LMFDB - Embedded newform 1849.2.a.n.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,2,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1849.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:	$14.7643393337$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} - 15 x^{16} + 106 x^{15} + 47 x^{14} - 897 x^{13} + 364 x^{12} + 3855 x^{11} + \cdots - 27 $ x^18 - 5x^17 - 15x^16 + 106x^15 + 47x^14 - 897x^13 + 364x^12 + 3855x^11 - 3223x^10 - 8851x^9 + 9909x^8 + 10400x^7 - 14483x^6 - 5118x^5 + 9945x^4 - 27x^3 - 2493x^2 + 513*x - 27
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$-1.09100$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.09100 q^{2} +1.45952 q^{3} -0.809726 q^{4} +1.35087 q^{5} +1.59233 q^{6} +0.216325 q^{7} -3.06540 q^{8} -0.869803 q^{9} +O(q^{10})$	\(q+1.09100 q^{2} +1.45952 q^{3} -0.809726 q^{4} +1.35087 q^{5} +1.59233 q^{6} +0.216325 q^{7} -3.06540 q^{8} -0.869803 q^{9} +1.47379 q^{10} -6.03107 q^{11} -1.18181 q^{12} -2.87520 q^{13} +0.236010 q^{14} +1.97161 q^{15} -1.72489 q^{16} +0.282609 q^{17} -0.948953 q^{18} -1.13727 q^{19} -1.09383 q^{20} +0.315731 q^{21} -6.57988 q^{22} -3.94262 q^{23} -4.47401 q^{24} -3.17516 q^{25} -3.13683 q^{26} -5.64805 q^{27} -0.175164 q^{28} +6.90413 q^{29} +2.15103 q^{30} -9.89090 q^{31} +4.24895 q^{32} -8.80247 q^{33} +0.308326 q^{34} +0.292226 q^{35} +0.704302 q^{36} +7.54258 q^{37} -1.24076 q^{38} -4.19641 q^{39} -4.14095 q^{40} +5.12997 q^{41} +0.344461 q^{42} +4.88351 q^{44} -1.17499 q^{45} -4.30138 q^{46} +0.462299 q^{47} -2.51752 q^{48} -6.95320 q^{49} -3.46409 q^{50} +0.412474 q^{51} +2.32812 q^{52} +8.35339 q^{53} -6.16201 q^{54} -8.14717 q^{55} -0.663124 q^{56} -1.65987 q^{57} +7.53238 q^{58} -8.35544 q^{59} -1.59647 q^{60} +13.4329 q^{61} -10.7909 q^{62} -0.188160 q^{63} +8.08538 q^{64} -3.88401 q^{65} -9.60347 q^{66} -6.29357 q^{67} -0.228836 q^{68} -5.75433 q^{69} +0.318818 q^{70} -1.47896 q^{71} +2.66630 q^{72} -0.820130 q^{73} +8.22893 q^{74} -4.63421 q^{75} +0.920878 q^{76} -1.30467 q^{77} -4.57827 q^{78} +6.15595 q^{79} -2.33010 q^{80} -5.63403 q^{81} +5.59678 q^{82} -7.20537 q^{83} -0.255655 q^{84} +0.381767 q^{85} +10.0767 q^{87} +18.4877 q^{88} +4.43399 q^{89} -1.28191 q^{90} -0.621978 q^{91} +3.19244 q^{92} -14.4360 q^{93} +0.504367 q^{94} -1.53630 q^{95} +6.20143 q^{96} -4.46918 q^{97} -7.58592 q^{98} +5.24585 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) $ 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9	\( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9} - 7 q^{10} - 2 q^{11} - 16 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 9 q^{16} - 11 q^{17} - 25 q^{18} - 31 q^{19} - 25 q^{20} - 19 q^{22} - 11 q^{23} + 18 q^{24} + 9 q^{25} - 27 q^{26} - 23 q^{27} - 20 q^{28} - 37 q^{29} + 17 q^{30} - 12 q^{31} - 39 q^{32} - 38 q^{33} - 14 q^{34} + 16 q^{35} + 47 q^{36} + 19 q^{37} + 56 q^{38} - 46 q^{39} + 6 q^{40} - 7 q^{41} + q^{42} + 7 q^{44} - 23 q^{45} + 47 q^{46} - q^{47} - 15 q^{48} - 6 q^{49} + 3 q^{50} - 38 q^{51} + 15 q^{52} + 3 q^{53} - 67 q^{54} - 28 q^{55} - 81 q^{56} + 46 q^{57} + 34 q^{58} + 17 q^{59} - 83 q^{60} - 28 q^{61} - 33 q^{62} - 26 q^{63} + 10 q^{64} - 16 q^{65} - 72 q^{66} + 18 q^{67} + 53 q^{68} - 7 q^{69} + 34 q^{70} - 86 q^{71} + 2 q^{72} + 27 q^{73} - 79 q^{74} - 31 q^{75} - 59 q^{76} - 43 q^{77} + 91 q^{78} + 17 q^{79} - 8 q^{80} - 10 q^{81} - 13 q^{82} - 12 q^{83} - 32 q^{84} - 28 q^{85} - 43 q^{87} + 23 q^{88} - 51 q^{89} + 10 q^{90} + 20 q^{91} + 18 q^{92} + 30 q^{93} + 15 q^{94} - q^{95} - 20 q^{96} - 19 q^{97} + 5 q^{98} + 38 q^{99}+O(q^{100}) \) 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9 - 7 * q^10 - 2 * q^11 - 16 * q^12 - 7 * q^13 - 4 * q^14 + 3 * q^15 + 9 * q^16 - 11 * q^17 - 25 * q^18 - 31 * q^19 - 25 * q^20 - 19 * q^22 - 11 * q^23 + 18 * q^24 + 9 * q^25 - 27 * q^26 - 23 * q^27 - 20 * q^28 - 37 * q^29 + 17 * q^30 - 12 * q^31 - 39 * q^32 - 38 * q^33 - 14 * q^34 + 16 * q^35 + 47 * q^36 + 19 * q^37 + 56 * q^38 - 46 * q^39 + 6 * q^40 - 7 * q^41 + q^42 + 7 * q^44 - 23 * q^45 + 47 * q^46 - q^47 - 15 * q^48 - 6 * q^49 + 3 * q^50 - 38 * q^51 + 15 * q^52 + 3 * q^53 - 67 * q^54 - 28 * q^55 - 81 * q^56 + 46 * q^57 + 34 * q^58 + 17 * q^59 - 83 * q^60 - 28 * q^61 - 33 * q^62 - 26 * q^63 + 10 * q^64 - 16 * q^65 - 72 * q^66 + 18 * q^67 + 53 * q^68 - 7 * q^69 + 34 * q^70 - 86 * q^71 + 2 * q^72 + 27 * q^73 - 79 * q^74 - 31 * q^75 - 59 * q^76 - 43 * q^77 + 91 * q^78 + 17 * q^79 - 8 * q^80 - 10 * q^81 - 13 * q^82 - 12 * q^83 - 32 * q^84 - 28 * q^85 - 43 * q^87 + 23 * q^88 - 51 * q^89 + 10 * q^90 + 20 * q^91 + 18 * q^92 + 30 * q^93 + 15 * q^94 - q^95 - 20 * q^96 - 19 * q^97 + 5 * q^98 + 38 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.09100	0.771451	0.385726	−	0.922614i	$-0.373951\pi$
$2$	1.09100	0.771451	0.385726	+	0.922614i	$0.373951\pi$
$3$	1.45952	0.842654	0.421327	−	0.906909i	$-0.361565\pi$
$3$	1.45952	0.842654	0.421327	+	0.906909i	$0.361565\pi$
$4$	−0.809726	−0.404863
$5$	1.35087	0.604125	0.302063	−	0.953288i	$-0.402325\pi$
$5$	1.35087	0.604125	0.302063	+	0.953288i	$0.402325\pi$
$6$	1.59233	0.650066
$7$	0.216325	0.0817633	0.0408816	−	0.999164i	$-0.486983\pi$
$7$	0.216325	0.0817633	0.0408816	+	0.999164i	$0.486983\pi$
$8$	−3.06540	−1.08378
$9$	−0.869803	−0.289934
$10$	1.47379	0.466053
$11$	−6.03107	−1.81844	−0.909219	−	0.416319i	$-0.863320\pi$
$11$	−6.03107	−1.81844	−0.909219	+	0.416319i	$0.863320\pi$
$12$	−1.18181	−0.341159
$13$	−2.87520	−0.797436	−0.398718	−	0.917073i	$-0.630545\pi$
$13$	−2.87520	−0.797436	−0.398718	+	0.917073i	$0.630545\pi$
$14$	0.236010	0.0630764
$15$	1.97161	0.509069
$16$	−1.72489	−0.431223
$17$	0.282609	0.0685429	0.0342714	−	0.999413i	$-0.489089\pi$
$17$	0.282609	0.0685429	0.0342714	+	0.999413i	$0.489089\pi$
$18$	−0.948953	−0.223670
$19$	−1.13727	−0.260908	−0.130454	−	0.991454i	$-0.541644\pi$
$19$	−1.13727	−0.260908	−0.130454	+	0.991454i	$0.541644\pi$
$20$	−1.09383	−0.244588
$21$	0.315731	0.0688981
$22$	−6.57988	−1.40284
$23$	−3.94262	−0.822093	−0.411046	−	0.911614i	$-0.634837\pi$
$23$	−3.94262	−0.822093	−0.411046	+	0.911614i	$0.634837\pi$
$24$	−4.47401	−0.913254
$25$	−3.17516	−0.635033
$26$	−3.13683	−0.615183
$27$	−5.64805	−1.08697
$28$	−0.175164	−0.0331029
