LMFDB - Embedded newform 1849.2.a.h.1.2

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:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
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			1.2
Root			$1.61803$ 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)

$f(q)$	$=$	$q+2.61803 q^{2} +0.381966 q^{3} +4.85410 q^{4} +3.23607 q^{5} +1.00000 q^{6} -0.236068 q^{7} +7.47214 q^{8} -2.85410 q^{9} +O(q^{10})$	\(q+2.61803 q^{2} +0.381966 q^{3} +4.85410 q^{4} +3.23607 q^{5} +1.00000 q^{6} -0.236068 q^{7} +7.47214 q^{8} -2.85410 q^{9} +8.47214 q^{10} -1.38197 q^{11} +1.85410 q^{12} +3.61803 q^{13} -0.618034 q^{14} +1.23607 q^{15} +9.85410 q^{16} -5.09017 q^{17} -7.47214 q^{18} -3.23607 q^{19} +15.7082 q^{20} -0.0901699 q^{21} -3.61803 q^{22} +6.61803 q^{23} +2.85410 q^{24} +5.47214 q^{25} +9.47214 q^{26} -2.23607 q^{27} -1.14590 q^{28} -3.00000 q^{29} +3.23607 q^{30} +10.8541 q^{32} -0.527864 q^{33} -13.3262 q^{34} -0.763932 q^{35} -13.8541 q^{36} -1.85410 q^{37} -8.47214 q^{38} +1.38197 q^{39} +24.1803 q^{40} +0.527864 q^{41} -0.236068 q^{42} -6.70820 q^{44} -9.23607 q^{45} +17.3262 q^{46} +7.85410 q^{47} +3.76393 q^{48} -6.94427 q^{49} +14.3262 q^{50} -1.94427 q^{51} +17.5623 q^{52} -3.61803 q^{53} -5.85410 q^{54} -4.47214 q^{55} -1.76393 q^{56} -1.23607 q^{57} -7.85410 q^{58} -6.09017 q^{59} +6.00000 q^{60} +3.85410 q^{61} +0.673762 q^{63} +8.70820 q^{64} +11.7082 q^{65} -1.38197 q^{66} +2.85410 q^{67} -24.7082 q^{68} +2.52786 q^{69} -2.00000 q^{70} -13.7984 q^{71} -21.3262 q^{72} +4.85410 q^{73} -4.85410 q^{74} +2.09017 q^{75} -15.7082 q^{76} +0.326238 q^{77} +3.61803 q^{78} -3.61803 q^{79} +31.8885 q^{80} +7.70820 q^{81} +1.38197 q^{82} -13.0344 q^{83} -0.437694 q^{84} -16.4721 q^{85} -1.14590 q^{87} -10.3262 q^{88} -4.85410 q^{89} -24.1803 q^{90} -0.854102 q^{91} +32.1246 q^{92} +20.5623 q^{94} -10.4721 q^{95} +4.14590 q^{96} -4.76393 q^{97} -18.1803 q^{98} +3.94427 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{7} + 6 q^{8} + q^{9}+O(q^{10}) $ 2 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^7 + 6 * q^8 + q^9	$ 2 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{7} + 6 q^{8} + q^{9} + 8 q^{10} - 5 q^{11} - 3 q^{12} + 5 q^{13} + q^{14} - 2 q^{15} + 13 q^{16} + q^{17} - 6 q^{18} - 2 q^{19} + 18 q^{20} + 11 q^{21} - 5 q^{22} + 11 q^{23} - q^{24} + 2 q^{25} + 10 q^{26} - 9 q^{28} - 6 q^{29} + 2 q^{30} + 15 q^{32} - 10 q^{33} - 11 q^{34} - 6 q^{35} - 21 q^{36} + 3 q^{37} - 8 q^{38} + 5 q^{39} + 26 q^{40} + 10 q^{41} + 4 q^{42} - 14 q^{45} + 19 q^{46} + 9 q^{47} + 12 q^{48} + 4 q^{49} + 13 q^{50} + 14 q^{51} + 15 q^{52} - 5 q^{53} - 5 q^{54} - 8 q^{56} + 2 q^{57} - 9 q^{58} - q^{59} + 12 q^{60} + q^{61} + 17 q^{63} + 4 q^{64} + 10 q^{65} - 5 q^{66} - q^{67} - 36 q^{68} + 14 q^{69} - 4 q^{70} - 3 q^{71} - 27 q^{72} + 3 q^{73} - 3 q^{74} - 7 q^{75} - 18 q^{76} - 15 q^{77} + 5 q^{78} - 5 q^{79} + 28 q^{80} + 2 q^{81} + 5 q^{82} + 3 q^{83} - 21 q^{84} - 24 q^{85} - 9 q^{87} - 5 q^{88} - 3 q^{89} - 26 q^{90} + 5 q^{91} + 24 q^{92} + 21 q^{94} - 12 q^{95} + 15 q^{96} - 14 q^{97} - 14 q^{98} - 10 q^{99}+O(q^{100}) $ 2 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^7 + 6 * q^8 + q^9 + 8 * q^10 - 5 * q^11 - 3 * q^12 + 5 * q^13 + q^14 - 2 * q^15 + 13 * q^16 + q^17 - 6 * q^18 - 2 * q^19 + 18 * q^20 + 11 * q^21 - 5 * q^22 + 11 * q^23 - q^24 + 2 * q^25 + 10 * q^26 - 9 * q^28 - 6 * q^29 + 2 * q^30 + 15 * q^32 - 10 * q^33 - 11 * q^34 - 6 * q^35 - 21 * q^36 + 3 * q^37 - 8 * q^38 + 5 * q^39 + 26 * q^40 + 10 * q^41 + 4 * q^42 - 14 * q^45 + 19 * q^46 + 9 * q^47 + 12 * q^48 + 4 * q^49 + 13 * q^50 + 14 * q^51 + 15 * q^52 - 5 * q^53 - 5 * q^54 - 8 * q^56 + 2 * q^57 - 9 * q^58 - q^59 + 12 * q^60 + q^61 + 17 * q^63 + 4 * q^64 + 10 * q^65 - 5 * q^66 - q^67 - 36 * q^68 + 14 * q^69 - 4 * q^70 - 3 * q^71 - 27 * q^72 + 3 * q^73 - 3 * q^74 - 7 * q^75 - 18 * q^76 - 15 * q^77 + 5 * q^78 - 5 * q^79 + 28 * q^80 + 2 * q^81 + 5 * q^82 + 3 * q^83 - 21 * q^84 - 24 * q^85 - 9 * q^87 - 5 * q^88 - 3 * q^89 - 26 * q^90 + 5 * q^91 + 24 * q^92 + 21 * q^94 - 12 * q^95 + 15 * q^96 - 14 * q^97 - 14 * q^98 - 10 * 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 $

$2$	2.61803	1.85123	0.925615	−	0.378467i	$-0.123549\pi$
$2$	2.61803	1.85123	0.925615	+	0.378467i	$0.123549\pi$
$3$	0.381966	0.220528	0.110264	−	0.993902i	$-0.464830\pi$
$3$	0.381966	0.220528	0.110264	+	0.993902i	$0.464830\pi$
$4$	4.85410	2.42705
$5$	3.23607	1.44721	0.723607	−	0.690212i	$-0.242483\pi$
$5$	3.23607	1.44721	0.723607	+	0.690212i	$0.242483\pi$
$6$	1.00000	0.408248
$7$	−0.236068	−0.0892253	−0.0446127	−	0.999004i	$-0.514205\pi$
$7$	−0.236068	−0.0892253	−0.0446127	+	0.999004i	$0.514205\pi$
$8$	7.47214	2.64180
$9$	−2.85410	−0.951367
$10$	8.47214	2.67912
$11$	−1.38197	−0.416678	−0.208339	−	0.978057i	$-0.566806\pi$
$11$	−1.38197	−0.416678	−0.208339	+	0.978057i	$0.566806\pi$
$12$	1.85410	0.535233
$13$	3.61803	1.00346	0.501731	−	0.865024i	$-0.332697\pi$
$13$	3.61803	1.00346	0.501731	+	0.865024i	$0.332697\pi$
$14$	−0.618034	−0.165177
$15$	1.23607	0.319151
$16$	9.85410	2.46353
$17$	−5.09017	−1.23455	−0.617274	−	0.786748i	$-0.711763\pi$
$17$	−5.09017	−1.23455	−0.617274	+	0.786748i	$0.711763\pi$
$18$	−7.47214	−1.76120
$19$	−3.23607	−0.742405	−0.371202	−	0.928552i	$-0.621054\pi$
$19$	−3.23607	−0.742405	−0.371202	+	0.928552i	$0.621054\pi$
$20$	15.7082	3.51246
$21$	−0.0901699	−0.0196767
$22$	−3.61803	−0.771367
$23$	6.61803	1.37996	0.689978	−	0.723831i	$-0.257620\pi$
$23$	6.61803	1.37996	0.689978	+	0.723831i	$0.257620\pi$
$24$	2.85410	0.582591
$25$	5.47214	1.09443
$26$	9.47214	1.85764
$27$	−2.23607	−0.430331
$28$	−1.14590	−0.216554
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	3.23607	0.590822
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	10.8541	1.91875
$33$	−0.527864	−0.0918893
$34$	−13.3262	−2.28543
$35$	−0.763932	−0.129128
$36$	−13.8541	−2.30902
$37$	−1.85410	−0.304812	−0.152406	−	0.988318i	$-0.548702\pi$
$37$	−1.85410	−0.304812	−0.152406	+	0.988318i	$0.548702\pi$
