LMFDB - Embedded newform 3549.2.a.bf.1.3

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:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 11x^{7} + 8x^{6} + 37x^{5} - 18x^{4} - 41x^{3} + 12x^{2} + 6x - 1 $ x^9 - x^8 - 11x^7 + 8x^6 + 37x^5 - 18x^4 - 41x^3 + 12x^2 + 6*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.36450$ 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)

$f(q)$	$=$	$q-1.36450 q^{2} -1.00000 q^{3} -0.138150 q^{4} -3.32059 q^{5} +1.36450 q^{6} -1.00000 q^{7} +2.91750 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.36450 q^{2} -1.00000 q^{3} -0.138150 q^{4} -3.32059 q^{5} +1.36450 q^{6} -1.00000 q^{7} +2.91750 q^{8} +1.00000 q^{9} +4.53093 q^{10} +1.11378 q^{11} +0.138150 q^{12} +1.36450 q^{14} +3.32059 q^{15} -3.70462 q^{16} +0.665810 q^{17} -1.36450 q^{18} +3.22931 q^{19} +0.458738 q^{20} +1.00000 q^{21} -1.51975 q^{22} +5.07298 q^{23} -2.91750 q^{24} +6.02631 q^{25} -1.00000 q^{27} +0.138150 q^{28} -0.615375 q^{29} -4.53093 q^{30} -8.84343 q^{31} -0.780060 q^{32} -1.11378 q^{33} -0.908495 q^{34} +3.32059 q^{35} -0.138150 q^{36} -3.79560 q^{37} -4.40639 q^{38} -9.68781 q^{40} +0.916015 q^{41} -1.36450 q^{42} +8.09576 q^{43} -0.153868 q^{44} -3.32059 q^{45} -6.92207 q^{46} -13.0955 q^{47} +3.70462 q^{48} +1.00000 q^{49} -8.22287 q^{50} -0.665810 q^{51} +3.52862 q^{53} +1.36450 q^{54} -3.69841 q^{55} -2.91750 q^{56} -3.22931 q^{57} +0.839676 q^{58} +5.48952 q^{59} -0.458738 q^{60} -14.1106 q^{61} +12.0668 q^{62} -1.00000 q^{63} +8.47362 q^{64} +1.51975 q^{66} -3.47625 q^{67} -0.0919813 q^{68} -5.07298 q^{69} -4.53093 q^{70} +4.77075 q^{71} +2.91750 q^{72} -7.86139 q^{73} +5.17908 q^{74} -6.02631 q^{75} -0.446128 q^{76} -1.11378 q^{77} -11.8320 q^{79} +12.3015 q^{80} +1.00000 q^{81} -1.24990 q^{82} -16.4426 q^{83} -0.138150 q^{84} -2.21088 q^{85} -11.0466 q^{86} +0.615375 q^{87} +3.24946 q^{88} +16.1871 q^{89} +4.53093 q^{90} -0.700830 q^{92} +8.84343 q^{93} +17.8688 q^{94} -10.7232 q^{95} +0.780060 q^{96} -1.42122 q^{97} -1.36450 q^{98} +1.11378 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + q^{2} - 9 q^{3} + 5 q^{4} - 9 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + q^2 - 9 * q^3 + 5 * q^4 - 9 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 9 * q^9	$ 9 q + q^{2} - 9 q^{3} + 5 q^{4} - 9 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 9 q^{9} + q^{10} + q^{11} - 5 q^{12} - q^{14} + 9 q^{15} + 5 q^{16} + 11 q^{17} + q^{18} - 7 q^{19} - 23 q^{20} + 9 q^{21} - 3 q^{22} + 22 q^{23} - 6 q^{24} - 8 q^{25} - 9 q^{27} - 5 q^{28} + 11 q^{29} - q^{30} - 7 q^{31} + 18 q^{32} - q^{33} + 6 q^{34} + 9 q^{35} + 5 q^{36} + q^{37} - 6 q^{38} - 14 q^{40} - 16 q^{41} + q^{42} + 32 q^{43} - 18 q^{44} - 9 q^{45} + 9 q^{46} + 12 q^{47} - 5 q^{48} + 9 q^{49} - 10 q^{50} - 11 q^{51} + 13 q^{53} - q^{54} + 9 q^{55} - 6 q^{56} + 7 q^{57} - 4 q^{58} - 29 q^{59} + 23 q^{60} - 12 q^{61} + 30 q^{62} - 9 q^{63} + 6 q^{64} + 3 q^{66} + 20 q^{67} + 34 q^{68} - 22 q^{69} - q^{70} + 2 q^{71} + 6 q^{72} - q^{73} + 43 q^{74} + 8 q^{75} - 13 q^{76} - q^{77} + 3 q^{79} + 39 q^{80} + 9 q^{81} - 19 q^{82} - 24 q^{83} + 5 q^{84} - 15 q^{85} + 28 q^{86} - 11 q^{87} - 19 q^{88} - 11 q^{89} + q^{90} + 73 q^{92} + 7 q^{93} + 15 q^{94} + 39 q^{95} - 18 q^{96} - 20 q^{97} + q^{98} + q^{99}+O(q^{100}) $ 9 * q + q^2 - 9 * q^3 + 5 * q^4 - 9 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 9 * q^9 + q^10 + q^11 - 5 * q^12 - q^14 + 9 * q^15 + 5 * q^16 + 11 * q^17 + q^18 - 7 * q^19 - 23 * q^20 + 9 * q^21 - 3 * q^22 + 22 * q^23 - 6 * q^24 - 8 * q^25 - 9 * q^27 - 5 * q^28 + 11 * q^29 - q^30 - 7 * q^31 + 18 * q^32 - q^33 + 6 * q^34 + 9 * q^35 + 5 * q^36 + q^37 - 6 * q^38 - 14 * q^40 - 16 * q^41 + q^42 + 32 * q^43 - 18 * q^44 - 9 * q^45 + 9 * q^46 + 12 * q^47 - 5 * q^48 + 9 * q^49 - 10 * q^50 - 11 * q^51 + 13 * q^53 - q^54 + 9 * q^55 - 6 * q^56 + 7 * q^57 - 4 * q^58 - 29 * q^59 + 23 * q^60 - 12 * q^61 + 30 * q^62 - 9 * q^63 + 6 * q^64 + 3 * q^66 + 20 * q^67 + 34 * q^68 - 22 * q^69 - q^70 + 2 * q^71 + 6 * q^72 - q^73 + 43 * q^74 + 8 * q^75 - 13 * q^76 - q^77 + 3 * q^79 + 39 * q^80 + 9 * q^81 - 19 * q^82 - 24 * q^83 + 5 * q^84 - 15 * q^85 + 28 * q^86 - 11 * q^87 - 19 * q^88 - 11 * q^89 + q^90 + 73 * q^92 + 7 * q^93 + 15 * q^94 + 39 * q^95 - 18 * q^96 - 20 * q^97 + q^98 + 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 $

$2$	−1.36450	−0.964845	−0.482422	−	0.875939i	$-0.660243\pi$
$2$	−1.36450	−0.964845	−0.482422	+	0.875939i	$0.660243\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.138150	−0.0690748
$5$	−3.32059	−1.48501	−0.742506	−	0.669839i	$-0.766363\pi$
$5$	−3.32059	−1.48501	−0.742506	+	0.669839i	$0.766363\pi$
$6$	1.36450	0.557053
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.91750	1.03149
$9$	1.00000	0.333333
$10$	4.53093	1.43281
$11$	1.11378	0.335818	0.167909	−	0.985803i	$-0.446299\pi$
$11$	1.11378	0.335818	0.167909	+	0.985803i	$0.446299\pi$
$12$	0.138150	0.0398803
$13$	0	0
$13$	0	0
$14$	1.36450	0.364677
$15$	3.32059	0.857372
$16$	−3.70462	−0.926154
$17$	0.665810	0.161483	0.0807413	−	0.996735i	$-0.474271\pi$
$17$	0.665810	0.161483	0.0807413	+	0.996735i	$0.474271\pi$
$18$	−1.36450	−0.321615
$19$	3.22931	0.740855	0.370428	−	0.928861i	$-0.379211\pi$
$19$	3.22931	0.740855	0.370428	+	0.928861i	$0.379211\pi$
$20$	0.458738	0.102577
$21$	1.00000	0.218218
$22$	−1.51975	−0.324012
$23$	5.07298	1.05779	0.528895	−	0.848687i	$-0.322606\pi$
$23$	5.07298	1.05779	0.528895	+	0.848687i	$0.322606\pi$
$24$	−2.91750	−0.595532
$25$	6.02631	1.20526
$26$	0	0
$27$	−1.00000	−0.192450
$28$	0.138150	0.0261078
$29$	−0.615375	−0.114272	−0.0571361	−	0.998366i	$-0.518197\pi$
$29$	−0.615375	−0.114272	−0.0571361	+	0.998366i	$0.518197\pi$
$30$	−4.53093	−0.827231
$31$	−8.84343	−1.58833	−0.794163	−	0.607704i	$-0.792091\pi$
$31$	−8.84343	−1.58833	−0.794163	+	0.607704i	$0.792091\pi$
$32$	−0.780060	−0.137896
$33$	−1.11378	−0.193885
$34$	−0.908495	−0.155806
$35$	3.32059	0.561282
$36$	−0.138150	−0.0230249
