LMFDB - Embedded newform 3549.2.a.w.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3549, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$28.3389076774$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.17428.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 6x^{2} + 4x + 6 $ x^4 - x^3 - 6x^2 + 4x + 6
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.787711$ of defining polynomial
Character	$\chi$	$=$	3549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.37951	1.68257	0.841285	−	0.540593i	$-0.181800\pi$
$2$	2.37951	1.68257	0.841285	+	0.540593i	$0.181800\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.66208	1.83104
$5$	2.66208	1.19052	0.595259	−	0.803534i	$-0.297050\pi$
$5$	2.66208	1.19052	0.595259	+	0.803534i	$0.297050\pi$
$6$	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	$-0.576329\pi$
$11$	−1.57542	−0.475007	−0.237504	+	0.971387i	$0.576329\pi$
$12$	3.66208	1.05715
$13$	0	0
$13$	0	0
$14$	−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	$-0.417378\pi$
$19$	2.23750	0.513317	0.256659	+	0.966502i	$0.417378\pi$
$20$	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
$26$	0	0
$27$	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	$-0.726832\pi$
$31$	−7.28055	−1.30763	−0.653813	+	0.756656i	$0.726832\pi$
$32$	−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	$-0.830186\pi$
$37$	−10.4750	−1.72208	−0.861039	+	0.508538i	$0.830186\pi$
$38$	5.32415	0.863692
$39$	0	0
$40$	10.5283	1.66468
$41$	2.25127	0.351589	0.175794	−	0.984427i	$-0.443751\pi$
$41$	2.25127	0.351589	0.175794	+	0.984427i	$0.443751\pi$
$42$	−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	$-0.451127\pi$
$47$	2.09695	0.305871	0.152936	+	0.988236i	$0.451127\pi$
$48$	2.08666	0.301183
$49$	1.00000	0.142857
$50$	4.96522	0.702189
$51$	4.75902	0.666397
$52$	0	0
$53$	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	$-0.203287\pi$
$59$	12.3344	1.60581	0.802904	+	0.596108i	$0.203287\pi$
$60$	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
$65$	0	0
$66$	−3.74873	−0.461437
$67$	15.6914	1.91700	0.958502	−	0.285084i	$-0.0920217\pi$
$67$	15.6914	1.91700	0.958502	+	0.285084i	$0.0920217\pi$
$68$	17.4279	2.11345
$69$	5.84568	0.703737
$70$	−6.33445	−0.757111
$71$	−10.0504	−1.19277	−0.596383	−	0.802700i	$-0.703396\pi$
$71$	−10.0504	−1.19277	−0.596383	+	0.802700i	$0.703396\pi$
$72$	3.95493	0.466093
$73$	−15.0797	−1.76495	−0.882473	−	0.470363i	$-0.844123\pi$
$73$	−15.0797	−1.76495	−0.882473	+	0.470363i	$0.844123\pi$
$74$	−24.9254	−2.89752
$75$	2.08666	0.240946
$76$	8.19389	0.939904
$77$	1.57542	0.179536
$78$	0	0
$79$	−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	$-0.633525\pi$
$83$	−7.42110	−0.814572	−0.407286	+	0.913301i	$0.633525\pi$
$84$	−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	$-0.299024\pi$
$89$	11.1371	1.18053	0.590264	+	0.807210i	$0.299024\pi$
$90$	6.33445	0.667709
$91$	0	0
$92$	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	$-0.234142\pi$
$97$	14.6047	1.48288	0.741442	+	0.671017i	$0.234142\pi$
$98$	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	$0.314871\pi$
$104$	0	0
$105$	−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	$-0.747938\pi$
$109$	−14.6689	−1.40502	−0.702512	+	0.711671i	$0.747938\pi$
$110$	−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
$117$	0	0
$118$	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
$130$	0	0
$131$	−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	$-0.220244\pi$
$137$	18.0258	1.54005	0.770024	+	0.638015i	$0.220244\pi$
$138$	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
$143$	0	0
$144$	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	$-0.401087\pi$
$149$	7.46471	0.611533	0.305766	+	0.952107i	$0.401087\pi$
$150$	4.96522	0.405409
$151$	−13.0155	−1.05919	−0.529594	−	0.848251i	$-0.677656\pi$
$151$	−13.0155	−1.05919	−0.529594	+	0.848251i	$0.677656\pi$