$38$	−8.47214	−1.37436
$39$	1.38197	0.221292
$40$	24.1803	3.82325
$41$	0.527864	0.0824385	0.0412193	−	0.999150i	$-0.486876\pi$
$41$	0.527864	0.0824385	0.0412193	+	0.999150i	$0.486876\pi$
$42$	−0.236068	−0.0364261
$43$	0	0
$43$	0	0
$44$	−6.70820	−1.01130
$45$	−9.23607	−1.37683
$46$	17.3262	2.55461
$47$	7.85410	1.14564	0.572819	−	0.819682i	$-0.305850\pi$
$47$	7.85410	1.14564	0.572819	+	0.819682i	$0.305850\pi$
$48$	3.76393	0.543277
$49$	−6.94427	−0.992039
$50$	14.3262	2.02604
$51$	−1.94427	−0.272253
$52$	17.5623	2.43545
$53$	−3.61803	−0.496975	−0.248488	−	0.968635i	$-0.579934\pi$
$53$	−3.61803	−0.496975	−0.248488	+	0.968635i	$0.579934\pi$
$54$	−5.85410	−0.796642
$55$	−4.47214	−0.603023
$56$	−1.76393	−0.235715
$57$	−1.23607	−0.163721
$58$	−7.85410	−1.03129
$59$	−6.09017	−0.792873	−0.396436	−	0.918062i	$-0.629753\pi$
$59$	−6.09017	−0.792873	−0.396436	+	0.918062i	$0.629753\pi$
$60$	6.00000	0.774597
$61$	3.85410	0.493467	0.246734	−	0.969083i	$-0.420643\pi$
$61$	3.85410	0.493467	0.246734	+	0.969083i	$0.420643\pi$
$62$	0	0
$63$	0.673762	0.0848860
$64$	8.70820	1.08853
$65$	11.7082	1.45222
$66$	−1.38197	−0.170108
$67$	2.85410	0.348684	0.174342	−	0.984685i	$-0.444220\pi$
$67$	2.85410	0.348684	0.174342	+	0.984685i	$0.444220\pi$
$68$	−24.7082	−2.99631
$69$	2.52786	0.304319
$70$	−2.00000	−0.239046
$71$	−13.7984	−1.63757	−0.818783	−	0.574103i	$-0.805351\pi$
$71$	−13.7984	−1.63757	−0.818783	+	0.574103i	$0.805351\pi$
$72$	−21.3262	−2.51332
$73$	4.85410	0.568130	0.284065	−	0.958805i	$-0.408317\pi$
$73$	4.85410	0.568130	0.284065	+	0.958805i	$0.408317\pi$
$74$	−4.85410	−0.564278
$75$	2.09017	0.241352
$76$	−15.7082	−1.80185
$77$	0.326238	0.0371783
$78$	3.61803	0.409662
$79$	−3.61803	−0.407061	−0.203530	−	0.979069i	$-0.565242\pi$
$79$	−3.61803	−0.407061	−0.203530	+	0.979069i	$0.565242\pi$
$80$	31.8885	3.56525
$81$	7.70820	0.856467
$82$	1.38197	0.152613
$83$	−13.0344	−1.43072	−0.715358	−	0.698758i	$-0.753736\pi$
$83$	−13.0344	−1.43072	−0.715358	+	0.698758i	$0.753736\pi$
$84$	−0.437694	−0.0477563
$85$	−16.4721	−1.78665
$86$	0	0
$87$	−1.14590	−0.122853
$88$	−10.3262	−1.10078
$89$	−4.85410	−0.514534	−0.257267	−	0.966340i	$-0.582822\pi$
$89$	−4.85410	−0.514534	−0.257267	+	0.966340i	$0.582822\pi$
$90$	−24.1803	−2.54883
$91$	−0.854102	−0.0895342
$92$	32.1246	3.34922
$93$	0	0
$94$	20.5623	2.12084
$95$	−10.4721	−1.07442
$96$	4.14590	0.423139
$97$	−4.76393	−0.483704	−0.241852	−	0.970313i	$-0.577755\pi$
$97$	−4.76393	−0.483704	−0.241852	+	0.970313i	$0.577755\pi$
$98$	−18.1803	−1.83649
$99$	3.94427	0.396414
$100$	26.5623	2.65623
$101$	8.23607	0.819519	0.409760	−	0.912194i	$-0.365613\pi$
$101$	8.23607	0.819519	0.409760	+	0.912194i	$0.365613\pi$
$102$	−5.09017	−0.504002
$103$	10.4164	1.02636	0.513180	−	0.858281i	$-0.328467\pi$
$103$	10.4164	1.02636	0.513180	+	0.858281i	$0.328467\pi$
$104$	27.0344	2.65095
$105$	−0.291796	−0.0284764
$106$	−9.47214	−0.920015
$107$	16.4721	1.59242	0.796211	−	0.605019i	$-0.206835\pi$
$107$	16.4721	1.59242	0.796211	+	0.605019i	$0.206835\pi$
$108$	−10.8541	−1.04444
$109$	−7.14590	−0.684453	−0.342226	−	0.939618i	$-0.611181\pi$
$109$	−7.14590	−0.684453	−0.342226	+	0.939618i	$0.611181\pi$
$110$	−11.7082	−1.11633
$111$	−0.708204	−0.0672197
$112$	−2.32624	−0.219809
$113$	13.3820	1.25887	0.629435	−	0.777053i	$-0.283286\pi$
$113$	13.3820	1.25887	0.629435	+	0.777053i	$0.283286\pi$
$114$	−3.23607	−0.303086
$115$	21.4164	1.99709
$116$	−14.5623	−1.35208
$117$	−10.3262	−0.954661
$118$	−15.9443	−1.46779
$119$	1.20163	0.110153
$120$	9.23607	0.843134
$121$	−9.09017	−0.826379
$122$	10.0902	0.913521
$123$	0.201626	0.0181800
$124$	0	0
$125$	1.52786	0.136656
$126$	1.76393	0.157144
$127$	16.6525	1.47767	0.738834	−	0.673887i	$-0.235377\pi$
$127$	16.6525	1.47767	0.738834	+	0.673887i	$0.235377\pi$
$128$	1.09017	0.0963583
$129$	0	0
$130$	30.6525	2.68840
$131$	7.94427	0.694094	0.347047	−	0.937848i	$-0.387184\pi$
$131$	7.94427	0.694094	0.347047	+	0.937848i	$0.387184\pi$
$132$	−2.56231	−0.223020
$133$	0.763932	0.0662413
$134$	7.47214	0.645494
$135$	−7.23607	−0.622782
$136$	−38.0344	−3.26143
$137$	9.70820	0.829428	0.414714	−	0.909952i	$-0.363882\pi$
$137$	9.70820	0.829428	0.414714	+	0.909952i	$0.363882\pi$
$138$	6.61803	0.563364
$139$	−18.7082	−1.58681	−0.793405	−	0.608695i	$-0.791693\pi$
$139$	−18.7082	−1.58681	−0.793405	+	0.608695i	$0.791693\pi$
$140$	−3.70820	−0.313400
$141$	3.00000	0.252646
$142$	−36.1246	−3.03151
$143$	−5.00000	−0.418121
$144$	−28.1246	−2.34372
$145$	−9.70820	−0.806222
$146$	12.7082	1.05174
$147$	−2.65248	−0.218773
$148$	−9.00000	−0.739795
$149$	−9.00000	−0.737309	−0.368654	−	0.929567i	$-0.620181\pi$
$149$	−9.00000	−0.737309	−0.368654	+	0.929567i	$0.620181\pi$
$150$	5.47214	0.446798
$151$	2.14590	0.174631	0.0873154	−	0.996181i	$-0.472171\pi$
$151$	2.14590	0.174631	0.0873154	+	0.996181i	$0.472171\pi$
$152$	−24.1803	−1.96128
$153$	14.5279	1.17451
$154$	0.854102	0.0688255
$155$	0	0
$156$	6.70820	0.537086
$157$	11.8541	0.946060	0.473030	−	0.881046i	$-0.343160\pi$
$157$	11.8541	0.946060	0.473030	+	0.881046i	$0.343160\pi$
$158$	−9.47214	−0.753563
$159$	−1.38197	−0.109597
$160$	35.1246	2.77684
$161$	−1.56231	−0.123127
$162$	20.1803	1.58552
$163$	−14.0000	−1.09656	−0.548282	−	0.836293i	$-0.684718\pi$
$163$	−14.0000	−1.09656	−0.548282	+	0.836293i	$0.684718\pi$
$164$	2.56231	0.200082
$165$	−1.70820	−0.132983
$166$	−34.1246	−2.64858
$167$	9.76393	0.755556	0.377778	−	0.925896i	$-0.376688\pi$
$167$	9.76393	0.755556	0.377778	+	0.925896i	$0.376688\pi$
$168$	−0.673762	−0.0519819
$169$	0.0901699	0.00693615
$170$	−43.1246	−3.30751
$171$	9.23607	0.706300
$172$	0	0
$173$	−8.23607	−0.626177	−0.313088	−	0.949724i	$-0.601364\pi$
$173$	−8.23607	−0.626177	−0.313088	+	0.949724i	$0.601364\pi$
$174$	−3.00000	−0.227429
$175$	−1.29180	−0.0976506
$176$	−13.6180	−1.02650
$177$	−2.32624	−0.174851
$178$	−12.7082	−0.952520
$179$	21.6525	1.61838	0.809191	−	0.587546i	$-0.199906\pi$
$179$	21.6525	1.61838	0.809191	+	0.587546i	$0.199906\pi$
$180$	−44.8328	−3.34164
