi$
$947$	−47.8997	−1.55653	−0.778265	+	0.627936i	$0.783900\pi$
$948$	5.89911	0.191594
$949$	0	0
$950$	−205.472	−6.66640
$951$	29.3780	0.952647
$952$	23.3102	0.755487
$953$	−32.5181	−1.05337	−0.526683	−	0.850062i	$-0.676564\pi$
$953$	−32.5181	−1.05337	−0.526683	+	0.850062i	$0.676564\pi$
$954$	3.47323	0.112450
$955$	−21.1095	−0.683088
$956$	18.7167	0.605341
$957$	−7.32853	−0.236898
$958$	9.23949	0.298514
$959$	18.9134	0.610745
$960$	26.0851	0.841892
$961$	−30.2456	−0.975663
$962$	0	0
$963$	−0.846676	−0.0272838
$964$	121.545	3.91469
$965$	−28.6836	−0.923359
$966$	10.3637	0.333447
$967$	18.0387	0.580086	0.290043	−	0.957014i	$-0.406330\pi$
$967$	18.0387	0.580086	0.290043	+	0.957014i	$0.406330\pi$
$968$	−32.4794	−1.04393
$969$	27.1044	0.870719
$970$	−55.8239	−1.79240
$971$	30.2190	0.969774	0.484887	−	0.874577i	$-0.338861\pi$
$971$	30.2190	0.969774	0.484887	+	0.874577i	$0.338861\pi$
$972$	−4.78706	−0.153545
$973$	5.67501	0.181932
$974$	104.181	3.33819
$975$	0	0
$976$	−38.3097	−1.22626
$977$	−38.4652	−1.23061	−0.615305	−	0.788289i	$-0.710967\pi$
$977$	−38.4652	−1.23061	−0.615305	+	0.788289i	$0.710967\pi$
$978$	−9.83695	−0.314551
$979$	14.1130	0.451055
$980$	−18.1289	−0.579106
$981$	17.9949	0.574533
$982$	25.2664	0.806282
$983$	−12.1742	−0.388297	−0.194149	−	0.980972i	$-0.562194\pi$
$983$	−12.1742	−0.388297	−0.194149	+	0.980972i	$0.562194\pi$
$984$	24.2828	0.774109
$985$	50.5359	1.61021
$986$	−23.9920	−0.764062
$987$	11.0983	0.353264
$988$	0	0
$989$	19.3677	0.615856
$990$	25.2053	0.801077
$991$	14.4982	0.460552	0.230276	−	0.973125i	$-0.426037\pi$
$991$	14.4982	0.460552	0.230276	+	0.973125i	$0.426037\pi$
$992$	8.52567	0.270690
$993$	−23.9124	−0.758836
$994$	−6.65564	−0.211104
$995$	−63.9460	−2.02722
$996$	53.1284	1.68344
$997$	−9.35086	−0.296145	−0.148072	−	0.988977i	$-0.547307\pi$
$997$	−9.35086	−0.296145	−0.148072	+	0.988977i	$0.547307\pi$
$998$	62.6124	1.98196
$999$	−5.10951	−0.161658

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.v.1.4		4
13.5	odd	4		273.2.c.c.64.1	✓	8
13.8	odd	4		273.2.c.c.64.8	yes	8
13.12	even	2		3549.2.a.x.1.1		4
39.5	even	4		819.2.c.d.64.8		8
39.8	even	4		819.2.c.d.64.1		8
52.31	even	4		4368.2.h.q.337.8		8
52.47	even	4		4368.2.h.q.337.1		8
91.34	even	4		1911.2.c.l.883.8		8
91.83	even	4		1911.2.c.l.883.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.c.c.64.1	✓	8	13.5	odd	4
273.2.c.c.64.8	yes	8	13.8	odd	4
819.2.c.d.64.1		8	39.8	even	4
819.2.c.d.64.8		8	39.5	even	4
1911.2.c.l.883.1		8	91.83	even	4
1911.2.c.l.883.8		8	91.34	even	4
3549.2.a.v.1.4		4	1.1	even	1	trivial
3549.2.a.x.1.1		4	13.12	even	2
4368.2.h.q.337.1		8	52.47	even	4
4368.2.h.q.337.8		8	52.31	even	4

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)