$152$	8.84916	0.717761
$153$	4.75902	0.384744
$154$	3.74873	0.302082
$155$	−19.3814	−1.55675
$156$	0	0
$157$	−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	$-0.489412\pi$
$163$	0.849158	0.0665112	0.0332556	+	0.999447i	$0.489412\pi$
$164$	8.24431	0.643773
$165$	−4.19389	−0.326494
$166$	−17.6586	−1.37057
$167$	−18.3781	−1.42214	−0.711068	−	0.703123i	$-0.751788\pi$
$167$	−18.3781	−1.42214	−0.711068	+	0.703123i	$0.751788\pi$
$168$	−3.95493	−0.305130
$169$	0	0
$170$	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	$0.735920\pi$
$182$	0	0
$183$	−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	$-0.677922\pi$
$193$	−14.7344	−1.06061	−0.530303	+	0.847808i	$0.677922\pi$
$194$	34.7521	2.49505
$195$	0	0
$196$	3.66208	0.261577
$197$	−14.5008	−1.03314	−0.516570	−	0.856245i	$-0.672791\pi$
$197$	−14.5008	−1.03314	−0.516570	+	0.856245i	$0.672791\pi$
$198$	−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
$208$	0	0
$209$	−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
$221$	0	0
$222$	−24.9254	−1.67288
$223$	0.0641862	0.00429822	0.00214911	−	0.999998i	$-0.499316\pi$
$223$	0.0641862	0.00429822	0.00214911	+	0.999998i	$0.499316\pi$
$224$	2.94464	0.196747
$225$	2.08666	0.139110
$226$	−10.0832	−0.670723
$227$	1.68614	0.111913	0.0559564	−	0.998433i	$-0.482179\pi$
$227$	1.68614	0.111913	0.0559564	+	0.998433i	$0.482179\pi$
$228$	8.19389	0.542654
$229$	−0.648310	−0.0428415	−0.0214208	−	0.999771i	$-0.506819\pi$
$229$	−0.648310	−0.0428415	−0.0214208	+	0.999771i	$0.506819\pi$
$230$	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	$0.467546\pi$
$234$	0	0
$235$	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	$-0.337994\pi$
$239$	15.0659	0.974534	0.487267	+	0.873253i	$0.337994\pi$
$240$	5.55484	0.358563
$241$	−25.7280	−1.65729	−0.828643	−	0.559777i	$-0.810887\pi$
$241$	−25.7280	−1.65729	−0.828643	+	0.559777i	$0.810887\pi$
$242$	−20.2688	−1.30293
$243$	1.00000	0.0641500
$244$	−27.5317	−1.76253
$245$	2.66208	0.170074
$246$	5.35692	0.341544
$247$	0	0
$248$	−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
$260$	0	0
$261$	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	$-0.450198\pi$
$271$	5.13026	0.311641	0.155821	+	0.987785i	$0.450198\pi$
$272$	9.93045	0.602122
$273$	0	0
$274$	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	$-0.187900\pi$
$281$	27.8525	1.66154	0.830770	+	0.556616i	$0.187900\pi$
$282$	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
$286$	0	0
$287$	−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	$-0.340333\pi$
$293$	16.4612	0.961675	0.480838	+	0.876810i	$0.340333\pi$
$294$	2.37951	0.138776
$295$	32.8352	1.91174
$296$	−41.4279	−2.40795
$297$	−1.57542	−0.0914152
$298$	17.7624	1.02895
$299$	0	0
$300$	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	$-0.517780\pi$
$307$	−1.95639	−0.111657	−0.0558287	+	0.998440i	$0.517780\pi$
$308$	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	$0.560614\pi$
$312$	0	0
$313$	−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	$-0.169216\pi$
$317$	30.6947	1.72399	0.861993	+	0.506920i	$0.169216\pi$
$318$	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
$325$	0	0
$326$	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	$-0.375927\pi$
$331$	13.8267	0.759983	0.379992	+	0.924990i	$0.375927\pi$
$332$	−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	$0.274786\pi$
$338$	0	0
$339$	−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	$-0.355319\pi$
$349$	16.4039	0.878078	0.439039	+	0.898468i	$0.355319\pi$
$350$	−4.96522	−0.265402
$351$	0	0
$352$	4.63905	0.247262
$353$	4.73322	0.251924	0.125962	−	0.992035i	$-0.459798\pi$
$353$	4.73322	0.251924	0.125962	+	0.992035i	$0.459798\pi$
$354$	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	$-0.346747\pi$
$359$	17.5479	0.926142	0.463071	+	0.886321i	$0.346747\pi$
$360$	10.5283	0.554892
$361$	−13.9936	−0.736505