$181$	−21.6180	−1.60686	−0.803428	−	0.595402i	$-0.796993\pi$
$181$	−21.6180	−1.60686	−0.803428	+	0.595402i	$0.796993\pi$
$182$	−2.23607	−0.165748
$183$	1.47214	0.108823
$184$	49.4508	3.64557
$185$	−6.00000	−0.441129
$186$	0	0
$187$	7.03444	0.514409
$188$	38.1246	2.78052
$189$	0.527864	0.0383965
$190$	−27.4164	−1.98900
$191$	23.4721	1.69838	0.849192	−	0.528084i	$-0.177089\pi$
$191$	23.4721	1.69838	0.849192	+	0.528084i	$0.177089\pi$
$192$	3.32624	0.240051
$193$	−10.7082	−0.770793	−0.385397	−	0.922751i	$-0.625935\pi$
$193$	−10.7082	−0.770793	−0.385397	+	0.922751i	$0.625935\pi$
$194$	−12.4721	−0.895447
$195$	4.47214	0.320256
$196$	−33.7082	−2.40773
$197$	14.9443	1.06474	0.532368	−	0.846513i	$-0.321302\pi$
$197$	14.9443	1.06474	0.532368	+	0.846513i	$0.321302\pi$
$198$	10.3262	0.733854
$199$	15.9443	1.13026	0.565130	−	0.825002i	$-0.308826\pi$
$199$	15.9443	1.13026	0.565130	+	0.825002i	$0.308826\pi$
$200$	40.8885	2.89126
$201$	1.09017	0.0768947
$202$	21.5623	1.51712
$203$	0.708204	0.0497062
$204$	−9.43769	−0.660771
$205$	1.70820	0.119306
$206$	27.2705	1.90003
$207$	−18.8885	−1.31284
$208$	35.6525	2.47205
$209$	4.47214	0.309344
$210$	−0.763932	−0.0527163
$211$	4.76393	0.327963	0.163981	−	0.986463i	$-0.447566\pi$
$211$	4.76393	0.327963	0.163981	+	0.986463i	$0.447566\pi$
$212$	−17.5623	−1.20618
$213$	−5.27051	−0.361129
$214$	43.1246	2.94794
$215$	0	0
$216$	−16.7082	−1.13685
$217$	0	0
$218$	−18.7082	−1.26708
$219$	1.85410	0.125289
$220$	−21.7082	−1.46357
$221$	−18.4164	−1.23882
$222$	−1.85410	−0.124439
$223$	−7.23607	−0.484563	−0.242281	−	0.970206i	$-0.577896\pi$
$223$	−7.23607	−0.484563	−0.242281	+	0.970206i	$0.577896\pi$
$224$	−2.56231	−0.171201
$225$	−15.6180	−1.04120
$226$	35.0344	2.33046
$227$	−7.47214	−0.495943	−0.247972	−	0.968767i	$-0.579764\pi$
$227$	−7.47214	−0.495943	−0.247972	+	0.968767i	$0.579764\pi$
$228$	−6.00000	−0.397360
$229$	−15.7082	−1.03803	−0.519014	−	0.854766i	$-0.673701\pi$
$229$	−15.7082	−1.03803	−0.519014	+	0.854766i	$0.673701\pi$
$230$	56.0689	3.69707
$231$	0.124612	0.00819885
$232$	−22.4164	−1.47171
$233$	11.0344	0.722890	0.361445	−	0.932393i	$-0.382283\pi$
$233$	11.0344	0.722890	0.361445	+	0.932393i	$0.382283\pi$
$234$	−27.0344	−1.76730
$235$	25.4164	1.65798
$236$	−29.5623	−1.92434
$237$	−1.38197	−0.0897683
$238$	3.14590	0.203918
$239$	−21.7082	−1.40419	−0.702093	−	0.712085i	$-0.747751\pi$
$239$	−21.7082	−1.40419	−0.702093	+	0.712085i	$0.747751\pi$
$240$	12.1803	0.786238
$241$	29.2705	1.88548	0.942740	−	0.333530i	$-0.108240\pi$
$241$	29.2705	1.88548	0.942740	+	0.333530i	$0.108240\pi$
$242$	−23.7984	−1.52982
$243$	9.65248	0.619207
$244$	18.7082	1.19767
$245$	−22.4721	−1.43569
$246$	0.527864	0.0336554
$247$	−11.7082	−0.744975
$248$	0	0
$249$	−4.97871	−0.315513
$250$	4.00000	0.252982
$251$	−6.81966	−0.430453	−0.215227	−	0.976564i	$-0.569049\pi$
$251$	−6.81966	−0.430453	−0.215227	+	0.976564i	$0.569049\pi$
$252$	3.27051	0.206023
$253$	−9.14590	−0.574998
$254$	43.5967	2.73550
$255$	−6.29180	−0.394008
$256$	−14.5623	−0.910144
$257$	−23.5623	−1.46978	−0.734888	−	0.678188i	$-0.762765\pi$
$257$	−23.5623	−1.46978	−0.734888	+	0.678188i	$0.762765\pi$
$258$	0	0
$259$	0.437694	0.0271970
$260$	56.8328	3.52462
$261$	8.56231	0.529993
$262$	20.7984	1.28493
$263$	10.5066	0.647863	0.323932	−	0.946080i	$-0.394995\pi$
$263$	10.5066	0.647863	0.323932	+	0.946080i	$0.394995\pi$
$264$	−3.94427	−0.242753
$265$	−11.7082	−0.719229
$266$	2.00000	0.122628
$267$	−1.85410	−0.113469
$268$	13.8541	0.846274
$269$	−8.56231	−0.522053	−0.261027	−	0.965332i	$-0.584061\pi$
$269$	−8.56231	−0.522053	−0.261027	+	0.965332i	$0.584061\pi$
$270$	−18.9443	−1.15291
$271$	7.14590	0.434082	0.217041	−	0.976162i	$-0.430359\pi$
$271$	7.14590	0.434082	0.217041	+	0.976162i	$0.430359\pi$
$272$	−50.1591	−3.04134
$273$	−0.326238	−0.0197448
$274$	25.4164	1.53546
$275$	−7.56231	−0.456024
$276$	12.2705	0.738598
$277$	3.52786	0.211969	0.105984	−	0.994368i	$-0.466201\pi$
$277$	3.52786	0.211969	0.105984	+	0.994368i	$0.466201\pi$
$278$	−48.9787	−2.93755
$279$	0	0
$280$	−5.70820	−0.341130
$281$	−1.47214	−0.0878203	−0.0439101	−	0.999035i	$-0.513982\pi$
$281$	−1.47214	−0.0878203	−0.0439101	+	0.999035i	$0.513982\pi$
$282$	7.85410	0.467705
$283$	15.2361	0.905690	0.452845	−	0.891589i	$-0.350409\pi$
$283$	15.2361	0.905690	0.452845	+	0.891589i	$0.350409\pi$
$284$	−66.9787	−3.97446
$285$	−4.00000	−0.236940
$286$	−13.0902	−0.774038
$287$	−0.124612	−0.00735560
$288$	−30.9787	−1.82544
$289$	8.90983	0.524108
$290$	−25.4164	−1.49250
$291$	−1.81966	−0.106670
$292$	23.5623	1.37888
$293$	−0.909830	−0.0531528	−0.0265764	−	0.999647i	$-0.508461\pi$
$293$	−0.909830	−0.0531528	−0.0265764	+	0.999647i	$0.508461\pi$
$294$	−6.94427	−0.404998
$295$	−19.7082	−1.14746
$296$	−13.8541	−0.805253
$297$	3.09017	0.179310
$298$	−23.5623	−1.36493
$299$	23.9443	1.38473
$300$	10.1459	0.585774
$301$	0	0
$302$	5.61803	0.323282
$303$	3.14590	0.180727
$304$	−31.8885	−1.82893
$305$	12.4721	0.714152
$306$	38.0344	2.17428
$307$	28.2148	1.61030	0.805151	−	0.593069i	$-0.202084\pi$
$307$	28.2148	1.61030	0.805151	+	0.593069i	$0.202084\pi$
$308$	1.58359	0.0902335
$309$	3.97871	0.226341
$310$	0	0
$311$	23.8328	1.35143	0.675717	−	0.737161i	$-0.263834\pi$
$311$	23.8328	1.35143	0.675717	+	0.737161i	$0.263834\pi$
$312$	10.3262	0.584608
$313$	27.1246	1.53317	0.766587	−	0.642141i	$-0.221953\pi$
$313$	27.1246	1.53317	0.766587	+	0.642141i	$0.221953\pi$
$314$	31.0344	1.75137
$315$	2.18034	0.122848
$316$	−17.5623	−0.987957
$317$	−29.3050	−1.64593	−0.822965	−	0.568092i	$-0.807682\pi$
$317$	−29.3050	−1.64593	−0.822965	+	0.568092i	$0.807682\pi$
$318$	−3.61803	−0.202889
$319$	4.14590	0.232126
$320$	28.1803	1.57533
$321$	6.29180	0.351174
$322$	−4.09017	−0.227936
$323$	16.4721	0.916534
$324$	37.4164	2.07869
$325$	19.7984	1.09822
$326$	−36.6525	−2.02999
$327$	−2.72949	−0.150941
$328$	3.94427	0.217786
$329$	−1.85410	−0.102220
$330$	−4.47214	−0.246183
$331$	−3.47214	−0.190846	−0.0954229	−	0.995437i	$-0.530420\pi$
