LMFDB - Embedded newform 1849.2.a.j.1.3

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:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 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			1.3
Root			$-1.24698$ 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)

$f(q)$	$=$	$q+1.24698 q^{2} -0.445042 q^{3} -0.445042 q^{4} -0.554958 q^{5} -0.554958 q^{6} -1.35690 q^{7} -3.04892 q^{8} -2.80194 q^{9} +O(q^{10})$	\(q+1.24698 q^{2} -0.445042 q^{3} -0.445042 q^{4} -0.554958 q^{5} -0.554958 q^{6} -1.35690 q^{7} -3.04892 q^{8} -2.80194 q^{9} -0.692021 q^{10} -2.15883 q^{11} +0.198062 q^{12} +1.58211 q^{13} -1.69202 q^{14} +0.246980 q^{15} -2.91185 q^{16} +2.49396 q^{17} -3.49396 q^{18} +5.80194 q^{19} +0.246980 q^{20} +0.603875 q^{21} -2.69202 q^{22} +5.09783 q^{23} +1.35690 q^{24} -4.69202 q^{25} +1.97285 q^{26} +2.58211 q^{27} +0.603875 q^{28} +6.00000 q^{29} +0.307979 q^{30} +7.62565 q^{31} +2.46681 q^{32} +0.960771 q^{33} +3.10992 q^{34} +0.753020 q^{35} +1.24698 q^{36} +7.18598 q^{37} +7.23490 q^{38} -0.704103 q^{39} +1.69202 q^{40} +10.4940 q^{41} +0.753020 q^{42} +0.960771 q^{44} +1.55496 q^{45} +6.35690 q^{46} -10.9390 q^{47} +1.29590 q^{48} -5.15883 q^{49} -5.85086 q^{50} -1.10992 q^{51} -0.704103 q^{52} -3.07606 q^{53} +3.21983 q^{54} +1.19806 q^{55} +4.13706 q^{56} -2.58211 q^{57} +7.48188 q^{58} -7.29590 q^{59} -0.109916 q^{60} -8.09783 q^{61} +9.50902 q^{62} +3.80194 q^{63} +8.89977 q^{64} -0.878002 q^{65} +1.19806 q^{66} +7.38404 q^{67} -1.10992 q^{68} -2.26875 q^{69} +0.939001 q^{70} +1.68233 q^{71} +8.54288 q^{72} +3.97823 q^{73} +8.96077 q^{74} +2.08815 q^{75} -2.58211 q^{76} +2.92931 q^{77} -0.878002 q^{78} -2.08815 q^{79} +1.61596 q^{80} +7.25667 q^{81} +13.0858 q^{82} +0.917231 q^{83} -0.268750 q^{84} -1.38404 q^{85} -2.67025 q^{87} +6.58211 q^{88} +1.48858 q^{89} +1.93900 q^{90} -2.14675 q^{91} -2.26875 q^{92} -3.39373 q^{93} -13.6407 q^{94} -3.21983 q^{95} -1.09783 q^{96} -15.1250 q^{97} -6.43296 q^{98} +6.04892 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - q^{2} - q^{3} - q^{4} - 2 q^{5} - 2 q^{6} - 4 q^{9}+O(q^{10}) $ 3 * q - q^2 - q^3 - q^4 - 2 * q^5 - 2 * q^6 - 4 * q^9	$ 3 q - q^{2} - q^{3} - q^{4} - 2 q^{5} - 2 q^{6} - 4 q^{9} + 3 q^{10} + 2 q^{11} + 5 q^{12} - q^{13} - 4 q^{15} - 5 q^{16} - 2 q^{17} - q^{18} + 13 q^{19} - 4 q^{20} - 7 q^{21} - 3 q^{22} - 3 q^{23} - 9 q^{25} + 12 q^{26} + 2 q^{27} - 7 q^{28} + 18 q^{29} + 6 q^{30} + 11 q^{31} + 4 q^{32} - 10 q^{33} + 10 q^{34} + 7 q^{35} - q^{36} + 7 q^{37} - 2 q^{38} - 16 q^{39} + 22 q^{41} + 7 q^{42} - 10 q^{44} + 5 q^{45} + 15 q^{46} - 23 q^{47} - 10 q^{48} - 7 q^{49} - 4 q^{50} - 4 q^{51} - 16 q^{52} + 6 q^{53} + 11 q^{54} + 8 q^{55} + 7 q^{56} - 2 q^{57} - 6 q^{58} - 8 q^{59} - q^{60} - 6 q^{61} - 6 q^{62} + 7 q^{63} + 4 q^{64} + 17 q^{65} + 8 q^{66} + 12 q^{67} - 4 q^{68} + q^{69} - 7 q^{70} + 22 q^{71} + 7 q^{72} + 15 q^{73} + 14 q^{74} + 10 q^{75} - 2 q^{76} + 21 q^{77} + 17 q^{78} - 10 q^{79} + 15 q^{80} - 5 q^{81} + 2 q^{82} - 4 q^{83} + 7 q^{84} + 6 q^{85} - 6 q^{87} + 14 q^{88} - 2 q^{89} - 4 q^{90} + 21 q^{91} + q^{92} + 22 q^{93} - 4 q^{94} - 11 q^{95} + 15 q^{96} - 21 q^{97} + 9 q^{99}+O(q^{100}) $ 3 * q - q^2 - q^3 - q^4 - 2 * q^5 - 2 * q^6 - 4 * q^9 + 3 * q^10 + 2 * q^11 + 5 * q^12 - q^13 - 4 * q^15 - 5 * q^16 - 2 * q^17 - q^18 + 13 * q^19 - 4 * q^20 - 7 * q^21 - 3 * q^22 - 3 * q^23 - 9 * q^25 + 12 * q^26 + 2 * q^27 - 7 * q^28 + 18 * q^29 + 6 * q^30 + 11 * q^31 + 4 * q^32 - 10 * q^33 + 10 * q^34 + 7 * q^35 - q^36 + 7 * q^37 - 2 * q^38 - 16 * q^39 + 22 * q^41 + 7 * q^42 - 10 * q^44 + 5 * q^45 + 15 * q^46 - 23 * q^47 - 10 * q^48 - 7 * q^49 - 4 * q^50 - 4 * q^51 - 16 * q^52 + 6 * q^53 + 11 * q^54 + 8 * q^55 + 7 * q^56 - 2 * q^57 - 6 * q^58 - 8 * q^59 - q^60 - 6 * q^61 - 6 * q^62 + 7 * q^63 + 4 * q^64 + 17 * q^65 + 8 * q^66 + 12 * q^67 - 4 * q^68 + q^69 - 7 * q^70 + 22 * q^71 + 7 * q^72 + 15 * q^73 + 14 * q^74 + 10 * q^75 - 2 * q^76 + 21 * q^77 + 17 * q^78 - 10 * q^79 + 15 * q^80 - 5 * q^81 + 2 * q^82 - 4 * q^83 + 7 * q^84 + 6 * q^85 - 6 * q^87 + 14 * q^88 - 2 * q^89 - 4 * q^90 + 21 * q^91 + q^92 + 22 * q^93 - 4 * q^94 - 11 * q^95 + 15 * q^96 - 21 * q^97 + 9 * 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 $

$2$	1.24698	0.881748	0.440874	−	0.897569i	$-0.354669\pi$
$2$	1.24698	0.881748	0.440874	+	0.897569i	$0.354669\pi$
$3$	−0.445042	−0.256945	−0.128473	−	0.991713i	$-0.541007\pi$
$3$	−0.445042	−0.256945	−0.128473	+	0.991713i	$0.541007\pi$
$4$	−0.445042	−0.222521
$5$	−0.554958	−0.248185	−0.124092	−	0.992271i	$-0.539602\pi$
$5$	−0.554958	−0.248185	−0.124092	+	0.992271i	$0.539602\pi$
$6$	−0.554958	−0.226561
$7$	−1.35690	−0.512858	−0.256429	−	0.966563i	$-0.582546\pi$
$7$	−1.35690	−0.512858	−0.256429	+	0.966563i	$0.582546\pi$
$8$	−3.04892	−1.07796
$9$	−2.80194	−0.933979
$10$	−0.692021	−0.218836
$11$	−2.15883	−0.650913	−0.325456	−	0.945557i	$-0.605518\pi$
$11$	−2.15883	−0.650913	−0.325456	+	0.945557i	$0.605518\pi$
$12$	0.198062	0.0571757
$13$	1.58211	0.438797	0.219399	−	0.975635i	$-0.429591\pi$
$13$	1.58211	0.438797	0.219399	+	0.975635i	$0.429591\pi$
$14$	−1.69202	−0.452212
$15$	0.246980	0.0637699
$16$	−2.91185	−0.727963
$17$	2.49396	0.604874	0.302437	−	0.953169i	$-0.402200\pi$
$17$	2.49396	0.604874	0.302437	+	0.953169i	$0.402200\pi$
$18$	−3.49396	−0.823534
$19$	5.80194	1.33106	0.665528	−	0.746373i	$-0.268206\pi$
$19$	5.80194	1.33106	0.665528	+	0.746373i	$0.268206\pi$
$20$	0.246980	0.0552263
$21$	0.603875	0.131776
$22$	−2.69202	−0.573941
$23$	5.09783	1.06297	0.531486	−	0.847067i	$-0.321634\pi$
$23$	5.09783	1.06297	0.531486	+	0.847067i	$0.321634\pi$
$24$	1.35690	0.276975
$25$	−4.69202	−0.938404
$26$	1.97285	0.386908
$27$	2.58211	0.496926
$28$	0.603875	0.114122
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	0.307979	0.0562289
$31$	7.62565	1.36961	0.684803	−	0.728728i	$-0.259888\pi$
$31$	7.62565	1.36961	0.684803	+	0.728728i	$0.259888\pi$
$32$	2.46681	0.436075
$33$	0.960771	0.167249
$34$	3.10992	0.533346
$35$	0.753020	0.127284
$36$	1.24698	0.207830
$37$	7.18598	1.18137	0.590684	−	0.806903i	$-0.298858\pi$