$37$	−3.79560	−0.623992	−0.311996	−	0.950083i	$-0.600998\pi$
$37$	−3.79560	−0.623992	−0.311996	+	0.950083i	$0.600998\pi$
$38$	−4.40639	−0.714810
$39$	0	0
$40$	−9.68781	−1.53178
$41$	0.916015	0.143058	0.0715288	−	0.997439i	$-0.477212\pi$
$41$	0.916015	0.143058	0.0715288	+	0.997439i	$0.477212\pi$
$42$	−1.36450	−0.210546
$43$	8.09576	1.23459	0.617296	−	0.786731i	$-0.288228\pi$
$43$	8.09576	1.23459	0.617296	+	0.786731i	$0.288228\pi$
$44$	−0.153868	−0.0231965
$45$	−3.32059	−0.495004
$46$	−6.92207	−1.02060
$47$	−13.0955	−1.91018	−0.955090	−	0.296316i	$-0.904242\pi$
$47$	−13.0955	−1.91018	−0.955090	+	0.296316i	$0.904242\pi$
$48$	3.70462	0.534715
$49$	1.00000	0.142857
$50$	−8.22287	−1.16289
$51$	−0.665810	−0.0932320
$52$	0	0
$53$	3.52862	0.484694	0.242347	−	0.970190i	$-0.422083\pi$
$53$	3.52862	0.484694	0.242347	+	0.970190i	$0.422083\pi$
$54$	1.36450	0.185684
$55$	−3.69841	−0.498694
$56$	−2.91750	−0.389867
$57$	−3.22931	−0.427733
$58$	0.839676	0.110255
$59$	5.48952	0.714674	0.357337	−	0.933975i	$-0.383685\pi$
$59$	5.48952	0.714674	0.357337	+	0.933975i	$0.383685\pi$
$60$	−0.458738	−0.0592228
$61$	−14.1106	−1.80667	−0.903336	−	0.428934i	$-0.858889\pi$
$61$	−14.1106	−1.80667	−0.903336	+	0.428934i	$0.858889\pi$
$62$	12.0668	1.53249
$63$	−1.00000	−0.125988
$64$	8.47362	1.05920
$65$	0	0
$66$	1.51975	0.187069
$67$	−3.47625	−0.424691	−0.212345	−	0.977195i	$-0.568110\pi$
$67$	−3.47625	−0.424691	−0.212345	+	0.977195i	$0.568110\pi$
$68$	−0.0919813	−0.0111544
$69$	−5.07298	−0.610716
$70$	−4.53093	−0.541550
$71$	4.77075	0.566184	0.283092	−	0.959093i	$-0.408640\pi$
$71$	4.77075	0.566184	0.283092	+	0.959093i	$0.408640\pi$
$72$	2.91750	0.343830
$73$	−7.86139	−0.920106	−0.460053	−	0.887892i	$-0.652170\pi$
$73$	−7.86139	−0.920106	−0.460053	+	0.887892i	$0.652170\pi$
$74$	5.17908	0.602056
$75$	−6.02631	−0.695858
$76$	−0.446128	−0.0511744
$77$	−1.11378	−0.126927
$78$	0	0
$79$	−11.8320	−1.33120	−0.665601	−	0.746307i	$-0.731825\pi$
$79$	−11.8320	−1.33120	−0.665601	+	0.746307i	$0.731825\pi$
$80$	12.3015	1.37535
$81$	1.00000	0.111111
$82$	−1.24990	−0.138028
$83$	−16.4426	−1.80481	−0.902406	−	0.430887i	$-0.858201\pi$
$83$	−16.4426	−1.80481	−0.902406	+	0.430887i	$0.858201\pi$
$84$	−0.138150	−0.0150733
$85$	−2.21088	−0.239804
$86$	−11.0466	−1.19119
$87$	0.615375	0.0659751
$88$	3.24946	0.346393
$89$	16.1871	1.71583	0.857913	−	0.513796i	$-0.171761\pi$
$89$	16.1871	1.71583	0.857913	+	0.513796i	$0.171761\pi$
$90$	4.53093	0.477602
$91$	0	0
$92$	−0.700830	−0.0730666
$93$	8.84343	0.917021
$94$	17.8688	1.84303
$95$	−10.7232	−1.10018
$96$	0.780060	0.0796145
$97$	−1.42122	−0.144303	−0.0721516	−	0.997394i	$-0.522987\pi$
$97$	−1.42122	−0.144303	−0.0721516	+	0.997394i	$0.522987\pi$
$98$	−1.36450	−0.137835
$99$	1.11378	0.111939
$100$	−0.832531	−0.0832531
$101$	−0.720751	−0.0717174	−0.0358587	−	0.999357i	$-0.511417\pi$
$101$	−0.720751	−0.0717174	−0.0358587	+	0.999357i	$0.511417\pi$
$102$	0.908495	0.0899544
$103$	14.9632	1.47437	0.737186	−	0.675690i	$-0.236154\pi$
$103$	14.9632	1.47437	0.737186	+	0.675690i	$0.236154\pi$
$104$	0	0
$105$	−3.32059	−0.324056
$106$	−4.81479	−0.467654
$107$	11.6187	1.12323	0.561613	−	0.827400i	$-0.310181\pi$
$107$	11.6187	1.12323	0.561613	+	0.827400i	$0.310181\pi$
$108$	0.138150	0.0132934
$109$	−4.94550	−0.473693	−0.236846	−	0.971547i	$-0.576114\pi$
$109$	−4.94550	−0.473693	−0.236846	+	0.971547i	$0.576114\pi$
$110$	5.04647	0.481162
$111$	3.79560	0.360262
$112$	3.70462	0.350053
$113$	16.2144	1.52532	0.762661	−	0.646798i	$-0.223892\pi$
$113$	16.2144	1.52532	0.762661	+	0.646798i	$0.223892\pi$
$114$	4.40639	0.412696
$115$	−16.8453	−1.57083
$116$	0.0850137	0.00789332
$117$	0	0
$118$	−7.49043	−0.689550
$119$	−0.665810	−0.0610347
$120$	9.68781	0.884372
$121$	−9.75949	−0.887226
$122$	19.2538	1.74316
$123$	−0.916015	−0.0825943
$124$	1.22172	0.109713
$125$	−3.40794	−0.304815
$126$	1.36450	0.121559
$127$	−11.4819	−1.01886	−0.509429	−	0.860513i	$-0.670143\pi$
$127$	−11.4819	−1.01886	−0.509429	+	0.860513i	$0.670143\pi$
$128$	−10.0021	−0.884070
$129$	−8.09576	−0.712792
$130$	0	0
$131$	−18.3232	−1.60090	−0.800451	−	0.599398i	$-0.795407\pi$
$131$	−18.3232	−1.60090	−0.800451	+	0.599398i	$0.795407\pi$
$132$	0.153868	0.0133925
$133$	−3.22931	−0.280017
$134$	4.74332	0.409761
$135$	3.32059	0.285791
$136$	1.94250	0.166568
$137$	−13.5829	−1.16047	−0.580233	−	0.814451i	$-0.697038\pi$
$137$	−13.5829	−1.16047	−0.580233	+	0.814451i	$0.697038\pi$
$138$	6.92207	0.589246
$139$	−0.226772	−0.0192345	−0.00961726	−	0.999954i	$-0.503061\pi$
$139$	−0.226772	−0.0192345	−0.00961726	+	0.999954i	$0.503061\pi$
$140$	−0.458738	−0.0387704
$141$	13.0955	1.10284
$142$	−6.50967	−0.546279
$143$	0	0
$144$	−3.70462	−0.308718
$145$	2.04341	0.169696
$146$	10.7268	0.887759
$147$	−1.00000	−0.0824786
$148$	0.524360	0.0431021
$149$	7.17188	0.587543	0.293772	−	0.955876i	$-0.405089\pi$
$149$	7.17188	0.587543	0.293772	+	0.955876i	$0.405089\pi$
$150$	8.22287	0.671395
$151$	−7.19280	−0.585342	−0.292671	−	0.956213i	$-0.594544\pi$
$151$	−7.19280	−0.585342	−0.292671	+	0.956213i	$0.594544\pi$
$152$	9.42151	0.764186
$153$	0.665810	0.0538275
$154$	1.51975	0.122465
$155$	29.3654	2.35868
$156$	0	0
$157$	7.18613	0.573515	0.286758	−	0.958003i	$-0.407423\pi$
$157$	7.18613	0.573515	0.286758	+	0.958003i	$0.407423\pi$
$158$	16.1447	1.28440
$159$	−3.52862	−0.279838
$160$	2.59026	0.204778
$161$	−5.07298	−0.399807
$162$	−1.36450	−0.107205
$163$	−22.1597	−1.73568	−0.867839	−	0.496845i	$-0.834492\pi$
$163$	−22.1597	−1.73568	−0.867839	+	0.496845i	$0.834492\pi$
$164$	−0.126547	−0.00988167
$165$	3.69841	0.287921
$166$	22.4359	1.74136
$167$	14.9897	1.15994	0.579969	−	0.814638i	$-0.303064\pi$
$167$	14.9897	1.15994	0.579969	+	0.814638i	$0.303064\pi$
$168$	2.91750	0.225090
$169$	0	0
$170$	3.01674	0.231373
$171$	3.22931	0.246952
$172$	−1.11843	−0.0852791
$173$	0.425335	0.0323376	0.0161688	−	0.999869i	$-0.494853\pi$
$173$	0.425335	0.0323376	0.0161688	+	0.999869i	$0.494853\pi$
$174$	−0.839676	−0.0636557
$175$	−6.02631	−0.455546
$176$	−4.12614	−0.311019