$362$	−43.2271	−2.27196
$363$	−8.51805	−0.447082
$364$	0	0
$365$	−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
$377$	0	0
$378$	−2.37951	−0.122389
$379$	−10.8422	−0.556927	−0.278463	−	0.960447i	$-0.589825\pi$
$379$	−10.8422	−0.556927	−0.278463	+	0.960447i	$0.589825\pi$
$380$	21.8128	1.11897
$381$	4.84916	0.248430
$382$	55.9545	2.86288
$383$	−10.5353	−0.538328	−0.269164	−	0.963094i	$-0.586747\pi$
$383$	−10.5353	−0.538328	−0.269164	+	0.963094i	$0.586747\pi$
$384$	−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	$0.451394\pi$
$390$	0	0
$391$	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	$-0.151164\pi$
$397$	35.4400	1.77868	0.889340	+	0.457246i	$0.151164\pi$
$398$	−32.1664	−1.61235
$399$	−2.23750	−0.112015
$400$	4.35413	0.217707
$401$	−23.7241	−1.18473	−0.592363	−	0.805671i	$-0.701805\pi$
$401$	−23.7241	−1.18473	−0.592363	+	0.805671i	$0.701805\pi$
$402$	37.3378	1.86224
$403$	0	0
$404$	−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	$-0.468814\pi$
$409$	3.95639	0.195631	0.0978156	+	0.995205i	$0.468814\pi$
$410$	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
$416$	0	0
$417$	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	$-0.703609\pi$
$421$	−24.4956	−1.19384	−0.596921	+	0.802300i	$0.703609\pi$
$422$	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
$429$	0	0
$430$	5.78553	0.279003
$431$	40.7779	1.96420	0.982101	−	0.188357i	$-0.0603163\pi$
$431$	40.7779	1.96420	0.982101	+	0.188357i	$0.0603163\pi$
$432$	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
$442$	0	0
$443$	−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	$-0.824595\pi$
$449$	−36.1061	−1.70395	−0.851975	+	0.523582i	$0.824595\pi$
$450$	4.96522	0.234063
$451$	−3.54669	−0.167007
$452$	−15.5180	−0.729908
$453$	−13.0155	−0.611522
$454$	4.01218	0.188301
$455$	0	0
$456$	8.84916	0.414400
$457$	6.54052	0.305953	0.152976	−	0.988230i	$-0.451114\pi$
$457$	6.54052	0.305953	0.152976	+	0.988230i	$0.451114\pi$
$458$	−1.54266	−0.0720838
$459$	4.75902	0.222132
$460$	56.9880	2.65708
$461$	14.6987	0.684588	0.342294	−	0.939593i	$-0.388796\pi$
$461$	14.6987	0.684588	0.342294	+	0.939593i	$0.388796\pi$
$462$	3.74873	0.174407
$463$	−21.7775	−1.01208	−0.506042	−	0.862509i	$-0.668892\pi$
$463$	−21.7775	−1.01208	−0.506042	+	0.862509i	$0.668892\pi$
$464$	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	$0.199466\pi$
$468$	0	0
$469$	−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	$-0.758652\pi$
$479$	−31.7814	−1.45213	−0.726064	+	0.687628i	$0.758652\pi$
$480$	−7.83887	−0.357794
$481$	0	0
$482$	−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	$-0.275781\pi$
$487$	28.5817	1.29516	0.647580	+	0.761998i	$0.275781\pi$
$488$	−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
$494$	0	0
$495$	−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	$-0.0952934\pi$
$499$	42.6895	1.91104	0.955522	+	0.294921i	$0.0952934\pi$
$500$	−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
$507$	0	0
$508$	17.7580	0.787883
$509$	5.36546	0.237820	0.118910	−	0.992905i	$-0.462060\pi$
$509$	5.36546	0.237820	0.118910	+	0.992905i	$0.462060\pi$
$510$	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
$520$	0	0
$521$	−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
$533$	0	0
$534$	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	$-0.795338\pi$
$541$	−37.2300	−1.60064	−0.800321	+	0.599572i	$0.795338\pi$
$542$	12.2075	0.524358
$543$	−18.1664	−0.779593
$544$	−14.0136	−0.600829
$545$	−39.0497	−1.67271
$546$	0	0
$547$	−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	$-0.702179\pi$
$557$	−28.0052	−1.18662	−0.593310	+	0.804974i	$0.702179\pi$
$558$	−17.3242	−0.733390
$559$	0	0
$560$	−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	$0.387246\pi$
$572$	0	0
$573$	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	$-0.450422\pi$
$577$	7.45253	0.310253	0.155126	+	0.987895i	$0.450422\pi$
