LMFDB - Embedded newform 1805.2.a.u.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1,1805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.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:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 12x^{7} - 4x^{6} + 48x^{5} + 27x^{4} - 72x^{3} - 51x^{2} + 27x + 19 $ x^9 - 12x^7 - 4x^6 + 48x^5 + 27x^4 - 72x^3 - 51x^2 + 27*x + 19
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-2.02162$ of defining polynomial
Character	$\chi$	$=$	1805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.02162 q^{2} +1.90055 q^{3} +2.08694 q^{4} -1.00000 q^{5} +3.84218 q^{6} +3.09218 q^{7} +0.175759 q^{8} +0.612075 q^{9} +O(q^{10})$	\(q+2.02162 q^{2} +1.90055 q^{3} +2.08694 q^{4} -1.00000 q^{5} +3.84218 q^{6} +3.09218 q^{7} +0.175759 q^{8} +0.612075 q^{9} -2.02162 q^{10} +0.963188 q^{11} +3.96633 q^{12} +2.95920 q^{13} +6.25120 q^{14} -1.90055 q^{15} -3.81856 q^{16} +0.0389621 q^{17} +1.23738 q^{18} -2.08694 q^{20} +5.87682 q^{21} +1.94720 q^{22} +3.88160 q^{23} +0.334039 q^{24} +1.00000 q^{25} +5.98236 q^{26} -4.53836 q^{27} +6.45319 q^{28} +9.32783 q^{29} -3.84218 q^{30} +9.37788 q^{31} -8.07119 q^{32} +1.83058 q^{33} +0.0787664 q^{34} -3.09218 q^{35} +1.27736 q^{36} +1.11739 q^{37} +5.62409 q^{39} -0.175759 q^{40} -12.0747 q^{41} +11.8807 q^{42} -4.95348 q^{43} +2.01012 q^{44} -0.612075 q^{45} +7.84711 q^{46} +8.01557 q^{47} -7.25735 q^{48} +2.56155 q^{49} +2.02162 q^{50} +0.0740492 q^{51} +6.17566 q^{52} -6.05981 q^{53} -9.17483 q^{54} -0.963188 q^{55} +0.543479 q^{56} +18.8573 q^{58} -2.77465 q^{59} -3.96633 q^{60} -10.0302 q^{61} +18.9585 q^{62} +1.89264 q^{63} -8.67975 q^{64} -2.95920 q^{65} +3.70074 q^{66} -9.34881 q^{67} +0.0813115 q^{68} +7.37716 q^{69} -6.25120 q^{70} -12.5894 q^{71} +0.107578 q^{72} +0.897116 q^{73} +2.25894 q^{74} +1.90055 q^{75} +2.97835 q^{77} +11.3698 q^{78} -8.89241 q^{79} +3.81856 q^{80} -10.4616 q^{81} -24.4104 q^{82} -9.60447 q^{83} +12.2646 q^{84} -0.0389621 q^{85} -10.0140 q^{86} +17.7280 q^{87} +0.169289 q^{88} +8.74675 q^{89} -1.23738 q^{90} +9.15035 q^{91} +8.10067 q^{92} +17.8231 q^{93} +16.2044 q^{94} -15.3397 q^{96} -7.78824 q^{97} +5.17848 q^{98} +0.589543 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 3 q^{3} + 6 q^{4} - 9 q^{5} - 12 q^{6} - 12 q^{8} + 6 q^{9}+O(q^{10}) $ 9 * q + 3 * q^3 + 6 * q^4 - 9 * q^5 - 12 * q^6 - 12 * q^8 + 6 * q^9	$ 9 q + 3 q^{3} + 6 q^{4} - 9 q^{5} - 12 q^{6} - 12 q^{8} + 6 q^{9} + 6 q^{12} - 3 q^{13} + 12 q^{14} - 3 q^{15} - 12 q^{16} - 9 q^{17} + 6 