$177$	−5.48952	−0.412617
$178$	−22.0872	−1.65550
$179$	13.7825	1.03015	0.515076	−	0.857145i	$-0.327764\pi$
$179$	13.7825	1.03015	0.515076	+	0.857145i	$0.327764\pi$
$180$	0.458738	0.0341923
$181$	21.8738	1.62587	0.812933	−	0.582357i	$-0.197870\pi$
$181$	21.8738	1.62587	0.812933	+	0.582357i	$0.197870\pi$
$182$	0	0
$183$	14.1106	1.04308
$184$	14.8004	1.09110
$185$	12.6036	0.926636
$186$	−12.0668	−0.884783
$187$	0.741567	0.0542287
$188$	1.80914	0.131945
$189$	1.00000	0.0727393
$190$	14.6318	1.06150
$191$	10.8936	0.788231	0.394115	−	0.919061i	$-0.371051\pi$
$191$	10.8936	0.788231	0.394115	+	0.919061i	$0.371051\pi$
$192$	−8.47362	−0.611531
$193$	17.0935	1.23042	0.615208	−	0.788365i	$-0.289072\pi$
$193$	17.0935	1.23042	0.615208	+	0.788365i	$0.289072\pi$
$194$	1.93925	0.139230
$195$	0	0
$196$	−0.138150	−0.00986782
$197$	4.58665	0.326785	0.163393	−	0.986561i	$-0.447756\pi$
$197$	4.58665	0.326785	0.163393	+	0.986561i	$0.447756\pi$
$198$	−1.51975	−0.108004
$199$	6.08803	0.431569	0.215785	−	0.976441i	$-0.430769\pi$
$199$	6.08803	0.431569	0.215785	+	0.976441i	$0.430769\pi$
$200$	17.5817	1.24322
$201$	3.47625	0.245195
$202$	0.983462	0.0691961
$203$	0.615375	0.0431908
$204$	0.0919813	0.00643998
$205$	−3.04171	−0.212442
$206$	−20.4173	−1.42254
$207$	5.07298	0.352597
$208$	0	0
$209$	3.59675	0.248793
$210$	4.53093	0.312664
$211$	10.3803	0.714606	0.357303	−	0.933988i	$-0.383696\pi$
$211$	10.3803	0.714606	0.357303	+	0.933988i	$0.383696\pi$
$212$	−0.487478	−0.0334801
$213$	−4.77075	−0.326886
$214$	−15.8537	−1.08374
$215$	−26.8827	−1.83338
$216$	−2.91750	−0.198511
$217$	8.84343	0.600331
$218$	6.74811	0.457040
$219$	7.86139	0.531223
$220$	0.510934	0.0344471
$221$	0	0
$222$	−5.17908	−0.347597
$223$	−12.7655	−0.854840	−0.427420	−	0.904053i	$-0.640577\pi$
$223$	−12.7655	−0.854840	−0.427420	+	0.904053i	$0.640577\pi$
$224$	0.780060	0.0521199
$225$	6.02631	0.401754
$226$	−22.1245	−1.47170
$227$	13.3301	0.884747	0.442374	−	0.896831i	$-0.354136\pi$
$227$	13.3301	0.884747	0.442374	+	0.896831i	$0.354136\pi$
$228$	0.446128	0.0295456
$229$	−9.63903	−0.636965	−0.318482	−	0.947929i	$-0.603173\pi$
$229$	−9.63903	−0.636965	−0.318482	+	0.947929i	$0.603173\pi$
$230$	22.9853	1.51561
$231$	1.11378	0.0732815
$232$	−1.79535	−0.117871
$233$	−22.0553	−1.44489	−0.722444	−	0.691429i	$-0.756981\pi$
$233$	−22.0553	−1.44489	−0.722444	+	0.691429i	$0.756981\pi$
$234$	0	0
$235$	43.4849	2.83664
$236$	−0.758374	−0.0493659
$237$	11.8320	0.768570
$238$	0.908495	0.0588890
$239$	23.6972	1.53285	0.766424	−	0.642335i	$-0.222034\pi$
$239$	23.6972	1.53285	0.766424	+	0.642335i	$0.222034\pi$
$240$	−12.3015	−0.794059
$241$	17.5586	1.13105	0.565525	−	0.824731i	$-0.308673\pi$
$241$	17.5586	1.13105	0.565525	+	0.824731i	$0.308673\pi$
$242$	13.3168	0.856036
$243$	−1.00000	−0.0641500
$244$	1.94937	0.124795
$245$	−3.32059	−0.212145
$246$	1.24990	0.0796907
$247$	0	0
$248$	−25.8007	−1.63834
$249$	16.4426	1.04201
$250$	4.65012	0.294099
$251$	30.2065	1.90662	0.953310	−	0.301994i	$-0.0976522\pi$
$251$	30.2065	1.90662	0.953310	+	0.301994i	$0.0976522\pi$
$252$	0.138150	0.00870260
$253$	5.65020	0.355225
$254$	15.6671	0.983039
$255$	2.21088	0.138451
$256$	−3.29940	−0.206213
$257$	−4.98163	−0.310746	−0.155373	−	0.987856i	$-0.549658\pi$
$257$	−4.98163	−0.310746	−0.155373	+	0.987856i	$0.549658\pi$
$258$	11.0466	0.687733
$259$	3.79560	0.235847
$260$	0	0
$261$	−0.615375	−0.0380907
$262$	25.0019	1.54462
$263$	−12.5614	−0.774571	−0.387286	−	0.921960i	$-0.626587\pi$
$263$	−12.5614	−0.774571	−0.387286	+	0.921960i	$0.626587\pi$
$264$	−3.24946	−0.199990
$265$	−11.7171	−0.719776
$266$	4.40639	0.270173
$267$	−16.1871	−0.990632
$268$	0.480242	0.0293354
$269$	−1.45811	−0.0889028	−0.0444514	−	0.999012i	$-0.514154\pi$
$269$	−1.45811	−0.0889028	−0.0444514	+	0.999012i	$0.514154\pi$
$270$	−4.53093	−0.275744
$271$	−15.5702	−0.945820	−0.472910	−	0.881111i	$-0.656797\pi$
$271$	−15.5702	−0.945820	−0.472910	+	0.881111i	$0.656797\pi$
$272$	−2.46657	−0.149558
$273$	0	0
$274$	18.5338	1.11967
$275$	6.71199	0.404748
$276$	0.700830	0.0421850
$277$	−18.0174	−1.08256	−0.541280	−	0.840842i	$-0.682060\pi$
$277$	−18.0174	−1.08256	−0.541280	+	0.840842i	$0.682060\pi$
$278$	0.309429	0.0185583
$279$	−8.84343	−0.529442
$280$	9.68781	0.578957
$281$	25.8821	1.54400	0.771999	−	0.635624i	$-0.219257\pi$
$281$	25.8821	1.54400	0.771999	+	0.635624i	$0.219257\pi$
$282$	−17.8688	−1.06407
$283$	9.98839	0.593748	0.296874	−	0.954917i	$-0.404056\pi$
$283$	9.98839	0.593748	0.296874	+	0.954917i	$0.404056\pi$
$284$	−0.659077	−0.0391090
$285$	10.7232	0.635189
$286$	0	0
$287$	−0.916015	−0.0540707
$288$	−0.780060	−0.0459655
$289$	−16.5567	−0.973923
$290$	−2.78822	−0.163730
$291$	1.42122	0.0833135
$292$	1.08605	0.0635561
$293$	−3.60381	−0.210537	−0.105268	−	0.994444i	$-0.533570\pi$
$293$	−3.60381	−0.210537	−0.105268	+	0.994444i	$0.533570\pi$
$294$	1.36450	0.0795790
$295$	−18.2284	−1.06130
$296$	−11.0736	−0.643642
$297$	−1.11378	−0.0646282
$298$	−9.78600	−0.566888
$299$	0	0
$300$	0.832531	0.0480662
$301$	−8.09576	−0.466632
$302$	9.81455	0.564764
$303$	0.720751	0.0414061
$304$	−11.9634	−0.686146
$305$	46.8553	2.68293
$306$	−0.908495	−0.0519352
$307$	17.4426	0.995500	0.497750	−	0.867321i	$-0.334160\pi$
$307$	17.4426	0.995500	0.497750	+	0.867321i	$0.334160\pi$
$308$	0.153868	0.00876747
$309$	−14.9632	−0.851229
$310$	−40.0690	−2.27576
$311$	−22.3025	−1.26466	−0.632330	−	0.774699i	$-0.717901\pi$
$311$	−22.3025	−1.26466	−0.632330	+	0.774699i	$0.717901\pi$
$312$	0	0
$313$	0.792995	0.0448227	0.0224114	−	0.999749i	$-0.492866\pi$
$313$	0.792995	0.0448227	0.0224114	+	0.999749i	$0.492866\pi$
$314$	−9.80545	−0.553353
$315$	3.32059	0.187094
$316$	1.63458	0.0919525
$317$	8.48350	0.476481	0.238240	−	0.971206i	$-0.423429\pi$
$317$	8.48350	0.476481	0.238240	+	0.971206i	$0.423429\pi$
$318$	4.81479	0.270000
$319$	−0.685393	−0.0383747
$320$	−28.1374	−1.57293
$321$	−11.6187	−0.648495
$322$	6.92207	0.385752
$323$	2.15011	0.119635
$324$	−0.138150	−0.00767497
$325$	0	0
$326$	30.2368	1.67466
