LMFDB - Embedded newform 273.2.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(1,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, 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("273.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.17428.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 6x^{2} + 4x + 6 $ x^4 - x^3 - 6x^2 + 4x + 6
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.787711$ of defining polynomial
Character	$\chi$	$=$	273.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.37951 q^{2} +1.00000 q^{3} +3.66208 q^{4} -2.66208 q^{5} -2.37951 q^{6} +1.00000 q^{7} -3.95493 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.37951 q^{2} +1.00000 q^{3} +3.66208 q^{4} -2.66208 q^{5} -2.37951 q^{6} +1.00000 q^{7} -3.95493 q^{8} +1.00000 q^{9} +6.33445 q^{10} +1.57542 q^{11} +3.66208 q^{12} +1.00000 q^{13} -2.37951 q^{14} -2.66208 q^{15} +2.08666 q^{16} +4.75902 q^{17} -2.37951 q^{18} -2.23750 q^{19} -9.74873 q^{20} +1.00000 q^{21} -3.74873 q^{22} +5.84568 q^{23} -3.95493 q^{24} +2.08666 q^{25} -2.37951 q^{26} +1.00000 q^{27} +3.66208 q^{28} +4.23750 q^{29} +6.33445 q^{30} +7.28055 q^{31} +2.94464 q^{32} +1.57542 q^{33} -11.3242 q^{34} -2.66208 q^{35} +3.66208 q^{36} +10.4750 q^{37} +5.32415 q^{38} +1.00000 q^{39} +10.5283 q^{40} -2.25127 q^{41} -2.37951 q^{42} +0.913344 q^{43} +5.76931 q^{44} -2.66208 q^{45} -13.9099 q^{46} -2.09695 q^{47} +2.08666 q^{48} +1.00000 q^{49} -4.96522 q^{50} +4.75902 q^{51} +3.66208 q^{52} +1.08666 q^{53} -2.37951 q^{54} -4.19389 q^{55} -3.95493 q^{56} -2.23750 q^{57} -10.0832 q^{58} -12.3344 q^{59} -9.74873 q^{60} -7.51805 q^{61} -17.3242 q^{62} +1.00000 q^{63} -11.1801 q^{64} -2.66208 q^{65} -3.74873 q^{66} -15.6914 q^{67} +17.4279 q^{68} +5.84568 q^{69} +6.33445 q^{70} +10.0504 q^{71} -3.95493 q^{72} +15.0797 q^{73} -24.9254 q^{74} +2.08666 q^{75} -8.19389 q^{76} +1.57542 q^{77} -2.37951 q^{78} -11.7555 q^{79} -5.55484 q^{80} +1.00000 q^{81} +5.35692 q^{82} +7.42110 q^{83} +3.66208 q^{84} -12.6689 q^{85} -2.17331 q^{86} +4.23750 q^{87} -6.23069 q^{88} -11.1371 q^{89} +6.33445 q^{90} +1.00000 q^{91} +21.4073 q^{92} +7.28055 q^{93} +4.98971 q^{94} +5.95639 q^{95} +2.94464 q^{96} -14.6047 q^{97} -2.37951 q^{98} +1.57542 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + 4 q^{3} + 7 q^{4} - 3 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + q^2 + 4 * q^3 + 7 * q^4 - 3 * q^5 + q^6 + 4 * q^7 + 3 * q^8 + 4 * q^9	\( 4 q + q^{2} + 4 q^{3} + 7 q^{4} - 3 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} + 4 q^{9} - 4 q^{10} - 2 q^{11} + 7 q^{12} + 4 q^{13} + q^{14} - 3 q^{15} + 9 q^{16} - 2 q^{17} + q^{18} + 7 q^{19} - 32 q^{20} + 4 q^{21} - 8 q^{22} + 3 q^{23} + 3 q^{24} + 9 q^{25} + q^{26} + 4 q^{27} + 7 q^{28} + q^{29} - 4 q^{30} + 3 q^{31} + 7 q^{32} - 2 q^{33} - 30 q^{34} - 3 q^{35} + 7 q^{36} + 10 q^{37} + 6 q^{38} + 4 q^{39} - 14 q^{40} - 16 q^{41} + q^{42} + 3 q^{43} - 12 q^{44} - 3 q^{45} - 18 q^{46} + 5 q^{47} + 9 q^{48} + 4 q^{49} + 13 q^{50} - 2 q^{51} + 7 q^{52} + 5 q^{53} + q^{54} + 10 q^{55} + 3 q^{56} + 7 q^{57} - 4 q^{58} - 20 q^{59} - 32 q^{60} + 12 q^{61} - 54 q^{62} + 4 q^{63} + 5 q^{64} - 3 q^{65} - 8 q^{66} - 22 q^{67} - 10 q^{68} + 3 q^{69} - 4 q^{70} + 3 q^{72} - 13 q^{73} - 6 q^{74} + 9 q^{75} - 6 q^{76} - 2 q^{77} + q^{78} + 11 q^{79} - 42 q^{80} + 4 q^{81} + 10 q^{82} + q^{83} + 7 q^{84} + 8 q^{85} - 10 q^{86} + q^{87} - 60 q^{88} - 5 q^{89} - 4 q^{90} + 4 q^{91} + 34 q^{92} + 3 q^{93} + 34 q^{94} + 13 q^{95} + 7 q^{96} - 17 q^{97} + q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q + q^2 + 4 * q^3 + 7 * q^4 - 3 * q^5 + q^6 + 4 * q^7 + 3 * q^8 + 4 * q^9 - 4 * q^10 - 2 * q^11 + 7 * q^12 + 4 * q^13 + q^14 - 3 * q^15 + 9 * q^16 - 2 * q^17 + q^18 + 7 * q^19 - 32 * q^20 + 4 * q^21 - 8 * q^22 + 3 * q^23 + 3 * q^24 + 9 * q^25 + q^26 + 4 * q^27 + 7 * q^28 + q^29 - 4 * q^30 + 3 * q^31 + 7 * q^32 - 2 * q^33 - 30 * q^34 - 3 * q^35 + 7 * q^36 + 10 * q^37 + 6 * q^38 + 4 * q^39 - 14 * q^40 - 16 * q^41 + q^42 + 3 * q^43 - 12 * q^44 - 3 * q^45 - 18 * q^46 + 5 * q^47 + 9 * q^48 + 4 * q^49 + 13 * q^50 - 2 * q^51 + 7 * q^52 + 5 * q^53 + q^54 + 10 * q^55 + 3 * q^56 + 7 * q^57 - 4 * q^58 - 20 * q^59 - 32 * q^60 + 12 * q^61 - 54 * q^62 + 4 * q^63 + 5 * q^64 - 3 * q^65 - 8 * q^66 - 22 * q^67 - 10 * q^68 + 3 * q^69 - 4 * q^70 + 3 * q^72 - 13 * q^73 - 6 * q^74 + 9 * q^75 - 6 * q^76 - 2 * q^77 + q^78 + 11 * q^79 - 42 * q^80 + 4 * q^81 + 10 * q^82 + q^83 + 7 * q^84 + 8 * q^85 - 10 * q^86 + q^87 - 60 * q^88 - 5 * q^89 - 4 * q^90 + 4 * q^91 + 34 * q^92 + 3 * q^93 + 34 * q^94 + 13 * q^95 + 7 * q^96 - 17 * q^97 + q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.37951	−1.68257	−0.841285	−	0.540593i	$-0.818200\pi$
$2$	−2.37951	−1.68257	−0.841285	+	0.540593i	$0.818200\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.66208	1.83104
$5$	−2.66208	−1.19052	−0.595259	−	0.803534i	$-0.702950\pi$
$5$	−2.66208	−1.19052	−0.595259	+	0.803534i	$0.702950\pi$
$6$	−2.37951	−0.971432
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−3.95493	−1.39828
$9$	1.00000	0.333333
$10$	6.33445	2.00313
$11$	1.57542	0.475007	0.237504	−	0.971387i	$-0.423671\pi$
$11$	1.57542	0.475007	0.237504	+	0.971387i	$0.423671\pi$
$12$	3.66208	1.05715
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−2.37951	−0.635951
$15$	−2.66208	−0.687345
$16$	2.08666	0.521664
$17$	4.75902	1.15423	0.577116	−	0.816662i	$-0.304178\pi$
$17$	4.75902	1.15423	0.577116	+	0.816662i	$0.304178\pi$
$18$	−2.37951	−0.560856
$19$	−2.23750	−0.513317	−0.256659	−	0.966502i	$-0.582622\pi$
$19$	−2.23750	−0.513317	−0.256659	+	0.966502i	$0.582622\pi$
$20$	−9.74873	−2.17988
$21$	1.00000	0.218218
$22$	−3.74873	−0.799233
$23$	5.84568	1.21891	0.609454	−	0.792821i	$-0.291389\pi$
$23$	5.84568	1.21891	0.609454	+	0.792821i	$0.291389\pi$
$24$	−3.95493	−0.807297
$25$	2.08666	0.417331
$26$	−2.37951	−0.466661
$27$	1.00000	0.192450
$28$	3.66208	0.692068
$29$	4.23750	0.786884	0.393442	−	0.919349i	$-0.371284\pi$
$29$	4.23750	0.786884	0.393442	+	0.919349i	$0.371284\pi$
$30$	6.33445	1.15651
$31$	7.28055	1.30763	0.653813	−	0.756656i	$-0.273168\pi$
$31$	7.28055	1.30763	0.653813	+	0.756656i	$0.273168\pi$