$37$	7.18598	1.18137	0.590684	+	0.806903i	$0.298858\pi$
$38$	7.23490	1.17366
$39$	−0.704103	−0.112747
$40$	1.69202	0.267532
$41$	10.4940	1.63888	0.819441	−	0.573164i	$-0.194284\pi$
$41$	10.4940	1.63888	0.819441	+	0.573164i	$0.194284\pi$
$42$	0.753020	0.116194
$43$	0	0
$43$	0	0
$44$	0.960771	0.144842
$45$	1.55496	0.231799
$46$	6.35690	0.937273
$47$	−10.9390	−1.59562	−0.797809	−	0.602911i	$-0.794008\pi$
$47$	−10.9390	−1.59562	−0.797809	+	0.602911i	$0.794008\pi$
$48$	1.29590	0.187047
$49$	−5.15883	−0.736976
$50$	−5.85086	−0.827436
$51$	−1.10992	−0.155419
$52$	−0.704103	−0.0976415
$53$	−3.07606	−0.422530	−0.211265	−	0.977429i	$-0.567758\pi$
$53$	−3.07606	−0.422530	−0.211265	+	0.977429i	$0.567758\pi$
$54$	3.21983	0.438164
$55$	1.19806	0.161547
$56$	4.13706	0.552838
$57$	−2.58211	−0.342008
$58$	7.48188	0.982419
$59$	−7.29590	−0.949845	−0.474922	−	0.880028i	$-0.657524\pi$
$59$	−7.29590	−0.949845	−0.474922	+	0.880028i	$0.657524\pi$
$60$	−0.109916	−0.0141901
$61$	−8.09783	−1.03682	−0.518411	−	0.855132i	$-0.673476\pi$
$61$	−8.09783	−1.03682	−0.518411	+	0.855132i	$0.673476\pi$
$62$	9.50902	1.20765
$63$	3.80194	0.478999
$64$	8.89977	1.11247
$65$	−0.878002	−0.108903
$66$	1.19806	0.147471
$67$	7.38404	0.902104	0.451052	−	0.892498i	$-0.351049\pi$
$67$	7.38404	0.902104	0.451052	+	0.892498i	$0.351049\pi$
$68$	−1.10992	−0.134597
$69$	−2.26875	−0.273125
$70$	0.939001	0.112232
$71$	1.68233	0.199656	0.0998281	−	0.995005i	$-0.468171\pi$
$71$	1.68233	0.199656	0.0998281	+	0.995005i	$0.468171\pi$
$72$	8.54288	1.00679
$73$	3.97823	0.465617	0.232808	−	0.972523i	$-0.425209\pi$
$73$	3.97823	0.465617	0.232808	+	0.972523i	$0.425209\pi$
$74$	8.96077	1.04167
$75$	2.08815	0.241118
$76$	−2.58211	−0.296188
$77$	2.92931	0.333826
$78$	−0.878002	−0.0994142
$79$	−2.08815	−0.234935	−0.117467	−	0.993077i	$-0.537478\pi$
$79$	−2.08815	−0.234935	−0.117467	+	0.993077i	$0.537478\pi$
$80$	1.61596	0.180669
$81$	7.25667	0.806296
$82$	13.0858	1.44508
$83$	0.917231	0.100679	0.0503396	−	0.998732i	$-0.483970\pi$
$83$	0.917231	0.100679	0.0503396	+	0.998732i	$0.483970\pi$
$84$	−0.268750	−0.0293230
$85$	−1.38404	−0.150121
$86$	0	0
$87$	−2.67025	−0.286281
$88$	6.58211	0.701655
$89$	1.48858	0.157789	0.0788947	−	0.996883i	$-0.474861\pi$
$89$	1.48858	0.157789	0.0788947	+	0.996883i	$0.474861\pi$
$90$	1.93900	0.204389
$91$	−2.14675	−0.225041
$92$	−2.26875	−0.236534
$93$	−3.39373	−0.351914
$94$	−13.6407	−1.40693
$95$	−3.21983	−0.330348
$96$	−1.09783	−0.112047
$97$	−15.1250	−1.53571	−0.767855	−	0.640624i	$-0.778676\pi$
$97$	−15.1250	−1.53571	−0.767855	+	0.640624i	$0.778676\pi$
$98$	−6.43296	−0.649827
$99$	6.04892	0.607939
$100$	2.08815	0.208815
$101$	−3.39373	−0.337689	−0.168844	−	0.985643i	$-0.554004\pi$
$101$	−3.39373	−0.337689	−0.168844	+	0.985643i	$0.554004\pi$
$102$	−1.38404	−0.137041
$103$	−5.09783	−0.502305	−0.251152	−	0.967948i	$-0.580809\pi$
$103$	−5.09783	−0.502305	−0.251152	+	0.967948i	$0.580809\pi$
$104$	−4.82371	−0.473003
$105$	−0.335126	−0.0327049
$106$	−3.83579	−0.372565
$107$	0.307979	0.0297734	0.0148867	−	0.999889i	$-0.495261\pi$
$107$	0.307979	0.0297734	0.0148867	+	0.999889i	$0.495261\pi$
$108$	−1.14914	−0.110577
$109$	13.7017	1.31239	0.656193	−	0.754593i	$-0.272166\pi$
$109$	13.7017	1.31239	0.656193	+	0.754593i	$0.272166\pi$
$110$	1.49396	0.142443
$111$	−3.19806	−0.303547
$112$	3.95108	0.373342
$113$	18.8823	1.77630	0.888149	−	0.459555i	$-0.151991\pi$
$113$	18.8823	1.77630	0.888149	+	0.459555i	$0.151991\pi$
$114$	−3.21983	−0.301565
$115$	−2.82908	−0.263814
$116$	−2.67025	−0.247927
$117$	−4.43296	−0.409827
$118$	−9.09783	−0.837524
$119$	−3.38404	−0.310215
$120$	−0.753020	−0.0687410
$121$	−6.33944	−0.576312
$122$	−10.0978	−0.914215
$123$	−4.67025	−0.421102
$124$	−3.39373	−0.304766
$125$	5.37867	0.481083
$126$	4.74094	0.422356
$127$	−4.99462	−0.443201	−0.221601	−	0.975138i	$-0.571128\pi$
$127$	−4.99462	−0.443201	−0.221601	+	0.975138i	$0.571128\pi$
$128$	6.16421	0.544844
$129$	0	0
$130$	−1.09485	−0.0960248
$131$	17.9269	1.56628	0.783141	−	0.621844i	$-0.213616\pi$
$131$	17.9269	1.56628	0.783141	+	0.621844i	$0.213616\pi$
$132$	−0.427583	−0.0372164
$133$	−7.87263	−0.682643
$134$	9.20775	0.795429
$135$	−1.43296	−0.123330
$136$	−7.60388	−0.652027
$137$	12.5090	1.06872	0.534359	−	0.845258i	$-0.320553\pi$
$137$	12.5090	1.06872	0.534359	+	0.845258i	$0.320553\pi$
$138$	−2.82908	−0.240828
$139$	−6.07069	−0.514909	−0.257455	−	0.966290i	$-0.582884\pi$
$139$	−6.07069	−0.514909	−0.257455	+	0.966290i	$0.582884\pi$
$140$	−0.335126	−0.0283233
$141$	4.86831	0.409986
$142$	2.09783	0.176046
$143$	−3.41550	−0.285619
$144$	8.15883	0.679903
$145$	−3.32975	−0.276521
$146$	4.96077	0.410556
$147$	2.29590	0.189362
$148$	−3.19806	−0.262879
$149$	2.75302	0.225536	0.112768	−	0.993621i	$-0.464028\pi$
$149$	2.75302	0.225536	0.112768	+	0.993621i	$0.464028\pi$
$150$	2.60388	0.212606
$151$	18.6504	1.51775	0.758874	−	0.651237i	$-0.225750\pi$
$151$	18.6504	1.51775	0.758874	+	0.651237i	$0.225750\pi$
$152$	−17.6896	−1.43482
$153$	−6.98792	−0.564940
$154$	3.65279	0.294350
$155$	−4.23191	−0.339916
$156$	0.313355	0.0250885
$157$	−13.2295	−1.05583	−0.527915	−	0.849297i	$-0.677026\pi$
$157$	−13.2295	−1.05583	−0.527915	+	0.849297i	$0.677026\pi$
$158$	−2.60388	−0.207153
$159$	1.36898	0.108567
$160$	−1.36898	−0.108227
$161$	−6.91723	−0.545154
$162$	9.04892	0.710950
$163$	10.4668	0.819824	0.409912	−	0.912125i	$-0.365559\pi$
$163$	10.4668	0.819824	0.409912	+	0.912125i	$0.365559\pi$
$164$	−4.67025	−0.364685
$165$	−0.533188	−0.0415086
$166$	1.14377	0.0887736
$167$	14.5646	1.12705	0.563523	−	0.826100i	$-0.309446\pi$
$167$	14.5646	1.12705	0.563523	+	0.826100i	$0.309446\pi$
$168$	−1.84117	−0.142049
$169$	−10.4969	−0.807457
$170$	−1.72587	−0.132368
$171$	−16.2567	−1.24318
$172$	0	0
$173$	−8.78986	−0.668280	−0.334140	−	0.942523i	$-0.608446\pi$
$173$	−8.78986	−0.668280	−0.334140	+	0.942523i	$0.608446\pi$
$174$	−3.32975	−0.252428
$175$	6.36658	0.481269
$176$	6.28621	0.473841
$177$	3.24698	0.244058
$178$	1.85623	0.139130
$179$	21.4034	1.59977	0.799883	−	0.600155i	$-0.204895\pi$
$179$	21.4034	1.59977	0.799883	+	0.600155i	$0.204895\pi$
$180$	−0.692021	−0.0515802