$327$	4.94550	0.273487
$328$	2.67247	0.147563
$329$	13.0955	0.721980
$330$	−5.04647	−0.277799
$331$	33.5170	1.84226	0.921130	−	0.389256i	$-0.127268\pi$
$331$	33.5170	1.84226	0.921130	+	0.389256i	$0.127268\pi$
$332$	2.27154	0.124667
$333$	−3.79560	−0.207997
$334$	−20.4534	−1.11916
$335$	11.5432	0.630671
$336$	−3.70462	−0.202103
$337$	−19.4227	−1.05802	−0.529012	−	0.848614i	$-0.677437\pi$
$337$	−19.4227	−1.05802	−0.529012	+	0.848614i	$0.677437\pi$
$338$	0	0
$339$	−16.2144	−0.880645
$340$	0.305432	0.0165644
$341$	−9.84965	−0.533389
$342$	−4.40639	−0.238270
$343$	−1.00000	−0.0539949
$344$	23.6194	1.27347
$345$	16.8453	0.906920
$346$	−0.580368	−0.0312008
$347$	−11.1748	−0.599896	−0.299948	−	0.953956i	$-0.596969\pi$
$347$	−11.1748	−0.599896	−0.299948	+	0.953956i	$0.596969\pi$
$348$	−0.0850137	−0.00455721
$349$	−36.8109	−1.97044	−0.985222	−	0.171281i	$-0.945209\pi$
$349$	−36.8109	−1.97044	−0.985222	+	0.171281i	$0.945209\pi$
$350$	8.22287	0.439531
$351$	0	0
$352$	−0.868817	−0.0463081
$353$	−17.5115	−0.932041	−0.466021	−	0.884774i	$-0.654313\pi$
$353$	−17.5115	−0.932041	−0.466021	+	0.884774i	$0.654313\pi$
$354$	7.49043	0.398112
$355$	−15.8417	−0.840790
$356$	−2.23623	−0.118520
$357$	0.665810	0.0352384
$358$	−18.8062	−0.993936
$359$	−8.15731	−0.430527	−0.215263	−	0.976556i	$-0.569061\pi$
$359$	−8.15731	−0.430527	−0.215263	+	0.976556i	$0.569061\pi$
$360$	−9.68781	−0.510592
$361$	−8.57154	−0.451133
$362$	−29.8467	−1.56871
$363$	9.75949	0.512240
$364$	0	0
$365$	26.1044	1.36637
$366$	−19.2538	−1.00641
$367$	15.8536	0.827552	0.413776	−	0.910379i	$-0.364210\pi$
$367$	15.8536	0.827552	0.413776	+	0.910379i	$0.364210\pi$
$368$	−18.7935	−0.979677
$369$	0.916015	0.0476859
$370$	−17.1976	−0.894060
$371$	−3.52862	−0.183197
$372$	−1.22172	−0.0633430
$373$	11.3075	0.585482	0.292741	−	0.956192i	$-0.405433\pi$
$373$	11.3075	0.585482	0.292741	+	0.956192i	$0.405433\pi$
$374$	−1.01187	−0.0523223
$375$	3.40794	0.175985
$376$	−38.2062	−1.97033
$377$	0	0
$378$	−1.36450	−0.0701821
$379$	−14.8591	−0.763262	−0.381631	−	0.924315i	$-0.624638\pi$
$379$	−14.8591	−0.763262	−0.381631	+	0.924315i	$0.624638\pi$
$380$	1.48141	0.0759946
$381$	11.4819	0.588238
$382$	−14.8642	−0.760520
$383$	−19.5528	−0.999101	−0.499551	−	0.866285i	$-0.666502\pi$
$383$	−19.5528	−0.999101	−0.499551	+	0.866285i	$0.666502\pi$
$384$	10.0021	0.510418
$385$	3.69841	0.188489
$386$	−23.3240	−1.18716
$387$	8.09576	0.411531
$388$	0.196341	0.00996771
$389$	15.4987	0.785815	0.392907	−	0.919578i	$-0.371469\pi$
$389$	15.4987	0.785815	0.392907	+	0.919578i	$0.371469\pi$
$390$	0	0
$391$	3.37764	0.170815
$392$	2.91750	0.147356
$393$	18.3232	0.924281
$394$	−6.25847	−0.315297
$395$	39.2892	1.97685
$396$	−0.153868	−0.00773218
$397$	23.2126	1.16501	0.582503	−	0.812828i	$-0.302073\pi$
$397$	23.2126	1.16501	0.582503	+	0.812828i	$0.302073\pi$
$398$	−8.30710	−0.416397
$399$	3.22931	0.161668
$400$	−22.3251	−1.11626
$401$	39.2538	1.96024	0.980121	−	0.198403i	$-0.0635754\pi$
$401$	39.2538	1.96024	0.980121	+	0.198403i	$0.0635754\pi$
$402$	−4.74332	−0.236576
$403$	0	0
$404$	0.0995714	0.00495386
$405$	−3.32059	−0.165001
$406$	−0.839676	−0.0416724
$407$	−4.22747	−0.209548
$408$	−1.94250	−0.0961680
$409$	19.5916	0.968743	0.484371	−	0.874862i	$-0.339048\pi$
$409$	19.5916	0.968743	0.484371	+	0.874862i	$0.339048\pi$
$410$	4.15040	0.204974
$411$	13.5829	0.669995
$412$	−2.06716	−0.101842
$413$	−5.48952	−0.270121
$414$	−6.92207	−0.340201
$415$	54.5992	2.68017
$416$	0	0
$417$	0.226772	0.0111051
$418$	−4.90775	−0.240046
$419$	8.42940	0.411803	0.205902	−	0.978573i	$-0.433987\pi$
$419$	8.42940	0.411803	0.205902	+	0.978573i	$0.433987\pi$
$420$	0.458738	0.0223841
$421$	−2.84921	−0.138862	−0.0694309	−	0.997587i	$-0.522118\pi$
$421$	−2.84921	−0.138862	−0.0694309	+	0.997587i	$0.522118\pi$
$422$	−14.1638	−0.689484
$423$	−13.0955	−0.636727
$424$	10.2948	0.499957
$425$	4.01237	0.194629
$426$	6.50967	0.315394
$427$	14.1106	0.682858
$428$	−1.60512	−0.0775865
$429$	0	0
$430$	36.6813	1.76893
$431$	−35.8018	−1.72451	−0.862257	−	0.506472i	$-0.830950\pi$
$431$	−35.8018	−1.72451	−0.862257	+	0.506472i	$0.830950\pi$
$432$	3.70462	0.178238
$433$	8.92560	0.428937	0.214468	−	0.976731i	$-0.431198\pi$
$433$	8.92560	0.428937	0.214468	+	0.976731i	$0.431198\pi$
$434$	−12.0668	−0.579226
$435$	−2.04341	−0.0979738
$436$	0.683218	0.0327202
$437$	16.3823	0.783670
$438$	−10.7268	−0.512548
$439$	−4.92169	−0.234899	−0.117450	−	0.993079i	$-0.537472\pi$
$439$	−4.92169	−0.234899	−0.117450	+	0.993079i	$0.537472\pi$
$440$	−10.7901	−0.514398
$441$	1.00000	0.0476190
$442$	0	0
$443$	−4.96252	−0.235776	−0.117888	−	0.993027i	$-0.537612\pi$
$443$	−4.96252	−0.235776	−0.117888	+	0.993027i	$0.537612\pi$
$444$	−0.524360	−0.0248850
$445$	−53.7506	−2.54802
$446$	17.4185	0.824788
$447$	−7.17188	−0.339218
$448$	−8.47362	−0.400341
$449$	17.9792	0.848492	0.424246	−	0.905547i	$-0.360539\pi$
$449$	17.9792	0.848492	0.424246	+	0.905547i	$0.360539\pi$
$450$	−8.22287	−0.387630
$451$	1.02024	0.0480413
$452$	−2.24001	−0.105361
$453$	7.19280	0.337947
$454$	−18.1888	−0.853644
$455$	0	0
$456$	−9.42151	−0.441203
$457$	27.8074	1.30078	0.650389	−	0.759602i	$-0.274606\pi$
$457$	27.8074	1.30078	0.650389	+	0.759602i	$0.274606\pi$
$458$	13.1524	0.614572
$459$	−0.665810	−0.0310773
$460$	2.32717	0.108505
$461$	−16.5862	−0.772496	−0.386248	−	0.922395i	$-0.626229\pi$
$461$	−16.5862	−0.772496	−0.386248	+	0.922395i	$0.626229\pi$
$462$	−1.51975	−0.0707053
$463$	42.4947	1.97490	0.987449	−	0.157940i	$-0.0504853\pi$
$463$	42.4947	1.97490	0.987449	+	0.157940i	$0.0504853\pi$
$464$	2.27973	0.105834
$465$	−29.3654	−1.36179
$466$	30.0943	1.39409
$467$	−1.30217	−0.0602575	−0.0301287	−	0.999546i	$-0.509592\pi$
$467$	−1.30217	−0.0602575	−0.0301287	+	0.999546i	$0.509592\pi$
$468$	0	0
$469$	3.47625	0.160518
$470$	−59.3349	−2.73692
$471$	−7.18613	−0.331119
$472$	16.0157	0.737180
$473$	9.01691	0.414598
$474$	−16.1447	−0.741551
$475$	19.4608	0.892924
$476$	0.0919813	0.00421595
$477$	3.52862	0.161565
$478$	−32.3348	−1.47896