$32$	2.94464	0.520544
$33$	1.57542	0.274246
$34$	−11.3242	−1.94208
$35$	−2.66208	−0.449973
$36$	3.66208	0.610346
$37$	10.4750	1.72208	0.861039	−	0.508538i	$-0.169814\pi$
$37$	10.4750	1.72208	0.861039	+	0.508538i	$0.169814\pi$
$38$	5.32415	0.863692
$39$	1.00000	0.160128
$40$	10.5283	1.66468
$41$	−2.25127	−0.351589	−0.175794	−	0.984427i	$-0.556249\pi$
$41$	−2.25127	−0.351589	−0.175794	+	0.984427i	$0.556249\pi$
$42$	−2.37951	−0.367167
$43$	0.913344	0.139284	0.0696418	−	0.997572i	$-0.477814\pi$
$43$	0.913344	0.139284	0.0696418	+	0.997572i	$0.477814\pi$
$44$	5.76931	0.869757
$45$	−2.66208	−0.396839
$46$	−13.9099	−2.05090
$47$	−2.09695	−0.305871	−0.152936	−	0.988236i	$-0.548873\pi$
$47$	−2.09695	−0.305871	−0.152936	+	0.988236i	$0.548873\pi$
$48$	2.08666	0.301183
$49$	1.00000	0.142857
$50$	−4.96522	−0.702189
$51$	4.75902	0.666397
$52$	3.66208	0.507839
$53$	1.08666	0.149264	0.0746319	−	0.997211i	$-0.476222\pi$
$53$	1.08666	0.149264	0.0746319	+	0.997211i	$0.476222\pi$
$54$	−2.37951	−0.323811
$55$	−4.19389	−0.565504
$56$	−3.95493	−0.528500
$57$	−2.23750	−0.296364
$58$	−10.0832	−1.32399
$59$	−12.3344	−1.60581	−0.802904	−	0.596108i	$-0.796713\pi$
$59$	−12.3344	−1.60581	−0.802904	+	0.596108i	$0.796713\pi$
$60$	−9.74873	−1.25856
$61$	−7.51805	−0.962587	−0.481294	−	0.876559i	$-0.659833\pi$
$61$	−7.51805	−0.962587	−0.481294	+	0.876559i	$0.659833\pi$
$62$	−17.3242	−2.20017
$63$	1.00000	0.125988
$64$	−11.1801	−1.39752
$65$	−2.66208	−0.330190
$66$	−3.74873	−0.461437
$67$	−15.6914	−1.91700	−0.958502	−	0.285084i	$-0.907978\pi$
$67$	−15.6914	−1.91700	−0.958502	+	0.285084i	$0.907978\pi$
$68$	17.4279	2.11345
$69$	5.84568	0.703737
$70$	6.33445	0.757111
$71$	10.0504	1.19277	0.596383	−	0.802700i	$-0.296604\pi$
$71$	10.0504	1.19277	0.596383	+	0.802700i	$0.296604\pi$
$72$	−3.95493	−0.466093
$73$	15.0797	1.76495	0.882473	−	0.470363i	$-0.155877\pi$
$73$	15.0797	1.76495	0.882473	+	0.470363i	$0.155877\pi$
$74$	−24.9254	−2.89752
$75$	2.08666	0.240946
$76$	−8.19389	−0.939904
$77$	1.57542	0.179536
$78$	−2.37951	−0.269427
$79$	−11.7555	−1.32260	−0.661301	−	0.750121i	$-0.729995\pi$
$79$	−11.7555	−1.32260	−0.661301	+	0.750121i	$0.729995\pi$
$80$	−5.55484	−0.621050
$81$	1.00000	0.111111
$82$	5.35692	0.591572
$83$	7.42110	0.814572	0.407286	−	0.913301i	$-0.366475\pi$
$83$	7.42110	0.814572	0.407286	+	0.913301i	$0.366475\pi$
$84$	3.66208	0.399565
$85$	−12.6689	−1.37413
$86$	−2.17331	−0.234354
$87$	4.23750	0.454308
$88$	−6.23069	−0.664193
$89$	−11.1371	−1.18053	−0.590264	−	0.807210i	$-0.700976\pi$
$89$	−11.1371	−1.18053	−0.590264	+	0.807210i	$0.700976\pi$
$90$	6.33445	0.667709
$91$	1.00000	0.104828
$92$	21.4073	2.23187
$93$	7.28055	0.754958
$94$	4.98971	0.514649
$95$	5.95639	0.611113
$96$	2.94464	0.300536
$97$	−14.6047	−1.48288	−0.741442	−	0.671017i	$-0.765858\pi$
$97$	−14.6047	−1.48288	−0.741442	+	0.671017i	$0.765858\pi$
$98$	−2.37951	−0.240367
$99$	1.57542	0.158336
$100$	7.64150	0.764150
$101$	−11.4349	−1.13781	−0.568906	−	0.822403i	$-0.692633\pi$
$101$	−11.4349	−1.13781	−0.568906	+	0.822403i	$0.692633\pi$
$102$	−11.3242	−1.12126
$103$	11.1508	1.09873	0.549363	−	0.835584i	$-0.314871\pi$
$103$	11.1508	1.09873	0.549363	+	0.835584i	$0.314871\pi$
$104$	−3.95493	−0.387813
$105$	−2.66208	−0.259792
$106$	−2.58571	−0.251147
$107$	2.28403	0.220805	0.110403	−	0.993887i	$-0.464786\pi$
$107$	2.28403	0.220805	0.110403	+	0.993887i	$0.464786\pi$
$108$	3.66208	0.352384
$109$	14.6689	1.40502	0.702512	−	0.711671i	$-0.252062\pi$
$109$	14.6689	1.40502	0.702512	+	0.711671i	$0.252062\pi$
$110$	9.97942	0.951500
$111$	10.4750	0.994243
$112$	2.08666	0.197170
$113$	−4.23750	−0.398630	−0.199315	−	0.979935i	$-0.563872\pi$
$113$	−4.23750	−0.398630	−0.199315	+	0.979935i	$0.563872\pi$
$114$	5.32415	0.498653
$115$	−15.5617	−1.45113
$116$	15.5180	1.44081
$117$	1.00000	0.0924500
$118$	29.3500	2.70188
$119$	4.75902	0.436259
$120$	10.5283	0.961101
$121$	−8.51805	−0.774368
$122$	17.8893	1.61962
$123$	−2.25127	−0.202990
$124$	26.6619	2.39431
$125$	7.75555	0.693677
$126$	−2.37951	−0.211984
$127$	4.84916	0.430293	0.215147	−	0.976582i	$-0.430977\pi$
$127$	4.84916	0.430293	0.215147	+	0.976582i	$0.430977\pi$
$128$	20.7140	1.83087
$129$	0.913344	0.0804154
$130$	6.33445	0.555568
$131$	−6.36721	−0.556305	−0.278153	−	0.960537i	$-0.589722\pi$
$131$	−6.36721	−0.556305	−0.278153	+	0.960537i	$0.589722\pi$
$132$	5.76931	0.502154
$133$	−2.23750	−0.194016
$134$	37.3378	3.22549
$135$	−2.66208	−0.229115
$136$	−18.8216	−1.61394
$137$	−18.0258	−1.54005	−0.770024	−	0.638015i	$-0.779756\pi$
$137$	−18.0258	−1.54005	−0.770024	+	0.638015i	$0.779756\pi$
$138$	−13.9099	−1.18409
$139$	2.67585	0.226962	0.113481	−	0.993540i	$-0.463800\pi$
$139$	2.67585	0.226962	0.113481	+	0.993540i	$0.463800\pi$
$140$	−9.74873	−0.823918
$141$	−2.09695	−0.176595
$142$	−23.9151	−2.00691
$143$	1.57542	0.131743
$144$	2.08666	0.173888
$145$	−11.2805	−0.936799
$146$	−35.8823	−2.96964
$147$	1.00000	0.0824786
$148$	38.3603	3.15319
$149$	−7.46471	−0.611533	−0.305766	−	0.952107i	$-0.598913\pi$
$149$	−7.46471	−0.611533	−0.305766	+	0.952107i	$0.598913\pi$
$150$	−4.96522	−0.405409
$151$	13.0155	1.05919	0.529594	−	0.848251i	$-0.322344\pi$
$151$	13.0155	1.05919	0.529594	+	0.848251i	$0.322344\pi$
$152$	8.84916	0.717761
$153$	4.75902	0.384744
$154$	−3.74873	−0.302082
$155$	−19.3814	−1.55675
$156$	3.66208	0.293201
$157$	−17.1233	−1.36659	−0.683294	−	0.730143i	$-0.739453\pi$
$157$	−17.1233	−1.36659	−0.683294	+	0.730143i	$0.739453\pi$
$158$	27.9725	2.22537
$159$	1.08666	0.0861774
$160$	−7.83887	−0.619717
$161$	5.84568	0.460704
$162$	−2.37951	−0.186952
$163$	−0.849158	−0.0665112	−0.0332556	−	0.999447i	$-0.510588\pi$
$163$	−0.849158	−0.0665112	−0.0332556	+	0.999447i	$0.510588\pi$
$164$	−8.24431	−0.643773
$165$	−4.19389	−0.326494
$166$	−17.6586	−1.37057
$167$	18.3781	1.42214	0.711068	−	0.703123i	$-0.248212\pi$
$167$	18.3781	1.42214	0.711068	+	0.703123i	$0.248212\pi$
$168$	−3.95493	−0.305130
$169$	1.00000	0.0769231
$170$	30.1458	2.31208
$171$	−2.23750	−0.171106
$172$	3.34474	0.255034
$173$	−12.2565	−0.931844	−0.465922	−	0.884826i	$-0.654277\pi$
$173$	−12.2565	−0.931844	−0.465922	+	0.884826i	$0.654277\pi$