$29$	6.90413	1.28206	0.641032	−	0.767514i	$-0.278506\pi$
$29$	6.90413	1.28206	0.641032	+	0.767514i	$0.278506\pi$
$30$	2.15103	0.392722
$31$	−9.89090	−1.77646	−0.888229	−	0.459400i	$-0.848064\pi$
$31$	−9.89090	−1.77646	−0.888229	+	0.459400i	$0.848064\pi$
$32$	4.24895	0.751115
$33$	−8.80247	−1.53231
$34$	0.308326	0.0528775
$35$	0.292226	0.0493953
$36$	0.704302	0.117384
$37$	7.54258	1.23999	0.619996	−	0.784605i	$-0.287134\pi$
$37$	7.54258	1.23999	0.619996	+	0.784605i	$0.287134\pi$
$38$	−1.24076	−0.201278
$39$	−4.19641	−0.671963
$40$	−4.14095	−0.654741
$41$	5.12997	0.801167	0.400584	−	0.916260i	$-0.368807\pi$
$41$	5.12997	0.801167	0.400584	+	0.916260i	$0.368807\pi$
$42$	0.344461	0.0531516
$43$	0	0
$43$	0	0
$44$	4.88351	0.736217
$45$	−1.17499	−0.175157
$46$	−4.30138	−0.634205
$47$	0.462299	0.0674332	0.0337166	−	0.999431i	$-0.489266\pi$
$47$	0.462299	0.0674332	0.0337166	+	0.999431i	$0.489266\pi$
$48$	−2.51752	−0.363372
$49$	−6.95320	−0.993315
$50$	−3.46409	−0.489897
$51$	0.412474	0.0577579
$52$	2.32812	0.322852
$53$	8.35339	1.14743	0.573713	−	0.819057i	$-0.305503\pi$
$53$	8.35339	1.14743	0.573713	+	0.819057i	$0.305503\pi$
$54$	−6.16201	−0.838543
$55$	−8.14717	−1.09856
$56$	−0.663124	−0.0886137
$57$	−1.65987	−0.219855
$58$	7.53238	0.989050
$59$	−8.35544	−1.08779	−0.543893	−	0.839155i	$-0.683050\pi$
$59$	−8.35544	−1.08779	−0.543893	+	0.839155i	$0.683050\pi$
$60$	−1.59647	−0.206103
$61$	13.4329	1.71990	0.859950	−	0.510377i	$-0.170494\pi$
$61$	13.4329	1.71990	0.859950	+	0.510377i	$0.170494\pi$
$62$	−10.7909	−1.37045
$63$	−0.188160	−0.0237060
$64$	8.08538	1.01067
$65$	−3.88401	−0.481752
$66$	−9.60347	−1.18210
$67$	−6.29357	−0.768882	−0.384441	−	0.923150i	$-0.625606\pi$
$67$	−6.29357	−0.768882	−0.384441	+	0.923150i	$0.625606\pi$
$68$	−0.228836	−0.0277504
$69$	−5.75433	−0.692740
$70$	0.318818	0.0381060
$71$	−1.47896	−0.175520	−0.0877600	−	0.996142i	$-0.527971\pi$
$71$	−1.47896	−0.175520	−0.0877600	+	0.996142i	$0.527971\pi$
$72$	2.66630	0.314226
$73$	−0.820130	−0.0959890	−0.0479945	−	0.998848i	$-0.515283\pi$
$73$	−0.820130	−0.0959890	−0.0479945	+	0.998848i	$0.515283\pi$
$74$	8.22893	0.956594
$75$	−4.63421	−0.535113
$76$	0.920878	0.105632
$77$	−1.30467	−0.148681
$78$	−4.57827	−0.518387
$79$	6.15595	0.692599	0.346299	−	0.938124i	$-0.387438\pi$
$79$	6.15595	0.692599	0.346299	+	0.938124i	$0.387438\pi$
$80$	−2.33010	−0.260513
$81$	−5.63403	−0.626003
$82$	5.59678	0.618061
$83$	−7.20537	−0.790893	−0.395446	−	0.918489i	$-0.629410\pi$
$83$	−7.20537	−0.790893	−0.395446	+	0.918489i	$0.629410\pi$
$84$	−0.255655	−0.0278943
$85$	0.381767	0.0414085
$86$	0	0
$87$	10.0767	1.08034
$88$	18.4877	1.97079
$89$	4.43399	0.470002	0.235001	−	0.971995i	$-0.424491\pi$
$89$	4.43399	0.470002	0.235001	+	0.971995i	$0.424491\pi$
$90$	−1.28191	−0.135125
$91$	−0.621978	−0.0652010
$92$	3.19244	0.332835
$93$	−14.4360	−1.49694
$94$	0.504367	0.0520214
$95$	−1.53630	−0.157621
$96$	6.20143	0.632930
$97$	−4.46918	−0.453777	−0.226888	−	0.973921i	$-0.572855\pi$
$97$	−4.46918	−0.453777	−0.226888	+	0.973921i	$0.572855\pi$
$98$	−7.58592	−0.766294
$99$	5.24585	0.527228
$100$	2.57101	0.257101
$101$	−2.99466	−0.297980	−0.148990	−	0.988839i	$-0.547602\pi$
$101$	−2.99466	−0.297980	−0.148990	+	0.988839i	$0.547602\pi$
$102$	0.450008	0.0445574
$103$	8.44886	0.832491	0.416245	−	0.909252i	$-0.363346\pi$
$103$	8.44886	0.832491	0.416245	+	0.909252i	$0.363346\pi$
$104$	8.81364	0.864248
$105$	0.426510	0.0416231
$106$	9.11352	0.885183
$107$	6.26653	0.605808	0.302904	−	0.953021i	$-0.402044\pi$
$107$	6.26653	0.605808	0.302904	+	0.953021i	$0.402044\pi$
$108$	4.57337	0.440073
$109$	0.212675	0.0203705	0.0101853	−	0.999948i	$-0.496758\pi$
$109$	0.212675	0.0203705	0.0101853	+	0.999948i	$0.496758\pi$
$110$	−8.88854	−0.847489
$111$	11.0085	1.04488
$112$	−0.373138	−0.0352582
$113$	−11.0725	−1.04161	−0.520807	−	0.853674i	$-0.674369\pi$
$113$	−11.0725	−1.04161	−0.520807	+	0.853674i	$0.674369\pi$
$114$	−1.81091	−0.169608
$115$	−5.32595	−0.496647
$116$	−5.59045	−0.519060
$117$	2.50086	0.231204
$118$	−9.11576	−0.839174
$119$	0.0611356	0.00560429
$120$	−6.04379	−0.551720
$121$	25.3738	2.30671
$122$	14.6552	1.32682
$123$	7.48729	0.675107
$124$	8.00892	0.719222
$125$	−11.0435	−0.987765
$126$	−0.205282	−0.0182880
$127$	7.81423	0.693401	0.346700	−	0.937976i	$-0.387302\pi$
$127$	7.81423	0.693401	0.346700	+	0.937976i	$0.387302\pi$
$128$	0.323224	0.0285692
$129$	0	0
$130$	−4.23744	−0.371648
$131$	−17.9581	−1.56901	−0.784505	−	0.620123i	$-0.787083\pi$
$131$	−17.9581	−1.56901	−0.784505	+	0.620123i	$0.787083\pi$
$132$	7.12758	0.620376
$133$	−0.246021	−0.0213327
$134$	−6.86627	−0.593155
$135$	−7.62976	−0.656665
$136$	−0.866312	−0.0742856
$137$	10.0468	0.858359	0.429180	−	0.903219i	$-0.358803\pi$
$137$	10.0468	0.858359	0.429180	+	0.903219i	$0.358803\pi$
$138$	−6.27795	−0.534415
$139$	−12.4203	−1.05348	−0.526738	−	0.850028i	$-0.676585\pi$
$139$	−12.4203	−1.05348	−0.526738	+	0.850028i	$0.676585\pi$
$140$	−0.236623	−0.0199983
$141$	0.674734	0.0568229
$142$	−1.61354	−0.135405
$143$	17.3405	1.45009
$144$	1.50032	0.125027
$145$	9.32655	0.774528
$146$	−0.894760	−0.0740508
$147$	−10.1483	−0.837021
$148$	−6.10742	−0.502027
$149$	−3.69719	−0.302886	−0.151443	−	0.988466i	$-0.548392\pi$
$149$	−3.69719	−0.302886	−0.151443	+	0.988466i	$0.548392\pi$
$150$	−5.05591	−0.412813
$151$	−11.5179	−0.937316	−0.468658	−	0.883380i	$-0.655262\pi$
$151$	−11.5179	−0.937316	−0.468658	+	0.883380i	$0.655262\pi$
$152$	3.48620	0.282768
$153$	−0.245815	−0.0198729
$154$	−1.42339	−0.114700
$155$	−13.3613	−1.07320
$156$	3.39794	0.272053
$157$	−20.5978	−1.64388	−0.821940	−	0.569574i	$-0.807108\pi$
$157$	−20.5978	−1.64388	−0.821940	+	0.569574i	$0.807108\pi$
$158$	6.71612	0.534306
$159$	12.1919	0.966883
$160$	5.73976	0.453768
$161$	−0.852888	−0.0672170
$162$	−6.14671	−0.482931
$163$	6.91536	0.541653	0.270826	−	0.962628i	$-0.412703\pi$
$163$	6.91536	0.541653	0.270826	+	0.962628i	$0.412703\pi$
$164$	−4.15387	−0.324363
$165$	−11.8909	−0.925709
$166$	−7.86104	−0.610135
$167$	3.55518	0.275108	0.137554	−	0.990494i	$-0.456076\pi$
$167$	3.55518	0.275108	0.137554	+	0.990494i	$0.456076\pi$
$168$	−0.967842	−0.0746706
$169$	−4.73324	−0.364095
$170$	0.416507	0.0319446
$171$	0.989203	0.0756463
$172$	0	0