$479$	8.28495	0.378549	0.189274	−	0.981924i	$-0.439386\pi$
$479$	8.28495	0.378549	0.189274	+	0.981924i	$0.439386\pi$
$480$	−2.59026	−0.118229
$481$	0	0
$482$	−23.9587	−1.09129
$483$	5.07298	0.230829
$484$	1.34827	0.0612849
$485$	4.71929	0.214292
$486$	1.36450	0.0618948
$487$	43.5629	1.97402	0.987011	−	0.160651i	$-0.0513595\pi$
$487$	43.5629	1.97402	0.987011	+	0.160651i	$0.0513595\pi$
$488$	−41.1675	−1.86357
$489$	22.1597	1.00209
$490$	4.53093	0.204687
$491$	41.8051	1.88664	0.943318	−	0.331890i	$-0.107686\pi$
$491$	41.8051	1.88664	0.943318	+	0.331890i	$0.107686\pi$
$492$	0.126547	0.00570518
$493$	−0.409722	−0.0184530
$494$	0	0
$495$	−3.69841	−0.166231
$496$	32.7615	1.47103
$497$	−4.77075	−0.213997
$498$	−22.4359	−1.00538
$499$	6.28962	0.281562	0.140781	−	0.990041i	$-0.455039\pi$
$499$	6.28962	0.281562	0.140781	+	0.990041i	$0.455039\pi$
$500$	0.470805	0.0210550
$501$	−14.9897	−0.669691
$502$	−41.2167	−1.83959
$503$	18.5950	0.829109	0.414554	−	0.910025i	$-0.363937\pi$
$503$	18.5950	0.829109	0.414554	+	0.910025i	$0.363937\pi$
$504$	−2.91750	−0.129956
$505$	2.39332	0.106501
$506$	−7.70968	−0.342737
$507$	0	0
$508$	1.58622	0.0703773
$509$	2.87537	0.127448	0.0637242	−	0.997968i	$-0.479702\pi$
$509$	2.87537	0.127448	0.0637242	+	0.997968i	$0.479702\pi$
$510$	−3.01674	−0.133583
$511$	7.86139	0.347767
$512$	24.5062	1.08303
$513$	−3.22931	−0.142578
$514$	6.79742	0.299821
$515$	−49.6868	−2.18946
$516$	1.11843	0.0492359
$517$	−14.5856	−0.641473
$518$	−5.17908	−0.227556
$519$	−0.425335	−0.0186701
$520$	0	0
$521$	18.3937	0.805843	0.402922	−	0.915234i	$-0.367995\pi$
$521$	18.3937	0.805843	0.402922	+	0.915234i	$0.367995\pi$
$522$	0.839676	0.0367516
$523$	2.24583	0.0982031	0.0491016	−	0.998794i	$-0.484364\pi$
$523$	2.24583	0.0982031	0.0491016	+	0.998794i	$0.484364\pi$
$524$	2.53134	0.110582
$525$	6.02631	0.263010
$526$	17.1400	0.747341
$527$	−5.88804	−0.256487
$528$	4.12614	0.179567
$529$	2.73517	0.118920
$530$	15.9879	0.694472
$531$	5.48952	0.238225
$532$	0.446128	0.0193421
$533$	0	0
$534$	22.0872	0.955806
$535$	−38.5810	−1.66800
$536$	−10.1419	−0.438065
$537$	−13.7825	−0.594758
$538$	1.98959	0.0857774
$539$	1.11378	0.0479740
$540$	−0.458738	−0.0197409
$541$	22.4028	0.963170	0.481585	−	0.876399i	$-0.340061\pi$
$541$	22.4028	0.963170	0.481585	+	0.876399i	$0.340061\pi$
$542$	21.2454	0.912570
$543$	−21.8738	−0.938694
$544$	−0.519371	−0.0222679
$545$	16.4220	0.703440
$546$	0	0
$547$	−22.5948	−0.966084	−0.483042	−	0.875597i	$-0.660468\pi$
$547$	−22.5948	−0.966084	−0.483042	+	0.875597i	$0.660468\pi$
$548$	1.87647	0.0801589
$549$	−14.1106	−0.602224
$550$	−9.15849	−0.390519
$551$	−1.98724	−0.0846591
$552$	−14.8004	−0.629948
$553$	11.8320	0.503147
$554$	24.5847	1.04450
$555$	−12.6036	−0.534994
$556$	0.0313284	0.00132862
$557$	18.0550	0.765014	0.382507	−	0.923953i	$-0.375061\pi$
$557$	18.0550	0.765014	0.382507	+	0.923953i	$0.375061\pi$
$558$	12.0668	0.510829
$559$	0	0
$560$	−12.3015	−0.519833
$561$	−0.741567	−0.0313090
$562$	−35.3161	−1.48972
$563$	11.9664	0.504322	0.252161	−	0.967685i	$-0.418859\pi$
$563$	11.9664	0.504322	0.252161	+	0.967685i	$0.418859\pi$
$564$	−1.80914	−0.0761786
$565$	−53.8413	−2.26512
$566$	−13.6291	−0.572875
$567$	−1.00000	−0.0419961
$568$	13.9186	0.584013
$569$	35.7491	1.49868	0.749339	−	0.662186i	$-0.230371\pi$
$569$	35.7491	1.49868	0.749339	+	0.662186i	$0.230371\pi$
$570$	−14.6318	−0.612858
$571$	18.4132	0.770570	0.385285	−	0.922798i	$-0.374103\pi$
$571$	18.4132	0.770570	0.385285	+	0.922798i	$0.374103\pi$
$572$	0	0
$573$	−10.8936	−0.455085
$574$	1.24990	0.0521698
$575$	30.5714	1.27491
$576$	8.47362	0.353068
$577$	−27.4531	−1.14289	−0.571444	−	0.820641i	$-0.693617\pi$
$577$	−27.4531	−1.14289	−0.571444	+	0.820641i	$0.693617\pi$
$578$	22.5916	0.939685
$579$	−17.0935	−0.710381
$580$	−0.282295	−0.0117217
$581$	16.4426	0.682155
$582$	−1.93925	−0.0803846
$583$	3.93012	0.162769
$584$	−22.9356	−0.949081
$585$	0	0
$586$	4.91738	0.203135
$587$	−23.5141	−0.970531	−0.485265	−	0.874367i	$-0.661277\pi$
$587$	−23.5141	−0.970531	−0.485265	+	0.874367i	$0.661277\pi$
$588$	0.138150	0.00569719
$589$	−28.5582	−1.17672
$590$	24.8726	1.02399
$591$	−4.58665	−0.188670
$592$	14.0612	0.577913
$593$	31.0493	1.27504	0.637520	−	0.770433i	$-0.279960\pi$
$593$	31.0493	1.27504	0.637520	+	0.770433i	$0.279960\pi$
$594$	1.51975	0.0623562
$595$	2.21088	0.0906372
$596$	−0.990792	−0.0405844
$597$	−6.08803	−0.249167
$598$	0	0
$599$	−23.3733	−0.955007	−0.477503	−	0.878630i	$-0.658458\pi$
$599$	−23.3733	−0.955007	−0.477503	+	0.878630i	$0.658458\pi$
$600$	−17.5817	−0.717771
$601$	−25.5738	−1.04318	−0.521588	−	0.853197i	$-0.674660\pi$
$601$	−25.5738	−1.04318	−0.521588	+	0.853197i	$0.674660\pi$
$602$	11.0466	0.450227
$603$	−3.47625	−0.141564
$604$	0.993682	0.0404323
$605$	32.4072	1.31754
$606$	−0.983462	−0.0399504
$607$	−31.2846	−1.26980	−0.634902	−	0.772593i	$-0.718959\pi$
$607$	−31.2846	−1.26980	−0.634902	+	0.772593i	$0.718959\pi$
$608$	−2.51906	−0.102161
$609$	−0.615375	−0.0249362
$610$	−63.9339	−2.58861
$611$	0	0
$612$	−0.0919813	−0.00371812
$613$	−8.72726	−0.352491	−0.176245	−	0.984346i	$-0.556395\pi$
$613$	−8.72726	−0.352491	−0.176245	+	0.984346i	$0.556395\pi$
$614$	−23.8003	−0.960502
$615$	3.04171	0.122654
$616$	−3.24946	−0.130924
$617$	−19.2871	−0.776470	−0.388235	−	0.921560i	$-0.626915\pi$
$617$	−19.2871	−0.776470	−0.388235	+	0.921560i	$0.626915\pi$
$618$	20.4173	0.821304
$619$	42.3279	1.70130	0.850650	−	0.525732i	$-0.176209\pi$
$619$	42.3279	1.70130	0.850650	+	0.525732i	$0.176209\pi$
$620$	−4.05681	−0.162926
$621$	−5.07298	−0.203572
$622$	30.4317	1.22020
$623$	−16.1871	−0.648521
$624$	0	0
$625$	−18.8152	−0.752607
$626$	−1.08204	−0.0432470
$627$	−3.59675	−0.143640
$628$	−0.992760	−0.0396154
$629$	−2.52714	−0.100764
$630$	−4.53093	−0.180517
$631$	15.0098	0.597531	0.298766	−	0.954326i	$-0.403425\pi$
$631$	15.0098	0.597531	0.298766	+	0.954326i	$0.403425\pi$
$632$	−34.5198	−1.37312
$633$	−10.3803	−0.412578
$634$	−11.5757	−0.459730
$635$	38.1268	1.51302