q^{18} - 6 q^{20} + 12 q^{21} + 12 q^{22} + 15 q^{24} + 9 q^{25} + 21 q^{26} + 6 q^{27} - 15 q^{28} + 15 q^{29} + 12 q^{30} + 30 q^{31} - 9 q^{32} + 9 q^{33} - 6 q^{36} + 30 q^{37} + 6 q^{39} + 12 q^{40} + 18 q^{41} + 36 q^{42} - 6 q^{43} - 24 q^{44} - 6 q^{45} + 21 q^{46} + 21 q^{47} + 15 q^{48} + 3 q^{49} + 18 q^{51} - 3 q^{52} - 9 q^{53} - 9 q^{54} + 36 q^{56} + 18 q^{58} + 27 q^{59} - 6 q^{60} + 12 q^{61} - 6 q^{62} - 15 q^{63} + 24 q^{64} + 3 q^{65} + 3 q^{66} + 36 q^{67} + 3 q^{68} + 27 q^{69} - 12 q^{70} - 6 q^{71} + 12 q^{72} - 9 q^{73} - 9 q^{74} + 3 q^{75} + 12 q^{77} + 54 q^{78} + 45 q^{79} + 12 q^{80} - 15 q^{81} - 48 q^{82} - 12 q^{84} + 9 q^{85} - 9 q^{86} + 45 q^{87} + 39 q^{88} - 9 q^{89} - 6 q^{90} + 51 q^{91} - 54 q^{92} + 9 q^{93} + 33 q^{94} - 9 q^{96} + 45 q^{97} + 33 q^{98} + 12 q^{99}+O(q^{100}) $ 9 * q + 3 * q^3 + 6 * q^4 - 9 * q^5 - 12 * q^6 - 12 * q^8 + 6 * q^9 + 6 * q^12 - 3 * q^13 + 12 * q^14 - 3 * q^15 - 12 * q^16 - 9 * q^17 + 6 * q^18 - 6 * q^20 + 12 * q^21 + 12 * q^22 + 15 * q^24 + 9 * q^25 + 21 * q^26 + 6 * q^27 - 15 * q^28 + 15 * q^29 + 12 * q^30 + 30 * q^31 - 9 * q^32 + 9 * q^33 - 6 * q^36 + 30 * q^37 + 6 * q^39 + 12 * q^40 + 18 * q^41 + 36 * q^42 - 6 * q^43 - 24 * q^44 - 6 * q^45 + 21 * q^46 + 21 * q^47 + 15 * q^48 + 3 * q^49 + 18 * q^51 - 3 * q^52 - 9 * q^53 - 9 * q^54 + 36 * q^56 + 18 * q^58 + 27 * q^59 - 6 * q^60 + 12 * q^61 - 6 * q^62 - 15 * q^63 + 24 * q^64 + 3 * q^65 + 3 * q^66 + 36 * q^67 + 3 * q^68 + 27 * q^69 - 12 * q^70 - 6 * q^71 + 12 * q^72 - 9 * q^73 - 9 * q^74 + 3 * q^75 + 12 * q^77 + 54 * q^78 + 45 * q^79 + 12 * q^80 - 15 * q^81 - 48 * q^82 - 12 * q^84 + 9 * q^85 - 9 * q^86 + 45 * q^87 + 39 * q^88 - 9 * q^89 - 6 * q^90 + 51 * q^91 - 54 * q^92 + 9 * q^93 + 33 * q^94 - 9 * q^96 + 45 * q^97 + 33 * q^98 + 12 * 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 $

$2$	2.02162	1.42950	0.714750	−	0.699380i	$-0.246540\pi$
$2$	2.02162	1.42950	0.714750	+	0.699380i	$0.246540\pi$
$3$	1.90055	1.09728	0.548640	−	0.836058i	$-0.315146\pi$
$3$	1.90055	1.09728	0.548640	+	0.836058i	$0.315146\pi$
$4$	2.08694	1.04347
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.84218	1.56856
$7$	3.09218	1.16873	0.584366	−	0.811490i	$-0.301343\pi$
$7$	3.09218	1.16873	0.584366	+	0.811490i	$0.301343\pi$
$8$	0.175759	0.0621403
$9$	0.612075	0.204025
$10$	−2.02162	−0.639292
$11$	0.963188	0.290412	0.145206	−	0.989401i	$-0.453615\pi$
$11$	0.963188	0.290412	0.145206	+	0.989401i	$0.453615\pi$
$12$	3.96633	1.14498
$13$	2.95920	0.820733	0.410367	−	0.911921i	$-0.365401\pi$