$174$	−10.0832	−0.764404
$175$	2.08666	0.157736
$176$	3.28736	0.247794
$177$	−12.3344	−0.927114
$178$	26.5008	1.98632
$179$	18.5146	1.38384	0.691922	−	0.721972i	$-0.256764\pi$
$179$	18.5146	1.38384	0.691922	+	0.721972i	$0.256764\pi$
$180$	−9.74873	−0.726628
$181$	−18.1664	−1.35029	−0.675147	−	0.737683i	$-0.735920\pi$
$181$	−18.1664	−1.35029	−0.675147	+	0.737683i	$0.735920\pi$
$182$	−2.37951	−0.176381
$183$	−7.51805	−0.555750
$184$	−23.1193	−1.70438
$185$	−27.8853	−2.05016
$186$	−17.3242	−1.27027
$187$	7.49747	0.548269
$188$	−7.67918	−0.560062
$189$	1.00000	0.0727393
$190$	−14.1733	−1.02824
$191$	23.5151	1.70149	0.850747	−	0.525575i	$-0.176150\pi$
$191$	23.5151	1.70149	0.850747	+	0.525575i	$0.176150\pi$
$192$	−11.1801	−0.806856
$193$	14.7344	1.06061	0.530303	−	0.847808i	$-0.322078\pi$
$193$	14.7344	1.06061	0.530303	+	0.847808i	$0.322078\pi$
$194$	34.7521	2.49505
$195$	−2.66208	−0.190635
$196$	3.66208	0.261577
$197$	14.5008	1.03314	0.516570	−	0.856245i	$-0.327209\pi$
$197$	14.5008	1.03314	0.516570	+	0.856245i	$0.327209\pi$
$198$	−3.74873	−0.266411
$199$	−13.5180	−0.958269	−0.479135	−	0.877741i	$-0.659049\pi$
$199$	−13.5180	−0.958269	−0.479135	+	0.877741i	$0.659049\pi$
$200$	−8.25259	−0.583546
$201$	−15.6914	−1.10678
$202$	27.2094	1.91445
$203$	4.23750	0.297414
$204$	17.4279	1.22020
$205$	5.99305	0.418572
$206$	−26.5336	−1.84868
$207$	5.84568	0.406303
$208$	2.08666	0.144684
$209$	−3.52500	−0.243830
$210$	6.33445	0.437118
$211$	4.06419	0.279790	0.139895	−	0.990166i	$-0.455323\pi$
$211$	4.06419	0.279790	0.139895	+	0.990166i	$0.455323\pi$
$212$	3.97942	0.273308
$213$	10.0504	0.688643
$214$	−5.43487	−0.371520
$215$	−2.43139	−0.165820
$216$	−3.95493	−0.269099
$217$	7.28055	0.494236
$218$	−34.9048	−2.36405
$219$	15.0797	1.01899
$220$	−15.3584	−1.03546
$221$	4.75902	0.320127
$222$	−24.9254	−1.67288
$223$	−0.0641862	−0.00429822	−0.00214911	−	0.999998i	$-0.500684\pi$
$223$	−0.0641862	−0.00429822	−0.00214911	+	0.999998i	$0.500684\pi$
$224$	2.94464	0.196747
$225$	2.08666	0.139110
$226$	10.0832	0.670723
$227$	−1.68614	−0.111913	−0.0559564	−	0.998433i	$-0.517821\pi$
$227$	−1.68614	−0.111913	−0.0559564	+	0.998433i	$0.517821\pi$
$228$	−8.19389	−0.542654
$229$	0.648310	0.0428415	0.0214208	−	0.999771i	$-0.493181\pi$
$229$	0.648310	0.0428415	0.0214208	+	0.999771i	$0.493181\pi$
$230$	37.0291	2.44163
$231$	1.57542	0.103655
$232$	−16.7590	−1.10028
$233$	3.10724	0.203562	0.101781	−	0.994807i	$-0.467546\pi$
$233$	3.10724	0.203562	0.101781	+	0.994807i	$0.467546\pi$
$234$	−2.37951	−0.155554
$235$	5.58223	0.364145
$236$	−45.1697	−2.94030
$237$	−11.7555	−0.763605
$238$	−11.3242	−0.734036
$239$	−15.0659	−0.974534	−0.487267	−	0.873253i	$-0.662006\pi$
$239$	−15.0659	−0.974534	−0.487267	+	0.873253i	$0.662006\pi$
$240$	−5.55484	−0.358563
$241$	25.7280	1.65729	0.828643	−	0.559777i	$-0.189113\pi$
$241$	25.7280	1.65729	0.828643	+	0.559777i	$0.189113\pi$
$242$	20.2688	1.30293
$243$	1.00000	0.0641500
$244$	−27.5317	−1.76253
$245$	−2.66208	−0.170074
$246$	5.35692	0.341544
$247$	−2.23750	−0.142369
$248$	−28.7941	−1.82843
$249$	7.42110	0.470293
$250$	−18.4544	−1.16716
$251$	−11.6258	−0.733816	−0.366908	−	0.930257i	$-0.619584\pi$
$251$	−11.6258	−0.733816	−0.366908	+	0.930257i	$0.619584\pi$
$252$	3.66208	0.230689
$253$	9.20941	0.578991
$254$	−11.5386	−0.723998
$255$	−12.6689	−0.793357
$256$	−26.9289	−1.68305
$257$	−12.5651	−0.783791	−0.391896	−	0.920010i	$-0.628181\pi$
$257$	−12.5651	−0.783791	−0.391896	+	0.920010i	$0.628181\pi$
$258$	−2.17331	−0.135305
$259$	10.4750	0.650885
$260$	−9.74873	−0.604591
$261$	4.23750	0.262295
$262$	15.1508	0.936022
$263$	9.37068	0.577821	0.288911	−	0.957356i	$-0.406707\pi$
$263$	9.37068	0.577821	0.288911	+	0.957356i	$0.406707\pi$
$264$	−6.23069	−0.383472
$265$	−2.89276	−0.177701
$266$	5.32415	0.326445
$267$	−11.1371	−0.681578
$268$	−57.4630	−3.51011
$269$	−10.3918	−0.633600	−0.316800	−	0.948492i	$-0.602608\pi$
$269$	−10.3918	−0.633600	−0.316800	+	0.948492i	$0.602608\pi$
$270$	6.33445	0.385502
$271$	−5.13026	−0.311641	−0.155821	−	0.987785i	$-0.549802\pi$
$271$	−5.13026	−0.311641	−0.155821	+	0.987785i	$0.549802\pi$
$272$	9.93045	0.602122
$273$	1.00000	0.0605228
$274$	42.8926	2.59124
$275$	3.28736	0.198235
$276$	21.4073	1.28857
$277$	8.04361	0.483293	0.241647	−	0.970364i	$-0.422312\pi$
$277$	8.04361	0.483293	0.241647	+	0.970364i	$0.422312\pi$
$278$	−6.36721	−0.381880
$279$	7.28055	0.435875
$280$	10.5283	0.629189
$281$	−27.8525	−1.66154	−0.830770	−	0.556616i	$-0.812100\pi$
$281$	−27.8525	−1.66154	−0.830770	+	0.556616i	$0.812100\pi$
$282$	4.98971	0.297133
$283$	23.8197	1.41594	0.707968	−	0.706244i	$-0.249612\pi$
$283$	23.8197	1.41594	0.707968	+	0.706244i	$0.249612\pi$
$284$	36.8054	2.18400
$285$	5.95639	0.352826
$286$	−3.74873	−0.221667
$287$	−2.25127	−0.132888
$288$	2.94464	0.173515
$289$	5.64831	0.332254
$290$	26.8422	1.57623
$291$	−14.6047	−0.856143
$292$	55.2230	3.23168
$293$	−16.4612	−0.961675	−0.480838	−	0.876810i	$-0.659667\pi$
$293$	−16.4612	−0.961675	−0.480838	+	0.876810i	$0.659667\pi$
$294$	−2.37951	−0.138776
$295$	32.8352	1.91174
$296$	−41.4279	−2.40795
$297$	1.57542	0.0914152
$298$	17.7624	1.02895
$299$	5.84568	0.338064
$300$	7.64150	0.441182
$301$	0.913344	0.0526443
$302$	−30.9706	−1.78216
$303$	−11.4349	−0.656916
$304$	−4.66889	−0.267779
$305$	20.0136	1.14598
$306$	−11.3242	−0.647359
$307$	1.95639	0.111657	0.0558287	−	0.998440i	$-0.482220\pi$
$307$	1.95639	0.111657	0.0558287	+	0.998440i	$0.482220\pi$
$308$	5.76931	0.328737
$309$	11.1508	0.634349
$310$	46.1182	2.61934
$311$	−6.67585	−0.378552	−0.189276	−	0.981924i	$-0.560614\pi$
$311$	−6.67585	−0.378552	−0.189276	+	0.981924i	$0.560614\pi$
$312$	−3.95493	−0.223904
$313$	−6.78364	−0.383434	−0.191717	−	0.981450i	$-0.561406\pi$
$313$	−6.78364	−0.383434	−0.191717	+	0.981450i	$0.561406\pi$
$314$	40.7451	2.29938
$315$	−2.66208	−0.149991
$316$	−43.0497	−2.42174
$317$	−30.6947	−1.72399	−0.861993	−	0.506920i	$-0.830784\pi$
$317$	−30.6947	−1.72399	−0.861993	+	0.506920i	$0.830784\pi$
$318$	−2.58571	−0.145000
$319$	6.67585	0.373776
$320$	29.7624	1.66377
$321$	2.28403	0.127482
$322$	−13.9099	−0.775167
$323$	−10.6483	−0.592488
$324$	3.66208	0.203449