$636$	0.487478	0.0193297
$637$	0	0
$638$	0.935217	0.0370256
$639$	4.77075	0.188728
$640$	33.2129	1.31285
$641$	24.5344	0.969050	0.484525	−	0.874777i	$-0.338992\pi$
$641$	24.5344	0.969050	0.484525	+	0.874777i	$0.338992\pi$
$642$	15.8537	0.625697
$643$	−29.4303	−1.16062	−0.580309	−	0.814396i	$-0.697068\pi$
$643$	−29.4303	−1.16062	−0.580309	+	0.814396i	$0.697068\pi$
$644$	0.700830	0.0276166
$645$	26.8827	1.05850
$646$	−2.93381	−0.115429
$647$	−8.01884	−0.315253	−0.157627	−	0.987499i	$-0.550384\pi$
$647$	−8.01884	−0.315253	−0.157627	+	0.987499i	$0.550384\pi$
$648$	2.91750	0.114610
$649$	6.11413	0.240000
$650$	0	0
$651$	−8.84343	−0.346601
$652$	3.06135	0.119892
$653$	5.06783	0.198320	0.0991598	−	0.995072i	$-0.468385\pi$
$653$	5.06783	0.198320	0.0991598	+	0.995072i	$0.468385\pi$
$654$	−6.74811	−0.263872
$655$	60.8437	2.37736
$656$	−3.39348	−0.132493
$657$	−7.86139	−0.306702
$658$	−17.8688	−0.696599
$659$	−16.9404	−0.659904	−0.329952	−	0.943998i	$-0.607033\pi$
$659$	−16.9404	−0.659904	−0.329952	+	0.943998i	$0.607033\pi$
$660$	−0.510934	−0.0198881
$661$	36.7741	1.43035	0.715174	−	0.698947i	$-0.246348\pi$
$661$	36.7741	1.43035	0.715174	+	0.698947i	$0.246348\pi$
$662$	−45.7338	−1.77749
$663$	0	0
$664$	−47.9713	−1.86165
$665$	10.7232	0.415829
$666$	5.17908	0.200685
$667$	−3.12179	−0.120876
$668$	−2.07082	−0.0801225
$669$	12.7655	0.493542
$670$	−15.7506	−0.608500
$671$	−15.7161	−0.606713
$672$	−0.780060	−0.0300915
$673$	−45.5657	−1.75643	−0.878214	−	0.478268i	$-0.841265\pi$
$673$	−45.5657	−1.75643	−0.878214	+	0.478268i	$0.841265\pi$
$674$	26.5023	1.02083
$675$	−6.02631	−0.231953
$676$	0	0
$677$	11.9937	0.460956	0.230478	−	0.973077i	$-0.425971\pi$
$677$	11.9937	0.460956	0.230478	+	0.973077i	$0.425971\pi$
$678$	22.1245	0.849686
$679$	1.42122	0.0545415
$680$	−6.45023	−0.247355
$681$	−13.3301	−0.510809
$682$	13.4398	0.514637
$683$	−23.9577	−0.916716	−0.458358	−	0.888768i	$-0.651562\pi$
$683$	−23.9577	−0.916716	−0.458358	+	0.888768i	$0.651562\pi$
$684$	−0.446128	−0.0170581
$685$	45.1032	1.72331
$686$	1.36450	0.0520967
$687$	9.63903	0.367752
$688$	−29.9917	−1.14342
$689$	0	0
$690$	−22.9853	−0.875037
$691$	23.9462	0.910958	0.455479	−	0.890247i	$-0.349468\pi$
$691$	23.9462	0.910958	0.455479	+	0.890247i	$0.349468\pi$
$692$	−0.0587598	−0.00223371
$693$	−1.11378	−0.0423091
$694$	15.2480	0.578806
$695$	0.753015	0.0285635
$696$	1.79535	0.0680527
$697$	0.609892	0.0231013
$698$	50.2284	1.90117
$699$	22.0553	0.834207
$700$	0.832531	0.0314667
$701$	−20.6807	−0.781099	−0.390550	−	0.920582i	$-0.627715\pi$
$701$	−20.6807	−0.781099	−0.390550	+	0.920582i	$0.627715\pi$
$702$	0	0
$703$	−12.2572	−0.462288
$704$	9.43777	0.355699
$705$	−43.4849	−1.63773
$706$	23.8943	0.899275
$707$	0.720751	0.0271066
$708$	0.758374	0.0285014
$709$	16.0902	0.604281	0.302141	−	0.953263i	$-0.402299\pi$
$709$	16.0902	0.604281	0.302141	+	0.953263i	$0.402299\pi$
$710$	21.6159	0.811231
$711$	−11.8320	−0.443734
$712$	47.2257	1.76986
$713$	−44.8626	−1.68012
$714$	−0.908495	−0.0339996
$715$	0	0
$716$	−1.90404	−0.0711575
$717$	−23.6972	−0.884990
$718$	11.1306	0.415391
$719$	−8.10172	−0.302143	−0.151072	−	0.988523i	$-0.548272\pi$
$719$	−8.10172	−0.302143	−0.151072	+	0.988523i	$0.548272\pi$
$720$	12.3015	0.458450
$721$	−14.9632	−0.557260
$722$	11.6958	0.435274
$723$	−17.5586	−0.653012
$724$	−3.02185	−0.112306
$725$	−3.70843	−0.137728
$726$	−13.3168	−0.494232
$727$	−8.37621	−0.310657	−0.155328	−	0.987863i	$-0.549644\pi$
$727$	−8.37621	−0.310657	−0.155328	+	0.987863i	$0.549644\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−35.6194	−1.31833
$731$	5.39023	0.199365
$732$	−1.94937	−0.0720506
$733$	−13.7644	−0.508399	−0.254199	−	0.967152i	$-0.581812\pi$
$733$	−13.7644	−0.508399	−0.254199	+	0.967152i	$0.581812\pi$
$734$	−21.6322	−0.798460
$735$	3.32059	0.122482
$736$	−3.95723	−0.145865
$737$	−3.87178	−0.142619
$738$	−1.24990	−0.0460094
$739$	39.2848	1.44511	0.722557	−	0.691311i	$-0.242967\pi$
$739$	39.2848	1.44511	0.722557	+	0.691311i	$0.242967\pi$
$740$	−1.74118	−0.0640072
$741$	0	0
$742$	4.81479	0.176757
$743$	−3.96163	−0.145338	−0.0726690	−	0.997356i	$-0.523152\pi$
$743$	−3.96163	−0.145338	−0.0726690	+	0.997356i	$0.523152\pi$
$744$	25.8007	0.945899
$745$	−23.8149	−0.872509
$746$	−15.4291	−0.564899
$747$	−16.4426	−0.601604
$748$	−0.102447	−0.00374584
$749$	−11.6187	−0.424539
$750$	−4.65012	−0.169798
$751$	−12.3197	−0.449553	−0.224776	−	0.974410i	$-0.572165\pi$
$751$	−12.3197	−0.449553	−0.224776	+	0.974410i	$0.572165\pi$
$752$	48.5139	1.76912
$753$	−30.2065	−1.10079
$754$	0	0
$755$	23.8843	0.869239
$756$	−0.138150	−0.00502445
$757$	27.1281	0.985988	0.492994	−	0.870033i	$-0.335902\pi$
$757$	27.1281	0.985988	0.492994	+	0.870033i	$0.335902\pi$
$758$	20.2752	0.736430
$759$	−5.65020	−0.205089
$760$	−31.2850	−1.13482
$761$	−8.01574	−0.290570	−0.145285	−	0.989390i	$-0.546410\pi$
$761$	−8.01574	−0.290570	−0.145285	+	0.989390i	$0.546410\pi$
$762$	−15.6671	−0.567558
$763$	4.94550	0.179039
$764$	−1.50494	−0.0544468
$765$	−2.21088	−0.0799345
$766$	26.6797	0.963978
$767$	0	0
$768$	3.29940	0.119057
$769$	31.3627	1.13097	0.565484	−	0.824759i	$-0.308689\pi$
$769$	31.3627	1.13097	0.565484	+	0.824759i	$0.308689\pi$
$770$	−5.04647	−0.181862
$771$	4.98163	0.179409
$772$	−2.36146	−0.0849907
$773$	−4.00669	−0.144111	−0.0720553	−	0.997401i	$-0.522956\pi$
$773$	−4.00669	−0.144111	−0.0720553	+	0.997401i	$0.522956\pi$
$774$	−11.0466	−0.397063
$775$	−53.2932	−1.91435
$776$	−4.14641	−0.148847
$777$	−3.79560	−0.136166
$778$	−21.1479	−0.758189
$779$	2.95810	0.105985
$780$	0	0
$781$	5.31357	0.190135
$782$	−4.60878	−0.164810
$783$	0.615375	0.0219917
$784$	−3.70462	−0.132308
$785$	−23.8622	−0.851677
$786$	−25.0019	−0.891788
$787$	10.2148	0.364117	0.182058	−	0.983288i	$-0.441724\pi$
$787$	10.2148	0.364117	0.182058	+	0.983288i	$0.441724\pi$
$788$	−0.633644	−0.0225726
$789$	12.5614	0.447199
$790$	−53.6099	−1.90736
$791$	−16.2144	−0.576518
$792$	3.24946	0.115464
$793$	0	0
$794$	−31.6735	−1.12405
$795$	11.7171	0.415563