$13$	2.95920	0.820733	0.410367	+	0.911921i	$0.365401\pi$
$14$	6.25120	1.67070
$15$	−1.90055	−0.490719
$16$	−3.81856	−0.954640
$17$	0.0389621	0.00944969	0.00472484	−	0.999989i	$-0.498496\pi$
$17$	0.0389621	0.00944969	0.00472484	+	0.999989i	$0.498496\pi$
$18$	1.23738	0.291654
$19$	0	0
$19$	0	0
$20$	−2.08694	−0.466654
$21$	5.87682	1.28243
$22$	1.94720	0.415144
$23$	3.88160	0.809370	0.404685	−	0.914456i	$-0.367381\pi$
$23$	3.88160	0.809370	0.404685	+	0.914456i	$0.367381\pi$
$24$	0.334039	0.0681853
$25$	1.00000	0.200000
$26$	5.98236	1.17324
$27$	−4.53836	−0.873408
$28$	6.45319	1.21954
$29$	9.32783	1.73213	0.866067	−	0.499928i	$-0.166640\pi$
$29$	9.32783	1.73213	0.866067	+	0.499928i	$0.166640\pi$
$30$	−3.84218	−0.701483
$31$	9.37788	1.68432	0.842158	−	0.539231i	$-0.181285\pi$
$31$	9.37788	1.68432	0.842158	+	0.539231i	$0.181285\pi$
$32$	−8.07119	−1.42680
$33$	1.83058	0.318664
$34$	0.0787664	0.0135083
$35$	−3.09218	−0.522673
$36$	1.27736	0.212894
$37$	1.11739	0.183698	0.0918491	−	0.995773i	$-0.470722\pi$
$37$	1.11739	0.183698	0.0918491	+	0.995773i	$0.470722\pi$
$38$	0	0
$39$	5.62409	0.900575
$40$	−0.175759	−0.0277900
$41$	−12.0747	−1.88575	−0.942873	−	0.333152i	$-0.891888\pi$
$41$	−12.0747	−1.88575	−0.942873	+	0.333152i	$0.891888\pi$
$42$	11.8807	1.83323
$43$	−4.95348	−0.755399	−0.377699	−	0.925928i	$-0.623285\pi$
$43$	−4.95348	−0.755399	−0.377699	+	0.925928i	$0.623285\pi$
$44$	2.01012	0.303036
$45$	−0.612075	−0.0912427
$46$	7.84711	1.15699
$47$	8.01557	1.16919	0.584595	−	0.811325i	$-0.301253\pi$
$47$	8.01557	1.16919	0.584595	+	0.811325i	$0.301253\pi$
$48$	−7.25735	−1.04751
$49$	2.56155	0.365936
$50$	2.02162	0.285900
$51$	0.0740492	0.0103690
$52$	6.17566	0.856410
$53$	−6.05981	−0.832379	−0.416189	−	0.909278i	$-0.636635\pi$
$53$	−6.05981	−0.832379	−0.416189	+	0.909278i	$0.636635\pi$
$54$	−9.17483	−1.24854
$55$	−0.963188	−0.129876
$56$	0.543479	0.0726254
$57$	0	0
$58$	18.8573	2.47609
$59$	−2.77465	−0.361229	−0.180615	−	0.983554i	$-0.557809\pi$
$59$	−2.77465	−0.361229	−0.180615	+	0.983554i	$0.557809\pi$
$60$	−3.96633	−0.512050
$61$	−10.0302	−1.28424	−0.642119	−	0.766605i	$-0.721945\pi$
$61$	−10.0302	−1.28424	−0.642119	+	0.766605i	$0.721945\pi$
$62$	18.9585	2.40773
$63$	1.89264	0.238451
$64$	−8.67975	−1.08497
$65$	−2.95920	−0.367043
$66$	3.70074	0.455530
$67$	−9.34881	−1.14214	−0.571070	−	0.820902i	$-0.693471\pi$
$67$	−9.34881	−1.14214	−0.571070	+	0.820902i	$0.693471\pi$
$68$	0.0813115	0.00986047
$69$	7.37716	0.888106
$70$	−6.25120	−0.747161
$71$	−12.5894	−1.49409	−0.747043	−	0.664775i	$-0.768527\pi$