$331$	−3.47214	−0.190846	−0.0954229	+	0.995437i	$0.530420\pi$
$332$	−63.2705	−3.47242
$333$	5.29180	0.289989
$334$	25.5623	1.39871
$335$	9.23607	0.504620
$336$	−0.888544	−0.0484740
$337$	28.0000	1.52526	0.762629	−	0.646837i	$-0.223908\pi$
$337$	28.0000	1.52526	0.762629	+	0.646837i	$0.223908\pi$
$338$	0.236068	0.0128404
$339$	5.11146	0.277616
$340$	−79.9574	−4.33630
$341$	0	0
$342$	24.1803	1.30752
$343$	3.29180	0.177740
$344$	0	0
$345$	8.18034	0.440415
$346$	−21.5623	−1.15920
$347$	1.09017	0.0585234	0.0292617	−	0.999572i	$-0.490684\pi$
$347$	1.09017	0.0585234	0.0292617	+	0.999572i	$0.490684\pi$
$348$	−5.56231	−0.298171
$349$	−7.29180	−0.390321	−0.195160	−	0.980771i	$-0.562523\pi$
$349$	−7.29180	−0.390321	−0.195160	+	0.980771i	$0.562523\pi$
$350$	−3.38197	−0.180774
$351$	−8.09017	−0.431821
$352$	−15.0000	−0.799503
$353$	−12.7639	−0.679356	−0.339678	−	0.940542i	$-0.610318\pi$
$353$	−12.7639	−0.679356	−0.339678	+	0.940542i	$0.610318\pi$
$354$	−6.09017	−0.323689
$355$	−44.6525	−2.36991
$356$	−23.5623	−1.24880
$357$	0.458980	0.0242918
$358$	56.6869	2.99600
$359$	−36.6525	−1.93444	−0.967222	−	0.253933i	$-0.918276\pi$
$359$	−36.6525	−1.93444	−0.967222	+	0.253933i	$0.918276\pi$
$360$	−69.0132	−3.63731
$361$	−8.52786	−0.448835
$362$	−56.5967	−2.97466
$363$	−3.47214	−0.182240
$364$	−4.14590	−0.217304
$365$	15.7082	0.822205
$366$	3.85410	0.201457
$367$	−3.18034	−0.166012	−0.0830062	−	0.996549i	$-0.526452\pi$
$367$	−3.18034	−0.166012	−0.0830062	+	0.996549i	$0.526452\pi$
$368$	65.2148	3.39956
$369$	−1.50658	−0.0784293
$370$	−15.7082	−0.816631
$371$	0.854102	0.0443428
$372$	0	0
$373$	−6.00000	−0.310668	−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000	−0.310668	−0.155334	+	0.987862i	$0.549645\pi$
$374$	18.4164	0.952290
$375$	0.583592	0.0301366
$376$	58.6869	3.02655
$377$	−10.8541	−0.559015
$378$	1.38197	0.0710807
$379$	17.3607	0.891758	0.445879	−	0.895093i	$-0.352891\pi$
$379$	17.3607	0.891758	0.445879	+	0.895093i	$0.352891\pi$
$380$	−50.8328	−2.60767
$381$	6.36068	0.325867
$382$	61.4508	3.14410
$383$	2.12461	0.108563	0.0542813	−	0.998526i	$-0.482713\pi$
$383$	2.12461	0.108563	0.0542813	+	0.998526i	$0.482713\pi$
$384$	0.416408	0.0212497
$385$	1.05573	0.0538049
$386$	−28.0344	−1.42692
$387$	0	0
$388$	−23.1246	−1.17397
$389$	−23.0689	−1.16964	−0.584819	−	0.811164i	$-0.698835\pi$
$389$	−23.0689	−1.16964	−0.584819	+	0.811164i	$0.698835\pi$
$390$	11.7082	0.592868
$391$	−33.6869	−1.70362
$392$	−51.8885	−2.62077
$393$	3.03444	0.153067
$394$	39.1246	1.97107
$395$	−11.7082	−0.589104
$396$	19.1459	0.962118
$397$	5.58359	0.280232	0.140116	−	0.990135i	$-0.455252\pi$
$397$	5.58359	0.280232	0.140116	+	0.990135i	$0.455252\pi$
$398$	41.7426	2.09237
$399$	0.291796	0.0146081
$400$	53.9230	2.69615
$401$	1.41641	0.0707320	0.0353660	−	0.999374i	$-0.488740\pi$
$401$	1.41641	0.0707320	0.0353660	+	0.999374i	$0.488740\pi$
$402$	2.85410	0.142350
$403$	0	0
$404$	39.9787	1.98902
$405$	24.9443	1.23949
$406$	1.85410	0.0920175
$407$	2.56231	0.127009
$408$	−14.5279	−0.719236
$409$	−20.0902	−0.993395	−0.496697	−	0.867924i	$-0.665454\pi$
$409$	−20.0902	−0.993395	−0.496697	+	0.867924i	$0.665454\pi$
$410$	4.47214	0.220863
$411$	3.70820	0.182912
$412$	50.5623	2.49103
$413$	1.43769	0.0707443
$414$	−49.4508	−2.43038
$415$	−42.1803	−2.07055
$416$	39.2705	1.92540
$417$	−7.14590	−0.349936
$418$	11.7082	0.572667
$419$	5.76393	0.281587	0.140793	−	0.990039i	$-0.455035\pi$
$419$	5.76393	0.281587	0.140793	+	0.990039i	$0.455035\pi$
$420$	−1.41641	−0.0691136
$421$	−23.6525	−1.15275	−0.576376	−	0.817185i	$-0.695533\pi$
$421$	−23.6525	−1.15275	−0.576376	+	0.817185i	$0.695533\pi$
$422$	12.4721	0.607134
$423$	−22.4164	−1.08992
$424$	−27.0344	−1.31291
$425$	−27.8541	−1.35112
$426$	−13.7984	−0.668533
$427$	−0.909830	−0.0440298
$428$	79.9574	3.86489
$429$	−1.90983	−0.0922075
$430$	0	0
$431$	−0.201626	−0.00971199	−0.00485599	−	0.999988i	$-0.501546\pi$
$431$	−0.201626	−0.00971199	−0.00485599	+	0.999988i	$0.501546\pi$
$432$	−22.0344	−1.06013
$433$	21.2918	1.02322	0.511609	−	0.859218i	$-0.329050\pi$
$433$	21.2918	1.02322	0.511609	+	0.859218i	$0.329050\pi$
$434$	0	0
$435$	−3.70820	−0.177795
$436$	−34.6869	−1.66120
$437$	−21.4164	−1.02449
$438$	4.85410	0.231938
$439$	7.85410	0.374856	0.187428	−	0.982278i	$-0.439985\pi$
$439$	7.85410	0.374856	0.187428	+	0.982278i	$0.439985\pi$
$440$	−33.4164	−1.59306
$441$	19.8197	0.943793
$442$	−48.2148	−2.29334
$443$	−6.47214	−0.307500	−0.153750	−	0.988110i	$-0.549135\pi$
$443$	−6.47214	−0.307500	−0.153750	+	0.988110i	$0.549135\pi$
$444$	−3.43769	−0.163146
$445$	−15.7082	−0.744640
$446$	−18.9443	−0.897037
$447$	−3.43769	−0.162597
$448$	−2.05573	−0.0971240
$449$	−20.8328	−0.983161	−0.491581	−	0.870832i	$-0.663581\pi$
$449$	−20.8328	−0.983161	−0.491581	+	0.870832i	$0.663581\pi$
$450$	−40.8885	−1.92750
$451$	−0.729490	−0.0343504
$452$	64.9574	3.05534
$453$	0.819660	0.0385110
$454$	−19.5623	−0.918105
$455$	−2.76393	−0.129575
$456$	−9.23607	−0.432519
$457$	2.29180	0.107206	0.0536028	−	0.998562i	$-0.482930\pi$
$457$	2.29180	0.107206	0.0536028	+	0.998562i	$0.482930\pi$
$458$	−41.1246	−1.92163
$459$	11.3820	0.531265
$460$	103.957	4.84704
$461$	17.5967	0.819562	0.409781	−	0.912184i	$-0.365605\pi$
$461$	17.5967	0.819562	0.409781	+	0.912184i	$0.365605\pi$
$462$	0.326238	0.0151780
$463$	−23.8328	−1.10760	−0.553802	−	0.832648i	$-0.686824\pi$
$463$	−23.8328	−1.10760	−0.553802	+	0.832648i	$0.686824\pi$
$464$	−29.5623	−1.37240
$465$	0	0
$466$	28.8885	1.33824
$467$	32.9443	1.52448	0.762240	−	0.647295i	$-0.224100\pi$
$467$	32.9443	1.52448	0.762240	+	0.647295i	$0.224100\pi$
$468$	−50.1246	−2.31701
$469$	−0.673762	−0.0311114
$470$	66.5410	3.06931
$471$	4.52786	0.208633
$472$	−45.5066	−2.09461
$473$	0	0
$474$	−3.61803	−0.166182
$475$	−17.7082	−0.812508
$476$	5.83282	0.267347
$477$	10.3262	0.472806
$478$	−56.8328	−2.59947
$479$	−36.1803	−1.65312	−0.826561	−	0.562847i	$-0.809706\pi$
$479$	−36.1803	−1.65312	−0.826561	+	0.562847i	$0.809706\pi$
$480$	13.4164	0.612372
$481$	−6.70820	−0.305868