$181$	26.3327	1.95730	0.978648	−	0.205542i	$-0.0658957\pi$
$181$	26.3327	1.95730	0.978648	+	0.205542i	$0.0658957\pi$
$182$	−2.67696	−0.198429
$183$	3.60388	0.266406
$184$	−15.5429	−1.14584
$185$	−3.98792	−0.293198
$186$	−4.23191	−0.310299
$187$	−5.38404	−0.393720
$188$	4.86831	0.355058
$189$	−3.50365	−0.254853
$190$	−4.01507	−0.291283
$191$	−8.68963	−0.628759	−0.314380	−	0.949297i	$-0.601797\pi$
$191$	−8.68963	−0.628759	−0.314380	+	0.949297i	$0.601797\pi$
$192$	−3.96077	−0.285844
$193$	2.06100	0.148354	0.0741770	−	0.997245i	$-0.476367\pi$
$193$	2.06100	0.148354	0.0741770	+	0.997245i	$0.476367\pi$
$194$	−18.8605	−1.35411
$195$	0.390748	0.0279820
$196$	2.29590	0.163993
$197$	0.457123	0.0325687	0.0162843	−	0.999867i	$-0.494816\pi$
$197$	0.457123	0.0325687	0.0162843	+	0.999867i	$0.494816\pi$
$198$	7.54288	0.536049
$199$	−2.06398	−0.146312	−0.0731559	−	0.997321i	$-0.523307\pi$
$199$	−2.06398	−0.146312	−0.0731559	+	0.997321i	$0.523307\pi$
$200$	14.3056	1.01156
$201$	−3.28621	−0.231791
$202$	−4.23191	−0.297756
$203$	−8.14138	−0.571413
$204$	0.493959	0.0345841
$205$	−5.82371	−0.406745
$206$	−6.35690	−0.442906
$207$	−14.2838	−0.992794
$208$	−4.60686	−0.319428
$209$	−12.5254	−0.866401
$210$	−0.417895	−0.0288375
$211$	−0.845478	−0.0582051	−0.0291026	−	0.999576i	$-0.509265\pi$
$211$	−0.845478	−0.0582051	−0.0291026	+	0.999576i	$0.509265\pi$
$212$	1.36898	0.0940218
$213$	−0.748709	−0.0513007
$214$	0.384043	0.0262526
$215$	0	0
$216$	−7.87263	−0.535664
$217$	−10.3472	−0.702414
$218$	17.0858	1.15719
$219$	−1.77048	−0.119638
$220$	−0.533188	−0.0359475
$221$	3.94571	0.265417
$222$	−3.98792	−0.267652
$223$	23.9366	1.60291	0.801457	−	0.598053i	$-0.204059\pi$
$223$	23.9366	1.60291	0.801457	+	0.598053i	$0.204059\pi$
$224$	−3.34721	−0.223645
$225$	13.1468	0.876450
$226$	23.5459	1.56625
$227$	5.29052	0.351144	0.175572	−	0.984467i	$-0.443822\pi$
$227$	5.29052	0.351144	0.175572	+	0.984467i	$0.443822\pi$
$228$	1.14914	0.0761040
$229$	15.3032	1.01126	0.505632	−	0.862749i	$-0.331259\pi$
$229$	15.3032	1.01126	0.505632	+	0.862749i	$0.331259\pi$
$230$	−3.52781	−0.232617
$231$	−1.30367	−0.0857750
$232$	−18.2935	−1.20103
$233$	25.6233	1.67864	0.839318	−	0.543641i	$-0.182955\pi$
$233$	25.6233	1.67864	0.839318	+	0.543641i	$0.182955\pi$
$234$	−5.52781	−0.361364
$235$	6.07069	0.396008
$236$	3.24698	0.211360
$237$	0.929312	0.0603653
$238$	−4.21983	−0.273531
$239$	−6.66248	−0.430960	−0.215480	−	0.976508i	$-0.569132\pi$
$239$	−6.66248	−0.430960	−0.215480	+	0.976508i	$0.569132\pi$
$240$	−0.719169	−0.0464221
$241$	−2.60388	−0.167730	−0.0838652	−	0.996477i	$-0.526727\pi$
$241$	−2.60388	−0.167730	−0.0838652	+	0.996477i	$0.526727\pi$
$242$	−7.90515	−0.508162
$243$	−10.9758	−0.704100
$244$	3.60388	0.230714
$245$	2.86294	0.182906
$246$	−5.82371	−0.371306
$247$	9.17928	0.584063
$248$	−23.2500	−1.47637
$249$	−0.408206	−0.0258690
$250$	6.70709	0.424193
$251$	6.64609	0.419497	0.209749	−	0.977755i	$-0.432735\pi$
$251$	6.64609	0.419497	0.209749	+	0.977755i	$0.432735\pi$
$252$	−1.69202	−0.106587
$253$	−11.0054	−0.691902
$254$	−6.22819	−0.390792
$255$	0.615957	0.0385727
$256$	−10.1129	−0.632056
$257$	−1.40581	−0.0876922	−0.0438461	−	0.999038i	$-0.513961\pi$
$257$	−1.40581	−0.0876922	−0.0438461	+	0.999038i	$0.513961\pi$
$258$	0	0
$259$	−9.75063	−0.605875
$260$	0.390748	0.0242331
$261$	−16.8116	−1.04061
$262$	22.3545	1.38107
$263$	3.14377	0.193853	0.0969265	−	0.995292i	$-0.469099\pi$
$263$	3.14377	0.193853	0.0969265	+	0.995292i	$0.469099\pi$
$264$	−2.92931	−0.180287
$265$	1.70709	0.104866
$266$	−9.81700	−0.601919
$267$	−0.662481	−0.0405432
$268$	−3.28621	−0.200737
$269$	−11.5284	−0.702899	−0.351450	−	0.936207i	$-0.614311\pi$
$269$	−11.5284	−0.702899	−0.351450	+	0.936207i	$0.614311\pi$
$270$	−1.78687	−0.108746
$271$	−13.3569	−0.811374	−0.405687	−	0.914012i	$-0.632968\pi$
$271$	−13.3569	−0.811374	−0.405687	+	0.914012i	$0.632968\pi$
$272$	−7.26205	−0.440326
$273$	0.955395	0.0578231
$274$	15.5985	0.942340
$275$	10.1293	0.610819
$276$	1.00969	0.0607761
$277$	−13.2717	−0.797421	−0.398711	−	0.917077i	$-0.630542\pi$
$277$	−13.2717	−0.797421	−0.398711	+	0.917077i	$0.630542\pi$
$278$	−7.57002	−0.454020
$279$	−21.3666	−1.27918
$280$	−2.29590	−0.137206
$281$	−15.9172	−0.949542	−0.474771	−	0.880109i	$-0.657469\pi$
$281$	−15.9172	−0.949542	−0.474771	+	0.880109i	$0.657469\pi$
$282$	6.07069	0.361504
$283$	23.7802	1.41358	0.706792	−	0.707421i	$-0.250142\pi$
$283$	23.7802	1.41358	0.706792	+	0.707421i	$0.250142\pi$
$284$	−0.748709	−0.0444277
$285$	1.43296	0.0848812
$286$	−4.25906	−0.251844
$287$	−14.2392	−0.840514
$288$	−6.91185	−0.407285
$289$	−10.7802	−0.634127
$290$	−4.15213	−0.243821
$291$	6.73125	0.394593
$292$	−1.77048	−0.103609
$293$	12.6896	0.741336	0.370668	−	0.928765i	$-0.379129\pi$
$293$	12.6896	0.741336	0.370668	+	0.928765i	$0.379129\pi$
$294$	2.86294	0.166970
$295$	4.04892	0.235737
$296$	−21.9095	−1.27346
$297$	−5.57434	−0.323456
$298$	3.43296	0.198866
$299$	8.06531	0.466429
$300$	−0.929312	−0.0536539
$301$	0	0
$302$	23.2567	1.33827
$303$	1.51035	0.0867675
$304$	−16.8944	−0.968960
$305$	4.49396	0.257323
$306$	−8.71379	−0.498134
$307$	18.1903	1.03817	0.519087	−	0.854721i	$-0.326272\pi$
$307$	18.1903	1.03817	0.519087	+	0.854721i	$0.326272\pi$
$308$	−1.30367	−0.0742833
$309$	2.26875	0.129065
$310$	−5.27711	−0.299720
$311$	7.28382	0.413027	0.206514	−	0.978444i	$-0.433788\pi$
$311$	7.28382	0.413027	0.206514	+	0.978444i	$0.433788\pi$
$312$	2.14675	0.121536
$313$	18.7332	1.05886	0.529431	−	0.848353i	$-0.322406\pi$
$313$	18.7332	1.05886	0.529431	+	0.848353i	$0.322406\pi$
$314$	−16.4969	−0.930976
$315$	−2.10992	−0.118880
$316$	0.929312	0.0522779
$317$	3.46921	0.194850	0.0974250	−	0.995243i	$-0.468939\pi$
$317$	3.46921	0.194850	0.0974250	+	0.995243i	$0.468939\pi$
$318$	1.70709	0.0957287
$319$	−12.9530	−0.725229
$320$	−4.93900	−0.276099
$321$	−0.137063	−0.00765013
$322$	−8.62565	−0.480688
$323$	14.4698	0.805121
$324$	−3.22952	−0.179418
$325$	−7.42327	−0.411769
$326$	13.0519	0.722878
$327$	−6.09783	−0.337211
$328$	−31.9952	−1.76664
$329$	14.8431	0.818326
$330$	−0.664874	−0.0366001
$331$	13.9148	0.764829	0.382414	−	0.923991i	$-0.375093\pi$