$71$	−12.5894	−1.49409	−0.747043	+	0.664775i	$0.768527\pi$
$72$	0.107578	0.0126782
$73$	0.897116	0.104999	0.0524997	−	0.998621i	$-0.483281\pi$
$73$	0.897116	0.104999	0.0524997	+	0.998621i	$0.483281\pi$
$74$	2.25894	0.262597
$75$	1.90055	0.219456
$76$	0	0
$77$	2.97835	0.339414
$78$	11.3698	1.28737
$79$	−8.89241	−1.00047	−0.500237	−	0.865888i	$-0.666754\pi$
$79$	−8.89241	−1.00047	−0.500237	+	0.865888i	$0.666754\pi$
$80$	3.81856	0.426928
$81$	−10.4616	−1.16240
$82$	−24.4104	−2.69567
$83$	−9.60447	−1.05423	−0.527114	−	0.849795i	$-0.676726\pi$
$83$	−9.60447	−1.05423	−0.527114	+	0.849795i	$0.676726\pi$
$84$	12.2646	1.33817
$85$	−0.0389621	−0.00422603
$86$	−10.0140	−1.07984
$87$	17.7280	1.90064
$88$	0.169289	0.0180463
$89$	8.74675	0.927153	0.463577	−	0.886057i	$-0.346566\pi$
$89$	8.74675	0.927153	0.463577	+	0.886057i	$0.346566\pi$
$90$	−1.23738	−0.130431
$91$	9.15035	0.959218
$92$	8.10067	0.844553
$93$	17.8231	1.84817
$94$	16.2044	1.67136
$95$	0	0
$96$	−15.3397	−1.56560
$97$	−7.78824	−0.790776	−0.395388	−	0.918514i	$-0.629390\pi$
$97$	−7.78824	−0.790776	−0.395388	+	0.918514i	$0.629390\pi$
$98$	5.17848	0.523105
$99$	0.589543	0.0592513
$100$	2.08694	0.208694
$101$	−3.04363	−0.302852	−0.151426	−	0.988469i	$-0.548387\pi$
$101$	−3.04363	−0.302852	−0.151426	+	0.988469i	$0.548387\pi$
$102$	0.149699	0.0148224
$103$	0.328573	0.0323753	0.0161876	−	0.999869i	$-0.494847\pi$
$103$	0.328573	0.0323753	0.0161876	+	0.999869i	$0.494847\pi$
$104$	0.520106	0.0510006
$105$	−5.87682	−0.573519
$106$	−12.2506	−1.18989
$107$	12.7873	1.23620	0.618099	−	0.786101i	$-0.287903\pi$
$107$	12.7873	1.23620	0.618099	+	0.786101i	$0.287903\pi$
$108$	−9.47129	−0.911375
$109$	15.2412	1.45984	0.729919	−	0.683534i	$-0.239558\pi$
$109$	15.2412	1.45984	0.729919	+	0.683534i	$0.239558\pi$
$110$	−1.94720	−0.185658
$111$	2.12366	0.201569
$112$	−11.8077	−1.11572
$113$	−2.56380	−0.241182	−0.120591	−	0.992702i	$-0.538479\pi$
$113$	−2.56380	−0.241182	−0.120591	+	0.992702i	$0.538479\pi$
$114$	0	0
$115$	−3.88160	−0.361961
$116$	19.4666	1.80743
$117$	1.81125	0.167450
$118$	−5.60929	−0.516377
$119$	0.120478	0.0110442
$120$	−0.334039	−0.0304934
$121$	−10.0723	−0.915661
$122$	−20.2773	−1.83582
$123$	−22.9485	−2.06919
$124$	19.5711	1.75753
$125$	−1.00000	−0.0894427
$126$	3.82620	0.340865
$127$	15.4761	1.37328	0.686641	−	0.726997i	$-0.259084\pi$
$127$	15.4761	1.37328	0.686641	+	0.726997i	$0.259084\pi$
$128$	−1.40475	−0.124163
$129$	−9.41432	−0.828884
$130$	−5.98236	−0.524688
$131$	0.842204	0.0735837	0.0367919	−	0.999323i	$-0.488286\pi$