$482$	76.6312	3.49046
$483$	−0.596748	−0.0271530
$484$	−44.1246	−2.00566
$485$	−15.4164	−0.700023
$486$	25.2705	1.14629
$487$	−14.3262	−0.649184	−0.324592	−	0.945854i	$-0.605227\pi$
$487$	−14.3262	−0.649184	−0.324592	+	0.945854i	$0.605227\pi$
$488$	28.7984	1.30364
$489$	−5.34752	−0.241823
$490$	−58.8328	−2.65780
$491$	9.65248	0.435610	0.217805	−	0.975992i	$-0.430110\pi$
$491$	9.65248	0.435610	0.217805	+	0.975992i	$0.430110\pi$
$492$	0.978714	0.0441238
$493$	15.2705	0.687749
$494$	−30.6525	−1.37912
$495$	12.7639	0.573696
$496$	0	0
$497$	3.25735	0.146112
$498$	−13.0344	−0.584087
$499$	−7.14590	−0.319894	−0.159947	−	0.987126i	$-0.551132\pi$
$499$	−7.14590	−0.319894	−0.159947	+	0.987126i	$0.551132\pi$
$500$	7.41641	0.331672
$501$	3.72949	0.166621
$502$	−17.8541	−0.796868
$503$	4.52786	0.201887	0.100944	−	0.994892i	$-0.467814\pi$
$503$	4.52786	0.201887	0.100944	+	0.994892i	$0.467814\pi$
$504$	5.03444	0.224252
$505$	26.6525	1.18602
$506$	−23.9443	−1.06445
$507$	0.0344419	0.00152962
$508$	80.8328	3.58638
$509$	5.29180	0.234555	0.117277	−	0.993099i	$-0.462583\pi$
$509$	5.29180	0.234555	0.117277	+	0.993099i	$0.462583\pi$
$510$	−16.4721	−0.729398
$511$	−1.14590	−0.0506915
$512$	−40.3050	−1.78124
$513$	7.23607	0.319480
$514$	−61.6869	−2.72089
$515$	33.7082	1.48536
$516$	0	0
$517$	−10.8541	−0.477363
$518$	1.14590	0.0503479
$519$	−3.14590	−0.138090
$520$	87.4853	3.83648
$521$	−7.03444	−0.308184	−0.154092	−	0.988056i	$-0.549245\pi$
$521$	−7.03444	−0.308184	−0.154092	+	0.988056i	$0.549245\pi$
$522$	22.4164	0.981140
$523$	17.8328	0.779775	0.389887	−	0.920863i	$-0.372514\pi$
$523$	17.8328	0.779775	0.389887	+	0.920863i	$0.372514\pi$
$524$	38.5623	1.68460
$525$	−0.493422	−0.0215347
$526$	27.5066	1.19934
$527$	0	0
$528$	−5.20163	−0.226372
$529$	20.7984	0.904277
$530$	−30.6525	−1.33146
$531$	17.3820	0.754313
$532$	3.70820	0.160771
$533$	1.90983	0.0827239
$534$	−4.85410	−0.210058
$535$	53.3050	2.30457
$536$	21.3262	0.921153
$537$	8.27051	0.356899
$538$	−22.4164	−0.966440
$539$	9.59675	0.413361
$540$	−35.1246	−1.51152
$541$	−20.0557	−0.862263	−0.431132	−	0.902289i	$-0.641886\pi$
$541$	−20.0557	−0.862263	−0.431132	+	0.902289i	$0.641886\pi$
$542$	18.7082	0.803586
$543$	−8.25735	−0.354357
$544$	−55.2492	−2.36879
$545$	−23.1246	−0.990550
$546$	−0.854102	−0.0365522
$547$	21.0000	0.897895	0.448948	−	0.893558i	$-0.351799\pi$
$547$	21.0000	0.897895	0.448948	+	0.893558i	$0.351799\pi$
$548$	47.1246	2.01306
$549$	−11.0000	−0.469469
$550$	−19.7984	−0.844205
$551$	9.70820	0.413583
$552$	18.8885	0.803950
$553$	0.854102	0.0363201
$554$	9.23607	0.392403
$555$	−2.29180	−0.0972813
$556$	−90.8115	−3.85127
$557$	−18.4377	−0.781230	−0.390615	−	0.920554i	$-0.627738\pi$
$557$	−18.4377	−0.781230	−0.390615	+	0.920554i	$0.627738\pi$
$558$	0	0
$559$	0	0
$560$	−7.52786	−0.318110
$561$	2.68692	0.113442
$562$	−3.85410	−0.162575
$563$	14.3262	0.603779	0.301889	−	0.953343i	$-0.402383\pi$
$563$	14.3262	0.603779	0.301889	+	0.953343i	$0.402383\pi$
$564$	14.5623	0.613184
$565$	43.3050	1.82185
$566$	39.8885	1.67664
$567$	−1.81966	−0.0764185
$568$	−103.103	−4.32612
$569$	−8.05573	−0.337714	−0.168857	−	0.985641i	$-0.554008\pi$
$569$	−8.05573	−0.337714	−0.168857	+	0.985641i	$0.554008\pi$
$570$	−10.4721	−0.438630
$571$	20.8197	0.871276	0.435638	−	0.900122i	$-0.356523\pi$
$571$	20.8197	0.871276	0.435638	+	0.900122i	$0.356523\pi$
$572$	−24.2705	−1.01480
$573$	8.96556	0.374542
$574$	−0.326238	−0.0136169
$575$	36.2148	1.51026
$576$	−24.8541	−1.03559
$577$	−23.2148	−0.966444	−0.483222	−	0.875498i	$-0.660534\pi$
$577$	−23.2148	−0.966444	−0.483222	+	0.875498i	$0.660534\pi$
$578$	23.3262	0.970244
$579$	−4.09017	−0.169982
$580$	−47.1246	−1.95674
$581$	3.07701	0.127656
$582$	−4.76393	−0.197471
$583$	5.00000	0.207079
$584$	36.2705	1.50088
$585$	−33.4164	−1.38160
$586$	−2.38197	−0.0983981
$587$	26.7426	1.10379	0.551894	−	0.833915i	$-0.313905\pi$
$587$	26.7426	1.10379	0.551894	+	0.833915i	$0.313905\pi$
$588$	−12.8754	−0.530972
$589$	0	0
$590$	−51.5967	−2.12420
$591$	5.70820	0.234804
$592$	−18.2705	−0.750913
$593$	21.5279	0.884043	0.442022	−	0.897004i	$-0.354261\pi$
$593$	21.5279	0.884043	0.442022	+	0.897004i	$0.354261\pi$
$594$	8.09017	0.331944
$595$	3.88854	0.159415
$596$	−43.6869	−1.78949
$597$	6.09017	0.249254
$598$	62.6869	2.56346
$599$	31.7639	1.29784	0.648920	−	0.760857i	$-0.275221\pi$
$599$	31.7639	1.29784	0.648920	+	0.760857i	$0.275221\pi$
$600$	15.6180	0.637604
$601$	−2.58359	−0.105387	−0.0526935	−	0.998611i	$-0.516781\pi$
$601$	−2.58359	−0.105387	−0.0526935	+	0.998611i	$0.516781\pi$
$602$	0	0
$603$	−8.14590	−0.331727
$604$	10.4164	0.423838
$605$	−29.4164	−1.19595
$606$	8.23607	0.334567
$607$	17.1459	0.695931	0.347965	−	0.937507i	$-0.386873\pi$
$607$	17.1459	0.695931	0.347965	+	0.937507i	$0.386873\pi$
$608$	−35.1246	−1.42449
$609$	0.270510	0.0109616
$610$	32.6525	1.32206
$611$	28.4164	1.14960
$612$	70.5197	2.85059
$613$	29.7984	1.20354	0.601772	−	0.798668i	$-0.294461\pi$
$613$	29.7984	1.20354	0.601772	+	0.798668i	$0.294461\pi$
$614$	73.8673	2.98104
$615$	0.652476	0.0263104
$616$	2.43769	0.0982175
$617$	−3.70820	−0.149287	−0.0746433	−	0.997210i	$-0.523782\pi$
$617$	−3.70820	−0.149287	−0.0746433	+	0.997210i	$0.523782\pi$
$618$	10.4164	0.419009
$619$	3.27051	0.131453	0.0657264	−	0.997838i	$-0.479064\pi$
$619$	3.27051	0.131453	0.0657264	+	0.997838i	$0.479064\pi$
$620$	0	0
$621$	−14.7984	−0.593838
$622$	62.3951	2.50182
$623$	1.14590	0.0459094
$624$	13.6180	0.545158
$625$	−22.4164	−0.896656
$626$	71.0132	2.83826
$627$	1.70820	0.0682191
$628$	57.5410	2.29614
$629$	9.43769	0.376306
$630$	5.70820	0.227420
$631$	15.9098	0.633360	0.316680	−	0.948532i	$-0.397432\pi$
$631$	15.9098	0.633360	0.316680	+	0.948532i	$0.397432\pi$
$632$	−27.0344	−1.07537
$633$	1.81966	0.0723250
$634$	−76.7214	−3.04699
$635$	53.8885	2.13850
$636$	−6.70820	−0.265998
$637$	−25.1246	−0.995473
$638$	10.8541	0.429718
$639$	39.3820	1.55793
$640$	3.52786	0.139451
$641$	−33.1803	−1.31054	−0.655272	−	0.755393i	$-0.727446\pi$