$331$	13.9148	0.764829	0.382414	+	0.923991i	$0.375093\pi$
$332$	−0.408206	−0.0224032
$333$	−20.1347	−1.10337
$334$	18.1618	0.993770
$335$	−4.09783	−0.223889
$336$	−1.75840	−0.0959284
$337$	−3.05323	−0.166320	−0.0831600	−	0.996536i	$-0.526501\pi$
$337$	−3.05323	−0.166320	−0.0831600	+	0.996536i	$0.526501\pi$
$338$	−13.0895	−0.711974
$339$	−8.40342	−0.456411
$340$	0.615957	0.0334050
$341$	−16.4625	−0.891494
$342$	−20.2717	−1.09617
$343$	16.4983	0.890823
$344$	0	0
$345$	1.25906	0.0677856
$346$	−10.9608	−0.589255
$347$	−14.4252	−0.774385	−0.387192	−	0.921999i	$-0.626555\pi$
$347$	−14.4252	−0.774385	−0.387192	+	0.921999i	$0.626555\pi$
$348$	1.18837	0.0637035
$349$	−28.3884	−1.51959	−0.759797	−	0.650160i	$-0.774702\pi$
$349$	−28.3884	−1.51959	−0.759797	+	0.650160i	$0.774702\pi$
$350$	7.93900	0.424357
$351$	4.08516	0.218050
$352$	−5.32544	−0.283847
$353$	−13.6160	−0.724704	−0.362352	−	0.932041i	$-0.618026\pi$
$353$	−13.6160	−0.724704	−0.362352	+	0.932041i	$0.618026\pi$
$354$	4.04892	0.215198
$355$	−0.933624	−0.0495516
$356$	−0.662481	−0.0351114
$357$	1.50604	0.0797081
$358$	26.6896	1.41059
$359$	−32.7875	−1.73046	−0.865228	−	0.501378i	$-0.832826\pi$
$359$	−32.7875	−1.73046	−0.865228	+	0.501378i	$0.832826\pi$
$360$	−4.74094	−0.249869
$361$	14.6625	0.771710
$362$	32.8364	1.72584
$363$	2.82132	0.148081
$364$	0.955395	0.0500763
$365$	−2.20775	−0.115559
$366$	4.49396	0.234903
$367$	25.4969	1.33093	0.665465	−	0.746429i	$-0.268233\pi$
$367$	25.4969	1.33093	0.665465	+	0.746429i	$0.268233\pi$
$368$	−14.8442	−0.773805
$369$	−29.4034	−1.53068
$370$	−4.97285	−0.258526
$371$	4.17390	0.216698
$372$	1.51035	0.0783081
$373$	−27.5646	−1.42724	−0.713622	−	0.700531i	$-0.752946\pi$
$373$	−27.5646	−1.42724	−0.713622	+	0.700531i	$0.752946\pi$
$374$	−6.71379	−0.347162
$375$	−2.39373	−0.123612
$376$	33.3521	1.72000
$377$	9.49263	0.488895
$378$	−4.36898	−0.224716
$379$	28.1594	1.44645	0.723226	−	0.690611i	$-0.242658\pi$
$379$	28.1594	1.44645	0.723226	+	0.690611i	$0.242658\pi$
$380$	1.43296	0.0735093
$381$	2.22282	0.113878
$382$	−10.8358	−0.554407
$383$	−28.6233	−1.46258	−0.731290	−	0.682067i	$-0.761081\pi$
$383$	−28.6233	−1.46258	−0.731290	+	0.682067i	$0.761081\pi$
$384$	−2.74333	−0.139995
$385$	−1.62565	−0.0828506
$386$	2.57002	0.130811
$387$	0	0
$388$	6.73125	0.341727
$389$	−35.3183	−1.79071	−0.895353	−	0.445356i	$-0.853077\pi$
$389$	−35.3183	−1.79071	−0.895353	+	0.445356i	$0.853077\pi$
$390$	0.487254	0.0246731
$391$	12.7138	0.642964
$392$	15.7289	0.794427
$393$	−7.97823	−0.402448
$394$	0.570024	0.0287174
$395$	1.15883	0.0583072
$396$	−2.69202	−0.135279
$397$	3.37867	0.169570	0.0847852	−	0.996399i	$-0.472980\pi$
$397$	3.37867	0.169570	0.0847852	+	0.996399i	$0.472980\pi$
$398$	−2.57374	−0.129010
$399$	3.50365	0.175402
$400$	13.6625	0.683124
$401$	−16.9095	−0.844418	−0.422209	−	0.906498i	$-0.638745\pi$
$401$	−16.9095	−0.844418	−0.422209	+	0.906498i	$0.638745\pi$
$402$	−4.09783	−0.204381
$403$	12.0646	0.600979
$404$	1.51035	0.0751429
$405$	−4.02715	−0.200111
$406$	−10.1521	−0.503842
$407$	−15.5133	−0.768968
$408$	3.38404	0.167535
$409$	−1.86054	−0.0919980	−0.0459990	−	0.998941i	$-0.514647\pi$
$409$	−1.86054	−0.0919980	−0.0459990	+	0.998941i	$0.514647\pi$
$410$	−7.26205	−0.358647
$411$	−5.56704	−0.274602
$412$	2.26875	0.111773
$413$	9.89977	0.487136
$414$	−17.8116	−0.875394
$415$	−0.509025	−0.0249870
$416$	3.90276	0.191348
$417$	2.70171	0.132303
$418$	−15.6189	−0.763947
$419$	16.5114	0.806636	0.403318	−	0.915060i	$-0.367857\pi$
$419$	16.5114	0.806636	0.403318	+	0.915060i	$0.367857\pi$
$420$	0.149145	0.00727753
$421$	−21.9879	−1.07163	−0.535813	−	0.844337i	$-0.679995\pi$
$421$	−21.9879	−1.07163	−0.535813	+	0.844337i	$0.679995\pi$
$422$	−1.05429	−0.0513222
$423$	30.6504	1.49027
$424$	9.37867	0.455468
$425$	−11.7017	−0.567616
$426$	−0.933624	−0.0452342
$427$	10.9879	0.531743
$428$	−0.137063	−0.00662521
$429$	1.52004	0.0733883
$430$	0	0
$431$	19.1884	0.924271	0.462136	−	0.886809i	$-0.347083\pi$
$431$	19.1884	0.924271	0.462136	+	0.886809i	$0.347083\pi$
$432$	−7.51871	−0.361744
$433$	−13.8073	−0.663537	−0.331769	−	0.943361i	$-0.607645\pi$
$433$	−13.8073	−0.663537	−0.331769	+	0.943361i	$0.607645\pi$
$434$	−12.9028	−0.619352
$435$	1.48188	0.0710506
$436$	−6.09783	−0.292033
$437$	29.5773	1.41488
$438$	−2.20775	−0.105490
$439$	11.9608	0.570856	0.285428	−	0.958400i	$-0.407864\pi$
$439$	11.9608	0.570856	0.285428	+	0.958400i	$0.407864\pi$
$440$	−3.65279	−0.174140
$441$	14.4547	0.688321
$442$	4.92021	0.234031
$443$	−14.8224	−0.704233	−0.352116	−	0.935956i	$-0.614538\pi$
$443$	−14.8224	−0.704233	−0.352116	+	0.935956i	$0.614538\pi$
$444$	1.42327	0.0675455
$445$	−0.826101	−0.0391609
$446$	29.8485	1.41337
$447$	−1.22521	−0.0579504
$448$	−12.0761	−0.570540
$449$	19.3884	0.914993	0.457497	−	0.889211i	$-0.348746\pi$
$449$	19.3884	0.914993	0.457497	+	0.889211i	$0.348746\pi$
$450$	16.3937	0.772808
$451$	−22.6547	−1.06677
$452$	−8.40342	−0.395264
$453$	−8.30021	−0.389978
$454$	6.59717	0.309621
$455$	1.19136	0.0558517
$456$	7.87263	0.368669
$457$	−21.5181	−1.00658	−0.503288	−	0.864119i	$-0.667876\pi$
$457$	−21.5181	−1.00658	−0.503288	+	0.864119i	$0.667876\pi$
$458$	19.0828	0.891679
$459$	6.43967	0.300578
$460$	1.25906	0.0587040
$461$	33.2553	1.54886	0.774428	−	0.632662i	$-0.218038\pi$
$461$	33.2553	1.54886	0.774428	+	0.632662i	$0.218038\pi$
$462$	−1.62565	−0.0756319
$463$	17.5579	0.815987	0.407993	−	0.912985i	$-0.366229\pi$
$463$	17.5579	0.815987	0.407993	+	0.912985i	$0.366229\pi$
$464$	−17.4711	−0.811077
$465$	1.88338	0.0873396
$466$	31.9517	1.48013
$467$	15.8398	0.732980	0.366490	−	0.930422i	$-0.380559\pi$
$467$	15.8398	0.732980	0.366490	+	0.930422i	$0.380559\pi$
$468$	1.97285	0.0911952
$469$	−10.0194	−0.462652
$470$	7.57002	0.349179
$471$	5.88769	0.271290
$472$	22.2446	1.02389
$473$	0	0
$474$	1.15883	0.0532270
$475$	−27.2228	−1.24907
$476$	1.50604	0.0690293
$477$	8.61894	0.394634
$478$	−8.30798	−0.379998
$479$	28.5652	1.30518	0.652590	−	0.757712i	$-0.273683\pi$
$479$	28.5652	1.30518	0.652590	+	0.757712i	$0.273683\pi$
$480$	0.609252	0.0278084
$481$	11.3690	0.518381
$482$	−3.24698	−0.147896