$796$	−0.841059	−0.0298105
$797$	−15.5770	−0.551767	−0.275884	−	0.961191i	$-0.588970\pi$
$797$	−15.5770	−0.551767	−0.275884	+	0.961191i	$0.588970\pi$
$798$	−4.40639	−0.155984
$799$	−8.71913	−0.308461
$800$	−4.70088	−0.166201
$801$	16.1871	0.571942
$802$	−53.5617	−1.89133
$803$	−8.75587	−0.308988
$804$	−0.480242	−0.0169368
$805$	16.8453	0.593718
$806$	0	0
$807$	1.45811	0.0513281
$808$	−2.10279	−0.0739758
$809$	−30.9360	−1.08765	−0.543826	−	0.839198i	$-0.683025\pi$
$809$	−30.9360	−1.08765	−0.543826	+	0.839198i	$0.683025\pi$
$810$	4.53093	0.159201
$811$	14.2471	0.500284	0.250142	−	0.968209i	$-0.419523\pi$
$811$	14.2471	0.500284	0.250142	+	0.968209i	$0.419523\pi$
$812$	−0.0850137	−0.00298340
$813$	15.5702	0.546070
$814$	5.76837	0.202181
$815$	73.5831	2.57750
$816$	2.46657	0.0863472
$817$	26.1437	0.914654
$818$	−26.7327	−0.934686
$819$	0	0
$820$	0.420211	0.0146744
$821$	−8.23270	−0.287323	−0.143662	−	0.989627i	$-0.545888\pi$
$821$	−8.23270	−0.287323	−0.143662	+	0.989627i	$0.545888\pi$
$822$	−18.5338	−0.646441
$823$	−7.03818	−0.245336	−0.122668	−	0.992448i	$-0.539145\pi$
$823$	−7.03818	−0.245336	−0.122668	+	0.992448i	$0.539145\pi$
$824$	43.6552	1.52080
$825$	−6.71199	−0.233682
$826$	7.49043	0.260625
$827$	43.3827	1.50856	0.754282	−	0.656550i	$-0.227985\pi$
$827$	43.3827	1.50856	0.754282	+	0.656550i	$0.227985\pi$
$828$	−0.700830	−0.0243555
$829$	32.7843	1.13865	0.569323	−	0.822114i	$-0.307206\pi$
$829$	32.7843	1.13865	0.569323	+	0.822114i	$0.307206\pi$
$830$	−74.5004	−2.58594
$831$	18.0174	0.625016
$832$	0	0
$833$	0.665810	0.0230689
$834$	−0.309429	−0.0107147
$835$	−49.7747	−1.72252
$836$	−0.496889	−0.0171853
$837$	8.84343	0.305674
$838$	−11.5019	−0.397326
$839$	26.5096	0.915212	0.457606	−	0.889155i	$-0.348707\pi$
$839$	26.5096	0.915212	0.457606	+	0.889155i	$0.348707\pi$
$840$	−9.68781	−0.334261
$841$	−28.6213	−0.986942
$842$	3.88773	0.133980
$843$	−25.8821	−0.891427
$844$	−1.43403	−0.0493613
$845$	0	0
$846$	17.8688	0.614342
$847$	9.75949	0.335340
$848$	−13.0722	−0.448901
$849$	−9.98839	−0.342801
$850$	−5.47487	−0.187786
$851$	−19.2550	−0.660053
$852$	0.659077	0.0225796
$853$	−23.0901	−0.790589	−0.395295	−	0.918554i	$-0.629357\pi$
$853$	−23.0901	−0.790589	−0.395295	+	0.918554i	$0.629357\pi$
$854$	−19.2538	−0.658851
$855$	−10.7232	−0.366726
$856$	33.8976	1.15860
$857$	0.861504	0.0294284	0.0147142	−	0.999892i	$-0.495316\pi$
$857$	0.861504	0.0294284	0.0147142	+	0.999892i	$0.495316\pi$
$858$	0	0
$859$	−18.6223	−0.635386	−0.317693	−	0.948194i	$-0.602908\pi$
$859$	−18.6223	−0.635386	−0.317693	+	0.948194i	$0.602908\pi$
$860$	3.71383	0.126641
$861$	0.916015	0.0312177
$862$	48.8515	1.66389
$863$	−22.5310	−0.766965	−0.383482	−	0.923548i	$-0.625275\pi$
$863$	−22.5310	−0.766965	−0.383482	+	0.923548i	$0.625275\pi$
$864$	0.780060	0.0265382
$865$	−1.41236	−0.0480218
$866$	−12.1789	−0.413858
$867$	16.5567	0.562295
$868$	−1.22172	−0.0414677
$869$	−13.1783	−0.447042
$870$	2.78822	0.0945295
$871$	0	0
$872$	−14.4285	−0.488610
$873$	−1.42122	−0.0481011
$874$	−22.3535	−0.756119
$875$	3.40794	0.115209
$876$	−1.08605	−0.0366941
$877$	−46.8180	−1.58093	−0.790466	−	0.612506i	$-0.790161\pi$
$877$	−46.8180	−1.58093	−0.790466	+	0.612506i	$0.790161\pi$
$878$	6.71563	0.226641
$879$	3.60381	0.121553
$880$	13.7012	0.461867
$881$	−12.3276	−0.415326	−0.207663	−	0.978200i	$-0.566586\pi$
$881$	−12.3276	−0.415326	−0.207663	+	0.978200i	$0.566586\pi$
$882$	−1.36450	−0.0459450
$883$	−20.2249	−0.680622	−0.340311	−	0.940313i	$-0.610532\pi$
$883$	−20.2249	−0.680622	−0.340311	+	0.940313i	$0.610532\pi$
$884$	0	0
$885$	18.2284	0.612742
$886$	6.77134	0.227488
$887$	−41.4430	−1.39152	−0.695760	−	0.718274i	$-0.744932\pi$
$887$	−41.4430	−1.39152	−0.695760	+	0.718274i	$0.744932\pi$
$888$	11.0736	0.371607
$889$	11.4819	0.385092
$890$	73.3425	2.45844
$891$	1.11378	0.0373131
$892$	1.76355	0.0590479
$893$	−42.2896	−1.41517
$894$	9.78600	0.327293
$895$	−45.7660	−1.52979
$896$	10.0021	0.334147
$897$	0	0
$898$	−24.5326	−0.818663
$899$	5.44202	0.181502
$900$	−0.832531	−0.0277510
$901$	2.34939	0.0782696
$902$	−1.39212	−0.0463524
$903$	8.09576	0.269410
$904$	47.3055	1.57336
$905$	−72.6338	−2.41443
$906$	−9.81455	−0.326067
$907$	18.4094	0.611275	0.305638	−	0.952148i	$-0.401130\pi$
$907$	18.4094	0.611275	0.305638	+	0.952148i	$0.401130\pi$
$908$	−1.84154	−0.0611137
$909$	−0.720751	−0.0239058
$910$	0	0
$911$	36.7759	1.21844	0.609220	−	0.793001i	$-0.291483\pi$
$911$	36.7759	1.21844	0.609220	+	0.793001i	$0.291483\pi$
$912$	11.9634	0.396147
$913$	−18.3135	−0.606088
$914$	−37.9432	−1.25505
$915$	−46.8553	−1.54899
$916$	1.33163	0.0439982
$917$	18.3232	0.605084
$918$	0.908495	0.0299848
$919$	55.6734	1.83649	0.918247	−	0.396008i	$-0.129605\pi$
$919$	55.6734	1.83649	0.918247	+	0.396008i	$0.129605\pi$
$920$	−49.1461	−1.62030
$921$	−17.4426	−0.574752
$922$	22.6318	0.745339
$923$	0	0
$924$	−0.153868	−0.00506190
$925$	−22.8734	−0.752074
$926$	−57.9839	−1.90547
$927$	14.9632	0.491457
$928$	0.480029	0.0157577
$929$	−34.2055	−1.12224	−0.561122	−	0.827733i	$-0.689630\pi$
$929$	−34.2055	−1.12224	−0.561122	+	0.827733i	$0.689630\pi$
$930$	40.0690	1.31391
$931$	3.22931	0.105836
$932$	3.04692	0.0998053
$933$	22.3025	0.730152
$934$	1.77681	0.0581391
$935$	−2.46244	−0.0805303
$936$	0	0
$937$	−50.2091	−1.64026	−0.820130	−	0.572177i	$-0.806099\pi$
$937$	−50.2091	−1.64026	−0.820130	+	0.572177i	$0.806099\pi$
$938$	−4.74332	−0.154875
$939$	−0.792995	−0.0258784
$940$	−6.00741	−0.195940
$941$	3.12662	0.101925	0.0509625	−	0.998701i	$-0.483771\pi$
$941$	3.12662	0.101925	0.0509625	+	0.998701i	$0.483771\pi$
$942$	9.80545	0.319479
$943$	4.64693	0.151325
$944$	−20.3366	−0.661898
$945$	−3.32059	−0.108019
$946$	−12.3035	−0.400023
$947$	−2.54412	−0.0826729	−0.0413364	−	0.999145i	$-0.513162\pi$
$947$	−2.54412	−0.0826729	−0.0413364	+	0.999145i	$0.513162\pi$
$948$	−1.63458	−0.0530888
$949$	0	0
$950$	−26.5542	−0.861533
$951$	−8.48350	−0.275096
$952$	−1.94250	−0.0629567
$953$	42.2175	1.36756	0.683780	−	0.729688i	$-0.260335\pi$