$641$	−33.1803	−1.31054	−0.655272	+	0.755393i	$0.727446\pi$
$642$	16.4721	0.650103
$643$	29.5623	1.16582	0.582912	−	0.812535i	$-0.301913\pi$
$643$	29.5623	1.16582	0.582912	+	0.812535i	$0.301913\pi$
$644$	−7.58359	−0.298835
$645$	0	0
$646$	43.1246	1.69672
$647$	37.3262	1.46745	0.733723	−	0.679449i	$-0.237781\pi$
$647$	37.3262	1.46745	0.733723	+	0.679449i	$0.237781\pi$
$648$	57.5967	2.26261
$649$	8.41641	0.330373
$650$	51.8328	2.03305
$651$	0	0
$652$	−67.9574	−2.66142
$653$	−2.88854	−0.113037	−0.0565187	−	0.998402i	$-0.518000\pi$
$653$	−2.88854	−0.113037	−0.0565187	+	0.998402i	$0.518000\pi$
$654$	−7.14590	−0.279427
$655$	25.7082	1.00450
$656$	5.20163	0.203089
$657$	−13.8541	−0.540500
$658$	−4.85410	−0.189233
$659$	15.3607	0.598367	0.299184	−	0.954196i	$-0.403286\pi$
$659$	15.3607	0.598367	0.299184	+	0.954196i	$0.403286\pi$
$660$	−8.29180	−0.322758
$661$	30.3951	1.18223	0.591117	−	0.806586i	$-0.298687\pi$
$661$	30.3951	1.18223	0.591117	+	0.806586i	$0.298687\pi$
$662$	−9.09017	−0.353299
$663$	−7.03444	−0.273195
$664$	−97.3951	−3.77966
$665$	2.47214	0.0958653
$666$	13.8541	0.536836
$667$	−19.8541	−0.768754
$668$	47.3951	1.83377
$669$	−2.76393	−0.106860
$670$	24.1803	0.934168
$671$	−5.32624	−0.205617
$672$	−0.978714	−0.0377547
$673$	39.8328	1.53544	0.767721	−	0.640784i	$-0.221391\pi$
$673$	39.8328	1.53544	0.767721	+	0.640784i	$0.221391\pi$
$674$	73.3050	2.82360
$675$	−12.2361	−0.470966
$676$	0.437694	0.0168344
$677$	36.2361	1.39267	0.696333	−	0.717719i	$-0.254814\pi$
$677$	36.2361	1.39267	0.696333	+	0.717719i	$0.254814\pi$
$678$	13.3820	0.513931
$679$	1.12461	0.0431586
$680$	−123.082	−4.71998
$681$	−2.85410	−0.109369
$682$	0	0
$683$	29.1246	1.11442	0.557211	−	0.830371i	$-0.311871\pi$
$683$	29.1246	1.11442	0.557211	+	0.830371i	$0.311871\pi$
$684$	44.8328	1.71423
$685$	31.4164	1.20036
$686$	8.61803	0.329038
$687$	−6.00000	−0.228914
$688$	0	0
$689$	−13.0902	−0.498696
$690$	21.4164	0.815309
$691$	−49.2705	−1.87434	−0.937169	−	0.348875i	$-0.886564\pi$
$691$	−49.2705	−1.87434	−0.937169	+	0.348875i	$0.886564\pi$
$692$	−39.9787	−1.51976
$693$	−0.931116	−0.0353702
$694$	2.85410	0.108340
$695$	−60.5410	−2.29645
$696$	−8.56231	−0.324553
$697$	−2.68692	−0.101774
$698$	−19.0902	−0.722574
$699$	4.21478	0.159418
$700$	−6.27051	−0.237003
$701$	23.5066	0.887831	0.443916	−	0.896069i	$-0.353589\pi$
$701$	23.5066	0.887831	0.443916	+	0.896069i	$0.353589\pi$
$702$	−21.1803	−0.799400
$703$	6.00000	0.226294
$704$	−12.0344	−0.453565
$705$	9.70820	0.365632
$706$	−33.4164	−1.25764
$707$	−1.94427	−0.0731219
$708$	−11.2918	−0.424372
$709$	−6.88854	−0.258705	−0.129352	−	0.991599i	$-0.541290\pi$
$709$	−6.88854	−0.258705	−0.129352	+	0.991599i	$0.541290\pi$
$710$	−116.902	−4.38724
$711$	10.3262	0.387264
$712$	−36.2705	−1.35929
$713$	0	0
$714$	1.20163	0.0449697
$715$	−16.1803	−0.605110
$716$	105.103	3.92790
$717$	−8.29180	−0.309663
$718$	−95.9574	−3.58110
$719$	13.7984	0.514593	0.257296	−	0.966333i	$-0.417168\pi$
$719$	13.7984	0.514593	0.257296	+	0.966333i	$0.417168\pi$
$720$	−91.0132	−3.39186
$721$	−2.45898	−0.0915772
$722$	−22.3262	−0.830897
$723$	11.1803	0.415801
$724$	−104.936	−3.89992
$725$	−16.4164	−0.609690
$726$	−9.09017	−0.337368
$727$	−28.9787	−1.07476	−0.537381	−	0.843340i	$-0.680586\pi$
$727$	−28.9787	−1.07476	−0.537381	+	0.843340i	$0.680586\pi$
$728$	−6.38197	−0.236531
$729$	−19.4377	−0.719915
$730$	41.1246	1.52209
$731$	0	0
$732$	7.14590	0.264120
$733$	42.5410	1.57129	0.785644	−	0.618679i	$-0.212332\pi$
$733$	42.5410	1.57129	0.785644	+	0.618679i	$0.212332\pi$
$734$	−8.32624	−0.307327
$735$	−8.58359	−0.316611
$736$	71.8328	2.64779
$737$	−3.94427	−0.145289
$738$	−3.94427	−0.145191
$739$	17.5410	0.645257	0.322628	−	0.946526i	$-0.395434\pi$
$739$	17.5410	0.645257	0.322628	+	0.946526i	$0.395434\pi$
$740$	−29.1246	−1.07064
$741$	−4.47214	−0.164288
$742$	2.23607	0.0820886
$743$	11.3607	0.416783	0.208391	−	0.978045i	$-0.433177\pi$
$743$	11.3607	0.416783	0.208391	+	0.978045i	$0.433177\pi$
$744$	0	0
$745$	−29.1246	−1.06704
$746$	−15.7082	−0.575118
$747$	37.2016	1.36114
$748$	34.1459	1.24850
$749$	−3.88854	−0.142084
$750$	1.52786	0.0557897
$751$	−8.97871	−0.327638	−0.163819	−	0.986490i	$-0.552381\pi$
$751$	−8.97871	−0.327638	−0.163819	+	0.986490i	$0.552381\pi$
$752$	77.3951	2.82231
$753$	−2.60488	−0.0949270
$754$	−28.4164	−1.03486
$755$	6.94427	0.252728
$756$	2.56231	0.0931902
$757$	−15.9787	−0.580756	−0.290378	−	0.956912i	$-0.593781\pi$
$757$	−15.9787	−0.580756	−0.290378	+	0.956912i	$0.593781\pi$
$758$	45.4508	1.65085
$759$	−3.49342	−0.126803
$760$	−78.2492	−2.83840
$761$	10.0902	0.365768	0.182884	−	0.983134i	$-0.441457\pi$
$761$	10.0902	0.365768	0.182884	+	0.983134i	$0.441457\pi$
$762$	16.6525	0.603256
$763$	1.68692	0.0610705
$764$	113.936	4.12206
$765$	47.0132	1.69976
$766$	5.56231	0.200974
$767$	−22.0344	−0.795618
$768$	−5.56231	−0.200712
$769$	−15.8885	−0.572956	−0.286478	−	0.958087i	$-0.592484\pi$
$769$	−15.8885	−0.572956	−0.286478	+	0.958087i	$0.592484\pi$
$770$	2.76393	0.0996052
$771$	−9.00000	−0.324127
$772$	−51.9787	−1.87075
$773$	33.5967	1.20839	0.604196	−	0.796836i	$-0.293495\pi$
$773$	33.5967	1.20839	0.604196	+	0.796836i	$0.293495\pi$
$774$	0	0
$775$	0	0
$776$	−35.5967	−1.27785
$777$	0.167184	0.00599770
$778$	−60.3951	−2.16527
$779$	−1.70820	−0.0612028
$780$	21.7082	0.777278
$781$	19.0689	0.682338
$782$	−88.1935	−3.15379
$783$	6.70820	0.239732
$784$	−68.4296	−2.44391
$785$	38.3607	1.36915
$786$	7.94427	0.283363
$787$	−45.4508	−1.62015	−0.810074	−	0.586328i	$-0.800573\pi$
$787$	−45.4508	−1.62015	−0.810074	+	0.586328i	$0.800573\pi$
$788$	72.5410	2.58417
$789$	4.01316	0.142872
$790$	−30.6525	−1.09057
$791$	−3.15905	−0.112323
$792$	29.4721	1.04725
$793$	13.9443	0.495176
$794$	14.6180	0.518775
$795$	−4.47214	−0.158610
$796$	77.3951	2.74320
$797$	−3.76393	−0.133325	−0.0666627	−	0.997776i	$-0.521235\pi$
$797$	−3.76393	−0.133325	−0.0666627	+	0.997776i	$0.521235\pi$
$798$	0.763932	0.0270429
$799$	−39.9787	−1.41435
$800$	59.3951	2.09993
$801$	13.8541	0.489511