$173$	−24.0563	−1.82897	−0.914483	−	0.404623i	$-0.867403\pi$
$173$	−24.0563	−1.82897	−0.914483	+	0.404623i	$0.867403\pi$
$174$	10.9937	0.833427
$175$	−0.686868	−0.0519223
$176$	10.4030	0.784153
$177$	−12.1949	−0.916627
$178$	4.83747	0.362584
$179$	−5.20188	−0.388807	−0.194403	−	0.980922i	$-0.562277\pi$
$179$	−5.20188	−0.388807	−0.194403	+	0.980922i	$0.562277\pi$
$180$	0.951417	0.0709145
$181$	−2.77405	−0.206193	−0.103097	−	0.994671i	$-0.532875\pi$
$181$	−2.77405	−0.206193	−0.103097	+	0.994671i	$0.532875\pi$
$182$	−0.678576	−0.0502994
$183$	19.6055	1.44928
$184$	12.0857	0.890970
$185$	10.1890	0.749111
$186$	−15.7496	−1.15482
$187$	−1.70444	−0.124641
$188$	−0.374335	−0.0273012
$189$	−1.22182	−0.0888741
$190$	−1.67610	−0.121597
$191$	−3.45560	−0.250038	−0.125019	−	0.992154i	$-0.539899\pi$
$191$	−3.45560	−0.250038	−0.125019	+	0.992154i	$0.539899\pi$
$192$	11.8008	0.851647
$193$	−18.2577	−1.31422	−0.657111	−	0.753794i	$-0.728222\pi$
$193$	−18.2577	−1.31422	−0.657111	+	0.753794i	$0.728222\pi$
$194$	−4.87587	−0.350067
$195$	−5.66878	−0.405950
$196$	5.63019	0.402156
$197$	10.1801	0.725299	0.362649	−	0.931926i	$-0.381872\pi$
$197$	10.1801	0.725299	0.362649	+	0.931926i	$0.381872\pi$
$198$	5.72321	0.406730
$199$	9.19652	0.651924	0.325962	−	0.945383i	$-0.394312\pi$
$199$	9.19652	0.651924	0.325962	+	0.945383i	$0.394312\pi$
$200$	9.73315	0.688238
$201$	−9.18559	−0.647902
$202$	−3.26717	−0.229877
$203$	1.49354	0.104826
$204$	−0.333991	−0.0233840
$205$	6.92990	0.484005
$206$	9.21768	0.642226
$207$	3.42930	0.238353
$208$	4.95941	0.343873
$209$	6.85897	0.474445
$210$	0.465321	0.0321102
$211$	−19.0580	−1.31201	−0.656005	−	0.754756i	$-0.727755\pi$
$211$	−19.0580	−1.31201	−0.656005	+	0.754756i	$0.727755\pi$
$212$	−6.76395	−0.464550
$213$	−2.15857	−0.147903
$214$	6.83676	0.467352
$215$	0	0
$216$	17.3136	1.17804
$217$	−2.13965	−0.145249
$218$	0.232027	0.0157149
$219$	−1.19700	−0.0808855
$220$	6.59697	0.444768
$221$	−0.812558	−0.0546586
$222$	12.0103	0.806078
$223$	−7.29778	−0.488695	−0.244348	−	0.969688i	$-0.578574\pi$
$223$	−7.29778	−0.488695	−0.244348	+	0.969688i	$0.578574\pi$
$224$	0.919155	0.0614136
$225$	2.76177	0.184118
$226$	−12.0801	−0.803555
$227$	15.6379	1.03792	0.518962	−	0.854797i	$-0.326319\pi$
$227$	15.6379	1.03792	0.518962	+	0.854797i	$0.326319\pi$
$228$	1.34404	0.0890112
$229$	−1.07522	−0.0710529	−0.0355264	−	0.999369i	$-0.511311\pi$
$229$	−1.07522	−0.0710529	−0.0355264	+	0.999369i	$0.511311\pi$
$230$	−5.81059	−0.383139
$231$	−1.90420	−0.125287
$232$	−21.1639	−1.38948
$233$	−1.33303	−0.0873298	−0.0436649	−	0.999046i	$-0.513903\pi$
$233$	−1.33303	−0.0873298	−0.0436649	+	0.999046i	$0.513903\pi$
$234$	2.72843	0.178363
$235$	0.624503	0.0407381
$236$	6.76561	0.440404
$237$	8.98473	0.583621
$238$	0.0666987	0.00432343
$239$	14.8772	0.962327	0.481164	−	0.876631i	$-0.340214\pi$
$239$	14.8772	0.962327	0.481164	+	0.876631i	$0.340214\pi$
$240$	−3.40082	−0.219522
$241$	23.9040	1.53979	0.769897	−	0.638168i	$-0.220307\pi$
$241$	23.9040	1.53979	0.769897	+	0.638168i	$0.220307\pi$
$242$	27.6828	1.77952
$243$	8.72118	0.559464
$244$	−10.8769	−0.696324
$245$	−9.39284	−0.600087
$246$	8.16862	0.520812
$247$	3.26988	0.208058
$248$	30.3196	1.92530
$249$	−10.5164	−0.666449
$250$	−12.0485	−0.762012
$251$	−20.5359	−1.29622	−0.648108	−	0.761548i	$-0.724440\pi$
$251$	−20.5359	−1.29622	−0.648108	+	0.761548i	$0.724440\pi$
$252$	0.152358	0.00959767
$253$	23.7782	1.49492
$254$	8.52530	0.534925
$255$	0.557197	0.0348930
$256$	−15.8181	−0.988633
$257$	−22.8388	−1.42464	−0.712322	−	0.701853i	$-0.752356\pi$
$257$	−22.8388	−1.42464	−0.712322	+	0.701853i	$0.752356\pi$
$258$	0	0
$259$	1.63165	0.101386
$260$	3.14498	0.195043
$261$	−6.00524	−0.371715
$262$	−19.5923	−1.21041
$263$	6.15818	0.379730	0.189865	−	0.981810i	$-0.439195\pi$
$263$	6.15818	0.379730	0.189865	+	0.981810i	$0.439195\pi$
$264$	26.9831	1.66070
$265$	11.2843	0.693189
$266$	−0.268408	−0.0164571
$267$	6.47150	0.396049
$268$	5.09607	0.311292
$269$	15.0181	0.915671	0.457835	−	0.889037i	$-0.348625\pi$
$269$	15.0181	0.915671	0.457835	+	0.889037i	$0.348625\pi$
$270$	−8.32404	−0.506585
$271$	3.09449	0.187977	0.0939886	−	0.995573i	$-0.470038\pi$
$271$	3.09449	0.187977	0.0939886	+	0.995573i	$0.470038\pi$
$272$	−0.487471	−0.0295573
$273$	−0.907789	−0.0549419
$274$	10.9611	0.662183
$275$	19.1496	1.15477
$276$	4.65943	0.280464
$277$	15.1134	0.908075	0.454037	−	0.890983i	$-0.349983\pi$
$277$	15.1134	0.908075	0.454037	+	0.890983i	$0.349983\pi$
$278$	−13.5505	−0.812706
$279$	8.60314	0.515057
$280$	−0.895791	−0.0535338
$281$	11.1617	0.665850	0.332925	−	0.942953i	$-0.391964\pi$
$281$	11.1617	0.665850	0.332925	+	0.942953i	$0.391964\pi$
$282$	0.736133	0.0438361
$283$	−16.0909	−0.956503	−0.478252	−	0.878223i	$-0.658729\pi$
$283$	−16.0909	−0.956503	−0.478252	+	0.878223i	$0.658729\pi$
$284$	1.19755	0.0710615
$285$	−2.24226	−0.132820
$286$	18.9185	1.11867
$287$	1.10974	0.0655060
$288$	−3.69575	−0.217774
$289$	−16.9201	−0.995302
$290$	10.1752	0.597510
$291$	−6.52286	−0.382377
$292$	0.664080	0.0388624
$293$	−14.6854	−0.857931	−0.428966	−	0.903321i	$-0.641122\pi$
$293$	−14.6854	−0.857931	−0.428966	+	0.903321i	$0.641122\pi$
$294$	−11.0718	−0.645721
$295$	−11.2871	−0.657159
$296$	−23.1210	−1.34388
$297$	34.0638	1.97658
$298$	−4.03363	−0.233662
$299$	11.3358	0.655567
$300$	3.75244	0.216647
$301$	0	0
$302$	−12.5660	−0.723094
$303$	−4.37077	−0.251094
$304$	1.96167	0.112510
$305$	18.1460	1.03904
$306$	−0.268183	−0.0153310
$307$	0.0283640	0.00161882	0.000809410	−	1.00000i	$-0.499742\pi$
$307$	0.0283640	0.00161882	0.000809410		1.00000i	$0.499742\pi$
$308$	1.05643	0.0601955
$309$	12.3313	0.701501
$310$	−14.5771	−0.827924
$311$	−10.2776	−0.582792	−0.291396	−	0.956603i	$-0.594120\pi$
$311$	−10.2776	−0.582792	−0.291396	+	0.956603i	$0.594120\pi$
$312$	12.8637	0.728262
$313$	17.9283	1.01337	0.506683	−	0.862132i	$-0.330871\pi$
$313$	17.9283	1.01337	0.506683	+	0.862132i	$0.330871\pi$
$314$	−22.4721	−1.26817
$315$	−0.254179	−0.0143214
$316$	−4.98463	−0.280407
$317$	−21.7299	−1.22047	−0.610237	−	0.792219i	$-0.708926\pi$
$317$	−21.7299	−1.22047	−0.610237	+	0.792219i	$0.708926\pi$
$318$	13.3014	0.745903
$319$	−41.6393	−2.33135
$320$	10.9223	0.610573
$321$	9.14612	0.510487