$483$	3.07846	0.140075
$484$	2.82132	0.128242
$485$	8.39373	0.381140
$486$	−13.6866	−0.620839
$487$	1.87263	0.0848568	0.0424284	−	0.999100i	$-0.486491\pi$
$487$	1.87263	0.0848568	0.0424284	+	0.999100i	$0.486491\pi$
$488$	24.6896	1.11765
$489$	−4.65817	−0.210650
$490$	3.57002	0.161277
$491$	29.2336	1.31929	0.659646	−	0.751576i	$-0.270706\pi$
$491$	29.2336	1.31929	0.659646	+	0.751576i	$0.270706\pi$
$492$	2.07846	0.0937041
$493$	14.9638	0.673934
$494$	11.4464	0.514997
$495$	−3.35690	−0.150881
$496$	−22.2048	−0.997023
$497$	−2.28275	−0.102395
$498$	−0.509025	−0.0228099
$499$	−24.9342	−1.11621	−0.558104	−	0.829771i	$-0.688471\pi$
$499$	−24.9342	−1.11621	−0.558104	+	0.829771i	$0.688471\pi$
$500$	−2.39373	−0.107051
$501$	−6.48188	−0.289589
$502$	8.28754	0.369891
$503$	−42.2814	−1.88524	−0.942618	−	0.333874i	$-0.891644\pi$
$503$	−42.2814	−1.88524	−0.942618	+	0.333874i	$0.891644\pi$
$504$	−11.5918	−0.516340
$505$	1.88338	0.0838093
$506$	−13.7235	−0.610083
$507$	4.67158	0.207472
$508$	2.22282	0.0986215
$509$	−18.1153	−0.802946	−0.401473	−	0.915871i	$-0.631502\pi$
$509$	−18.1153	−0.802946	−0.401473	+	0.915871i	$0.631502\pi$
$510$	0.768086	0.0340114
$511$	−5.39804	−0.238795
$512$	−24.9390	−1.10216
$513$	14.9812	0.661437
$514$	−1.75302	−0.0773224
$515$	2.82908	0.124664
$516$	0	0
$517$	23.6155	1.03861
$518$	−12.1588	−0.534228
$519$	3.91185	0.171711
$520$	2.67696	0.117392
$521$	−1.26098	−0.0552445	−0.0276223	−	0.999618i	$-0.508794\pi$
$521$	−1.26098	−0.0552445	−0.0276223	+	0.999618i	$0.508794\pi$
$522$	−20.9638	−0.917559
$523$	−36.9788	−1.61697	−0.808485	−	0.588516i	$-0.799712\pi$
$523$	−36.9788	−1.61697	−0.808485	+	0.588516i	$0.799712\pi$
$524$	−7.97823	−0.348531
$525$	−2.83340	−0.123660
$526$	3.92021	0.170929
$527$	19.0180	0.828439
$528$	−2.79763	−0.121751
$529$	2.98792	0.129909
$530$	2.12870	0.0924649
$531$	20.4426	0.887135
$532$	3.50365	0.151902
$533$	16.6025	0.719136
$534$	−0.826101	−0.0357489
$535$	−0.170915	−0.00738931
$536$	−22.5133	−0.972428
$537$	−9.52542	−0.411052
$538$	−14.3757	−0.619780
$539$	11.1371	0.479707
$540$	0.637727	0.0274434
$541$	−0.489647	−0.0210516	−0.0105258	−	0.999945i	$-0.503351\pi$
$541$	−0.489647	−0.0210516	−0.0105258	+	0.999945i	$0.503351\pi$
$542$	−16.6558	−0.715427
$543$	−11.7192	−0.502918
$544$	6.15213	0.263770
$545$	−7.60388	−0.325714
$546$	1.19136	0.0509854
$547$	−12.0871	−0.516806	−0.258403	−	0.966037i	$-0.583196\pi$
$547$	−12.0871	−0.516806	−0.258403	+	0.966037i	$0.583196\pi$
$548$	−5.56704	−0.237812
$549$	22.6896	0.968370
$550$	12.6310	0.538589
$551$	34.8116	1.48303
$552$	6.91723	0.294417
$553$	2.83340	0.120488
$554$	−16.5496	−0.703124
$555$	1.77479	0.0753357
$556$	2.70171	0.114578
$557$	41.4392	1.75583	0.877917	−	0.478812i	$-0.158932\pi$
$557$	41.4392	1.75583	0.877917	+	0.478812i	$0.158932\pi$
$558$	−26.6437	−1.12792
$559$	0	0
$560$	−2.19269	−0.0926579
$561$	2.39612	0.101164
$562$	−19.8485	−0.837257
$563$	−16.2567	−0.685137	−0.342568	−	0.939493i	$-0.611297\pi$
$563$	−16.2567	−0.685137	−0.342568	+	0.939493i	$0.611297\pi$
$564$	−2.16660	−0.0912305
$565$	−10.4789	−0.440850
$566$	29.6534	1.24642
$567$	−9.84654	−0.413516
$568$	−5.12929	−0.215220
$569$	31.6601	1.32726	0.663630	−	0.748061i	$-0.269015\pi$
$569$	31.6601	1.32726	0.663630	+	0.748061i	$0.269015\pi$
$570$	1.78687	0.0748438
$571$	−15.8984	−0.665329	−0.332665	−	0.943045i	$-0.607948\pi$
$571$	−15.8984	−0.665329	−0.332665	+	0.943045i	$0.607948\pi$
$572$	1.52004	0.0635561
$573$	3.86725	0.161557
$574$	−17.7560	−0.741121
$575$	−23.9191	−0.997497
$576$	−24.9366	−1.03903
$577$	−15.8398	−0.659421	−0.329711	−	0.944082i	$-0.606951\pi$
$577$	−15.8398	−0.659421	−0.329711	+	0.944082i	$0.606951\pi$
$578$	−13.4426	−0.559140
$579$	−0.917231	−0.0381188
$580$	1.48188	0.0615316
$581$	−1.24459	−0.0516342
$582$	8.39373	0.347931
$583$	6.64071	0.275030
$584$	−12.1293	−0.501914
$585$	2.46011	0.101713
$586$	15.8237	0.653671
$587$	30.2107	1.24693	0.623465	−	0.781851i	$-0.285724\pi$
$587$	30.2107	1.24693	0.623465	+	0.781851i	$0.285724\pi$
$588$	−1.02177	−0.0421371
$589$	44.2435	1.82302
$590$	5.04892	0.207861
$591$	−0.203439	−0.00836837
$592$	−20.9245	−0.859993
$593$	−27.5502	−1.13135	−0.565675	−	0.824628i	$-0.691384\pi$
$593$	−27.5502	−1.13135	−0.565675	+	0.824628i	$0.691384\pi$
$594$	−6.95108	−0.285206
$595$	1.87800	0.0769906
$596$	−1.22521	−0.0501865
$597$	0.918559	0.0375941
$598$	10.0573	0.411273
$599$	−15.4620	−0.631761	−0.315881	−	0.948799i	$-0.602300\pi$
$599$	−15.4620	−0.631761	−0.315881	+	0.948799i	$0.602300\pi$
$600$	−6.36658	−0.259915
$601$	−3.03684	−0.123875	−0.0619376	−	0.998080i	$-0.519728\pi$
$601$	−3.03684	−0.123875	−0.0619376	+	0.998080i	$0.519728\pi$
$602$	0	0
$603$	−20.6896	−0.842547
$604$	−8.30021	−0.337731
$605$	3.51812	0.143032
$606$	1.88338	0.0765070
$607$	−5.34588	−0.216983	−0.108491	−	0.994097i	$-0.534602\pi$
$607$	−5.34588	−0.216983	−0.108491	+	0.994097i	$0.534602\pi$
$608$	14.3123	0.580440
$609$	3.62325	0.146822
$610$	5.60388	0.226894
$611$	−17.3067	−0.700152
$612$	3.10992	0.125711
$613$	−8.68771	−0.350893	−0.175447	−	0.984489i	$-0.556137\pi$
$613$	−8.68771	−0.350893	−0.175447	+	0.984489i	$0.556137\pi$
$614$	22.6829	0.915408
$615$	2.59179	0.104511
$616$	−8.93123	−0.359850
$617$	−17.4004	−0.700515	−0.350258	−	0.936653i	$-0.613906\pi$
$617$	−17.4004	−0.700515	−0.350258	+	0.936653i	$0.613906\pi$
$618$	2.82908	0.113802
$619$	−2.58642	−0.103957	−0.0519784	−	0.998648i	$-0.516553\pi$
$619$	−2.58642	−0.103957	−0.0519784	+	0.998648i	$0.516553\pi$
$620$	1.88338	0.0756383
$621$	13.1631	0.528219
$622$	9.08277	0.364186
$623$	−2.01985	−0.0809236
$624$	2.05025	0.0820755
$625$	20.4752	0.819007
$626$	23.3599	0.933649
$627$	5.57434	0.222618
$628$	5.88769	0.234944
$629$	17.9215	0.714579
$630$	−2.63102	−0.104822
$631$	2.83877	0.113010	0.0565049	−	0.998402i	$-0.482004\pi$
$631$	2.83877	0.113010	0.0565049	+	0.998402i	$0.482004\pi$
$632$	6.36658	0.253249
$633$	0.376273	0.0149555
$634$	4.32603	0.171809
$635$	2.77181	0.109996
$636$	−0.609252	−0.0241584
$637$	−8.16182	−0.323383
$638$	−16.1521	−0.639469
$639$	−4.71379	−0.186475
$640$	−3.42088	−0.135222
$641$	23.3957	0.924073	0.462036	−	0.886861i	$-0.347119\pi$