$802$	3.70820	0.130941
$803$	−6.70820	−0.236727
$804$	5.29180	0.186627
$805$	−5.05573	−0.178191
$806$	0	0
$807$	−3.27051	−0.115127
$808$	61.5410	2.16501
$809$	−37.7426	−1.32696	−0.663480	−	0.748194i	$-0.730921\pi$
$809$	−37.7426	−1.32696	−0.663480	+	0.748194i	$0.730921\pi$
$810$	65.3050	2.29458
$811$	26.3951	0.926858	0.463429	−	0.886134i	$-0.346619\pi$
$811$	26.3951	0.926858	0.463429	+	0.886134i	$0.346619\pi$
$812$	3.43769	0.120639
$813$	2.72949	0.0957274
$814$	6.70820	0.235122
$815$	−45.3050	−1.58696
$816$	−19.1591	−0.670701
$817$	0	0
$818$	−52.5967	−1.83900
$819$	2.43769	0.0851799
$820$	8.29180	0.289562
$821$	−15.3262	−0.534889	−0.267445	−	0.963573i	$-0.586179\pi$
$821$	−15.3262	−0.534889	−0.267445	+	0.963573i	$0.586179\pi$
$822$	9.70820	0.338612
$823$	−24.0132	−0.837046	−0.418523	−	0.908206i	$-0.637452\pi$
$823$	−24.0132	−0.837046	−0.418523	+	0.908206i	$0.637452\pi$
$824$	77.8328	2.71143
$825$	−2.88854	−0.100566
$826$	3.76393	0.130964
$827$	−13.1803	−0.458325	−0.229163	−	0.973388i	$-0.573599\pi$
$827$	−13.1803	−0.458325	−0.229163	+	0.973388i	$0.573599\pi$
$828$	−91.6869	−3.18634
$829$	41.1591	1.42951	0.714757	−	0.699373i	$-0.246538\pi$
$829$	41.1591	1.42951	0.714757	+	0.699373i	$0.246538\pi$
$830$	−110.430	−3.83307
$831$	1.34752	0.0467451
$832$	31.5066	1.09229
$833$	35.3475	1.22472
$834$	−18.7082	−0.647812
$835$	31.5967	1.09345
$836$	21.7082	0.750794
$837$	0	0
$838$	15.0902	0.521281
$839$	9.88854	0.341390	0.170695	−	0.985324i	$-0.445399\pi$
$839$	9.88854	0.341390	0.170695	+	0.985324i	$0.445399\pi$
$840$	−2.18034	−0.0752289
$841$	−20.0000	−0.689655
$842$	−61.9230	−2.13401
$843$	−0.562306	−0.0193668
$844$	23.1246	0.795982
$845$	0.291796	0.0100381
$846$	−58.6869	−2.01770
$847$	2.14590	0.0737339
$848$	−35.6525	−1.22431
$849$	5.81966	0.199730
$850$	−72.9230	−2.50124
$851$	−12.2705	−0.420628
$852$	−25.5836	−0.876479
$853$	53.7426	1.84011	0.920057	−	0.391786i	$-0.128142\pi$
$853$	53.7426	1.84011	0.920057	+	0.391786i	$0.128142\pi$
$854$	−2.38197	−0.0815092
$855$	29.8885	1.02217
$856$	123.082	4.20686
$857$	−13.8197	−0.472071	−0.236035	−	0.971744i	$-0.575848\pi$
$857$	−13.8197	−0.472071	−0.236035	+	0.971744i	$0.575848\pi$
$858$	−5.00000	−0.170697
$859$	22.5836	0.770542	0.385271	−	0.922803i	$-0.374108\pi$
$859$	22.5836	0.770542	0.385271	+	0.922803i	$0.374108\pi$
$860$	0	0
$861$	−0.0475975	−0.00162212
$862$	−0.527864	−0.0179791
$863$	28.5066	0.970375	0.485188	−	0.874410i	$-0.338751\pi$
$863$	28.5066	0.970375	0.485188	+	0.874410i	$0.338751\pi$
$864$	−24.2705	−0.825700
$865$	−26.6525	−0.906211
$866$	55.7426	1.89421
$867$	3.40325	0.115581
$868$	0	0
$869$	5.00000	0.169613
$870$	−9.70820	−0.329139
$871$	10.3262	0.349891
$872$	−53.3951	−1.80819
$873$	13.5967	0.460180
$874$	−56.0689	−1.89656
$875$	−0.360680	−0.0121932
$876$	9.00000	0.304082
$877$	23.6525	0.798687	0.399344	−	0.916801i	$-0.369238\pi$
$877$	23.6525	0.798687	0.399344	+	0.916801i	$0.369238\pi$
$878$	20.5623	0.693944
$879$	−0.347524	−0.0117217
$880$	−44.0689	−1.48556
$881$	38.2361	1.28821	0.644103	−	0.764939i	$-0.277231\pi$
$881$	38.2361	1.28821	0.644103	+	0.764939i	$0.277231\pi$
$882$	51.8885	1.74718
$883$	−27.1246	−0.912816	−0.456408	−	0.889771i	$-0.650864\pi$
$883$	−27.1246	−0.912816	−0.456408	+	0.889771i	$0.650864\pi$
$884$	−89.3951	−3.00668
$885$	−7.52786	−0.253046
$886$	−16.9443	−0.569254
$887$	−40.9574	−1.37522	−0.687608	−	0.726082i	$-0.741339\pi$
$887$	−40.9574	−1.37522	−0.687608	+	0.726082i	$0.741339\pi$
$888$	−5.29180	−0.177581
$889$	−3.93112	−0.131845
$890$	−41.1246	−1.37850
$891$	−10.6525	−0.356871
$892$	−35.1246	−1.17606
$893$	−25.4164	−0.850528
$894$	−9.00000	−0.301005
$895$	70.0689	2.34214
$896$	−0.257354	−0.00859760
$897$	9.14590	0.305373
$898$	−54.5410	−1.82006
$899$	0	0
$900$	−75.8115	−2.52705
$901$	18.4164	0.613540
$902$	−1.90983	−0.0635904
$903$	0	0
$904$	99.9919	3.32568
$905$	−69.9574	−2.32546
$906$	2.14590	0.0712927
$907$	−8.29180	−0.275325	−0.137662	−	0.990479i	$-0.543959\pi$
$907$	−8.29180	−0.275325	−0.137662	+	0.990479i	$0.543959\pi$
$908$	−36.2705	−1.20368
$909$	−23.5066	−0.779664
$910$	−7.23607	−0.239873
$911$	−3.97871	−0.131821	−0.0659103	−	0.997826i	$-0.520995\pi$
$911$	−3.97871	−0.131821	−0.0659103	+	0.997826i	$0.520995\pi$
$912$	−12.1803	−0.403331
$913$	18.0132	0.596148
$914$	6.00000	0.198462
$915$	4.76393	0.157491
$916$	−76.2492	−2.51935
$917$	−1.87539	−0.0619308
$918$	29.7984	0.983493
$919$	−44.3951	−1.46446	−0.732230	−	0.681057i	$-0.761520\pi$
$919$	−44.3951	−1.46446	−0.732230	+	0.681057i	$0.761520\pi$
$920$	160.026	5.27591
$921$	10.7771	0.355117
$922$	46.0689	1.51720
$923$	−49.9230	−1.64324
$924$	0.604878	0.0198990
$925$	−10.1459	−0.333595
$926$	−62.3951	−2.05043
$927$	−29.7295	−0.976445
$928$	−32.5623	−1.06891
$929$	−30.7639	−1.00933	−0.504666	−	0.863315i	$-0.668384\pi$
$929$	−30.7639	−1.00933	−0.504666	+	0.863315i	$0.668384\pi$
$930$	0	0
$931$	22.4721	0.736495
$932$	53.5623	1.75449
$933$	9.10333	0.298029
$934$	86.2492	2.82216
$935$	22.7639	0.744460
$936$	−77.1591	−2.52202
$937$	39.6738	1.29609	0.648043	−	0.761604i	$-0.275588\pi$
$937$	39.6738	1.29609	0.648043	+	0.761604i	$0.275588\pi$
$938$	−1.76393	−0.0575944
$939$	10.3607	0.338108
$940$	123.374	4.02401
$941$	−21.7639	−0.709484	−0.354742	−	0.934964i	$-0.615431\pi$
$941$	−21.7639	−0.709484	−0.354742	+	0.934964i	$0.615431\pi$
$942$	11.8541	0.386228
$943$	3.49342	0.113761
$944$	−60.0132	−1.95326
$945$	1.70820	0.0555679
$946$	0	0
$947$	−19.3607	−0.629138	−0.314569	−	0.949235i	$-0.601860\pi$
$947$	−19.3607	−0.629138	−0.314569	+	0.949235i	$0.601860\pi$
$948$	−6.70820	−0.217872
$949$	17.5623	0.570097
$950$	−46.3607	−1.50414
$951$	−11.1935	−0.362974
$952$	8.97871	0.291002
$953$	3.11146	0.100790	0.0503950	−	0.998729i	$-0.483952\pi$
$953$	3.11146	0.100790	0.0503950	+	0.998729i	$0.483952\pi$
$954$	27.0344	0.875272
$955$	75.9574	2.45792
$956$	−105.374	−3.40803
$957$	1.58359	0.0511903
$958$	−94.7214	−3.06031
$959$	−2.29180	−0.0740060
$960$	10.7639	0.347404
$961$	−31.0000	−1.00000