$322$	−0.930498	−0.0518546
$323$	−0.321404	−0.0178834
$324$	4.56202	0.253446
$325$	9.12922	0.506398
$326$	7.54464	0.417859
$327$	0.310403	0.0171653
$328$	−15.7254	−0.868292
$329$	0.100007	0.00551356
$330$	−12.9730	−0.714140
$331$	13.2271	0.727028	0.363514	−	0.931589i	$-0.381577\pi$
$331$	13.2271	0.727028	0.363514	+	0.931589i	$0.381577\pi$
$332$	5.83438	0.320203
$333$	−6.56056	−0.359517
$334$	3.87869	0.212232
$335$	−8.50177	−0.464501
$336$	−0.544602	−0.0297105
$337$	−9.43072	−0.513724	−0.256862	−	0.966448i	$-0.582689\pi$
$337$	−9.43072	−0.513724	−0.256862	+	0.966448i	$0.582689\pi$
$338$	−5.16395	−0.280882
$339$	−16.1606	−0.877721
$340$	−0.309127	−0.0167648
$341$	59.6528	3.23038
$342$	1.07922	0.0583574
$343$	−3.01843	−0.162980
$344$	0	0
$345$	−7.77332	−0.418502
$346$	−26.2454	−1.41096
$347$	−17.4825	−0.938511	−0.469256	−	0.883062i	$-0.655478\pi$
$347$	−17.4825	−0.938511	−0.469256	+	0.883062i	$0.655478\pi$
$348$	−8.15937	−0.437388
$349$	9.33264	0.499565	0.249782	−	0.968302i	$-0.419641\pi$
$349$	9.33264	0.499565	0.249782	+	0.968302i	$0.419641\pi$
$350$	−0.749371	−0.0400556
$351$	16.2393	0.866788
$352$	−25.6257	−1.36586
$353$	10.3879	0.552893	0.276447	−	0.961029i	$-0.410843\pi$
$353$	10.3879	0.552893	0.276447	+	0.961029i	$0.410843\pi$
$354$	−13.3046	−0.707133
$355$	−1.99787	−0.106036
$356$	−3.59032	−0.190286
$357$	0.0892285	0.00472247
$358$	−5.67524	−0.299946
$359$	10.8048	0.570253	0.285127	−	0.958490i	$-0.407964\pi$
$359$	10.8048	0.570253	0.285127	+	0.958490i	$0.407964\pi$
$360$	3.60181	0.189832
$361$	−17.7066	−0.931927
$362$	−3.02648	−0.159068
$363$	37.0336	1.94376
$364$	0.503631	0.0263975
$365$	−1.10789	−0.0579894
$366$	21.3896	1.11805
$367$	19.3732	1.01128	0.505638	−	0.862746i	$-0.331257\pi$
$367$	19.3732	1.01128	0.505638	+	0.862746i	$0.331257\pi$
$368$	6.80060	0.354506
$369$	−4.46207	−0.232286
$370$	11.1162	0.577903
$371$	1.80705	0.0938173
$372$	11.6892	0.606055
$373$	34.3456	1.77835	0.889175	−	0.457568i	$-0.151279\pi$
$373$	34.3456	1.77835	0.889175	+	0.457568i	$0.151279\pi$
$374$	−1.85954	−0.0961544
$375$	−16.1183	−0.832344
$376$	−1.41713	−0.0730830
$377$	−19.8507	−1.02236
$378$	−1.33300	−0.0685620
$379$	2.58065	0.132559	0.0662794	−	0.997801i	$-0.478887\pi$
$379$	2.58065	0.132559	0.0662794	+	0.997801i	$0.478887\pi$
$380$	1.24398	0.0638150
$381$	11.4050	0.584297
$382$	−3.77004	−0.192892
$383$	14.3072	0.731065	0.365532	−	0.930799i	$-0.380887\pi$
$383$	14.3072	0.731065	0.365532	+	0.930799i	$0.380887\pi$
$384$	0.471751	0.0240739
$385$	−1.76244	−0.0898222
$386$	−19.9191	−1.01386
$387$	0	0
$388$	3.61881	0.183717
$389$	−15.7874	−0.800455	−0.400228	−	0.916416i	$-0.631069\pi$
$389$	−15.7874	−0.800455	−0.400228	+	0.916416i	$0.631069\pi$
$390$	−6.18462	−0.313171
$391$	−1.11422	−0.0563486
$392$	21.3144	1.07654
$393$	−26.2102	−1.32213
$394$	11.1064	0.559533
$395$	8.31586	0.418416
$396$	−4.24770	−0.213455
$397$	−29.1059	−1.46078	−0.730391	−	0.683029i	$-0.760662\pi$
$397$	−29.1059	−1.46078	−0.730391	+	0.683029i	$0.760662\pi$
$398$	10.0334	0.502928
$399$	−0.359072	−0.0179761
$400$	5.47682	0.273841
$401$	14.3104	0.714629	0.357314	−	0.933984i	$-0.383692\pi$
$401$	14.3104	0.714629	0.357314	+	0.933984i	$0.383692\pi$
$402$	−10.0215	−0.499825
$403$	28.4383	1.41661
$404$	2.42485	0.120641
$405$	−7.61082	−0.378185
$406$	1.62944	0.0808680
$407$	−45.4899	−2.25485
$408$	−1.26440	−0.0625970
$409$	30.4520	1.50575	0.752877	−	0.658161i	$-0.228665\pi$
$409$	30.4520	1.50575	0.752877	+	0.658161i	$0.228665\pi$
$410$	7.56050	0.373387
$411$	14.6636	0.723300
$412$	−6.84126	−0.337044
$413$	−1.80749	−0.0889409
$414$	3.74136	0.183878
$415$	−9.73349	−0.477798
$416$	−12.2166	−0.598967
$417$	−18.1277	−0.887716
$418$	7.48312	0.366011
$419$	35.5658	1.73750	0.868752	−	0.495247i	$-0.164922\pi$
$419$	35.5658	1.73750	0.868752	+	0.495247i	$0.164922\pi$
$420$	−0.345356	−0.0168516
$421$	16.4973	0.804028	0.402014	−	0.915634i	$-0.368310\pi$
$421$	16.4973	0.804028	0.402014	+	0.915634i	$0.368310\pi$
$422$	−20.7923	−1.01215
$423$	−0.402109	−0.0195512
$424$	−25.6065	−1.24356
$425$	−0.897331	−0.0435269
$426$	−2.35499	−0.114100
$427$	2.90587	0.140625
$428$	−5.07417	−0.245269
$429$	25.3088	1.22192
$430$	0	0
$431$	−9.05750	−0.436285	−0.218142	−	0.975917i	$-0.570000\pi$
$431$	−9.05750	−0.436285	−0.218142	+	0.975917i	$0.570000\pi$
$432$	9.74229	0.468726
$433$	17.2817	0.830506	0.415253	−	0.909706i	$-0.363693\pi$
$433$	17.2817	0.830506	0.415253	+	0.909706i	$0.363693\pi$
$434$	−2.33435	−0.112053
$435$	13.6123	0.652659
$436$	−0.172208	−0.00824727
$437$	4.48383	0.214491
$438$	−1.30592	−0.0623992
$439$	18.4756	0.881791	0.440896	−	0.897558i	$-0.354661\pi$
$439$	18.4756	0.881791	0.440896	+	0.897558i	$0.354661\pi$
$440$	24.9743	1.19061
$441$	6.04792	0.287996
$442$	−0.886498	−0.0421664
$443$	−8.94530	−0.425004	−0.212502	−	0.977161i	$-0.568161\pi$
$443$	−8.94530	−0.425004	−0.212502	+	0.977161i	$0.568161\pi$
$444$	−8.91390	−0.423035
$445$	5.98973	0.283940
$446$	−7.96185	−0.377005
$447$	−5.39612	−0.255228
$448$	1.74907	0.0826359
$449$	−20.2725	−0.956718	−0.478359	−	0.878164i	$-0.658768\pi$
$449$	−20.2725	−0.956718	−0.478359	+	0.878164i	$0.658768\pi$
$450$	3.01308	0.142038
$451$	−30.9392	−1.45687
$452$	8.96570	0.421711
$453$	−16.8106	−0.789833
$454$	17.0609	0.800708
$455$	−0.840208	−0.0393896
$456$	5.08817	0.238275
$457$	−10.7619	−0.503419	−0.251710	−	0.967803i	$-0.580993\pi$
$457$	−10.7619	−0.503419	−0.251710	+	0.967803i	$0.580993\pi$
$458$	−1.17307	−0.0548138
$459$	−1.59619	−0.0745039
$460$	4.31256	0.201074
$461$	−8.51750	−0.396700	−0.198350	−	0.980131i	$-0.563558\pi$
$461$	−8.51750	−0.396700	−0.198350	+	0.980131i	$0.563558\pi$
$462$	−2.07747	−0.0966528
$463$	−2.27432	−0.105697	−0.0528483	−	0.998603i	$-0.516830\pi$
$463$	−2.27432	−0.105697	−0.0528483	+	0.998603i	$0.516830\pi$
$464$	−11.9089	−0.552856
$465$	−19.5010	−0.904339
$466$	−1.45433	−0.0673707
$467$	−30.2512	−1.39986	−0.699930	−	0.714211i	$-0.746786\pi$
$467$	−30.2512	−1.39986	−0.699930	+	0.714211i	$0.746786\pi$
$468$	−2.02501	−0.0936060
$469$	−1.36146	−0.0628663
$470$	0.681331	0.0314275
$471$	−30.0628	−1.38522
$472$	25.6128	1.17892
$473$	0	0
$474$	9.80231	0.450235
$475$	3.61102	0.165685
$476$	−0.0495030	−0.00226897
$477$	−7.26580	−0.332678
$478$	16.2310	0.742389