$953$	42.2175	1.36756	0.683780	+	0.729688i	$0.260335\pi$
$954$	−4.81479	−0.155885
$955$	−36.1730	−1.17053
$956$	−3.27376	−0.105881
$957$	0.685393	0.0221556
$958$	−11.3048	−0.365241
$959$	13.5829	0.438615
$960$	28.1374	0.908131
$961$	47.2062	1.52278
$962$	0	0
$963$	11.6187	0.374409
$964$	−2.42572	−0.0781270
$965$	−56.7604	−1.82718
$966$	−6.92207	−0.222714
$967$	38.3214	1.23233	0.616166	−	0.787616i	$-0.288685\pi$
$967$	38.3214	1.23233	0.616166	+	0.787616i	$0.288685\pi$
$968$	−28.4733	−0.915166
$969$	−2.15011	−0.0690714
$970$	−6.43946	−0.206759
$971$	8.66075	0.277937	0.138968	−	0.990297i	$-0.455621\pi$
$971$	8.66075	0.277937	0.138968	+	0.990297i	$0.455621\pi$
$972$	0.138150	0.00443115
$973$	0.226772	0.00726997
$974$	−59.4414	−1.90463
$975$	0	0
$976$	52.2742	1.67326
$977$	−11.2083	−0.358585	−0.179292	−	0.983796i	$-0.557381\pi$
$977$	−11.2083	−0.358585	−0.179292	+	0.983796i	$0.557381\pi$
$978$	−30.2368	−0.966865
$979$	18.0289	0.576205
$980$	0.458738	0.0146538
$981$	−4.94550	−0.157898
$982$	−57.0429	−1.82031
$983$	24.8347	0.792102	0.396051	−	0.918228i	$-0.370380\pi$
$983$	24.8347	0.792102	0.396051	+	0.918228i	$0.370380\pi$
$984$	−2.67247	−0.0851953
$985$	−15.2304	−0.485280
$986$	0.559065	0.0178042
$987$	−13.0955	−0.416835
$988$	0	0
$989$	41.0697	1.30594
$990$	5.04647	0.160387
$991$	22.6526	0.719585	0.359793	−	0.933032i	$-0.382847\pi$
$991$	22.6526	0.719585	0.359793	+	0.933032i	$0.382847\pi$
$992$	6.89840	0.219025
$993$	−33.5170	−1.06363
$994$	6.50967	0.206474
$995$	−20.2159	−0.640886
$996$	−2.27154	−0.0719765
$997$	39.1382	1.23952	0.619760	−	0.784791i	$-0.287230\pi$
$997$	39.1382	1.23952	0.619760	+	0.784791i	$0.287230\pi$
$998$	−8.58217	−0.271664
$999$	3.79560	0.120087

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.bf.1.3	yes	9
13.12	even	2		3549.2.a.be.1.7	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3549.2.a.be.1.7	✓	9	13.12	even	2
3549.2.a.bf.1.3	yes	9	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.a (trivial)

\(f(q)\)	\(=\)	\(q-1.36450 q^{2} -1.00000 q^{3} -0.138150 q^{4} -3.32059 q^{5} +1.36450 q^{6} -1.00000 q^{7} +2.91750 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.36450 q^{2} -1.00000 q^{3} -0.138150 q^{4} -3.32059 q^{5} +1.36450 q^{6} -1.00000 q^{7} +2.91750 q^{8} +1.00000 q^{9} +4.53093 q^{10} +1.11378 q^{11} +0.138150 q^{12} +1.36450 q^{14} +3.32059 q^{15} -3.70462 q^{16} +0.665810 q^{17} -1.36450 q^{18} +3.22931 q^{19} +0.458738 q^{20} +1.00000 q^{21} -1.51975 q^{22} +5.07298 q^{23} -2.91750 q^{24} +6.02631 q^{25} -1.00000 q^{27} +0.138150 q^{28} -0.615375 q^{29} -4.53093 q^{30} -8.84343 q^{31} -0.780060 q^{32} -1.11378 q^{33} -0.908495 q^{34} +3.32059 q^{35} -0.138150 q^{36} -3.79560 q^{37} -4.40639 q^{38} -9.68781 q^{40} +0.916015 q^{41} -1.36450 q^{42} +8.09576 q^{43} -0.153868 q^{44} -3.32059 q^{45} -6.92207 q^{46} -13.0955 q^{47} +3.70462 q^{48} +1.00000 q^{49} -8.22287 q^{50} -0.665810 q^{51} +3.52862 q^{53} +1.36450 q^{54} -3.69841 q^{55} -2.91750 q^{56} -3.22931 q^{57} +0.839676 q^{58} +5.48952 q^{59} -0.458738 q^{60} -14.1106 q^{61} +12.0668 q^{62} -1.00000 q^{63} +8.47362 q^{64} +1.51975 q^{66} -3.47625 q^{67} -0.0919813 q^{68} -5.07298 q^{69} -4.53093 q^{70} +4.77075 q^{71} +2.91750 q^{72} -7.86139 q^{73} +5.17908 q^{74} -6.02631 q^{75} -0.446128 q^{76} -1.11378 q^{77} -11.8320 q^{79} +12.3015 q^{80} +1.00000 q^{81} -1.24990 q^{82} -16.4426 q^{83} -0.138150 q^{84} -2.21088 q^{85} -11.0466 q^{86} +0.615375 q^{87} +3.24946 q^{88} +16.1871 q^{89} +4.53093 q^{90} -0.700830 q^{92} +8.84343 q^{93} +17.8688 q^{94} -10.7232 q^{95} +0.780060 q^{96} -1.42122 q^{97} -1.36450 q^{98} +1.11378 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + q^{2} - 9 q^{3} + 5 q^{4} - 9 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + q^2 - 9 * q^3 + 5 * q^4 - 9 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 9 * q^9	\( 9 q + q^{2} - 9 q^{3} + 5 q^{4} - 9 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 9 q^{9} + q^{10} + q^{11} - 5 q^{12} - q^{14} + 9 q^{15} + 5 q^{16} + 11 q^{17} + q^{18} - 7 q^{19} - 23 q^{20} + 9 q^{21} - 3 q^{22} + 22 q^{23} - 6 q^{24} - 8 q^{25} - 9 q^{27} - 5 q^{28} + 11 q^{29} - q^{30} - 7 q^{31} + 18 q^{32} - q^{33} + 6 q^{34} + 9 q^{35} + 5 q^{36} + q^{37} - 6 q^{38} - 14 q^{40} - 16 q^{41} + q^{42} + 32 q^{43} - 18 q^{44} - 9 q^{45} + 9 q^{46} + 12 q^{47} - 5 q^{48} + 9 q^{49} - 10 q^{50} - 11 q^{51} + 13 q^{53} - q^{54} + 9 q^{55} - 6 q^{56} + 7 q^{57} - 4 q^{58} - 29 q^{59} + 23 q^{60} - 12 q^{61} + 30 q^{62} - 9 q^{63} + 6 q^{64} + 3 q^{66} + 20 q^{67} + 34 q^{68} - 22 q^{69} - q^{70} + 2 q^{71} + 6 q^{72} - q^{73} + 43 q^{74} + 8 q^{75} - 13 q^{76} - q^{77} + 3 q^{79} + 39 q^{80} + 9 q^{81} - 19 q^{82} - 24 q^{83} + 5 q^{84} - 15 q^{85} + 28 q^{86} - 11 q^{87} - 19 q^{88} - 11 q^{89} + q^{90} + 73 q^{92} + 7 q^{93} + 15 q^{94} + 39 q^{95} - 18 q^{96} - 20 q^{97} + q^{98} + q^{99}+O(q^{100}) \) 9 * q + q^2 - 9 * q^3 + 5 * q^4 - 9 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 9 * q^9 + q^10 + q^11 - 5 * q^12 - q^14 + 9 * q^15 + 5 * q^16 + 11 * q^17 + q^18 - 7 * q^19 - 23 * q^20 + 9 * q^21 - 3 * q^22 + 22 * q^23 - 6 * q^24 - 8 * q^25 - 9 * q^27 - 5 * q^28 + 11 * q^29 - q^30 - 7 * q^31 + 18 * q^32 - q^33 + 6 * q^34 + 9 * q^35 + 5 * q^36 + q^37 - 6 * q^38 - 14 * q^40 - 16 * q^41 + q^42 + 32 * q^43 - 18 * q^44 - 9 * q^45 + 9 * q^46 + 12 * q^47 - 5 * q^48 + 9 * q^49 - 10 * q^50 - 11 * q^51 + 13 * q^53 - q^54 + 9 * q^55 - 6 * q^56 + 7 * q^57 - 4 * q^58 - 29 * q^59 + 23 * q^60 - 12 * q^61 + 30 * q^62 - 9 * q^63 + 6 * q^64 + 3 * q^66 + 20 * q^67 + 34 * q^68 - 22 * q^69 - q^70 + 2 * q^71 + 6 * q^72 - q^73 + 43 * q^74 + 8 * q^75 - 13 * q^76 - q^77 + 3 * q^79 + 39 * q^80 + 9 * q^81 - 19 * q^82 - 24 * q^83 + 5 * q^84 - 15 * q^85 + 28 * q^86 - 11 * q^87 - 19 * q^88 - 11 * q^89 + q^90 + 73 * q^92 + 7 * q^93 + 15 * q^94 + 39 * q^95 - 18 * q^96 - 20 * q^97 + q^98 + q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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