$131$	0.842204	0.0735837	0.0367919	+	0.999323i	$0.488286\pi$
$132$	3.82032	0.332516
$133$	0	0
$134$	−18.8997	−1.63269
$135$	4.53836	0.390600
$136$	0.00684795	0.000587206 0
$137$	−5.07379	−0.433483	−0.216742	−	0.976229i	$-0.569543\pi$
$137$	−5.07379	−0.433483	−0.216742	+	0.976229i	$0.569543\pi$
$138$	14.9138	1.26955
$139$	2.73039	0.231589	0.115794	−	0.993273i	$-0.463059\pi$
$139$	2.73039	0.231589	0.115794	+	0.993273i	$0.463059\pi$
$140$	−6.45319	−0.545394
$141$	15.2340	1.28293
$142$	−25.4510	−2.13580
$143$	2.85026	0.238351
$144$	−2.33725	−0.194770
$145$	−9.32783	−0.774634
$146$	1.81363	0.150097
$147$	4.86835	0.401534
$148$	2.33193	0.191684
$149$	−6.64567	−0.544435	−0.272217	−	0.962236i	$-0.587757\pi$
$149$	−6.64567	−0.544435	−0.272217	+	0.962236i	$0.587757\pi$
$150$	3.84218	0.313713
$151$	5.19059	0.422404	0.211202	−	0.977442i	$-0.432262\pi$
$151$	5.19059	0.422404	0.211202	+	0.977442i	$0.432262\pi$
$152$	0	0
$153$	0.0238477	0.00192797
$154$	6.02108	0.485192
$155$	−9.37788	−0.753249
$156$	11.7371	0.939723
$157$	11.6478	0.929598	0.464799	−	0.885416i	$-0.346127\pi$
$157$	11.6478	0.929598	0.464799	+	0.885416i	$0.346127\pi$
$158$	−17.9771	−1.43018
$159$	−11.5169	−0.913353
$160$	8.07119	0.638084
$161$	12.0026	0.945937
$162$	−21.1493	−1.66165
$163$	−0.556796	−0.0436116	−0.0218058	−	0.999762i	$-0.506942\pi$
$163$	−0.556796	−0.0436116	−0.0218058	+	0.999762i	$0.506942\pi$
$164$	−25.1991	−1.96772
$165$	−1.83058	−0.142511
$166$	−19.4166	−1.50702
$167$	−22.1563	−1.71451	−0.857254	−	0.514894i	$-0.827831\pi$
$167$	−22.1563	−1.71451	−0.857254	+	0.514894i	$0.827831\pi$
$168$	1.03291	0.0796904
$169$	−4.24316	−0.326397
$170$	−0.0787664	−0.00604111
$171$	0	0
$172$	−10.3376	−0.788236
$173$	11.4561	0.870994	0.435497	−	0.900190i	$-0.356573\pi$
$173$	11.4561	0.870994	0.435497	+	0.900190i	$0.356573\pi$
$174$	35.8392	2.71696
$175$	3.09218	0.233747
$176$	−3.67799	−0.277239
$177$	−5.27336	−0.396370
$178$	17.6826	1.32537
$179$	−5.96612	−0.445928	−0.222964	−	0.974827i	$-0.571573\pi$
$179$	−5.96612	−0.445928	−0.222964	+	0.974827i	$0.571573\pi$
$180$	−1.27736	−0.0952090
$181$	6.17784	0.459195	0.229597	−	0.973286i	$-0.426259\pi$
$181$	6.17784	0.459195	0.229597	+	0.973286i	$0.426259\pi$
$182$	18.4985	1.37120
$183$	−19.0629	−1.40917
$184$	0.682227	0.0502945
$185$	−1.11739	−0.0821523
$186$	36.0315	2.64196
$187$	0.0375278	0.00274430
$188$	16.7280	1.22002
$189$	−14.0334	−1.02078
$190$	0	0
$191$	−18.6639	−1.35047	−0.675235	−	0.737602i	$-0.735958\pi$
$191$	−18.6639	−1.35047	−0.675235	+	0.737602i	$0.735958\pi$