$578$	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
$585$	0	0
$586$	39.1697	1.61809
$587$	−11.9892	−0.494845	−0.247423	−	0.968908i	$-0.579584\pi$
$587$	−11.9892	−0.494845	−0.247423	+	0.968908i	$0.579584\pi$
$588$	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	$-0.258768\pi$
$593$	33.4767	1.37473	0.687363	+	0.726314i	$0.258768\pi$
$594$	−3.74873	−0.153812
$595$	−12.6689	−0.519374
$596$	27.3363	1.11974
$597$	−13.5180	−0.553257
$598$	0	0
$599$	−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
$611$	0	0
$612$	17.4279	0.704482
$613$	38.2455	1.54472	0.772361	−	0.635184i	$-0.219076\pi$
$613$	38.2455	1.54472	0.772361	+	0.635184i	$0.219076\pi$
$614$	−4.65526	−0.187871
$615$	5.99305	0.241663
$616$	6.23069	0.251041
$617$	34.1542	1.37500	0.687498	−	0.726187i	$-0.258709\pi$
$617$	34.1542	1.37500	0.687498	+	0.726187i	$0.258709\pi$
$618$	26.5336	1.06734
$619$	8.56805	0.344379	0.172190	−	0.985064i	$-0.444916\pi$
$619$	8.56805	0.344379	0.172190	+	0.985064i	$0.444916\pi$
$620$	−70.9761	−2.85047
$621$	5.84568	0.234579
$622$	−15.8853	−0.636941
$623$	−11.1371	−0.446197
$624$	0	0
$625$	−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	$-0.385314\pi$
$631$	17.7119	0.705101	0.352551	+	0.935793i	$0.385314\pi$
$632$	−46.4924	−1.84937
$633$	4.06419	0.161537
$634$	73.0384	2.90073
$635$	12.9088	0.512271
$636$	3.97942	0.157794
$637$	0	0
$638$	−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	$-0.582190\pi$
$643$	−12.9500	−0.510698	−0.255349	+	0.966849i	$0.582190\pi$
$644$	−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
$650$	0	0
$651$	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	$-0.684362\pi$
$661$	−28.1444	−1.09469	−0.547346	+	0.836906i	$0.684362\pi$
$662$	32.9008	1.27872
$663$	0	0
$664$	−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
$676$	0	0
$677$	−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	$-0.424999\pi$
$683$	12.2020	0.466898	0.233449	+	0.972369i	$0.424999\pi$
$684$	8.19389	0.313301
$685$	47.9861	1.83345
$686$	−2.37951	−0.0908502
$687$	−0.648310	−0.0247346
$688$	1.90583	0.0726593
$689$	0	0
$690$	37.0291	1.40968
$691$	−32.0367	−1.21873	−0.609366	−	0.792889i	$-0.708576\pi$
$691$	−32.0367	−1.21873	−0.609366	+	0.792889i	$0.708576\pi$
$692$	−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	$0.591115\pi$
$702$	0	0
$703$	−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	$-0.448474\pi$
$709$	8.58279	0.322333	0.161167	+	0.986927i	$0.448474\pi$
$710$	−63.6638	−2.38926
$711$	−11.7555	−0.440867
$712$	44.0464	1.65071
$713$	−42.5598	−1.59388
$714$	−11.3242	−0.423796
$715$	0	0
$716$	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	$0.698647\pi$
$728$	0	0
$729$	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	$-0.336510\pi$
$733$	26.6047	0.982667	0.491334	+	0.870971i	$0.336510\pi$
$734$	−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	$-0.123319\pi$
$739$	50.3397	1.85177	0.925887	+	0.377800i	$0.123319\pi$
$740$	−102.118	−3.75393
$741$	0	0
$742$	−2.58571	−0.0949245
$743$	−23.4021	−0.858540	−0.429270	−	0.903176i	$-0.641229\pi$
$743$	−23.4021	−0.858540	−0.429270	+	0.903176i	$0.641229\pi$
$744$	−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
$754$	0	0
$755$	−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	$-0.667459\pi$
$761$	−27.7051	−1.00431	−0.502155	+	0.864778i	$0.667459\pi$
$762$	11.5386	0.418000
$763$	14.6689	0.531049
$764$	86.1142	3.11550
$765$	12.6689	0.458045
$766$	−25.0689	−0.905775
$767$	0	0
$768$	−26.9289	−0.971712
$769$	−21.1383	−0.762265	−0.381133	−	0.924520i	$-0.624466\pi$
$769$	−21.1383	−0.762265	−0.381133	+	0.924520i	$0.624466\pi$
$770$	9.97942	0.359633
$771$	−12.5651	−0.452522
$772$	−53.9586	−1.94201
$773$	41.4537	1.49099	0.745493	−	0.666513i	$-0.232214\pi$
$773$	41.4537	1.49099	0.745493	+	0.666513i	$0.232214\pi$
$774$	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