$325$	2.08666	0.115747
$326$	2.02058	0.111910
$327$	14.6689	0.811191
$328$	8.90361	0.491620
$329$	−2.09695	−0.115608
$330$	9.97942	0.549349
$331$	−13.8267	−0.759983	−0.379992	−	0.924990i	$-0.624073\pi$
$331$	−13.8267	−0.759983	−0.379992	+	0.924990i	$0.624073\pi$
$332$	27.1766	1.49151
$333$	10.4750	0.574026
$334$	−43.7308	−2.39284
$335$	41.7716	2.28223
$336$	2.08666	0.113836
$337$	23.8633	1.29992	0.649959	−	0.759969i	$-0.274786\pi$
$337$	23.8633	1.29992	0.649959	+	0.759969i	$0.274786\pi$
$338$	−2.37951	−0.129428
$339$	−4.23750	−0.230149
$340$	−46.3945	−2.51609
$341$	11.4699	0.621132
$342$	5.32415	0.287897
$343$	1.00000	0.0539949
$344$	−3.61221	−0.194758
$345$	−15.5617	−0.837811
$346$	29.1645	1.56789
$347$	−13.6012	−0.730152	−0.365076	−	0.930978i	$-0.618957\pi$
$347$	−13.6012	−0.730152	−0.365076	+	0.930978i	$0.618957\pi$
$348$	15.5180	0.831855
$349$	−16.4039	−0.878078	−0.439039	−	0.898468i	$-0.644681\pi$
$349$	−16.4039	−0.878078	−0.439039	+	0.898468i	$0.644681\pi$
$350$	−4.96522	−0.265402
$351$	1.00000	0.0533761
$352$	4.63905	0.247262
$353$	−4.73322	−0.251924	−0.125962	−	0.992035i	$-0.540202\pi$
$353$	−4.73322	−0.251924	−0.125962	+	0.992035i	$0.540202\pi$
$354$	29.3500	1.55993
$355$	−26.7550	−1.42001
$356$	−40.7848	−2.16159
$357$	4.75902	0.251874
$358$	−44.0556	−2.32841
$359$	−17.5479	−0.926142	−0.463071	−	0.886321i	$-0.653253\pi$
$359$	−17.5479	−0.926142	−0.463071	+	0.886321i	$0.653253\pi$
$360$	10.5283	0.554892
$361$	−13.9936	−0.736505
$362$	43.2271	2.27196
$363$	−8.51805	−0.447082
$364$	3.66208	0.191945
$365$	−40.1433	−2.10120
$366$	17.8893	0.935088
$367$	−11.1888	−0.584052	−0.292026	−	0.956410i	$-0.594329\pi$
$367$	−11.1888	−0.584052	−0.292026	+	0.956410i	$0.594329\pi$
$368$	12.1979	0.635861
$369$	−2.25127	−0.117196
$370$	66.3533	3.44954
$371$	1.08666	0.0564164
$372$	26.6619	1.38236
$373$	−5.43195	−0.281256	−0.140628	−	0.990063i	$-0.544912\pi$
$373$	−5.43195	−0.281256	−0.140628	+	0.990063i	$0.544912\pi$
$374$	−17.8403	−0.922501
$375$	7.75555	0.400495
$376$	8.29328	0.427693
$377$	4.23750	0.218242
$378$	−2.37951	−0.122389
$379$	10.8422	0.556927	0.278463	−	0.960447i	$-0.410175\pi$
$379$	10.8422	0.556927	0.278463	+	0.960447i	$0.410175\pi$
$380$	21.8128	1.11897
$381$	4.84916	0.248430
$382$	−55.9545	−2.86288
$383$	10.5353	0.538328	0.269164	−	0.963094i	$-0.413253\pi$
$383$	10.5353	0.538328	0.269164	+	0.963094i	$0.413253\pi$
$384$	20.7140	1.05705
$385$	−4.19389	−0.213741
$386$	−35.0607	−1.78454
$387$	0.913344	0.0464279
$388$	−53.4836	−2.71522
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	6.33445	0.320757
$391$	27.8197	1.40690
$392$	−3.95493	−0.199754
$393$	−6.36721	−0.321183
$394$	−34.5048	−1.73833
$395$	31.2942	1.57458
$396$	5.76931	0.289919
$397$	−35.4400	−1.77868	−0.889340	−	0.457246i	$-0.848836\pi$
$397$	−35.4400	−1.77868	−0.889340	+	0.457246i	$0.848836\pi$
$398$	32.1664	1.61235
$399$	−2.23750	−0.112015
$400$	4.35413	0.217707
$401$	23.7241	1.18473	0.592363	−	0.805671i	$-0.298195\pi$
$401$	23.7241	1.18473	0.592363	+	0.805671i	$0.298195\pi$
$402$	37.3378	1.86224
$403$	7.28055	0.362670
$404$	−41.8754	−2.08338
$405$	−2.66208	−0.132280
$406$	−10.0832	−0.500420
$407$	16.5025	0.818000
$408$	−18.8216	−0.931809
$409$	−3.95639	−0.195631	−0.0978156	−	0.995205i	$-0.531186\pi$
$409$	−3.95639	−0.195631	−0.0978156	+	0.995205i	$0.531186\pi$
$410$	−14.2605	−0.704277
$411$	−18.0258	−0.889147
$412$	40.8352	2.01181
$413$	−12.3344	−0.606938
$414$	−13.9099	−0.683633
$415$	−19.7555	−0.969762
$416$	2.94464	0.144373
$417$	2.67585	0.131037
$418$	8.38779	0.410260
$419$	−18.0586	−0.882219	−0.441109	−	0.897453i	$-0.645415\pi$
$419$	−18.0586	−0.882219	−0.441109	+	0.897453i	$0.645415\pi$
$420$	−9.74873	−0.475689
$421$	24.4956	1.19384	0.596921	−	0.802300i	$-0.296391\pi$
$421$	24.4956	1.19384	0.596921	+	0.802300i	$0.296391\pi$
$422$	−9.67078	−0.470766
$423$	−2.09695	−0.101957
$424$	−4.29765	−0.208712
$425$	9.93045	0.481697
$426$	−23.9151	−1.15869
$427$	−7.51805	−0.363824
$428$	8.36428	0.404303
$429$	1.57542	0.0760621
$430$	5.78553	0.279003
$431$	−40.7779	−1.96420	−0.982101	−	0.188357i	$-0.939684\pi$
$431$	−40.7779	−1.96420	−0.982101	+	0.188357i	$0.939684\pi$
$432$	2.08666	0.100394
$433$	−18.0791	−0.868828	−0.434414	−	0.900713i	$-0.643045\pi$
$433$	−18.0791	−0.868828	−0.434414	+	0.900713i	$0.643045\pi$
$434$	−17.3242	−0.831586
$435$	−11.2805	−0.540861
$436$	53.7186	2.57265
$437$	−13.0797	−0.625687
$438$	−35.8823	−1.71452
$439$	20.7561	0.990635	0.495317	−	0.868712i	$-0.335052\pi$
$439$	20.7561	0.990635	0.495317	+	0.868712i	$0.335052\pi$
$440$	16.5866	0.790734
$441$	1.00000	0.0476190
$442$	−11.3242	−0.538635
$443$	−8.24042	−0.391514	−0.195757	−	0.980652i	$-0.562716\pi$
$443$	−8.24042	−0.391514	−0.195757	+	0.980652i	$0.562716\pi$
$444$	38.3603	1.82050
$445$	29.6478	1.40544
$446$	0.152732	0.00723206
$447$	−7.46471	−0.353069
$448$	−11.1801	−0.528211
$449$	36.1061	1.70395	0.851975	−	0.523582i	$-0.175405\pi$
$449$	36.1061	1.70395	0.851975	+	0.523582i	$0.175405\pi$
$450$	−4.96522	−0.234063
$451$	−3.54669	−0.167007
$452$	−15.5180	−0.729908
$453$	13.0155	0.611522
$454$	4.01218	0.188301
$455$	−2.66208	−0.124800
$456$	8.84916	0.414400
$457$	−6.54052	−0.305953	−0.152976	−	0.988230i	$-0.548886\pi$
$457$	−6.54052	−0.305953	−0.152976	+	0.988230i	$0.548886\pi$
$458$	−1.54266	−0.0720838
$459$	4.75902	0.222132
$460$	−56.9880	−2.65708
$461$	−14.6987	−0.684588	−0.342294	−	0.939593i	$-0.611204\pi$
$461$	−14.6987	−0.684588	−0.342294	+	0.939593i	$0.611204\pi$
$462$	−3.74873	−0.174407
$463$	21.7775	1.01208	0.506042	−	0.862509i	$-0.331108\pi$
$463$	21.7775	1.01208	0.506042	+	0.862509i	$0.331108\pi$
$464$	8.84220	0.410489
$465$	−19.3814	−0.898790
$466$	−7.39371	−0.342507
$467$	35.0086	1.62000	0.810001	−	0.586428i	$-0.199466\pi$
$467$	35.0086	1.62000	0.810001	+	0.586428i	$0.199466\pi$
$468$	3.66208	0.169280
$469$	−15.6914	−0.724560
$470$	−13.2830	−0.612699
$471$	−17.1233	−0.789000
$472$	48.7819	2.24537
$473$	1.43890	0.0661607
$474$	27.9725	1.28482
$475$	−4.66889	−0.214223
$476$	17.4279	0.798807
$477$	1.08666	0.0497546
$478$	35.8496	1.63972
$479$	31.7814	1.45213	0.726064	−	0.687628i	$-0.241348\pi$
$479$	31.7814	1.45213	0.726064	+	0.687628i	$0.241348\pi$