$962$	−17.5623	−0.566231
$963$	−47.0132	−1.51498
$964$	142.082	4.57615
$965$	−34.6525	−1.11550
$966$	−1.56231	−0.0502664
$967$	−49.1033	−1.57906	−0.789528	−	0.613714i	$-0.789675\pi$
$967$	−49.1033	−1.57906	−0.789528	+	0.613714i	$0.789675\pi$
$968$	−67.9230	−2.18313
$969$	6.29180	0.202122
$970$	−40.3607	−1.29590
$971$	27.3607	0.878046	0.439023	−	0.898476i	$-0.355325\pi$
$971$	27.3607	0.878046	0.439023	+	0.898476i	$0.355325\pi$
$972$	46.8541	1.50285
$973$	4.41641	0.141584
$974$	−37.5066	−1.20179
$975$	7.56231	0.242188
$976$	37.9787	1.21567
$977$	36.7639	1.17618	0.588091	−	0.808795i	$-0.299880\pi$
$977$	36.7639	1.17618	0.588091	+	0.808795i	$0.299880\pi$
$978$	−14.0000	−0.447671
$979$	6.70820	0.214395
$980$	−109.082	−3.48450
$981$	20.3951	0.651166
$982$	25.2705	0.806414
$983$	1.52786	0.0487313	0.0243656	−	0.999703i	$-0.492243\pi$
$983$	1.52786	0.0487313	0.0243656	+	0.999703i	$0.492243\pi$
$984$	1.50658	0.0480279
$985$	48.3607	1.54090
$986$	39.9787	1.27318
$987$	−0.708204	−0.0225424
$988$	−56.8328	−1.80809
$989$	0	0
$990$	33.4164	1.06204
$991$	33.1803	1.05401	0.527004	−	0.849863i	$-0.323315\pi$
$991$	33.1803	1.05401	0.527004	+	0.849863i	$0.323315\pi$
$992$	0	0
$993$	−1.32624	−0.0420869
$994$	8.52786	0.270487
$995$	51.5967	1.63573
$996$	−24.1672	−0.765767
$997$	−36.4508	−1.15441	−0.577205	−	0.816599i	$-0.695857\pi$
$997$	−36.4508	−1.15441	−0.577205	+	0.816599i	$0.695857\pi$
$998$	−18.7082	−0.592198
$999$	4.14590	0.131170

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.h.1.2		2
43.7	odd	6		43.2.c.b.6.1	✓	4
43.37	odd	6		43.2.c.b.36.1	yes	4
43.42	odd	2		1849.2.a.e.1.1		2
129.50	even	6		387.2.h.d.307.2		4
129.80	even	6		387.2.h.d.208.2		4
172.7	even	6		688.2.i.e.49.2		4
172.123	even	6		688.2.i.e.337.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.c.b.6.1	✓	4	43.7	odd	6
43.2.c.b.36.1	yes	4	43.37	odd	6
387.2.h.d.208.2		4	129.80	even	6
387.2.h.d.307.2		4	129.50	even	6
688.2.i.e.49.2		4	172.7	even	6
688.2.i.e.337.2		4	172.123	even	6
1849.2.a.e.1.1		2	43.42	odd	2
1849.2.a.h.1.2		2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q+2.61803 q^{2} +0.381966 q^{3} +4.85410 q^{4} +3.23607 q^{5} +1.00000 q^{6} -0.236068 q^{7} +7.47214 q^{8} -2.85410 q^{9} +O(q^{10})\)	\(q+2.61803 q^{2} +0.381966 q^{3} +4.85410 q^{4} +3.23607 q^{5} +1.00000 q^{6} -0.236068 q^{7} +7.47214 q^{8} -2.85410 q^{9} +8.47214 q^{10} -1.38197 q^{11} +1.85410 q^{12} +3.61803 q^{13} -0.618034 q^{14} +1.23607 q^{15} +9.85410 q^{16} -5.09017 q^{17} -7.47214 q^{18} -3.23607 q^{19} +15.7082 q^{20} -0.0901699 q^{21} -3.61803 q^{22} +6.61803 q^{23} +2.85410 q^{24} +5.47214 q^{25} +9.47214 q^{26} -2.23607 q^{27} -1.14590 q^{28} -3.00000 q^{29} +3.23607 q^{30} +10.8541 q^{32} -0.527864 q^{33} -13.3262 q^{34} -0.763932 q^{35} -13.8541 q^{36} -1.85410 q^{37} -8.47214 q^{38} +1.38197 q^{39} +24.1803 q^{40} +0.527864 q^{41} -0.236068 q^{42} -6.70820 q^{44} -9.23607 q^{45} +17.3262 q^{46} +7.85410 q^{47} +3.76393 q^{48} -6.94427 q^{49} +14.3262 q^{50} -1.94427 q^{51} +17.5623 q^{52} -3.61803 q^{53} -5.85410 q^{54} -4.47214 q^{55} -1.76393 q^{56} -1.23607 q^{57} -7.85410 q^{58} -6.09017 q^{59} +6.00000 q^{60} +3.85410 q^{61} +0.673762 q^{63} +8.70820 q^{64} +11.7082 q^{65} -1.38197 q^{66} +2.85410 q^{67} -24.7082 q^{68} +2.52786 q^{69} -2.00000 q^{70} -13.7984 q^{71} -21.3262 q^{72} +4.85410 q^{73} -4.85410 q^{74} +2.09017 q^{75} -15.7082 q^{76} +0.326238 q^{77} +3.61803 q^{78} -3.61803 q^{79} +31.8885 q^{80} +7.70820 q^{81} +1.38197 q^{82} -13.0344 q^{83} -0.437694 q^{84} -16.4721 q^{85} -1.14590 q^{87} -10.3262 q^{88} -4.85410 q^{89} -24.1803 q^{90} -0.854102 q^{91} +32.1246 q^{92} +20.5623 q^{94} -10.4721 q^{95} +4.14590 q^{96} -4.76393 q^{97} -18.1803 q^{98} +3.94427 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{7} + 6 q^{8} + q^{9}+O(q^{10}) \) 2 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^7 + 6 * q^8 + q^9	\( 2 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{7} + 6 q^{8} + q^{9} + 8 q^{10} - 5 q^{11} - 3 q^{12} + 5 q^{13} + q^{14} - 2 q^{15} + 13 q^{16} + q^{17} - 6 q^{18} - 2 q^{19} + 18 q^{20} + 11 q^{21} - 5 q^{22} + 11 q^{23} - q^{24} + 2 q^{25} + 10 q^{26} - 9 q^{28} - 6 q^{29} + 2 q^{30} + 15 q^{32} - 10 q^{33} - 11 q^{34} - 6 q^{35} - 21 q^{36} + 3 q^{37} - 8 q^{38} + 5 q^{39} + 26 q^{40} + 10 q^{41} + 4 q^{42} - 14 q^{45} + 19 q^{46} + 9 q^{47} + 12 q^{48} + 4 q^{49} + 13 q^{50} + 14 q^{51} + 15 q^{52} - 5 q^{53} - 5 q^{54} - 8 q^{56} + 2 q^{57} - 9 q^{58} - q^{59} + 12 q^{60} + q^{61} + 17 q^{63} + 4 q^{64} + 10 q^{65} - 5 q^{66} - q^{67} - 36 q^{68} + 14 q^{69} - 4 q^{70} - 3 q^{71} - 27 q^{72} + 3 q^{73} - 3 q^{74} - 7 q^{75} - 18 q^{76} - 15 q^{77} + 5 q^{78} - 5 q^{79} + 28 q^{80} + 2 q^{81} + 5 q^{82} + 3 q^{83} - 21 q^{84} - 24 q^{85} - 9 q^{87} - 5 q^{88} - 3 q^{89} - 26 q^{90} + 5 q^{91} + 24 q^{92} + 21 q^{94} - 12 q^{95} + 15 q^{96} - 14 q^{97} - 14 q^{98} - 10 q^{99}+O(q^{100}) \) 2 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 2 * q^5 + 2 * q^6 + 4 * q^7 + 6 * q^8 + q^9 + 8 * q^10 - 5 * q^11 - 3 * q^12 + 5 * q^13 + q^14 - 2 * q^15 + 13 * q^16 + q^17 - 6 * q^18 - 2 * q^19 + 18 * q^20 + 11 * q^21 - 5 * q^22 + 11 * q^23 - q^24 + 2 * q^25 + 10 * q^26 - 9 * q^28 - 6 * q^29 + 2 * q^30 + 15 * q^32 - 10 * q^33 - 11 * q^34 - 6 * q^35 - 21 * q^36 + 3 * q^37 - 8 * q^38 + 5 * q^39 + 26 * q^40 + 10 * q^41 + 4 * q^42 - 14 * q^45 + 19 * q^46 + 9 * q^47 + 12 * q^48 + 4 * q^49 + 13 * q^50 + 14 * q^51 + 15 * q^52 - 5 * q^53 - 5 * q^54 - 8 * q^56 + 2 * q^57 - 9 * q^58 - q^59 + 12 * q^60 + q^61 + 17 * q^63 + 4 * q^64 + 10 * q^65 - 5 * q^66 - q^67 - 36 * q^68 + 14 * q^69 - 4 * q^70 - 3 * q^71 - 27 * q^72 + 3 * q^73 - 3 * q^74 - 7 * q^75 - 18 * q^76 - 15 * q^77 + 5 * q^78 - 5 * q^79 + 28 * q^80 + 2 * q^81 + 5 * q^82 + 3 * q^83 - 21 * q^84 - 24 * q^85 - 9 * q^87 - 5 * q^88 - 3 * q^89 - 26 * q^90 + 5 * q^91 + 24 * q^92 + 21 * q^94 - 12 * q^95 + 15 * q^96 - 14 * q^97 - 14 * q^98 - 10 * q^99

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