$479$	13.5795	0.620465	0.310233	−	0.950661i	$-0.399593\pi$
$479$	13.5795	0.620465	0.310233	+	0.950661i	$0.399593\pi$
$480$	8.37729	0.382369
$481$	−21.6864	−0.988816
$482$	26.0792	1.18788
$483$	−1.24481	−0.0566406
$484$	−20.5459	−0.933902
$485$	−6.03727	−0.274138
$486$	9.51478	0.431599
$487$	−37.2554	−1.68820	−0.844101	−	0.536184i	$-0.819865\pi$
$487$	−37.2554	−1.68820	−0.844101	+	0.536184i	$0.819865\pi$
$488$	−41.1771	−1.86400
$489$	10.0931	0.456426
$490$	−10.2476	−0.462938
$491$	20.5331	0.926644	0.463322	−	0.886190i	$-0.346657\pi$
$491$	20.5331	0.926644	0.463322	+	0.886190i	$0.346657\pi$
$492$	−6.06265	−0.273325
$493$	1.95117	0.0878764
$494$	3.56743	0.160506
$495$	7.08644	0.318512
$496$	17.0608	0.766050
$497$	−0.319936	−0.0143511
$498$	−11.4733	−0.514133
$499$	6.97052	0.312043	0.156022	−	0.987754i	$-0.450133\pi$
$499$	6.97052	0.312043	0.156022	+	0.987754i	$0.450133\pi$
$500$	8.94224	0.399909
$501$	5.18885	0.231821
$502$	−22.4046	−0.999968
$503$	12.9747	0.578513	0.289256	−	0.957252i	$-0.406592\pi$
$503$	12.9747	0.578513	0.289256	+	0.957252i	$0.406592\pi$
$504$	0.576787	0.0256922
$505$	−4.04539	−0.180017
$506$	25.9420	1.15326
$507$	−6.90825	−0.306806
$508$	−6.32738	−0.280732
$509$	29.8062	1.32114	0.660568	−	0.750766i	$-0.270315\pi$
$509$	29.8062	1.32114	0.660568	+	0.750766i	$0.270315\pi$
$510$	0.607900	0.0269183
$511$	−0.177415	−0.00784837
$512$	−17.9040	−0.791251
$513$	6.42337	0.283599
$514$	−24.9170	−1.09904
$515$	11.4133	0.502929
$516$	0	0
$517$	−2.78816	−0.122623
$518$	1.78013	0.0782143
$519$	−35.1106	−1.54119
$520$	11.9060	0.522114
$521$	−31.1756	−1.36583	−0.682914	−	0.730499i	$-0.739288\pi$
$521$	−31.1756	−1.36583	−0.682914	+	0.730499i	$0.739288\pi$
$522$	−6.55169	−0.286760
$523$	13.9018	0.607884	0.303942	−	0.952691i	$-0.401697\pi$
$523$	13.9018	0.607884	0.303942	+	0.952691i	$0.401697\pi$
$524$	14.5412	0.635234
$525$	−1.00250	−0.0437525
$526$	6.71856	0.292943
$527$	−2.79526	−0.121764
$528$	15.1833	0.660769
$529$	−7.45576	−0.324163
$530$	12.3111	0.534762
$531$	7.26759	0.315387
$532$	0.199209	0.00863681
$533$	−14.7497	−0.638880
$534$	7.06038	0.305533
$535$	8.46524	0.365984
$536$	19.2923	0.833302
$537$	−7.59224	−0.327630
$538$	16.3847	0.706395
$539$	41.9353	1.80628
$540$	6.17801	0.265859
$541$	−20.7378	−0.891587	−0.445793	−	0.895136i	$-0.647078\pi$
$541$	−20.7378	−0.891587	−0.445793	+	0.895136i	$0.647078\pi$
$542$	3.37608	0.145015
$543$	−4.04877	−0.173750
$544$	1.20079	0.0514836
$545$	0.287295	0.0123064
$546$	−0.990395	−0.0423850
$547$	20.4705	0.875255	0.437627	−	0.899156i	$-0.355819\pi$
$547$	20.4705	0.875255	0.437627	+	0.899156i	$0.355819\pi$
$548$	−8.13518	−0.347518
$549$	−11.6839	−0.498659
$550$	20.8922	0.890846
$551$	−7.85187	−0.334501
$552$	17.6393	0.750780
$553$	1.33169	0.0566291
$554$	16.4886	0.700535
$555$	14.8711	0.631241
$556$	10.0570	0.426513
$557$	−17.0851	−0.723920	−0.361960	−	0.932194i	$-0.617892\pi$
$557$	−17.0851	−0.723920	−0.361960	+	0.932194i	$0.617892\pi$
$558$	9.38600	0.397341
$559$	0	0
$560$	−0.504059	−0.0213004
$561$	−2.48766	−0.105029
$562$	12.1774	0.513671
$563$	−11.2648	−0.474754	−0.237377	−	0.971418i	$-0.576288\pi$
$563$	−11.2648	−0.474754	−0.237377	+	0.971418i	$0.576288\pi$
$564$	−0.546349	−0.0230055
$565$	−14.9575	−0.629266
$566$	−17.5551	−0.737896
$567$	−1.21878	−0.0511841
$568$	4.53360	0.190226
$569$	−8.03597	−0.336885	−0.168443	−	0.985711i	$-0.553874\pi$
$569$	−8.03597	−0.336885	−0.168443	+	0.985711i	$0.553874\pi$
$570$	−2.44630	−0.102464
$571$	−29.1124	−1.21832	−0.609158	−	0.793049i	$-0.708493\pi$
$571$	−29.1124	−1.21832	−0.609158	+	0.793049i	$0.708493\pi$
$572$	−14.0411	−0.587087
$573$	−5.04351	−0.210696
$574$	1.21073	0.0505347
$575$	12.5185	0.522056
$576$	−7.03269	−0.293029
$577$	−7.18569	−0.299144	−0.149572	−	0.988751i	$-0.547790\pi$
$577$	−7.18569	−0.299144	−0.149572	+	0.988751i	$0.547790\pi$
$578$	−18.4598	−0.767827
$579$	−26.6475	−1.10743
$580$	−7.55194	−0.313577
$581$	−1.55870	−0.0646660
$582$	−7.11642	−0.294985
$583$	−50.3799	−2.08652
$584$	2.51403	0.104031
$585$	3.37832	0.139676
$586$	−16.0217	−0.661852
$587$	−29.7095	−1.22624	−0.613121	−	0.789989i	$-0.710086\pi$
$587$	−29.7095	−1.22624	−0.613121	+	0.789989i	$0.710086\pi$
$588$	8.21737	0.338878
$589$	11.2486	0.463492
$590$	−12.3142	−0.506966
$591$	14.8580	0.611176
$592$	−13.0102	−0.534714
$593$	32.2081	1.32263	0.661314	−	0.750109i	$-0.269999\pi$
$593$	32.2081	1.32263	0.661314	+	0.750109i	$0.269999\pi$
$594$	37.1635	1.52484
$595$	0.0825859	0.00338569
$596$	2.99371	0.122627
$597$	13.4225	0.549346
$598$	12.3673	0.505738
$599$	−15.2252	−0.622086	−0.311043	−	0.950396i	$-0.600678\pi$
$599$	−15.2252	−0.622086	−0.311043	+	0.950396i	$0.600678\pi$
$600$	14.2057	0.579946
$601$	−14.8489	−0.605699	−0.302849	−	0.953038i	$-0.597938\pi$
$601$	−14.8489	−0.605699	−0.302849	+	0.953038i	$0.597938\pi$
$602$	0	0
$603$	5.47417	0.222925
$604$	9.32636	0.379484
$605$	34.2767	1.39354
$606$	−4.76849	−0.193707
$607$	−9.34659	−0.379367	−0.189683	−	0.981845i	$-0.560746\pi$
$607$	−9.34659	−0.379367	−0.189683	+	0.981845i	$0.560746\pi$
$608$	−4.83221	−0.195972
$609$	2.17985	0.0883318
$610$	19.7972	0.801566
$611$	−1.32920	−0.0537737
$612$	0.199042	0.00804581
$613$	30.8057	1.24423	0.622116	−	0.782925i	$-0.286273\pi$
$613$	30.8057	1.24423	0.622116	+	0.782925i	$0.286273\pi$
$614$	0.0309450	0.00124884
$615$	10.1143	0.407849
$616$	3.99935	0.161138
$617$	−3.84050	−0.154613	−0.0773064	−	0.997007i	$-0.524632\pi$
$617$	−3.84050	−0.154613	−0.0773064	+	0.997007i	$0.524632\pi$
$618$	13.4534	0.541174
$619$	34.1580	1.37292	0.686462	−	0.727166i	$-0.259163\pi$
$619$	34.1580	1.37292	0.686462	+	0.727166i	$0.259163\pi$
$620$	10.8190	0.434500
$621$	22.2681	0.893589
$622$	−11.2129	−0.449596
$623$	0.959185	0.0384289
$624$	7.23836	0.289766
$625$	0.957471	0.0382988
$626$	19.5597	0.781763
$627$	10.0108	0.399793
$628$	16.6785	0.665546
$629$	2.13160	0.0849926
$630$	−0.277309	−0.0110483
$631$	−9.20560	−0.366469	−0.183235	−	0.983069i	$-0.558657\pi$
$631$	−9.20560	−0.366469	−0.183235	+	0.983069i	$0.558657\pi$
$632$	−18.8705	−0.750627
$633$	−27.8156	−1.10557
$634$	−23.7073	−0.941536
$635$	10.5560	0.418901
$636$	−9.87211	−0.391455
$637$	19.9918	0.792105
$638$	−45.4284	−1.79853
$639$	1.28640	0.0508893
$640$	0.436631	0.0172594