$480$	−7.83887	−0.357794
$481$	10.4750	0.477619
$482$	−61.2201	−2.78850
$483$	5.84568	0.265988
$484$	−31.1938	−1.41790
$485$	38.8789	1.76540
$486$	−2.37951	−0.107937
$487$	−28.5817	−1.29516	−0.647580	−	0.761998i	$-0.724219\pi$
$487$	−28.5817	−1.29516	−0.647580	+	0.761998i	$0.724219\pi$
$488$	29.7334	1.34597
$489$	−0.849158	−0.0384002
$490$	6.33445	0.286161
$491$	21.7160	0.980028	0.490014	−	0.871715i	$-0.336992\pi$
$491$	21.7160	0.980028	0.490014	+	0.871715i	$0.336992\pi$
$492$	−8.24431	−0.371682
$493$	20.1664	0.908247
$494$	5.32415	0.239545
$495$	−4.19389	−0.188501
$496$	15.1920	0.682141
$497$	10.0504	0.450823
$498$	−17.6586	−0.791301
$499$	−42.6895	−1.91104	−0.955522	−	0.294921i	$-0.904707\pi$
$499$	−42.6895	−1.91104	−0.955522	+	0.294921i	$0.904707\pi$
$500$	28.4014	1.27015
$501$	18.3781	0.821071
$502$	27.6638	1.23470
$503$	21.8922	0.976125	0.488063	−	0.872809i	$-0.337704\pi$
$503$	21.8922	0.976125	0.488063	+	0.872809i	$0.337704\pi$
$504$	−3.95493	−0.176167
$505$	30.4405	1.35458
$506$	−21.9139	−0.974192
$507$	1.00000	0.0444116
$508$	17.7580	0.787883
$509$	−5.36546	−0.237820	−0.118910	−	0.992905i	$-0.537940\pi$
$509$	−5.36546	−0.237820	−0.118910	+	0.992905i	$0.537940\pi$
$510$	30.1458	1.33488
$511$	15.0797	0.667087
$512$	22.6496	1.00098
$513$	−2.23750	−0.0987880
$514$	29.8989	1.31878
$515$	−29.6844	−1.30805
$516$	3.34474	0.147244
$517$	−3.30357	−0.145291
$518$	−24.9254	−1.09516
$519$	−12.2565	−0.538000
$520$	10.5283	0.461698
$521$	−11.5221	−0.504791	−0.252396	−	0.967624i	$-0.581218\pi$
$521$	−11.5221	−0.504791	−0.252396	+	0.967624i	$0.581218\pi$
$522$	−10.0832	−0.441329
$523$	−3.62584	−0.158547	−0.0792734	−	0.996853i	$-0.525260\pi$
$523$	−3.62584	−0.158547	−0.0792734	+	0.996853i	$0.525260\pi$
$524$	−23.3172	−1.01862
$525$	2.08666	0.0910691
$526$	−22.2977	−0.972224
$527$	34.6483	1.50930
$528$	3.28736	0.143064
$529$	11.1720	0.485738
$530$	6.88336	0.298994
$531$	−12.3344	−0.535269
$532$	−8.19389	−0.355250
$533$	−2.25127	−0.0975132
$534$	26.5008	1.14680
$535$	−6.08026	−0.262872
$536$	62.0583	2.68051
$537$	18.5146	0.798963
$538$	24.7275	1.06608
$539$	1.57542	0.0678582
$540$	−9.74873	−0.419519
$541$	37.2300	1.60064	0.800321	−	0.599572i	$-0.204662\pi$
$541$	37.2300	1.60064	0.800321	+	0.599572i	$0.204662\pi$
$542$	12.2075	0.524358
$543$	−18.1664	−0.779593
$544$	14.0136	0.600829
$545$	−39.0497	−1.67271
$546$	−2.37951	−0.101834
$547$	−4.34529	−0.185791	−0.0928956	−	0.995676i	$-0.529612\pi$
$547$	−4.34529	−0.185791	−0.0928956	+	0.995676i	$0.529612\pi$
$548$	−66.0119	−2.81989
$549$	−7.51805	−0.320862
$550$	−7.82232	−0.333545
$551$	−9.48140	−0.403921
$552$	−23.1193	−0.984022
$553$	−11.7555	−0.499897
$554$	−19.1399	−0.813175
$555$	−27.8853	−1.18366
$556$	9.79915	0.415577
$557$	28.0052	1.18662	0.593310	−	0.804974i	$-0.297821\pi$
$557$	28.0052	1.18662	0.593310	+	0.804974i	$0.297821\pi$
$558$	−17.3242	−0.733390
$559$	0.913344	0.0386303
$560$	−5.55484	−0.234735
$561$	7.49747	0.316543
$562$	66.2753	2.79566
$563$	−22.2525	−0.937829	−0.468915	−	0.883243i	$-0.655355\pi$
$563$	−22.2525	−0.937829	−0.468915	+	0.883243i	$0.655355\pi$
$564$	−7.67918	−0.323352
$565$	11.2805	0.474576
$566$	−56.6793	−2.38241
$567$	1.00000	0.0419961
$568$	−39.7487	−1.66782
$569$	3.10724	0.130262	0.0651311	−	0.997877i	$-0.479253\pi$
$569$	3.10724	0.130262	0.0651311	+	0.997877i	$0.479253\pi$
$570$	−14.1733	−0.593655
$571$	16.5772	0.693733	0.346866	−	0.937915i	$-0.387246\pi$
$571$	16.5772	0.693733	0.346866	+	0.937915i	$0.387246\pi$
$572$	5.76931	0.241227
$573$	23.5151	0.982358
$574$	5.35692	0.223593
$575$	12.1979	0.508689
$576$	−11.1801	−0.465839
$577$	−7.45253	−0.310253	−0.155126	−	0.987895i	$-0.549578\pi$
$577$	−7.45253	−0.310253	−0.155126	+	0.987895i	$0.549578\pi$
$578$	−13.4402	−0.559039
$579$	14.7344	0.612341
$580$	−41.3102	−1.71531
$581$	7.42110	0.307879
$582$	34.7521	1.44052
$583$	1.71194	0.0709014
$584$	−59.6392	−2.46789
$585$	−2.66208	−0.110063
$586$	39.1697	1.61809
$587$	11.9892	0.494845	0.247423	−	0.968908i	$-0.420416\pi$
$587$	11.9892	0.494845	0.247423	+	0.968908i	$0.420416\pi$
$588$	3.66208	0.151022
$589$	−16.2902	−0.671227
$590$	−78.1319	−3.21664
$591$	14.5008	0.596483
$592$	21.8577	0.898347
$593$	−33.4767	−1.37473	−0.687363	−	0.726314i	$-0.741232\pi$
$593$	−33.4767	−1.37473	−0.687363	+	0.726314i	$0.741232\pi$
$594$	−3.74873	−0.153812
$595$	−12.6689	−0.519374
$596$	−27.3363	−1.11974
$597$	−13.5180	−0.553257
$598$	−13.9099	−0.568817
$599$	−13.5863	−0.555120	−0.277560	−	0.960708i	$-0.589526\pi$
$599$	−13.5863	−0.555120	−0.277560	+	0.960708i	$0.589526\pi$
$600$	−8.25259	−0.336910
$601$	−6.78364	−0.276710	−0.138355	−	0.990383i	$-0.544182\pi$
$601$	−6.78364	−0.276710	−0.138355	+	0.990383i	$0.544182\pi$
$602$	−2.17331	−0.0885776
$603$	−15.6914	−0.639002
$604$	47.6638	1.93941
$605$	22.6757	0.921898
$606$	27.2094	1.10531
$607$	−17.4905	−0.709918	−0.354959	−	0.934882i	$-0.615505\pi$
$607$	−17.4905	−0.709918	−0.354959	+	0.934882i	$0.615505\pi$
$608$	−6.58863	−0.267204
$609$	4.23750	0.171712
$610$	−47.6227	−1.92819
$611$	−2.09695	−0.0848334
$612$	17.4279	0.704482
$613$	−38.2455	−1.54472	−0.772361	−	0.635184i	$-0.780924\pi$
$613$	−38.2455	−1.54472	−0.772361	+	0.635184i	$0.780924\pi$
$614$	−4.65526	−0.187871
$615$	5.99305	0.241663
$616$	−6.23069	−0.251041
$617$	−34.1542	−1.37500	−0.687498	−	0.726187i	$-0.741291\pi$
$617$	−34.1542	−1.37500	−0.687498	+	0.726187i	$0.741291\pi$
$618$	−26.5336	−1.06734
$619$	−8.56805	−0.344379	−0.172190	−	0.985064i	$-0.555084\pi$
$619$	−8.56805	−0.344379	−0.172190	+	0.985064i	$0.555084\pi$
$620$	−70.9761	−2.85047
$621$	5.84568	0.234579
$622$	15.8853	0.636941
$623$	−11.1371	−0.446197
$624$	2.08666	0.0835331
$625$	−31.0791	−1.24317
$626$	16.1417	0.645154
$627$	−3.52500	−0.140775
$628$	−62.7069	−2.50228
$629$	49.8508	1.98768
$630$	6.33445	0.252370
$631$	−17.7119	−0.705101	−0.352551	−	0.935793i	$-0.614686\pi$
$631$	−17.7119	−0.705101	−0.352551	+	0.935793i	$0.614686\pi$
$632$	46.4924	1.84937
$633$	4.06419	0.161537
$634$	73.0384	2.90073
$635$	−12.9088	−0.512271
$636$	3.97942	0.157794
$637$	1.00000	0.0396214
$638$	−15.8853	−0.628903
$639$	10.0504	0.397588
$640$	−55.1422	−2.17969