$192$	−16.4963	−1.19051
$193$	23.9067	1.72084	0.860421	−	0.509583i	$-0.170200\pi$
$193$	23.9067	1.72084	0.860421	+	0.509583i	$0.170200\pi$
$194$	−15.7449	−1.13041
$195$	−5.62409	−0.402749
$196$	5.34580	0.381843
$197$	−6.70152	−0.477463	−0.238732	−	0.971086i	$-0.576732\pi$
$197$	−6.70152	−0.477463	−0.238732	+	0.971086i	$0.576732\pi$
$198$	1.19183	0.0846997
$199$	3.15886	0.223926	0.111963	−	0.993712i	$-0.464286\pi$
$199$	3.15886	0.223926	0.111963	+	0.993712i	$0.464286\pi$
$200$	0.175759	0.0124281
$201$	−17.7678	−1.25325
$202$	−6.15306	−0.432928
$203$	28.8433	2.02440
$204$	0.154536	0.0108197
$205$	12.0747	0.843332
$206$	0.664250	0.0462805
$207$	2.37583	0.165132
$208$	−11.2999	−0.783505
$209$	0	0
$210$	−11.8807	−0.819846
$211$	11.4580	0.788801	0.394401	−	0.918939i	$-0.370952\pi$
$211$	11.4580	0.788801	0.394401	+	0.918939i	$0.370952\pi$
$212$	−12.6465	−0.868562
$213$	−23.9267	−1.63943
$214$	25.8511	1.76714
$215$	4.95348	0.337824
$216$	−0.797659	−0.0542738
$217$	28.9980	1.96852
$218$	30.8118	2.08684
$219$	1.70501	0.115214
$220$	−2.01012	−0.135522
$221$	0.115296	0.00775567
$222$	4.29322	0.288142
$223$	7.51422	0.503189	0.251595	−	0.967833i	$-0.419045\pi$
$223$	7.51422	0.503189	0.251595	+	0.967833i	$0.419045\pi$
$224$	−24.9575	−1.66755
$225$	0.612075	0.0408050
$226$	−5.18302	−0.344769
$227$	4.20184	0.278886	0.139443	−	0.990230i	$-0.455469\pi$
$227$	4.20184	0.278886	0.139443	+	0.990230i	$0.455469\pi$
$228$	0	0
$229$	22.5758	1.49185	0.745927	−	0.666028i	$-0.232007\pi$
$229$	22.5758	1.49185	0.745927	+	0.666028i	$0.232007\pi$
$230$	−7.84711	−0.517423
$231$	5.66048	0.372433
$232$	1.63945	0.107635
$233$	−10.9789	−0.719251	−0.359626	−	0.933097i	$-0.617096\pi$
$233$	−10.9789	−0.719251	−0.359626	+	0.933097i	$0.617096\pi$
$234$	3.66165	0.239370
$235$	−8.01557	−0.522878
$236$	−5.79054	−0.376932
$237$	−16.9004	−1.09780
$238$	0.243560	0.0157876
$239$	−2.72559	−0.176304	−0.0881520	−	0.996107i	$-0.528096\pi$
$239$	−2.72559	−0.176304	−0.0881520	+	0.996107i	$0.528096\pi$
$240$	7.25735	0.468460
$241$	−11.1540	−0.718493	−0.359246	−	0.933243i	$-0.616966\pi$
$241$	−11.1540	−0.718493	−0.359246	+	0.933243i	$0.616966\pi$
$242$	−20.3623	−1.30894
$243$	−6.26765	−0.402070
$244$	−20.9325	−1.34006
$245$	−2.56155	−0.163652
$246$	−46.3930	−2.95791
$247$	0	0
$248$	1.64825	0.104664
$249$	−18.2537	−1.15678
$250$	−2.02162	−0.127858
$251$	−27.3683	−1.72747	−0.863737	−	0.503944i	$-0.831882\pi$
$251$	−27.3683	−1.72747	−0.863737	+	0.503944i	$0.831882\pi$
$252$	3.94983	0.248816
$253$	3.73871	0.235051