$641$	23.3957	0.924073	0.462036	+	0.886861i	$0.347119\pi$
$642$	−0.170915	−0.00674548
$643$	−30.2150	−1.19157	−0.595783	−	0.803146i	$-0.703158\pi$
$643$	−30.2150	−1.19157	−0.595783	+	0.803146i	$0.703158\pi$
$644$	3.07846	0.121308
$645$	0	0
$646$	18.0435	0.709914
$647$	42.2368	1.66050	0.830250	−	0.557391i	$-0.188197\pi$
$647$	42.2368	1.66050	0.830250	+	0.557391i	$0.188197\pi$
$648$	−22.1250	−0.869151
$649$	15.7506	0.618266
$650$	−9.25667	−0.363076
$651$	4.60494	0.180482
$652$	−4.65817	−0.182428
$653$	1.47325	0.0576529	0.0288264	−	0.999584i	$-0.490823\pi$
$653$	1.47325	0.0576529	0.0288264	+	0.999584i	$0.490823\pi$
$654$	−7.60388	−0.297335
$655$	−9.94869	−0.388727
$656$	−30.5569	−1.19305
$657$	−11.1468	−0.434876
$658$	18.5090	0.721557
$659$	−15.8183	−0.616195	−0.308097	−	0.951355i	$-0.599692\pi$
$659$	−15.8183	−0.616195	−0.308097	+	0.951355i	$0.599692\pi$
$660$	0.237291	0.00923654
$661$	9.19375	0.357595	0.178798	−	0.983886i	$-0.442779\pi$
$661$	9.19375	0.357595	0.178798	+	0.983886i	$0.442779\pi$
$662$	17.3515	0.674386
$663$	−1.75600	−0.0681976
$664$	−2.79656	−0.108528
$665$	4.36898	0.169422
$666$	−25.1075	−0.972897
$667$	30.5870	1.18433
$668$	−6.48188	−0.250791
$669$	−10.6528	−0.411861
$670$	−5.10992	−0.197413
$671$	17.4819	0.674880
$672$	1.48965	0.0574644
$673$	−36.1250	−1.39252	−0.696258	−	0.717792i	$-0.745153\pi$
$673$	−36.1250	−1.39252	−0.696258	+	0.717792i	$0.745153\pi$
$674$	−3.80731	−0.146652
$675$	−12.1153	−0.466318
$676$	4.67158	0.179676
$677$	−10.2107	−0.392430	−0.196215	−	0.980561i	$-0.562865\pi$
$677$	−10.2107	−0.392430	−0.196215	+	0.980561i	$0.562865\pi$
$678$	−10.4789	−0.402439
$679$	20.5230	0.787601
$680$	4.21983	0.161823
$681$	−2.35450	−0.0902247
$682$	−20.5284	−0.786073
$683$	27.4215	1.04925	0.524627	−	0.851332i	$-0.324205\pi$
$683$	27.4215	1.04925	0.524627	+	0.851332i	$0.324205\pi$
$684$	7.23490	0.276633
$685$	−6.94198	−0.265240
$686$	20.5730	0.785481
$687$	−6.81056	−0.259839
$688$	0	0
$689$	−4.86666	−0.185405
$690$	1.57002	0.0597698
$691$	21.1172	0.803337	0.401668	−	0.915785i	$-0.368430\pi$
$691$	21.1172	0.803337	0.401668	+	0.915785i	$0.368430\pi$
$692$	3.91185	0.148706
$693$	−8.20775	−0.311787
$694$	−17.9879	−0.682812
$695$	3.36898	0.127793
$696$	8.14138	0.308598
$697$	26.1715	0.991316
$698$	−35.3997	−1.33990
$699$	−11.4034	−0.431317
$700$	−2.83340	−0.107092
$701$	−0.232505	−0.00878160	−0.00439080	−	0.999990i	$-0.501398\pi$
$701$	−0.232505	−0.00878160	−0.00439080	+	0.999990i	$0.501398\pi$
$702$	5.09411	0.192265
$703$	41.6926	1.57247
$704$	−19.2131	−0.724122
$705$	−2.70171	−0.101752
$706$	−16.9788	−0.639006
$707$	4.60494	0.173187
$708$	−1.44504	−0.0543080
$709$	17.9065	0.672492	0.336246	−	0.941774i	$-0.390843\pi$
$709$	17.9065	0.672492	0.336246	+	0.941774i	$0.390843\pi$
$710$	−1.16421	−0.0436920
$711$	5.85086	0.219424
$712$	−4.53856	−0.170090
$713$	38.8743	1.45585
$714$	1.87800	0.0702825
$715$	1.89546	0.0708862
$716$	−9.52542	−0.355982
$717$	2.96508	0.110733
$718$	−40.8853	−1.52583
$719$	−6.34242	−0.236532	−0.118266	−	0.992982i	$-0.537734\pi$
$719$	−6.34242	−0.236532	−0.118266	+	0.992982i	$0.537734\pi$
$720$	−4.52781	−0.168742
$721$	6.91723	0.257611
$722$	18.2838	0.680453
$723$	1.15883	0.0430975
$724$	−11.7192	−0.435539
$725$	−28.1521	−1.04554
$726$	3.51812	0.130570
$727$	10.2048	0.378474	0.189237	−	0.981931i	$-0.439399\pi$
$727$	10.2048	0.378474	0.189237	+	0.981931i	$0.439399\pi$
$728$	6.54527	0.242584
$729$	−16.8853	−0.625381
$730$	−2.75302	−0.101894
$731$	0	0
$732$	−1.60388	−0.0592809
$733$	4.84117	0.178813	0.0894063	−	0.995995i	$-0.471503\pi$
$733$	4.84117	0.178813	0.0894063	+	0.995995i	$0.471503\pi$
$734$	31.7942	1.17354
$735$	−1.27413	−0.0469969
$736$	12.5754	0.463535
$737$	−15.9409	−0.587191
$738$	−36.6655	−1.34967
$739$	−24.5066	−0.901491	−0.450746	−	0.892652i	$-0.648842\pi$
$739$	−24.5066	−0.901491	−0.450746	+	0.892652i	$0.648842\pi$
$740$	1.77479	0.0652426
$741$	−4.08516	−0.150072
$742$	5.20477	0.191073
$743$	25.5888	0.938762	0.469381	−	0.882996i	$-0.344477\pi$
$743$	25.5888	0.938762	0.469381	+	0.882996i	$0.344477\pi$
$744$	10.3472	0.379347
$745$	−1.52781	−0.0559747
$746$	−34.3726	−1.25847
$747$	−2.57002	−0.0940322
$748$	2.39612	0.0876110
$749$	−0.417895	−0.0152695
$750$	−2.98493	−0.108994
$751$	−21.8877	−0.798693	−0.399347	−	0.916800i	$-0.630763\pi$
$751$	−21.8877	−0.798693	−0.399347	+	0.916800i	$0.630763\pi$
$752$	31.8528	1.16155
$753$	−2.95779	−0.107788
$754$	11.8371	0.431082
$755$	−10.3502	−0.376682
$756$	1.55927	0.0567101
$757$	28.4252	1.03313	0.516566	−	0.856248i	$-0.327210\pi$
$757$	28.4252	1.03313	0.516566	+	0.856248i	$0.327210\pi$
$758$	35.1142	1.27541
$759$	4.89785	0.177781
$760$	9.81700	0.356100
$761$	29.4088	1.06607	0.533034	−	0.846094i	$-0.321052\pi$
$761$	29.4088	1.06607	0.533034	+	0.846094i	$0.321052\pi$
$762$	2.77181	0.100412
$763$	−18.5918	−0.673068
$764$	3.86725	0.139912
$765$	3.87800	0.140209
$766$	−35.6926	−1.28963
$767$	−11.5429	−0.416789
$768$	4.50066	0.162404
$769$	19.1752	0.691476	0.345738	−	0.938331i	$-0.387629\pi$
$769$	19.1752	0.691476	0.345738	+	0.938331i	$0.387629\pi$
$770$	−2.02715	−0.0730533
$771$	0.625646	0.0225321
$772$	−0.917231	−0.0330119
$773$	39.5725	1.42333	0.711663	−	0.702521i	$-0.247943\pi$
$773$	39.5725	1.42333	0.711663	+	0.702521i	$0.247943\pi$
$774$	0	0
$775$	−35.7797	−1.28524
$776$	46.1148	1.65543
$777$	4.33944	0.155676
$778$	−44.0411	−1.57895
$779$	60.8853	2.18144
$780$	−0.173899	−0.00622659
$781$	−3.63188	−0.129959
$782$	15.8538	0.566932
$783$	15.4926	0.553661
$784$	15.0218	0.536492
$785$	7.34183	0.262041
$786$	−9.94869	−0.354858
$787$	−13.7060	−0.488567	−0.244283	−	0.969704i	$-0.578553\pi$
$787$	−13.7060	−0.488567	−0.244283	+	0.969704i	$0.578553\pi$
$788$	−0.203439	−0.00724722
$789$	−1.39911	−0.0498096
$790$	1.44504	0.0514123
$791$	−25.6213	−0.910990
$792$	−18.4426	−0.655331
$793$	−12.8116	−0.454954
$794$	4.21313	0.149518
$795$	−0.759725	−0.0269447
$796$	0.918559	0.0325575
$797$	−36.3773	−1.28855	−0.644276	−	0.764793i	$-0.722841\pi$
$797$	−36.3773	−1.28855	−0.644276	+	0.764793i	$0.722841\pi$
$798$	4.36898	0.154660
$799$	−27.2814	−0.965147