\(f(q)\)	\(=\)	\(q+2.60520 q^{2} -1.00000 q^{3} +4.78706 q^{4} -3.78706 q^{5} -2.60520 q^{6} +1.00000 q^{7} +7.26084 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.60520 q^{2} -1.00000 q^{3} +4.78706 q^{4} -3.78706 q^{5} -2.60520 q^{6} +1.00000 q^{7} +7.26084 q^{8} +1.00000 q^{9} -9.86604 q^{10} -2.55475 q^{11} -4.78706 q^{12} +2.60520 q^{14} +3.78706 q^{15} +9.34181 q^{16} +3.21040 q^{17} +2.60520 q^{18} -8.44270 q^{19} -18.1289 q^{20} -1.00000 q^{21} -6.65564 q^{22} -3.97809 q^{23} -7.26084 q^{24} +9.34181 q^{25} -1.00000 q^{27} +4.78706 q^{28} -2.86858 q^{29} +9.86604 q^{30} +0.868584 q^{31} +9.81560 q^{32} +2.55475 q^{33} +8.36372 q^{34} -3.78706 q^{35} +4.78706 q^{36} +5.10951 q^{37} -21.9949 q^{38} -27.4972 q^{40} -3.34436 q^{41} -2.60520 q^{42} -4.86858 q^{43} -12.2298 q^{44} -3.78706 q^{45} -10.3637 q^{46} -11.0983 q^{47} -9.34181 q^{48} +1.00000 q^{49} +24.3373 q^{50} -3.21040 q^{51} +1.33319 q^{53} -2.60520 q^{54} +9.67501 q^{55} +7.26084 q^{56} +8.44270 q^{57} -7.47323 q^{58} -10.6556 q^{59} +18.1289 q^{60} -4.10089 q^{61} +2.26283 q^{62} +1.00000 q^{63} +6.88795 q^{64} +6.65564 q^{66} -10.8467 q^{67} +15.3684 q^{68} +3.97809 q^{69} -9.86604 q^{70} -2.55475 q^{71} +7.26084 q^{72} +6.76770 q^{73} +13.3113 q^{74} -9.34181 q^{75} -40.4157 q^{76} -2.55475 q^{77} -1.23230 q^{79} -35.3780 q^{80} +1.00000 q^{81} -8.71272 q^{82} -11.0983 q^{83} -4.78706 q^{84} -12.1580 q^{85} -12.6836 q^{86} +2.86858 q^{87} -18.5497 q^{88} -5.52423 q^{89} -9.86604 q^{90} -19.0434 q^{92} -0.868584 q^{93} -28.9134 q^{94} +31.9730 q^{95} -9.81560 q^{96} +5.65819 q^{97} +2.60520 q^{98} -2.55475 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 4 q^{3} + 7 q^{4} - 3 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - q^2 - 4 * q^3 + 7 * q^4 - 3 * q^5 + q^6 + 4 * q^7 + 3 * q^8 + 4 * q^9	\( 4 q - q^{2} - 4 q^{3} + 7 q^{4} - 3 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} + 4 q^{9} - 2 q^{10} - 2 q^{11} - 7 q^{12} - q^{14} + 3 q^{15} + 17 q^{16} - 10 q^{17} - q^{18} - 7 q^{19} - 40 q^{20} - 4 q^{21} - 12 q^{22} + 3 q^{23} - 3 q^{24} + 17 q^{25} - 4 q^{27} + 7 q^{28} - 9 q^{29} + 2 q^{30} + q^{31} + 5 q^{32} + 2 q^{33} + 32 q^{34} - 3 q^{35} + 7 q^{36} + 4 q^{37} - 18 q^{38} - 4 q^{40} - 28 q^{41} + q^{42} - 17 q^{43} - 10 q^{44} - 3 q^{45} - 40 q^{46} - 3 q^{47} - 17 q^{48} + 4 q^{49} + 11 q^{50} + 10 q^{51} - 5 q^{53} + q^{54} + 8 q^{55} + 3 q^{56} + 7 q^{57} - 12 q^{58} - 28 q^{59} + 40 q^{60} - 10 q^{61} + 14 q^{62} + 4 q^{63} + 9 q^{64} + 12 q^{66} - 22 q^{67} - 12 q^{68} - 3 q^{69} - 2 q^{70} - 2 q^{71} + 3 q^{72} + 31 q^{73} + 24 q^{74} - 17 q^{75} - 46 q^{76} - 2 q^{77} - q^{79} - 54 q^{80} + 4 q^{81} + 24 q^{82} - 3 q^{83} - 7 q^{84} + 2 q^{85} - 10 q^{86} + 9 q^{87} + 4 q^{88} - 5 q^{89} - 2 q^{90} + 28 q^{92} - q^{93} - 36 q^{94} + 39 q^{95} - 5 q^{96} + 43 q^{97} - q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q - q^2 - 4 * q^3 + 7 * q^4 - 3 * q^5 + q^6 + 4 * q^7 + 3 * q^8 + 4 * q^9 - 2 * q^10 - 2 * q^11 - 7 * q^12 - q^14 + 3 * q^15 + 17 * q^16 - 10 * q^17 - q^18 - 7 * q^19 - 40 * q^20 - 4 * q^21 - 12 * q^22 + 3 * q^23 - 3 * q^24 + 17 * q^25 - 4 * q^27 + 7 * q^28 - 9 * q^29 + 2 * q^30 + q^31 + 5 * q^32 + 2 * q^33 + 32 * q^34 - 3 * q^35 + 7 * q^36 + 4 * q^37 - 18 * q^38 - 4 * q^40 - 28 * q^41 + q^42 - 17 * q^43 - 10 * q^44 - 3 * q^45 - 40 * q^46 - 3 * q^47 - 17 * q^48 + 4 * q^49 + 11 * q^50 + 10 * q^51 - 5 * q^53 + q^54 + 8 * q^55 + 3 * q^56 + 7 * q^57 - 12 * q^58 - 28 * q^59 + 40 * q^60 - 10 * q^61 + 14 * q^62 + 4 * q^63 + 9 * q^64 + 12 * q^66 - 22 * q^67 - 12 * q^68 - 3 * q^69 - 2 * q^70 - 2 * q^71 + 3 * q^72 + 31 * q^73 + 24 * q^74 - 17 * q^75 - 46 * q^76 - 2 * q^77 - q^79 - 54 * q^80 + 4 * q^81 + 24 * q^82 - 3 * q^83 - 7 * q^84 + 2 * q^85 - 10 * q^86 + 9 * q^87 + 4 * q^88 - 5 * q^89 - 2 * q^90 + 28 * q^92 - q^93 - 36 * q^94 + 39 * q^95 - 5 * q^96 + 43 * q^97 - q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more