$254$	31.2868	1.96311
$255$	−0.0740492	−0.00463714
$256$	14.5196	0.907477
$257$	20.2628	1.26396	0.631980	−	0.774985i	$-0.282243\pi$
$257$	20.2628	1.26396	0.631980	+	0.774985i	$0.282243\pi$
$258$	−19.0322	−1.18489
$259$	3.45517	0.214694
$260$	−6.17566	−0.382998
$261$	5.70933	0.353399
$262$	1.70261	0.105188
$263$	9.56235	0.589640	0.294820	−	0.955553i	$-0.404740\pi$
$263$	9.56235	0.589640	0.294820	+	0.955553i	$0.404740\pi$
$264$	0.321742	0.0198019
$265$	6.05981	0.372251
$266$	0	0
$267$	16.6236	1.01735
$268$	−19.5104	−1.19179
$269$	−4.57455	−0.278915	−0.139458	−	0.990228i	$-0.544536\pi$
$269$	−4.57455	−0.278915	−0.139458	+	0.990228i	$0.544536\pi$
$270$	9.17483	0.558363
$271$	−22.1359	−1.34466	−0.672330	−	0.740252i	$-0.734706\pi$
$271$	−22.1359	−1.34466	−0.672330	+	0.740252i	$0.734706\pi$
$272$	−0.148779	−0.00902105
$273$	17.3907	1.05253
$274$	−10.2573	−0.619665
$275$	0.963188	0.0580824
$276$	15.3957	0.926712
$277$	23.5542	1.41523	0.707617	−	0.706597i	$-0.249770\pi$
$277$	23.5542	1.41523	0.707617	+	0.706597i	$0.249770\pi$
$278$	5.51981	0.331056
$279$	5.73996	0.343643
$280$	−0.543479	−0.0324791
$281$	−10.3229	−0.615815	−0.307907	−	0.951416i	$-0.599629\pi$
$281$	−10.3229	−0.615815	−0.307907	+	0.951416i	$0.599629\pi$
$282$	30.7972	1.83395
$283$	−30.8729	−1.83520	−0.917602	−	0.397501i	$-0.869877\pi$
$283$	−30.8729	−1.83520	−0.917602	+	0.397501i	$0.869877\pi$
$284$	−26.2733	−1.55903
$285$	0	0
$286$	5.76214	0.340722
$287$	−37.3370	−2.20393
$288$	−4.94017	−0.291103
$289$	−16.9985	−0.999911
$290$	−18.8573	−1.10734
$291$	−14.8019	−0.867703
$292$	1.87223	0.109564
$293$	−6.36103	−0.371616	−0.185808	−	0.982586i	$-0.559490\pi$
$293$	−6.36103	−0.371616	−0.185808	+	0.982586i	$0.559490\pi$
$294$	9.84194	0.573993
$295$	2.77465	0.161547
$296$	0.196392	0.0114151
$297$	−4.37130	−0.253648
$298$	−13.4350	−0.778270
$299$	11.4864	0.664276
$300$	3.96633	0.228996
$301$	−15.3170	−0.882859
$302$	10.4934	0.603826
$303$	−5.78456	−0.332314
$304$	0	0
$305$	10.0302	0.574329
$306$	0.0482109	0.00275604
$307$	5.88645	0.335958	0.167979	−	0.985791i	$-0.446276\pi$
$307$	5.88645	0.335958	0.167979	+	0.985791i	$0.446276\pi$
$308$	6.21563	0.354168
$309$	0.624469	0.0355248
$310$	−18.9585	−1.07677
$311$	−25.3885	−1.43965	−0.719825	−	0.694156i	$-0.755778\pi$
$311$	−25.3885	−1.43965	−0.719825	+	0.694156i	$0.755778\pi$
$312$	0.988486	0.0559620
$313$	6.03850	0.341316	0.170658	−	0.985330i	$-0.445411\pi$
$313$	6.03850	0.341316	0.170658	+	0.985330i	$0.445411\pi$
$314$	23.5475	1.32886
$315$	−1.89264	−0.106638
$316$	−18.5579	−1.04396