$641$	16.6117	0.656121	0.328061	−	0.944657i	$-0.393605\pi$
$641$	16.6117	0.656121	0.328061	+	0.944657i	$0.393605\pi$
$642$	−5.43487	−0.214497
$643$	12.9500	0.510698	0.255349	−	0.966849i	$-0.417810\pi$
$643$	12.9500	0.510698	0.255349	+	0.966849i	$0.417810\pi$
$644$	21.4073	0.843567
$645$	−2.43139	−0.0957360
$646$	25.3378	0.996902
$647$	−23.6775	−0.930857	−0.465428	−	0.885086i	$-0.654100\pi$
$647$	−23.6775	−0.930857	−0.465428	+	0.885086i	$0.654100\pi$
$648$	−3.95493	−0.155364
$649$	−19.4319	−0.762771
$650$	−4.96522	−0.194752
$651$	7.28055	0.285347
$652$	−3.10968	−0.121785
$653$	22.2811	0.871927	0.435963	−	0.899964i	$-0.356408\pi$
$653$	22.2811	0.871927	0.435963	+	0.899964i	$0.356408\pi$
$654$	−34.9048	−1.36489
$655$	16.9500	0.662291
$656$	−4.69762	−0.183411
$657$	15.0797	0.588315
$658$	4.98971	0.194519
$659$	15.5165	0.604435	0.302218	−	0.953239i	$-0.402273\pi$
$659$	15.5165	0.604435	0.302218	+	0.953239i	$0.402273\pi$
$660$	−15.3584	−0.597823
$661$	28.1444	1.09469	0.547346	−	0.836906i	$-0.315638\pi$
$661$	28.1444	1.09469	0.547346	+	0.836906i	$0.315638\pi$
$662$	32.9008	1.27872
$663$	4.75902	0.184825
$664$	−29.3500	−1.13900
$665$	5.95639	0.230979
$666$	−24.9254	−0.965839
$667$	24.7711	0.959139
$668$	67.3018	2.60399
$669$	−0.0641862	−0.00248158
$670$	−99.3961	−3.84000
$671$	−11.8441	−0.457236
$672$	2.94464	0.113592
$673$	7.13477	0.275025	0.137513	−	0.990500i	$-0.456089\pi$
$673$	7.13477	0.275025	0.137513	+	0.990500i	$0.456089\pi$
$674$	−56.7831	−2.18720
$675$	2.08666	0.0803154
$676$	3.66208	0.140849
$677$	−10.7660	−0.413770	−0.206885	−	0.978365i	$-0.566333\pi$
$677$	−10.7660	−0.413770	−0.206885	+	0.978365i	$0.566333\pi$
$678$	10.0832	0.387242
$679$	−14.6047	−0.560477
$680$	50.1046	1.92142
$681$	−1.68614	−0.0646129
$682$	−27.2928	−1.04510
$683$	−12.2020	−0.466898	−0.233449	−	0.972369i	$-0.575001\pi$
$683$	−12.2020	−0.466898	−0.233449	+	0.972369i	$0.575001\pi$
$684$	−8.19389	−0.313301
$685$	47.9861	1.83345
$686$	−2.37951	−0.0908502
$687$	0.648310	0.0247346
$688$	1.90583	0.0726593
$689$	1.08666	0.0413983
$690$	37.0291	1.40968
$691$	32.0367	1.21873	0.609366	−	0.792889i	$-0.291424\pi$
$691$	32.0367	1.21873	0.609366	+	0.792889i	$0.291424\pi$
$692$	−44.8842	−1.70624
$693$	1.57542	0.0598453
$694$	32.3643	1.22853
$695$	−7.12331	−0.270202
$696$	−16.7590	−0.635249
$697$	−10.7138	−0.405815
$698$	39.0332	1.47743
$699$	3.10724	0.117526
$700$	7.64150	0.288821
$701$	−14.9513	−0.564704	−0.282352	−	0.959311i	$-0.591115\pi$
$701$	−14.9513	−0.564704	−0.282352	+	0.959311i	$0.591115\pi$
$702$	−2.37951	−0.0898089
$703$	−23.4378	−0.883973
$704$	−17.6134	−0.663830
$705$	5.58223	0.210239
$706$	11.2627	0.423879
$707$	−11.4349	−0.430053
$708$	−45.1697	−1.69758
$709$	−8.58279	−0.322333	−0.161167	−	0.986927i	$-0.551526\pi$
$709$	−8.58279	−0.322333	−0.161167	+	0.986927i	$0.551526\pi$
$710$	63.6638	2.38926
$711$	−11.7555	−0.440867
$712$	44.0464	1.65071
$713$	42.5598	1.59388
$714$	−11.3242	−0.423796
$715$	−4.19389	−0.156843
$716$	67.8018	2.53387
$717$	−15.0659	−0.562648
$718$	41.7554	1.55830
$719$	35.9644	1.34125	0.670623	−	0.741798i	$-0.266027\pi$
$719$	35.9644	1.34125	0.670623	+	0.741798i	$0.266027\pi$
$720$	−5.55484	−0.207017
$721$	11.1508	0.415279
$722$	33.2979	1.23922
$723$	25.7280	0.956835
$724$	−66.5266	−2.47244
$725$	8.84220	0.328391
$726$	20.2688	0.752246
$727$	−31.5111	−1.16868	−0.584341	−	0.811508i	$-0.698647\pi$
$727$	−31.5111	−1.16868	−0.584341	+	0.811508i	$0.698647\pi$
$728$	−3.95493	−0.146580
$729$	1.00000	0.0370370
$730$	95.5215	3.53541
$731$	4.34662	0.160766
$732$	−27.5317	−1.01760
$733$	−26.6047	−0.982667	−0.491334	−	0.870971i	$-0.663490\pi$
$733$	−26.6047	−0.982667	−0.491334	+	0.870971i	$0.663490\pi$
$734$	26.6240	0.982708
$735$	−2.66208	−0.0981922
$736$	17.2134	0.634496
$737$	−24.7205	−0.910591
$738$	5.35692	0.197191
$739$	−50.3397	−1.85177	−0.925887	−	0.377800i	$-0.876681\pi$
$739$	−50.3397	−1.85177	−0.925887	+	0.377800i	$0.876681\pi$
$740$	−102.118	−3.75393
$741$	−2.23750	−0.0821966
$742$	−2.58571	−0.0949245
$743$	23.4021	0.858540	0.429270	−	0.903176i	$-0.358771\pi$
$743$	23.4021	0.858540	0.429270	+	0.903176i	$0.358771\pi$
$744$	−28.7941	−1.05564
$745$	19.8716	0.728040
$746$	12.9254	0.473232
$747$	7.42110	0.271524
$748$	27.4563	1.00390
$749$	2.28403	0.0834565
$750$	−18.4544	−0.673860
$751$	49.0305	1.78915	0.894574	−	0.446920i	$-0.147479\pi$
$751$	49.0305	1.78915	0.894574	+	0.446920i	$0.147479\pi$
$752$	−4.37561	−0.159562
$753$	−11.6258	−0.423669
$754$	−10.0832	−0.367208
$755$	−34.6483	−1.26098
$756$	3.66208	0.133188
$757$	−35.3883	−1.28621	−0.643106	−	0.765778i	$-0.722354\pi$
$757$	−35.3883	−1.28621	−0.643106	+	0.765778i	$0.722354\pi$
$758$	−25.7992	−0.937067
$759$	9.20941	0.334280
$760$	−23.5571	−0.854507
$761$	27.7051	1.00431	0.502155	−	0.864778i	$-0.332541\pi$
$761$	27.7051	1.00431	0.502155	+	0.864778i	$0.332541\pi$
$762$	−11.5386	−0.418000
$763$	14.6689	0.531049
$764$	86.1142	3.11550
$765$	−12.6689	−0.458045
$766$	−25.0689	−0.905775
$767$	−12.3344	−0.445371
$768$	−26.9289	−0.971712
$769$	21.1383	0.762265	0.381133	−	0.924520i	$-0.375534\pi$
$769$	21.1383	0.762265	0.381133	+	0.924520i	$0.375534\pi$
$770$	9.97942	0.359633
$771$	−12.5651	−0.452522
$772$	53.9586	1.94201
$773$	−41.4537	−1.49099	−0.745493	−	0.666513i	$-0.767786\pi$
$773$	−41.4537	−1.49099	−0.745493	+	0.666513i	$0.767786\pi$
$774$	−2.17331	−0.0781181
$775$	15.1920	0.545713
$776$	57.7606	2.07349
$777$	10.4750	0.375788
$778$	−14.2771	−0.511858
$779$	5.03721	0.180477
$780$	−9.74873	−0.349061
$781$	15.8336	0.566572
$782$	−66.1974	−2.36721
$783$	4.23750	0.151436
$784$	2.08666	0.0745234
$785$	45.5836	1.62695
$786$	15.1508	0.540413
$787$	−28.7711	−1.02558	−0.512789	−	0.858515i	$-0.671388\pi$
$787$	−28.7711	−1.02558	−0.512789	+	0.858515i	$0.671388\pi$
$788$	53.1031	1.89172
$789$	9.37068	0.333605
$790$	−74.4649	−2.64934
$791$	−4.23750	−0.150668
$792$	−6.23069	−0.221398
$793$	−7.51805	−0.266974
$794$	84.3298	2.99275
$795$	−2.89276	−0.102596
$796$	−49.5041	−1.75463
$797$	19.5357	0.691990	0.345995	−	0.938236i	$-0.387541\pi$
$797$	19.5357	0.691990	0.345995	+	0.938236i	$0.387541\pi$
$798$	5.32415	0.188473
$799$	−9.97942	−0.353046
$800$	6.14446	0.217239