$641$	3.38335	0.133634	0.0668171	−	0.997765i	$-0.478716\pi$
$641$	3.38335	0.133634	0.0668171	+	0.997765i	$0.478716\pi$
$642$	9.97839	0.393816
$643$	11.3071	0.445910	0.222955	−	0.974829i	$-0.428430\pi$
$643$	11.3071	0.445910	0.222955	+	0.974829i	$0.428430\pi$
$644$	0.690605	0.0272137
$645$	0	0
$646$	−0.350651	−0.0137962
$647$	−22.7411	−0.894046	−0.447023	−	0.894522i	$-0.647516\pi$
$647$	−22.7411	−0.894046	−0.447023	+	0.894522i	$0.647516\pi$
$648$	17.2706	0.678452
$649$	50.3923	1.97807
$650$	9.95995	0.390662
$651$	−3.12286	−0.122395
$652$	−5.59954	−0.219295
$653$	25.8110	1.01006	0.505032	−	0.863101i	$-0.331481\pi$
$653$	25.8110	1.01006	0.505032	+	0.863101i	$0.331481\pi$
$654$	0.338648	0.0132422
$655$	−24.2590	−0.947878
$656$	−8.84866	−0.345482
$657$	0.713352	0.0278305
$658$	0.109107	0.00425344
$659$	10.1927	0.397053	0.198526	−	0.980096i	$-0.436384\pi$
$659$	10.1927	0.397053	0.198526	+	0.980096i	$0.436384\pi$
$660$	9.62841	0.374785
$661$	−13.3155	−0.517913	−0.258957	−	0.965889i	$-0.583379\pi$
$661$	−13.3155	−0.517913	−0.258957	+	0.965889i	$0.583379\pi$
$662$	14.4308	0.560867
$663$	−1.18594	−0.0460583
$664$	22.0874	0.857156
$665$	−0.332341	−0.0128876
$666$	−7.15756	−0.277350
$667$	−27.2203	−1.05398
$668$	−2.87872	−0.111381
$669$	−10.6512	−0.411801
$670$	−9.27540	−0.358340
$671$	−81.0145	−3.12753
$672$	1.34152	0.0517504
$673$	−6.31447	−0.243405	−0.121703	−	0.992567i	$-0.538835\pi$
$673$	−6.31447	−0.243405	−0.121703	+	0.992567i	$0.538835\pi$
$674$	−10.2889	−0.396313
$675$	17.9335	0.690260
$676$	3.83262	0.147409
$677$	−26.0519	−1.00126	−0.500628	−	0.865662i	$-0.666898\pi$
$677$	−26.0519	−1.00126	−0.500628	+	0.865662i	$0.666898\pi$
$678$	−17.6311	−0.677119
$679$	−0.966797	−0.0371023
$680$	−1.17027	−0.0448778
$681$	22.8238	0.874610
$682$	65.0810	2.49208
$683$	−49.2576	−1.88479	−0.942395	−	0.334503i	$-0.891431\pi$
$683$	−49.2576	−1.88479	−0.942395	+	0.334503i	$0.891431\pi$
$684$	−0.800983	−0.0306264
$685$	13.5719	0.518557
$686$	−3.29310	−0.125731
$687$	−1.56931	−0.0598730
$688$	0	0
$689$	−24.0176	−0.914999
$690$	−8.48067	−0.322854
$691$	−49.3631	−1.87786	−0.938931	−	0.344106i	$-0.888182\pi$
$691$	−49.3631	−1.87786	−0.938931	+	0.344106i	$0.888182\pi$
$692$	19.4790	0.740481
$693$	1.13481	0.0431078
$694$	−19.0734	−0.724016
$695$	−16.7782	−0.636432
$696$	−30.8892	−1.17085
$697$	1.44978	0.0549143
$698$	10.1819	0.385390
$699$	−1.94558	−0.0735888
$700$	0.556174	0.0210214
$701$	−17.4990	−0.660929	−0.330464	−	0.943818i	$-0.607205\pi$
$701$	−17.4990	−0.660929	−0.330464	+	0.943818i	$0.607205\pi$
$702$	17.7170	0.668685
$703$	−8.57797	−0.323524
$704$	−48.7635	−1.83784
$705$	0.911475	0.0343281
$706$	11.3332	0.426530
$707$	−0.647821	−0.0243638
$708$	9.87455	0.371108
$709$	31.8895	1.19763	0.598817	−	0.800886i	$-0.295638\pi$
$709$	31.8895	1.19763	0.598817	+	0.800886i	$0.295638\pi$
$710$	−2.17967	−0.0818017
$711$	−5.35447	−0.200808
$712$	−13.5920	−0.509381
$713$	38.9961	1.46041
$714$	0.0973480	0.00364316
$715$	23.4247	0.876035
$716$	4.21210	0.157413
$717$	21.7136	0.810909
$718$	11.7880	0.439923
$719$	43.2301	1.61221	0.806105	−	0.591773i	$-0.201572\pi$
$719$	43.2301	1.61221	0.806105	+	0.591773i	$0.201572\pi$
$720$	2.02673	0.0755317
$721$	1.82770	0.0680672
$722$	−19.3179	−0.718936
$723$	34.8884	1.29751
$724$	2.24622	0.0834800
$725$	−21.9217	−0.814153
$726$	40.4036	1.49952
$727$	−4.19063	−0.155422	−0.0777109	−	0.996976i	$-0.524761\pi$
$727$	−4.19063	−0.155422	−0.0777109	+	0.996976i	$0.524761\pi$
$728$	1.90661	0.0706638
$729$	29.6308	1.09744
$730$	−1.20870	−0.0447360
$731$	0	0
$732$	−15.8751	−0.586760
$733$	49.2097	1.81760	0.908802	−	0.417228i	$-0.136998\pi$
$733$	49.2097	1.81760	0.908802	+	0.417228i	$0.136998\pi$
$734$	21.1362	0.780150
$735$	−13.7090	−0.505665
$736$	−16.7520	−0.617487
$737$	37.9570	1.39816
$738$	−4.86810	−0.179197
$739$	−2.50823	−0.0922666	−0.0461333	−	0.998935i	$-0.514690\pi$
$739$	−2.50823	−0.0922666	−0.0461333	+	0.998935i	$0.514690\pi$
$740$	−8.25030	−0.303287
$741$	4.77246	0.175321
$742$	1.97148	0.0723755
$743$	17.8168	0.653636	0.326818	−	0.945087i	$-0.394024\pi$
$743$	17.8168	0.653636	0.326818	+	0.945087i	$0.394024\pi$
$744$	44.2520	1.62236
$745$	−4.99441	−0.182981
$746$	37.4710	1.37191
$747$	6.26726	0.229307
$748$	1.38013	0.0504624
$749$	1.35561	0.0495328
$750$	−17.5850	−0.642113
$751$	38.7221	1.41299	0.706495	−	0.707718i	$-0.250275\pi$
$751$	38.7221	1.41299	0.706495	+	0.707718i	$0.250275\pi$
$752$	−0.797416	−0.0290788
$753$	−29.9726	−1.09226
$754$	−21.6571	−0.788705
$755$	−15.5592	−0.566256
$756$	0.989336	0.0359818
$757$	30.9261	1.12403	0.562014	−	0.827127i	$-0.310027\pi$
$757$	30.9261	1.12403	0.562014	+	0.827127i	$0.310027\pi$
$758$	2.81548	0.102263
$759$	34.7048	1.25970
$760$	4.70938	0.170827
$761$	−42.9702	−1.55767	−0.778834	−	0.627231i	$-0.784188\pi$
$761$	−42.9702	−1.55767	−0.778834	+	0.627231i	$0.784188\pi$
$762$	12.4428	0.450757
$763$	0.0460069	0.00166556
$764$	2.79808	0.101231
$765$	−0.332063	−0.0120057
$766$	15.6091	0.563981
$767$	24.0236	0.867440
$768$	−23.0869	−0.833075
$769$	11.5254	0.415616	0.207808	−	0.978170i	$-0.433367\pi$
$769$	11.5254	0.415616	0.207808	+	0.978170i	$0.433367\pi$
$770$	−1.92281	−0.0692934
$771$	−33.3336	−1.20048
$772$	14.7838	0.532079
$773$	−24.2393	−0.871828	−0.435914	−	0.899988i	$-0.643575\pi$
$773$	−24.2393	−0.871828	−0.435914	+	0.899988i	$0.643575\pi$
$774$	0	0
$775$	31.4052	1.12811
$776$	13.6998	0.491796
$777$	2.38143	0.0854332
$778$	−17.2241	−0.617512
$779$	−5.83417	−0.209031
$780$	4.59016	0.164354
$781$	8.91970	0.319172
$782$	−1.21561	−0.0434702
$783$	−38.9949	−1.39356
$784$	11.9935	0.428341
$785$	−27.8248	−0.993109
$786$	−28.5953	−1.01996
$787$	10.0588	0.358559	0.179279	−	0.983798i	$-0.442623\pi$
$787$	10.0588	0.358559	0.179279	+	0.983798i	$0.442623\pi$
$788$	−8.24305	−0.293647
$789$	8.98799	0.319981
$790$	9.07258	0.322788
$791$	−2.39526	−0.0851658
$792$	−16.0806	−0.571401
$793$	−38.6221	−1.37151
$794$	−31.7544	−1.12692
$795$	16.4697	0.584118
$796$	−7.44666	−0.263940
$797$	−40.8078	−1.44549	−0.722744	−	0.691116i	$-0.757119\pi$
$797$	−40.8078	−1.44549	−0.722744	+	0.691116i	$0.757119\pi$
$798$	−0.391746	−0.0138677
$799$	0.130650	0.00462206
$800$	−13.4911	−0.476983
$801$	−3.85670	−0.136270
$802$	15.6126	0.551302