$800$	−11.5743	−0.409215
$801$	−4.17092	−0.147372
$802$	−21.0858	−0.744564
$803$	−8.58834	−0.303076
$804$	1.46250	0.0515784
$805$	3.83877	0.135299
$806$	15.0443	0.529912
$807$	5.13062	0.180606
$808$	10.3472	0.364013
$809$	−37.7676	−1.32784	−0.663919	−	0.747804i	$-0.731108\pi$
$809$	−37.7676	−1.32784	−0.663919	+	0.747804i	$0.731108\pi$
$810$	−5.02177	−0.176447
$811$	37.9694	1.33329	0.666643	−	0.745377i	$-0.267731\pi$
$811$	37.9694	1.33329	0.666643	+	0.745377i	$0.267731\pi$
$812$	3.62325	0.127151
$813$	5.94438	0.208478
$814$	−19.3448	−0.678035
$815$	−5.80864	−0.203468
$816$	3.23191	0.113140
$817$	0	0
$818$	−2.32006	−0.0811190
$819$	6.01507	0.210183
$820$	2.59179	0.0905094
$821$	16.8334	0.587490	0.293745	−	0.955884i	$-0.405098\pi$
$821$	16.8334	0.587490	0.293745	+	0.955884i	$0.405098\pi$
$822$	−6.94198	−0.242130
$823$	17.7205	0.617698	0.308849	−	0.951111i	$-0.400056\pi$
$823$	17.7205	0.617698	0.308849	+	0.951111i	$0.400056\pi$
$824$	15.5429	0.541462
$825$	−4.50796	−0.156947
$826$	12.3448	0.429531
$827$	−49.0019	−1.70396	−0.851982	−	0.523571i	$-0.824599\pi$
$827$	−49.0019	−1.70396	−0.851982	+	0.523571i	$0.824599\pi$
$828$	6.35690	0.220917
$829$	−45.7525	−1.58905	−0.794526	−	0.607230i	$-0.792281\pi$
$829$	−45.7525	−1.58905	−0.794526	+	0.607230i	$0.792281\pi$
$830$	−0.634743	−0.0220323
$831$	5.90648	0.204893
$832$	14.0804	0.488149
$833$	−12.8659	−0.445778
$834$	3.36898	0.116658
$835$	−8.08277	−0.279716
$836$	5.57434	0.192792
$837$	19.6902	0.680594
$838$	20.5894	0.711249
$839$	−21.8659	−0.754895	−0.377448	−	0.926031i	$-0.623198\pi$
$839$	−21.8659	−0.754895	−0.377448	+	0.926031i	$0.623198\pi$
$840$	1.02177	0.0352544
$841$	7.00000	0.241379
$842$	−27.4185	−0.944903
$843$	7.08383	0.243980
$844$	0.376273	0.0129519
$845$	5.82536	0.200399
$846$	38.2204	1.31405
$847$	8.60196	0.295567
$848$	8.95705	0.307586
$849$	−10.5832	−0.363213
$850$	−14.5918	−0.500494
$851$	36.6329	1.25576
$852$	0.333207	0.0114155
$853$	−32.3217	−1.10667	−0.553337	−	0.832957i	$-0.686646\pi$
$853$	−32.3217	−1.10667	−0.553337	+	0.832957i	$0.686646\pi$
$854$	13.7017	0.468863
$855$	9.02177	0.308538
$856$	−0.939001	−0.0320944
$857$	−18.1618	−0.620396	−0.310198	−	0.950672i	$-0.600395\pi$
$857$	−18.1618	−0.620396	−0.310198	+	0.950672i	$0.600395\pi$
$858$	1.89546	0.0647100
$859$	−53.6402	−1.83018	−0.915091	−	0.403248i	$-0.867881\pi$
$859$	−53.6402	−1.83018	−0.915091	+	0.403248i	$0.867881\pi$
$860$	0	0
$861$	6.33704	0.215966
$862$	23.9275	0.814974
$863$	55.0186	1.87286	0.936428	−	0.350859i	$-0.114110\pi$
$863$	55.0186	1.87286	0.936428	+	0.350859i	$0.114110\pi$
$864$	6.36957	0.216697
$865$	4.87800	0.165857
$866$	−17.2174	−0.585072
$867$	4.79763	0.162936
$868$	4.60494	0.156302
$869$	4.50796	0.152922
$870$	1.84787	0.0626487
$871$	11.6823	0.395841
$872$	−41.7754	−1.41469
$873$	42.3793	1.43432
$874$	36.8823	1.24756
$875$	−7.29829	−0.246727
$876$	0.787937	0.0266219
$877$	−10.1099	−0.341388	−0.170694	−	0.985324i	$-0.554601\pi$
$877$	−10.1099	−0.341388	−0.170694	+	0.985324i	$0.554601\pi$
$878$	14.9148	0.503351
$879$	−5.64742	−0.190483
$880$	−3.48858	−0.117600
$881$	40.5314	1.36554	0.682769	−	0.730635i	$-0.260776\pi$
$881$	40.5314	1.36554	0.682769	+	0.730635i	$0.260776\pi$
$882$	18.0248	0.606925
$883$	−0.470861	−0.0158457	−0.00792287	−	0.999969i	$-0.502522\pi$
$883$	−0.470861	−0.0158457	−0.00792287	+	0.999969i	$0.502522\pi$
$884$	−1.75600	−0.0590608
$885$	−1.80194	−0.0605715
$886$	−18.4832	−0.620955
$887$	35.1347	1.17971	0.589853	−	0.807510i	$-0.299186\pi$
$887$	35.1347	1.17971	0.589853	+	0.807510i	$0.299186\pi$
$888$	9.75063	0.327210
$889$	6.77718	0.227299
$890$	−1.03013	−0.0345301
$891$	−15.6659	−0.524829
$892$	−10.6528	−0.356682
$893$	−63.4674	−2.12386
$894$	−1.52781	−0.0510976
$895$	−11.8780	−0.397038
$896$	−8.36419	−0.279428
$897$	−3.58940	−0.119847
$898$	24.1769	0.806793
$899$	45.7539	1.52598
$900$	−5.85086	−0.195029
$901$	−7.67158	−0.255577
$902$	−28.2500	−0.940621
$903$	0	0
$904$	−57.5706	−1.91477
$905$	−14.6136	−0.485771
$906$	−10.3502	−0.343862
$907$	−8.84356	−0.293646	−0.146823	−	0.989163i	$-0.546905\pi$
$907$	−8.84356	−0.293646	−0.146823	+	0.989163i	$0.546905\pi$
$908$	−2.35450	−0.0781369
$909$	9.50902	0.315394
$910$	1.48560	0.0492471
$911$	15.8267	0.524362	0.262181	−	0.965019i	$-0.415558\pi$
$911$	15.8267	0.524362	0.262181	+	0.965019i	$0.415558\pi$
$912$	7.51871	0.248969
$913$	−1.98015	−0.0655334
$914$	−26.8327	−0.887545
$915$	−2.00000	−0.0661180
$916$	−6.81056	−0.225027
$917$	−24.3250	−0.803281
$918$	8.03013	0.265034
$919$	−38.6937	−1.27639	−0.638193	−	0.769876i	$-0.720318\pi$
$919$	−38.6937	−1.27639	−0.638193	+	0.769876i	$0.720318\pi$
$920$	8.62565	0.284379
$921$	−8.09544	−0.266754
$922$	41.4687	1.36570
$923$	2.66163	0.0876085
$924$	0.580186	0.0190867
$925$	−33.7168	−1.10860
$926$	21.8944	0.719494
$927$	14.2838	0.469142
$928$	14.8009	0.485862
$929$	−4.12844	−0.135450	−0.0677249	−	0.997704i	$-0.521574\pi$
$929$	−4.12844	−0.135450	−0.0677249	+	0.997704i	$0.521574\pi$
$930$	2.34854	0.0770115
$931$	−29.9312	−0.980956
$932$	−11.4034	−0.373531
$933$	−3.24160	−0.106125
$934$	19.7520	0.646304
$935$	2.98792	0.0977154
$936$	13.5157	0.441775
$937$	−2.25800	−0.0737655	−0.0368828	−	0.999320i	$-0.511743\pi$
$937$	−2.25800	−0.0737655	−0.0368828	+	0.999320i	$0.511743\pi$
$938$	−12.4940	−0.407942
$939$	−8.33704	−0.272069
$940$	−2.70171	−0.0881201
$941$	51.7555	1.68718	0.843591	−	0.536986i	$-0.180437\pi$
$941$	51.7555	1.68718	0.843591	+	0.536986i	$0.180437\pi$
$942$	7.34183	0.239210
$943$	53.4965	1.74208
$944$	21.2446	0.691452
$945$	1.94438	0.0632506
$946$	0	0
$947$	−24.0965	−0.783031	−0.391516	−	0.920171i	$-0.628049\pi$
$947$	−24.0965	−0.783031	−0.391516	+	0.920171i	$0.628049\pi$
$948$	−0.413583	−0.0134325
$949$	6.29398	0.204311
$950$	−33.9463	−1.10136
$951$	−1.54394	−0.0500657
$952$	10.3177	0.334398
$953$	−47.1189	−1.52633	−0.763165	−	0.646204i	$-0.776356\pi$
$953$	−47.1189	−1.52633	−0.763165	+	0.646204i	$0.776356\pi$
$954$	10.7476	0.347968
$955$	4.82238	0.156049
$956$	2.96508	0.0958976
$957$	5.76463	0.186344
$958$	35.6203	1.15084
$959$	−16.9734	−0.548101
$960$	2.19806	0.0709422
$961$	27.1505	0.875822
$962$	14.1769	0.457081