$801$	−11.1371	−0.393509
$802$	−56.4518	−1.99338
$803$	23.7569	0.838362
$804$	−57.4630	−2.02656
$805$	−15.5617	−0.548476
$806$	−17.3242	−0.610217
$807$	−10.3918	−0.365809
$808$	45.2241	1.59098
$809$	−36.1824	−1.27211	−0.636053	−	0.771645i	$-0.719434\pi$
$809$	−36.1824	−1.27211	−0.636053	+	0.771645i	$0.719434\pi$
$810$	6.33445	0.222570
$811$	0.794087	0.0278842	0.0139421	−	0.999903i	$-0.495562\pi$
$811$	0.794087	0.0278842	0.0139421	+	0.999903i	$0.495562\pi$
$812$	15.5180	0.544577
$813$	−5.13026	−0.179926
$814$	−39.2680	−1.37634
$815$	2.26052	0.0791827
$816$	9.93045	0.347635
$817$	−2.04361	−0.0714967
$818$	9.41429	0.329163
$819$	1.00000	0.0349428
$820$	21.9470	0.766422
$821$	−15.8525	−0.553256	−0.276628	−	0.960977i	$-0.589217\pi$
$821$	−15.8525	−0.553256	−0.276628	+	0.960977i	$0.589217\pi$
$822$	42.8926	1.49605
$823$	−20.0412	−0.698591	−0.349295	−	0.937013i	$-0.613579\pi$
$823$	−20.0412	−0.698591	−0.349295	+	0.937013i	$0.613579\pi$
$824$	−44.1008	−1.53633
$825$	3.28736	0.114451
$826$	29.3500	1.02122
$827$	34.7848	1.20959	0.604794	−	0.796382i	$-0.293256\pi$
$827$	34.7848	1.20959	0.604794	+	0.796382i	$0.293256\pi$
$828$	21.4073	0.743956
$829$	−30.6793	−1.06554	−0.532769	−	0.846261i	$-0.678848\pi$
$829$	−30.6793	−1.06554	−0.532769	+	0.846261i	$0.678848\pi$
$830$	47.0086	1.63169
$831$	8.04361	0.279030
$832$	−11.1801	−0.387601
$833$	4.75902	0.164890
$834$	−6.36721	−0.220478
$835$	−48.9238	−1.69308
$836$	−12.9088	−0.446461
$837$	7.28055	0.251653
$838$	42.9706	1.48439
$839$	39.8238	1.37487	0.687436	−	0.726245i	$-0.258736\pi$
$839$	39.8238	1.37487	0.687436	+	0.726245i	$0.258736\pi$
$840$	10.5283	0.363262
$841$	−11.0436	−0.380814
$842$	−58.2875	−2.00872
$843$	−27.8525	−0.959291
$844$	14.8834	0.512307
$845$	−2.66208	−0.0915782
$846$	4.98971	0.171550
$847$	−8.51805	−0.292684
$848$	2.26748	0.0778655
$849$	23.8197	0.817491
$850$	−23.6296	−0.810489
$851$	61.2335	2.09906
$852$	36.8054	1.26093
$853$	24.7505	0.847440	0.423720	−	0.905793i	$-0.360724\pi$
$853$	24.7505	0.847440	0.423720	+	0.905793i	$0.360724\pi$
$854$	17.8893	0.612159
$855$	5.95639	0.203704
$856$	−9.03317	−0.308748
$857$	6.47097	0.221044	0.110522	−	0.993874i	$-0.464748\pi$
$857$	6.47097	0.221044	0.110522	+	0.993874i	$0.464748\pi$
$858$	−3.74873	−0.127980
$859$	31.0741	1.06023	0.530117	−	0.847925i	$-0.322148\pi$
$859$	31.0741	1.06023	0.530117	+	0.847925i	$0.322148\pi$
$860$	−8.90395	−0.303622
$861$	−2.25127	−0.0767230
$862$	97.0314	3.30490
$863$	28.6391	0.974885	0.487442	−	0.873155i	$-0.337930\pi$
$863$	28.6391	0.974885	0.487442	+	0.873155i	$0.337930\pi$
$864$	2.94464	0.100179
$865$	32.6277	1.10938
$866$	43.0195	1.46186
$867$	5.64831	0.191827
$868$	26.6619	0.904965
$869$	−18.5199	−0.628246
$870$	26.8422	0.910036
$871$	−15.6914	−0.531681
$872$	−58.0145	−1.96462
$873$	−14.6047	−0.494294
$874$	31.1233	1.05276
$875$	7.75555	0.262185
$876$	55.2230	1.86581
$877$	0.00110921	3.74555e−5 0	1.87278e−5	−	1.00000i	$-0.499994\pi$
$877$	0.00110921	3.74555e−5 0	1.87278e−5		1.00000i	$0.499994\pi$
$878$	−49.3894	−1.66681
$879$	−16.4612	−0.555223
$880$	−8.75121	−0.295003
$881$	23.9479	0.806824	0.403412	−	0.915019i	$-0.367824\pi$
$881$	23.9479	0.806824	0.403412	+	0.915019i	$0.367824\pi$
$882$	−2.37951	−0.0801223
$883$	51.9965	1.74982	0.874911	−	0.484283i	$-0.160919\pi$
$883$	51.9965	1.74982	0.874911	+	0.484283i	$0.160919\pi$
$884$	17.4279	0.586164
$885$	32.8352	1.10374
$886$	19.6082	0.658750
$887$	10.8697	0.364970	0.182485	−	0.983209i	$-0.441586\pi$
$887$	10.8697	0.364970	0.182485	+	0.983209i	$0.441586\pi$
$888$	−41.4279	−1.39023
$889$	4.84916	0.162636
$890$	−70.5472	−2.36475
$891$	1.57542	0.0527786
$892$	−0.235055	−0.00787021
$893$	4.69192	0.157009
$894$	17.7624	0.594062
$895$	−49.2872	−1.64749
$896$	20.7140	0.692005
$897$	5.84568	0.195182
$898$	−85.9148	−2.86701
$899$	30.8513	1.02895
$900$	7.64150	0.254717
$901$	5.17142	0.172285
$902$	8.43940	0.281001
$903$	0.913344	0.0303942
$904$	16.7590	0.557397
$905$	48.3603	1.60755
$906$	−30.9706	−1.02893
$907$	−25.4892	−0.846354	−0.423177	−	0.906047i	$-0.639085\pi$
$907$	−25.4892	−0.846354	−0.423177	+	0.906047i	$0.639085\pi$
$908$	−6.17476	−0.204917
$909$	−11.4349	−0.379271
$910$	6.33445	0.209985
$911$	42.2059	1.39834	0.699172	−	0.714953i	$-0.253552\pi$
$911$	42.2059	1.39834	0.699172	+	0.714953i	$0.253552\pi$
$912$	−4.66889	−0.154602
$913$	11.6914	0.386928
$914$	15.5632	0.514786
$915$	20.0136	0.661630
$916$	2.37416	0.0784445
$917$	−6.36721	−0.210264
$918$	−11.3242	−0.373753
$919$	−29.4033	−0.969925	−0.484963	−	0.874535i	$-0.661167\pi$
$919$	−29.4033	−0.969925	−0.484963	+	0.874535i	$0.661167\pi$
$920$	61.5453	2.02909
$921$	1.95639	0.0644654
$922$	34.9758	1.15187
$923$	10.0504	0.330814
$924$	5.76931	0.189797
$925$	21.8577	0.718677
$926$	−51.8197	−1.70290
$927$	11.1508	0.366242
$928$	12.4779	0.409608
$929$	−13.3759	−0.438849	−0.219425	−	0.975629i	$-0.570418\pi$
$929$	−13.3759	−0.438849	−0.219425	+	0.975629i	$0.570418\pi$
$930$	46.1182	1.51228
$931$	−2.23750	−0.0733311
$932$	11.3789	0.372730
$933$	−6.67585	−0.218557
$934$	−83.3033	−2.72577
$935$	−19.9588	−0.652724
$936$	−3.95493	−0.129271
$937$	−24.9981	−0.816653	−0.408326	−	0.912836i	$-0.633887\pi$
$937$	−24.9981	−0.816653	−0.408326	+	0.912836i	$0.633887\pi$
$938$	37.3378	1.21912
$939$	−6.78364	−0.221376
$940$	20.4426	0.666763
$941$	10.5369	0.343493	0.171746	−	0.985141i	$-0.445059\pi$
$941$	10.5369	0.343493	0.171746	+	0.985141i	$0.445059\pi$
$942$	40.7451	1.32755
$943$	−13.1602	−0.428555
$944$	−25.7377	−0.837692
$945$	−2.66208	−0.0865974
$946$	−3.42388	−0.111320
$947$	−52.7779	−1.71505	−0.857525	−	0.514442i	$-0.827999\pi$
$947$	−52.7779	−1.71505	−0.857525	+	0.514442i	$0.827999\pi$
$948$	−43.0497	−1.39819
$949$	15.0797	0.489508
$950$	11.1097	0.360446
$951$	−30.6947	−0.995344
$952$	−18.8216	−0.610012
$953$	21.8486	0.707746	0.353873	−	0.935294i	$-0.384865\pi$
$953$	21.8486	0.707746	0.353873	+	0.935294i	$0.384865\pi$
$954$	−2.58571	−0.0837155
$955$	−62.5991	−2.02566
$956$	−55.1726	−1.78441
$957$	6.67585	0.215799
$958$	−75.6241	−2.44330
$959$	−18.0258	−0.582084
$960$	29.7624	0.960576
$961$	22.0064	0.709884
$962$	−24.9254	−0.803627
$963$	2.28403	0.0736017
$964$	94.2180	3.03456