$803$	4.94627	0.174550
$804$	7.43781	0.262311
$805$	−1.15214	−0.0406075
$806$	31.0261	1.09285
$807$	21.9192	0.771593
$808$	9.17984	0.322946
$809$	−46.8987	−1.64887	−0.824435	−	0.565957i	$-0.808507\pi$
$809$	−46.8987	−1.64887	−0.824435	+	0.565957i	$0.808507\pi$
$810$	−8.30338	−0.291751
$811$	34.2713	1.20343	0.601714	−	0.798711i	$-0.294485\pi$
$811$	34.2713	1.20343	0.601714	+	0.798711i	$0.294485\pi$
$812$	−1.20936	−0.0424400
$813$	4.51647	0.158400
$814$	−49.6293	−1.73951
$815$	9.34172	0.327226
$816$	−0.711474	−0.0249066
$817$	0	0
$818$	33.2230	1.16162
$819$	0.540999	0.0189040
$820$	−5.61132	−0.195956
$821$	−18.4513	−0.643956	−0.321978	−	0.946747i	$-0.604348\pi$
$821$	−18.4513	−0.643956	−0.321978	+	0.946747i	$0.604348\pi$
$822$	15.9979	0.557991
$823$	9.18853	0.320292	0.160146	−	0.987093i	$-0.448803\pi$
$823$	9.18853	0.320292	0.160146	+	0.987093i	$0.448803\pi$
$824$	−25.8991	−0.902240
$825$	27.9493	0.973069
$826$	−1.97197	−0.0686136
$827$	36.7050	1.27636	0.638179	−	0.769888i	$-0.279688\pi$
$827$	36.7050	1.27636	0.638179	+	0.769888i	$0.279688\pi$
$828$	−2.77679	−0.0965003
$829$	4.54590	0.157885	0.0789427	−	0.996879i	$-0.474846\pi$
$829$	4.54590	0.157885	0.0789427	+	0.996879i	$0.474846\pi$
$830$	−10.6192	−0.368598
$831$	22.0583	0.765193
$832$	−23.2471	−0.805947
$833$	−1.96504	−0.0680846
$834$	−19.7772	−0.684830
$835$	4.80257	0.166200
$836$	−5.55388	−0.192085
$837$	55.8643	1.93095
$838$	38.8022	1.34040
$839$	−24.0212	−0.829304	−0.414652	−	0.909980i	$-0.636097\pi$
$839$	−24.0212	−0.829304	−0.414652	+	0.909980i	$0.636097\pi$
$840$	−1.30742	−0.0451104
$841$	18.6670	0.643689
$842$	17.9985	0.620268
$843$	16.2907	0.561081
$844$	15.4318	0.531184
$845$	−6.39396	−0.219959
$846$	−0.438700	−0.0150828
$847$	5.48900	0.188604
$848$	−14.4087	−0.494797
$849$	−23.4849	−0.806001
$850$	−0.978985	−0.0335789
$851$	−29.7375	−1.01939
$852$	1.74785	0.0598803
$853$	−49.7259	−1.70258	−0.851292	−	0.524693i	$-0.824180\pi$
$853$	−49.7259	−1.70258	−0.851292	+	0.524693i	$0.824180\pi$
$854$	3.17029	0.108485
$855$	1.33628	0.0456998
$856$	−19.2094	−0.656565
$857$	−35.3238	−1.20664	−0.603320	−	0.797499i	$-0.706156\pi$
$857$	−35.3238	−1.20664	−0.603320	+	0.797499i	$0.706156\pi$
$858$	27.6119	0.942654
$859$	8.58814	0.293024	0.146512	−	0.989209i	$-0.453195\pi$
$859$	8.58814	0.293024	0.146512	+	0.989209i	$0.453195\pi$
$860$	0	0
$861$	1.61969	0.0551989
$862$	−9.88171	−0.336572
$863$	33.8631	1.15271	0.576357	−	0.817198i	$-0.304474\pi$
$863$	33.8631	1.15271	0.576357	+	0.817198i	$0.304474\pi$
$864$	−23.9983	−0.816439
$865$	−32.4968	−1.10493
$866$	18.8543	0.640695
$867$	−24.6953	−0.838695
$868$	1.73253	0.0588059
$869$	−37.1270	−1.25945
$870$	14.8510	0.503494
$871$	18.0953	0.613135
$872$	−0.651933	−0.0220772
$873$	3.88731	0.131566
$874$	4.89184	0.165469
$875$	−2.38900	−0.0807629
$876$	0.969238	0.0327475
$877$	−18.0007	−0.607842	−0.303921	−	0.952697i	$-0.598296\pi$
$877$	−18.0007	−0.607842	−0.303921	+	0.952697i	$0.598296\pi$
$878$	20.1568	0.680259
$879$	−21.4337	−0.722939
$880$	14.0530	0.473726
$881$	−26.2153	−0.883215	−0.441608	−	0.897208i	$-0.645592\pi$
$881$	−26.2153	−0.883215	−0.441608	+	0.897208i	$0.645592\pi$
$882$	6.59826	0.222175
$883$	−49.7624	−1.67464	−0.837319	−	0.546715i	$-0.815878\pi$
$883$	−49.7624	−1.67464	−0.837319	+	0.546715i	$0.815878\pi$
$884$	0.657949	0.0221292
$885$	−16.4737	−0.553758
$886$	−9.75930	−0.327870
$887$	−8.57645	−0.287969	−0.143985	−	0.989580i	$-0.545992\pi$
$887$	−8.57645	−0.287969	−0.143985	+	0.989580i	$0.545992\pi$
$888$	−33.7456	−1.13243
$889$	1.69042	0.0566947
$890$	6.53477	0.219046
$891$	33.9793	1.13835
$892$	5.90920	0.197855
$893$	−0.525759	−0.0175939
$894$	−5.88715	−0.196896
$895$	−7.02704	−0.234888
$896$	0.0699214	0.00233591
$897$	16.5448	0.552416
$898$	−22.1172	−0.738061
$899$	−68.2881	−2.27753
$900$	−2.23627	−0.0745425
$901$	2.36075	0.0786478
$902$	−33.7546	−1.12391
$903$	0	0
$904$	33.9417	1.12888
$905$	−3.74736	−0.124567
$906$	−18.3404	−0.609318
$907$	−28.1743	−0.935511	−0.467756	−	0.883858i	$-0.654937\pi$
$907$	−28.1743	−0.935511	−0.467756	+	0.883858i	$0.654937\pi$
$908$	−12.6624	−0.420217
$909$	2.60477	0.0863947
$910$	−0.916665	−0.0303871
$911$	−24.4367	−0.809623	−0.404811	−	0.914400i	$-0.632663\pi$
$911$	−24.4367	−0.809623	−0.404811	+	0.914400i	$0.632663\pi$
$912$	2.86310	0.0948067
$913$	43.4561	1.43819
$914$	−11.7412	−0.388363
$915$	26.4844	0.875548
$916$	0.870637	0.0287667
$917$	−3.88480	−0.128287
$918$	−1.74144	−0.0574761
$919$	−15.9543	−0.526284	−0.263142	−	0.964757i	$-0.584759\pi$
$919$	−15.9543	−0.526284	−0.263142	+	0.964757i	$0.584759\pi$
$920$	16.3262	0.538258
$921$	0.0413978	0.00136410
$922$	−9.29257	−0.306034
$923$	4.25230	0.139966
$924$	1.54188	0.0507240
$925$	−23.9489	−0.787436
$926$	−2.48127	−0.0815398
$927$	−7.34885	−0.241368
$928$	29.3353	0.962978
$929$	−6.25130	−0.205099	−0.102549	−	0.994728i	$-0.532700\pi$
$929$	−6.25130	−0.205099	−0.102549	+	0.994728i	$0.532700\pi$
$930$	−21.2756	−0.697654
$931$	7.90768	0.259164
$932$	1.07939	0.0353566
$933$	−15.0004	−0.491092
$934$	−33.0040	−1.07992
$935$	−2.30247	−0.0752987
$936$	−7.66613	−0.250575
$937$	−54.0642	−1.76620	−0.883101	−	0.469184i	$-0.844548\pi$
$937$	−54.0642	−1.76620	−0.883101	+	0.469184i	$0.844548\pi$
$938$	−1.48535	−0.0484983
$939$	26.1667	0.853917
$940$	−0.505676	−0.0164933
$941$	31.2455	1.01857	0.509287	−	0.860597i	$-0.329909\pi$
$941$	31.2455	1.01857	0.509287	+	0.860597i	$0.329909\pi$
$942$	−32.7984	−1.06863
$943$	−20.2255	−0.658634
$944$	14.4122	0.469079
$945$	−1.65051	−0.0536911
$946$	0	0
$947$	−38.7946	−1.26066	−0.630328	−	0.776329i	$-0.717080\pi$
$947$	−38.7946	−1.26066	−0.630328	+	0.776329i	$0.717080\pi$
$948$	−7.27516	−0.236286
$949$	2.35804	0.0765451
$950$	3.93962	0.127818
$951$	−31.7152	−1.02844
$952$	−0.187405	−0.00607383
$953$	−29.2296	−0.946839	−0.473420	−	0.880837i	$-0.656981\pi$
$953$	−29.2296	−0.946839	−0.473420	+	0.880837i	$0.656981\pi$
$954$	−7.92697	−0.256645
$955$	−4.66804	−0.151054
$956$	−12.0465	−0.389610
$957$	−60.7734	−1.96452
$958$	14.8152	0.478659
$959$	2.17338	0.0701823
$960$	15.9412	0.514502
$961$	66.8300	2.15581
$962$	−23.6598	−0.762823
$963$	−5.45065	−0.175645
$964$	−19.3557	−0.623406
$965$	−24.6638	−0.793954
$966$	−1.35808	−0.0436955