$963$	−0.862937	−0.0278077
$964$	1.15883	0.0373235
$965$	−1.14377	−0.0368192
$966$	3.83877	0.123511
$967$	−7.09352	−0.228112	−0.114056	−	0.993474i	$-0.536384\pi$
$967$	−7.09352	−0.228112	−0.114056	+	0.993474i	$0.536384\pi$
$968$	19.3284	0.621239
$969$	−6.43967	−0.206872
$970$	10.4668	0.336069
$971$	27.7995	0.892130	0.446065	−	0.895001i	$-0.352825\pi$
$971$	27.7995	0.892130	0.446065	+	0.895001i	$0.352825\pi$
$972$	4.88471	0.156677
$973$	8.23729	0.264075
$974$	2.33513	0.0748223
$975$	3.30367	0.105802
$976$	23.5797	0.754768
$977$	30.6601	0.980903	0.490452	−	0.871468i	$-0.336832\pi$
$977$	30.6601	0.980903	0.490452	+	0.871468i	$0.336832\pi$
$978$	−5.80864	−0.185740
$979$	−3.21360	−0.102707
$980$	−1.27413	−0.0407005
$981$	−38.3913	−1.22574
$982$	36.4537	1.16328
$983$	−14.7797	−0.471399	−0.235700	−	0.971826i	$-0.575738\pi$
$983$	−14.7797	−0.471399	−0.235700	+	0.971826i	$0.575738\pi$
$984$	14.2392	0.453929
$985$	−0.253684	−0.00808306
$986$	18.6595	0.594239
$987$	−6.60579	−0.210265
$988$	−4.08516	−0.129966
$989$	0	0
$990$	−4.18598	−0.133039
$991$	62.3223	1.97973	0.989867	−	0.142000i	$-0.0453533\pi$
$991$	62.3223	1.97973	0.989867	+	0.142000i	$0.0453533\pi$
$992$	18.8110	0.597251
$993$	−6.19269	−0.196519
$994$	−2.84654	−0.0902869
$995$	1.14542	0.0363124
$996$	0.181669	0.00575640
$997$	−30.8127	−0.975848	−0.487924	−	0.872886i	$-0.662246\pi$
$997$	−30.8127	−0.975848	−0.487924	+	0.872886i	$0.662246\pi$
$998$	−31.0925	−0.984215
$999$	18.5550	0.587053

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.j.1.3		3
43.2	odd	14		43.2.e.a.4.1	✓	6
43.22	odd	14		43.2.e.a.11.1	yes	6
43.42	odd	2		1849.2.a.k.1.1		3
129.2	even	14		387.2.u.c.262.1		6
129.65	even	14		387.2.u.c.226.1		6
172.131	even	14		688.2.u.b.305.1		6
172.151	even	14		688.2.u.b.97.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.2.e.a.4.1	✓	6	43.2	odd	14
43.2.e.a.11.1	yes	6	43.22	odd	14
387.2.u.c.226.1		6	129.65	even	14
387.2.u.c.262.1		6	129.2	even	14
688.2.u.b.97.1		6	172.151	even	14
688.2.u.b.305.1		6	172.131	even	14
1849.2.a.j.1.3		3	1.1	even	1	trivial
1849.2.a.k.1.1		3	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)

\(f(q)\)	\(=\)	\(q+1.24698 q^{2} -0.445042 q^{3} -0.445042 q^{4} -0.554958 q^{5} -0.554958 q^{6} -1.35690 q^{7} -3.04892 q^{8} -2.80194 q^{9} +O(q^{10})\)	\(q+1.24698 q^{2} -0.445042 q^{3} -0.445042 q^{4} -0.554958 q^{5} -0.554958 q^{6} -1.35690 q^{7} -3.04892 q^{8} -2.80194 q^{9} -0.692021 q^{10} -2.15883 q^{11} +0.198062 q^{12} +1.58211 q^{13} -1.69202 q^{14} +0.246980 q^{15} -2.91185 q^{16} +2.49396 q^{17} -3.49396 q^{18} +5.80194 q^{19} +0.246980 q^{20} +0.603875 q^{21} -2.69202 q^{22} +5.09783 q^{23} +1.35690 q^{24} -4.69202 q^{25} +1.97285 q^{26} +2.58211 q^{27} +0.603875 q^{28} +6.00000 q^{29} +0.307979 q^{30} +7.62565 q^{31} +2.46681 q^{32} +0.960771 q^{33} +3.10992 q^{34} +0.753020 q^{35} +1.24698 q^{36} +7.18598 q^{37} +7.23490 q^{38} -0.704103 q^{39} +1.69202 q^{40} +10.4940 q^{41} +0.753020 q^{42} +0.960771 q^{44} +1.55496 q^{45} +6.35690 q^{46} -10.9390 q^{47} +1.29590 q^{48} -5.15883 q^{49} -5.85086 q^{50} -1.10992 q^{51} -0.704103 q^{52} -3.07606 q^{53} +3.21983 q^{54} +1.19806 q^{55} +4.13706 q^{56} -2.58211 q^{57} +7.48188 q^{58} -7.29590 q^{59} -0.109916 q^{60} -8.09783 q^{61} +9.50902 q^{62} +3.80194 q^{63} +8.89977 q^{64} -0.878002 q^{65} +1.19806 q^{66} +7.38404 q^{67} -1.10992 q^{68} -2.26875 q^{69} +0.939001 q^{70} +1.68233 q^{71} +8.54288 q^{72} +3.97823 q^{73} +8.96077 q^{74} +2.08815 q^{75} -2.58211 q^{76} +2.92931 q^{77} -0.878002 q^{78} -2.08815 q^{79} +1.61596 q^{80} +7.25667 q^{81} +13.0858 q^{82} +0.917231 q^{83} -0.268750 q^{84} -1.38404 q^{85} -2.67025 q^{87} +6.58211 q^{88} +1.48858 q^{89} +1.93900 q^{90} -2.14675 q^{91} -2.26875 q^{92} -3.39373 q^{93} -13.6407 q^{94} -3.21983 q^{95} -1.09783 q^{96} -15.1250 q^{97} -6.43296 q^{98} +6.04892 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - q^{2} - q^{3} - q^{4} - 2 q^{5} - 2 q^{6} - 4 q^{9}+O(q^{10}) \) 3 * q - q^2 - q^3 - q^4 - 2 * q^5 - 2 * q^6 - 4 * q^9	\( 3 q - q^{2} - q^{3} - q^{4} - 2 q^{5} - 2 q^{6} - 4 q^{9} + 3 q^{10} + 2 q^{11} + 5 q^{12} - q^{13} - 4 q^{15} - 5 q^{16} - 2 q^{17} - q^{18} + 13 q^{19} - 4 q^{20} - 7 q^{21} - 3 q^{22} - 3 q^{23} - 9 q^{25} + 12 q^{26} + 2 q^{27} - 7 q^{28} + 18 q^{29} + 6 q^{30} + 11 q^{31} + 4 q^{32} - 10 q^{33} + 10 q^{34} + 7 q^{35} - q^{36} + 7 q^{37} - 2 q^{38} - 16 q^{39} + 22 q^{41} + 7 q^{42} - 10 q^{44} + 5 q^{45} + 15 q^{46} - 23 q^{47} - 10 q^{48} - 7 q^{49} - 4 q^{50} - 4 q^{51} - 16 q^{52} + 6 q^{53} + 11 q^{54} + 8 q^{55} + 7 q^{56} - 2 q^{57} - 6 q^{58} - 8 q^{59} - q^{60} - 6 q^{61} - 6 q^{62} + 7 q^{63} + 4 q^{64} + 17 q^{65} + 8 q^{66} + 12 q^{67} - 4 q^{68} + q^{69} - 7 q^{70} + 22 q^{71} + 7 q^{72} + 15 q^{73} + 14 q^{74} + 10 q^{75} - 2 q^{76} + 21 q^{77} + 17 q^{78} - 10 q^{79} + 15 q^{80} - 5 q^{81} + 2 q^{82} - 4 q^{83} + 7 q^{84} + 6 q^{85} - 6 q^{87} + 14 q^{88} - 2 q^{89} - 4 q^{90} + 21 q^{91} + q^{92} + 22 q^{93} - 4 q^{94} - 11 q^{95} + 15 q^{96} - 21 q^{97} + 9 q^{99}+O(q^{100}) \) 3 * q - q^2 - q^3 - q^4 - 2 * q^5 - 2 * q^6 - 4 * q^9 + 3 * q^10 + 2 * q^11 + 5 * q^12 - q^13 - 4 * q^15 - 5 * q^16 - 2 * q^17 - q^18 + 13 * q^19 - 4 * q^20 - 7 * q^21 - 3 * q^22 - 3 * q^23 - 9 * q^25 + 12 * q^26 + 2 * q^27 - 7 * q^28 + 18 * q^29 + 6 * q^30 + 11 * q^31 + 4 * q^32 - 10 * q^33 + 10 * q^34 + 7 * q^35 - q^36 + 7 * q^37 - 2 * q^38 - 16 * q^39 + 22 * q^41 + 7 * q^42 - 10 * q^44 + 5 * q^45 + 15 * q^46 - 23 * q^47 - 10 * q^48 - 7 * q^49 - 4 * q^50 - 4 * q^51 - 16 * q^52 + 6 * q^53 + 11 * q^54 + 8 * q^55 + 7 * q^56 - 2 * q^57 - 6 * q^58 - 8 * q^59 - q^60 - 6 * q^61 - 6 * q^62 + 7 * q^63 + 4 * q^64 + 17 * q^65 + 8 * q^66 + 12 * q^67 - 4 * q^68 + q^69 - 7 * q^70 + 22 * q^71 + 7 * q^72 + 15 * q^73 + 14 * q^74 + 10 * q^75 - 2 * q^76 + 21 * q^77 + 17 * q^78 - 10 * q^79 + 15 * q^80 - 5 * q^81 + 2 * q^82 - 4 * q^83 + 7 * q^84 + 6 * q^85 - 6 * q^87 + 14 * q^88 - 2 * q^89 - 4 * q^90 + 21 * q^91 + q^92 + 22 * q^93 - 4 * q^94 - 11 * q^95 + 15 * q^96 - 21 * q^97 + 9 * q^99

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