$965$	−39.2241	−1.26267
$966$	−13.9099	−0.447543
$967$	1.94143	0.0624323	0.0312162	−	0.999513i	$-0.490062\pi$
$967$	1.94143	0.0624323	0.0312162	+	0.999513i	$0.490062\pi$
$968$	33.6883	1.08278
$969$	−10.6483	−0.342073
$970$	−92.5127	−2.97040
$971$	−14.9077	−0.478412	−0.239206	−	0.970969i	$-0.576887\pi$
$971$	−14.9077	−0.478412	−0.239206	+	0.970969i	$0.576887\pi$
$972$	3.66208	0.117461
$973$	2.67585	0.0857837
$974$	68.0105	2.17920
$975$	2.08666	0.0668265
$976$	−15.6876	−0.502147
$977$	−16.5353	−0.529011	−0.264505	−	0.964384i	$-0.585209\pi$
$977$	−16.5353	−0.529011	−0.264505	+	0.964384i	$0.585209\pi$
$978$	2.02058	0.0646110
$979$	−17.5456	−0.560759
$980$	−9.74873	−0.311412
$981$	14.6689	0.468342
$982$	−51.6734	−1.64897
$983$	−30.0694	−0.959065	−0.479533	−	0.877524i	$-0.659194\pi$
$983$	−30.0694	−0.959065	−0.479533	+	0.877524i	$0.659194\pi$
$984$	8.90361	0.283837
$985$	−38.6023	−1.22997
$986$	−47.9861	−1.52819
$987$	−2.09695	−0.0667465
$988$	−8.19389	−0.260682
$989$	5.33912	0.169774
$990$	9.97942	0.317167
$991$	43.5902	1.38469	0.692345	−	0.721567i	$-0.256578\pi$
$991$	43.5902	1.38469	0.692345	+	0.721567i	$0.256578\pi$
$992$	21.4386	0.680677
$993$	−13.8267	−0.438777
$994$	−23.9151	−0.758541
$995$	35.9861	1.14084
$996$	27.1766	0.861125
$997$	57.8577	1.83237	0.916186	−	0.400753i	$-0.131251\pi$
$997$	57.8577	1.83237	0.916186	+	0.400753i	$0.131251\pi$
$998$	101.580	3.21546
$999$	10.4750	0.331414

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.a.e.1.1	✓	4
3.2	odd	2		819.2.a.k.1.4		4
4.3	odd	2		4368.2.a.br.1.2		4
5.4	even	2		6825.2.a.bg.1.4		4
7.6	odd	2		1911.2.a.s.1.1		4
13.12	even	2		3549.2.a.w.1.4		4
21.20	even	2		5733.2.a.bf.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.a.e.1.1	✓	4	1.1	even	1	trivial
819.2.a.k.1.4		4	3.2	odd	2
1911.2.a.s.1.1		4	7.6	odd	2
3549.2.a.w.1.4		4	13.12	even	2
4368.2.a.br.1.2		4	4.3	odd	2
5733.2.a.bf.1.4		4	21.20	even	2
6825.2.a.bg.1.4		4	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.a (trivial)

\(f(q)\)	\(=\)	\(q-2.37951 q^{2} +1.00000 q^{3} +3.66208 q^{4} -2.66208 q^{5} -2.37951 q^{6} +1.00000 q^{7} -3.95493 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.37951 q^{2} +1.00000 q^{3} +3.66208 q^{4} -2.66208 q^{5} -2.37951 q^{6} +1.00000 q^{7} -3.95493 q^{8} +1.00000 q^{9} +6.33445 q^{10} +1.57542 q^{11} +3.66208 q^{12} +1.00000 q^{13} -2.37951 q^{14} -2.66208 q^{15} +2.08666 q^{16} +4.75902 q^{17} -2.37951 q^{18} -2.23750 q^{19} -9.74873 q^{20} +1.00000 q^{21} -3.74873 q^{22} +5.84568 q^{23} -3.95493 q^{24} +2.08666 q^{25} -2.37951 q^{26} +1.00000 q^{27} +3.66208 q^{28} +4.23750 q^{29} +6.33445 q^{30} +7.28055 q^{31} +2.94464 q^{32} +1.57542 q^{33} -11.3242 q^{34} -2.66208 q^{35} +3.66208 q^{36} +10.4750 q^{37} +5.32415 q^{38} +1.00000 q^{39} +10.5283 q^{40} -2.25127 q^{41} -2.37951 q^{42} +0.913344 q^{43} +5.76931 q^{44} -2.66208 q^{45} -13.9099 q^{46} -2.09695 q^{47} +2.08666 q^{48} +1.00000 q^{49} -4.96522 q^{50} +4.75902 q^{51} +3.66208 q^{52} +1.08666 q^{53} -2.37951 q^{54} -4.19389 q^{55} -3.95493 q^{56} -2.23750 q^{57} -10.0832 q^{58} -12.3344 q^{59} -9.74873 q^{60} -7.51805 q^{61} -17.3242 q^{62} +1.00000 q^{63} -11.1801 q^{64} -2.66208 q^{65} -3.74873 q^{66} -15.6914 q^{67} +17.4279 q^{68} +5.84568 q^{69} +6.33445 q^{70} +10.0504 q^{71} -3.95493 q^{72} +15.0797 q^{73} -24.9254 q^{74} +2.08666 q^{75} -8.19389 q^{76} +1.57542 q^{77} -2.37951 q^{78} -11.7555 q^{79} -5.55484 q^{80} +1.00000 q^{81} +5.35692 q^{82} +7.42110 q^{83} +3.66208 q^{84} -12.6689 q^{85} -2.17331 q^{86} +4.23750 q^{87} -6.23069 q^{88} -11.1371 q^{89} +6.33445 q^{90} +1.00000 q^{91} +21.4073 q^{92} +7.28055 q^{93} +4.98971 q^{94} +5.95639 q^{95} +2.94464 q^{96} -14.6047 q^{97} -2.37951 q^{98} +1.57542 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + 4 q^{3} + 7 q^{4} - 3 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + q^2 + 4 * q^3 + 7 * q^4 - 3 * q^5 + q^6 + 4 * q^7 + 3 * q^8 + 4 * q^9	\( 4 q + q^{2} + 4 q^{3} + 7 q^{4} - 3 q^{5} + q^{6} + 4 q^{7} + 3 q^{8} + 4 q^{9} - 4 q^{10} - 2 q^{11} + 7 q^{12} + 4 q^{13} + q^{14} - 3 q^{15} + 9 q^{16} - 2 q^{17} + q^{18} + 7 q^{19} - 32 q^{20} + 4 q^{21} - 8 q^{22} + 3 q^{23} + 3 q^{24} + 9 q^{25} + q^{26} + 4 q^{27} + 7 q^{28} + q^{29} - 4 q^{30} + 3 q^{31} + 7 q^{32} - 2 q^{33} - 30 q^{34} - 3 q^{35} + 7 q^{36} + 10 q^{37} + 6 q^{38} + 4 q^{39} - 14 q^{40} - 16 q^{41} + q^{42} + 3 q^{43} - 12 q^{44} - 3 q^{45} - 18 q^{46} + 5 q^{47} + 9 q^{48} + 4 q^{49} + 13 q^{50} - 2 q^{51} + 7 q^{52} + 5 q^{53} + q^{54} + 10 q^{55} + 3 q^{56} + 7 q^{57} - 4 q^{58} - 20 q^{59} - 32 q^{60} + 12 q^{61} - 54 q^{62} + 4 q^{63} + 5 q^{64} - 3 q^{65} - 8 q^{66} - 22 q^{67} - 10 q^{68} + 3 q^{69} - 4 q^{70} + 3 q^{72} - 13 q^{73} - 6 q^{74} + 9 q^{75} - 6 q^{76} - 2 q^{77} + q^{78} + 11 q^{79} - 42 q^{80} + 4 q^{81} + 10 q^{82} + q^{83} + 7 q^{84} + 8 q^{85} - 10 q^{86} + q^{87} - 60 q^{88} - 5 q^{89} - 4 q^{90} + 4 q^{91} + 34 q^{92} + 3 q^{93} + 34 q^{94} + 13 q^{95} + 7 q^{96} - 17 q^{97} + q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q + q^2 + 4 * q^3 + 7 * q^4 - 3 * q^5 + q^6 + 4 * q^7 + 3 * q^8 + 4 * q^9 - 4 * q^10 - 2 * q^11 + 7 * q^12 + 4 * q^13 + q^14 - 3 * q^15 + 9 * q^16 - 2 * q^17 + q^18 + 7 * q^19 - 32 * q^20 + 4 * q^21 - 8 * q^22 + 3 * q^23 + 3 * q^24 + 9 * q^25 + q^26 + 4 * q^27 + 7 * q^28 + q^29 - 4 * q^30 + 3 * q^31 + 7 * q^32 - 2 * q^33 - 30 * q^34 - 3 * q^35 + 7 * q^36 + 10 * q^37 + 6 * q^38 + 4 * q^39 - 14 * q^40 - 16 * q^41 + q^42 + 3 * q^43 - 12 * q^44 - 3 * q^45 - 18 * q^46 + 5 * q^47 + 9 * q^48 + 4 * q^49 + 13 * q^50 - 2 * q^51 + 7 * q^52 + 5 * q^53 + q^54 + 10 * q^55 + 3 * q^56 + 7 * q^57 - 4 * q^58 - 20 * q^59 - 32 * q^60 + 12 * q^61 - 54 * q^62 + 4 * q^63 + 5 * q^64 - 3 * q^65 - 8 * q^66 - 22 * q^67 - 10 * q^68 + 3 * q^69 - 4 * q^70 + 3 * q^72 - 13 * q^73 - 6 * q^74 + 9 * q^75 - 6 * q^76 - 2 * q^77 + q^78 + 11 * q^79 - 42 * q^80 + 4 * q^81 + 10 * q^82 + q^83 + 7 * q^84 + 8 * q^85 - 10 * q^86 + q^87 - 60 * q^88 - 5 * q^89 - 4 * q^90 + 4 * q^91 + 34 * q^92 + 3 * q^93 + 34 * q^94 + 13 * q^95 + 7 * q^96 - 17 * q^97 + q^98 - 2 * q^99

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