$967$	25.5158	0.820532	0.410266	−	0.911966i	$-0.365436\pi$
$967$	25.5158	0.820532	0.410266	+	0.911966i	$0.365436\pi$
$968$	−77.7810	−2.49998
$969$	−0.469095	−0.0150695
$970$	−6.58664	−0.211484
$971$	20.8009	0.667534	0.333767	−	0.942656i	$-0.391680\pi$
$971$	20.8009	0.667534	0.333767	+	0.942656i	$0.391680\pi$
$972$	−7.06176	−0.226506
$973$	−2.68683	−0.0861357
$974$	−40.6455	−1.30237
$975$	13.3243	0.426718
$976$	−23.1702	−0.741661
$977$	−18.8229	−0.602198	−0.301099	−	0.953593i	$-0.597353\pi$
$977$	−18.8229	−0.602198	−0.301099	+	0.953593i	$0.597353\pi$
$978$	11.0115	0.352110
$979$	−26.7417	−0.854670
$980$	7.60562	0.242953
$981$	−0.184985	−0.00590612
$982$	22.4015	0.714861
$983$	−22.2313	−0.709068	−0.354534	−	0.935043i	$-0.615360\pi$
$983$	−22.2313	−0.709068	−0.354534	+	0.935043i	$0.615360\pi$
$984$	−22.9516	−0.731669
$985$	13.7519	0.438172
$986$	2.12872	0.0677923
$987$	0.145962	0.00464602
$988$	−2.64771	−0.0842348
$989$	0	0
$990$	7.73128	0.245716
$991$	15.3259	0.486842	0.243421	−	0.969921i	$-0.421730\pi$
$991$	15.3259	0.486842	0.243421	+	0.969921i	$0.421730\pi$
$992$	−42.0260	−1.33433
$993$	19.3052	0.612633
$994$	−0.349049	−0.0110712
$995$	12.4233	0.393844
$996$	8.51538	0.269820
$997$	7.09424	0.224677	0.112338	−	0.993670i	$-0.464166\pi$
$997$	7.09424	0.224677	0.112338	+	0.993670i	$0.464166\pi$
$998$	7.60481	0.240726
$999$	−42.6009	−1.34783

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.n.1.13		18
43.10	even	21		43.2.g.a.14.2	✓	36
43.13	even	21		43.2.g.a.40.2	yes	36
43.42	odd	2		1849.2.a.o.1.6		18
129.53	odd	42		387.2.y.c.100.2		36
129.56	odd	42		387.2.y.c.298.2		36
172.99	odd	42		688.2.bg.c.513.1		36
172.139	odd	42		688.2.bg.c.401.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.g.a.14.2	✓	36	43.10	even	21
43.2.g.a.40.2	yes	36	43.13	even	21
387.2.y.c.100.2		36	129.53	odd	42
387.2.y.c.298.2		36	129.56	odd	42
688.2.bg.c.401.1		36	172.139	odd	42
688.2.bg.c.513.1		36	172.99	odd	42
1849.2.a.n.1.13		18	1.1	even	1	trivial
1849.2.a.o.1.6		18	43.42	odd	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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q+1.09100 q^{2} +1.45952 q^{3} -0.809726 q^{4} +1.35087 q^{5} +1.59233 q^{6} +0.216325 q^{7} -3.06540 q^{8} -0.869803 q^{9} +O(q^{10})\)	\(q+1.09100 q^{2} +1.45952 q^{3} -0.809726 q^{4} +1.35087 q^{5} +1.59233 q^{6} +0.216325 q^{7} -3.06540 q^{8} -0.869803 q^{9} +1.47379 q^{10} -6.03107 q^{11} -1.18181 q^{12} -2.87520 q^{13} +0.236010 q^{14} +1.97161 q^{15} -1.72489 q^{16} +0.282609 q^{17} -0.948953 q^{18} -1.13727 q^{19} -1.09383 q^{20} +0.315731 q^{21} -6.57988 q^{22} -3.94262 q^{23} -4.47401 q^{24} -3.17516 q^{25} -3.13683 q^{26} -5.64805 q^{27} -0.175164 q^{28} +6.90413 q^{29} +2.15103 q^{30} -9.89090 q^{31} +4.24895 q^{32} -8.80247 q^{33} +0.308326 q^{34} +0.292226 q^{35} +0.704302 q^{36} +7.54258 q^{37} -1.24076 q^{38} -4.19641 q^{39} -4.14095 q^{40} +5.12997 q^{41} +0.344461 q^{42} +4.88351 q^{44} -1.17499 q^{45} -4.30138 q^{46} +0.462299 q^{47} -2.51752 q^{48} -6.95320 q^{49} -3.46409 q^{50} +0.412474 q^{51} +2.32812 q^{52} +8.35339 q^{53} -6.16201 q^{54} -8.14717 q^{55} -0.663124 q^{56} -1.65987 q^{57} +7.53238 q^{58} -8.35544 q^{59} -1.59647 q^{60} +13.4329 q^{61} -10.7909 q^{62} -0.188160 q^{63} +8.08538 q^{64} -3.88401 q^{65} -9.60347 q^{66} -6.29357 q^{67} -0.228836 q^{68} -5.75433 q^{69} +0.318818 q^{70} -1.47896 q^{71} +2.66630 q^{72} -0.820130 q^{73} +8.22893 q^{74} -4.63421 q^{75} +0.920878 q^{76} -1.30467 q^{77} -4.57827 q^{78} +6.15595 q^{79} -2.33010 q^{80} -5.63403 q^{81} +5.59678 q^{82} -7.20537 q^{83} -0.255655 q^{84} +0.381767 q^{85} +10.0767 q^{87} +18.4877 q^{88} +4.43399 q^{89} -1.28191 q^{90} -0.621978 q^{91} +3.19244 q^{92} -14.4360 q^{93} +0.504367 q^{94} -1.53630 q^{95} +6.20143 q^{96} -4.46918 q^{97} -7.58592 q^{98} +5.24585 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) \) 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9	\( 18 q - 5 q^{2} - 5 q^{3} + 19 q^{4} - 11 q^{5} + 4 q^{6} - 6 q^{7} - 12 q^{8} + 15 q^{9} - 7 q^{10} - 2 q^{11} - 16 q^{12} - 7 q^{13} - 4 q^{14} + 3 q^{15} + 9 q^{16} - 11 q^{17} - 25 q^{18} - 31 q^{19} - 25 q^{20} - 19 q^{22} - 11 q^{23} + 18 q^{24} + 9 q^{25} - 27 q^{26} - 23 q^{27} - 20 q^{28} - 37 q^{29} + 17 q^{30} - 12 q^{31} - 39 q^{32} - 38 q^{33} - 14 q^{34} + 16 q^{35} + 47 q^{36} + 19 q^{37} + 56 q^{38} - 46 q^{39} + 6 q^{40} - 7 q^{41} + q^{42} + 7 q^{44} - 23 q^{45} + 47 q^{46} - q^{47} - 15 q^{48} - 6 q^{49} + 3 q^{50} - 38 q^{51} + 15 q^{52} + 3 q^{53} - 67 q^{54} - 28 q^{55} - 81 q^{56} + 46 q^{57} + 34 q^{58} + 17 q^{59} - 83 q^{60} - 28 q^{61} - 33 q^{62} - 26 q^{63} + 10 q^{64} - 16 q^{65} - 72 q^{66} + 18 q^{67} + 53 q^{68} - 7 q^{69} + 34 q^{70} - 86 q^{71} + 2 q^{72} + 27 q^{73} - 79 q^{74} - 31 q^{75} - 59 q^{76} - 43 q^{77} + 91 q^{78} + 17 q^{79} - 8 q^{80} - 10 q^{81} - 13 q^{82} - 12 q^{83} - 32 q^{84} - 28 q^{85} - 43 q^{87} + 23 q^{88} - 51 q^{89} + 10 q^{90} + 20 q^{91} + 18 q^{92} + 30 q^{93} + 15 q^{94} - q^{95} - 20 q^{96} - 19 q^{97} + 5 q^{98} + 38 q^{99}+O(q^{100}) \) 18 * q - 5 * q^2 - 5 * q^3 + 19 * q^4 - 11 * q^5 + 4 * q^6 - 6 * q^7 - 12 * q^8 + 15 * q^9 - 7 * q^10 - 2 * q^11 - 16 * q^12 - 7 * q^13 - 4 * q^14 + 3 * q^15 + 9 * q^16 - 11 * q^17 - 25 * q^18 - 31 * q^19 - 25 * q^20 - 19 * q^22 - 11 * q^23 + 18 * q^24 + 9 * q^25 - 27 * q^26 - 23 * q^27 - 20 * q^28 - 37 * q^29 + 17 * q^30 - 12 * q^31 - 39 * q^32 - 38 * q^33 - 14 * q^34 + 16 * q^35 + 47 * q^36 + 19 * q^37 + 56 * q^38 - 46 * q^39 + 6 * q^40 - 7 * q^41 + q^42 + 7 * q^44 - 23 * q^45 + 47 * q^46 - q^47 - 15 * q^48 - 6 * q^49 + 3 * q^50 - 38 * q^51 + 15 * q^52 + 3 * q^53 - 67 * q^54 - 28 * q^55 - 81 * q^56 + 46 * q^57 + 34 * q^58 + 17 * q^59 - 83 * q^60 - 28 * q^61 - 33 * q^62 - 26 * q^63 + 10 * q^64 - 16 * q^65 - 72 * q^66 + 18 * q^67 + 53 * q^68 - 7 * q^69 + 34 * q^70 - 86 * q^71 + 2 * q^72 + 27 * q^73 - 79 * q^74 - 31 * q^75 - 59 * q^76 - 43 * q^77 + 91 * q^78 + 17 * q^79 - 8 * q^80 - 10 * q^81 - 13 * q^82 - 12 * q^83 - 32 * q^84 - 28 * q^85 - 43 * q^87 + 23 * q^88 - 51 * q^89 + 10 * q^90 + 20 * q^91 + 18 * q^92 + 30 * q^93 + 15 * q^94 - q^95 - 20 * q^96 - 19 * q^97 + 5 * q^98 + 38 * q^99

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