$780$	0	0
$781$	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	$-0.328612\pi$
$787$	28.7711	1.02558	0.512789	+	0.858515i	$0.328612\pi$
$788$	−53.1031	−1.89172
$789$	9.37068	0.333605
$790$	−74.4649	−2.64934
$791$	4.23750	0.150668
$792$	−6.23069	−0.221398
$793$	0	0
$794$	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
$806$	0	0
$807$	−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	$-0.504438\pi$
$811$	−0.794087	−0.0278842	−0.0139421	+	0.999903i	$0.504438\pi$
$812$	−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
$819$	0	0
$820$	21.9470	0.766422
$821$	15.8525	0.553256	0.276628	−	0.960977i	$-0.410783\pi$
$821$	15.8525	0.553256	0.276628	+	0.960977i	$0.410783\pi$
$822$	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	$-0.706744\pi$
$827$	−34.7848	−1.20959	−0.604794	+	0.796382i	$0.706744\pi$
$828$	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
$832$	0	0
$833$	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	$-0.741264\pi$
$839$	−39.8238	−1.37487	−0.687436	+	0.726245i	$0.741264\pi$
$840$	−10.5283	−0.363262
$841$	−11.0436	−0.380814
$842$	−58.2875	−2.00872
$843$	27.8525	0.959291
$844$	14.8834	0.512307
$845$	0	0
$846$	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	$-0.639276\pi$
$853$	−24.7505	−0.847440	−0.423720	+	0.905793i	$0.639276\pi$
$854$	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	$0.464748\pi$
$858$	0	0
$859$	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	$-0.662070\pi$
$863$	−28.6391	−0.974885	−0.487442	+	0.873155i	$0.662070\pi$
$864$	−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
$871$	0	0
$872$	−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	$-0.500006\pi$
$877$	−0.00110921	−3.74555e−5 0	−1.87278e−5		1.00000i	$0.500006\pi$
$878$	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	$0.160919\pi$
$884$	0	0
$885$	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
$897$	0	0
$898$	−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
$910$	0	0
$911$	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
$923$	0	0
$924$	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	$-0.429582\pi$
$929$	13.3759	0.438849	0.219425	+	0.975629i	$0.429582\pi$
$930$	−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
$936$	0	0
$937$	−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	$-0.554941\pi$
$941$	−10.5369	−0.343493	−0.171746	+	0.985141i	$0.554941\pi$
$942$	−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	$-0.172001\pi$
$947$	52.7779	1.71505	0.857525	+	0.514442i	$0.172001\pi$
$948$	−43.0497	−1.39819
$949$	0	0
$950$	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
$962$	0	0
$963$	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	$-0.509938\pi$
$967$	−1.94143	−0.0624323	−0.0312162	+	0.999513i	$0.509938\pi$
$968$	−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
$975$	0	0
$976$	−15.6876	−0.502147
$977$	16.5353	0.529011	0.264505	−	0.964384i	$-0.414791\pi$
$977$	16.5353	0.529011	0.264505	+	0.964384i	$0.414791\pi$
$978$	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	$-0.340806\pi$
$983$	30.0694	0.959065	0.479533	+	0.877524i	$0.340806\pi$
$984$	8.90361	0.283837
$985$	−38.6023	−1.22997
$986$	47.9861	1.52819
$987$	−2.09695	−0.0667465
$988$	0	0
$989$	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	3549.2.a.w.1.4		4
13.12	even	2		273.2.a.e.1.1	✓	4
39.38	odd	2		819.2.a.k.1.4		4
52.51	odd	2		4368.2.a.br.1.2		4
65.64	even	2		6825.2.a.bg.1.4		4
91.90	odd	2		1911.2.a.s.1.1		4
273.272	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	13.12	even	2
819.2.a.k.1.4		4	39.38	odd	2
1911.2.a.s.1.1		4	91.90	odd	2
3549.2.a.w.1.4		4	1.1	even	1	trivial
4368.2.a.br.1.2		4	52.51	odd	2
5733.2.a.bf.1.4		4	273.272	even	2
6825.2.a.bg.1.4		4	65.64	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

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