$317$	−15.8757	−0.891670	−0.445835	−	0.895115i	$-0.647093\pi$
$317$	−15.8757	−0.891670	−0.445835	+	0.895115i	$0.647093\pi$
$318$	−23.2829	−1.30564
$319$	8.98445	0.503033
$320$	8.67975	0.485212
$321$	24.3029	1.35646
$322$	24.2647	1.35222
$323$	0	0
$324$	−21.8327	−1.21293
$325$	2.95920	0.164147
$326$	−1.12563	−0.0623428
$327$	28.9665	1.60185
$328$	−2.12224	−0.117181
$329$	24.7855	1.36647
$330$	−3.70074	−0.203719
$331$	14.1696	0.778829	0.389414	−	0.921063i	$-0.372677\pi$
$331$	14.1696	0.778829	0.389414	+	0.921063i	$0.372677\pi$
$332$	−20.0440	−1.10005
$333$	0.683928	0.0374790
$334$	−44.7916	−2.45089
$335$	9.34881	0.510780
$336$	−22.4410	−1.22426
$337$	2.14993	0.117114	0.0585571	−	0.998284i	$-0.481350\pi$
$337$	2.14993	0.117114	0.0585571	+	0.998284i	$0.481350\pi$
$338$	−8.57806	−0.466585
$339$	−4.87261	−0.264644
$340$	−0.0813115	−0.00440973
$341$	9.03266	0.489146
$342$	0	0
$343$	−13.7245	−0.741051
$344$	−0.870620	−0.0469407
$345$	−7.37716	−0.397173
$346$	23.1599	1.24509
$347$	−11.0525	−0.593329	−0.296664	−	0.954982i	$-0.595874\pi$
$347$	−11.0525	−0.593329	−0.296664	+	0.954982i	$0.595874\pi$
$348$	36.9972	1.98326
$349$	35.3451	1.89198	0.945989	−	0.324199i	$-0.105095\pi$
$349$	35.3451	1.89198	0.945989	+	0.324199i	$0.105095\pi$
$350$	6.25120	0.334141
$351$	−13.4299	−0.716835
$352$	−7.77407	−0.414360
$353$	22.1904	1.18108	0.590538	−	0.807010i	$-0.298916\pi$
$353$	22.1904	1.18108	0.590538	+	0.807010i	$0.298916\pi$
$354$	−10.6607	−0.566611
$355$	12.5894	0.668176
$356$	18.2539	0.967457
$357$	0.228973	0.0121185
$358$	−12.0612	−0.637455
$359$	−9.50861	−0.501845	−0.250923	−	0.968007i	$-0.580734\pi$
$359$	−9.50861	−0.501845	−0.250923	+	0.968007i	$0.580734\pi$
$360$	−0.107578	−0.00566985
$361$	0	0
$362$	12.4892	0.656419
$363$	−19.1428	−1.00474
$364$	19.0962	1.00091
$365$	−0.897116	−0.0469572
$366$	−38.5379	−2.01441
$367$	−2.18321	−0.113963	−0.0569813	−	0.998375i	$-0.518148\pi$
$367$	−2.18321	−0.113963	−0.0569813	+	0.998375i	$0.518148\pi$
$368$	−14.8221	−0.772657
$369$	−7.39060	−0.384739
$370$	−2.25894	−0.117437
$371$	−18.7380	−0.972828
$372$	37.1957	1.92851
$373$	12.3407	0.638977	0.319488	−	0.947590i	$-0.396489\pi$
$373$	12.3407	0.638977	0.319488	+	0.947590i	$0.396489\pi$
$374$	0.0758669	0.00392298
$375$	−1.90055	−0.0981438
$376$	1.40881	0.0726538
$377$	27.6029	1.42162
$378$	−28.3702	−1.45921
$379$	18.5014	0.950352	0.475176	−	0.879891i	$-0.342384\pi$
$379$	18.5014	0.950352	0.475176	+	0.879891i	$0.342384\pi$
$380$	0	0
$381$	29.4130	1.50688
$382$	−37.7312	−1.93050
$383$	11.4322	0.584156	0.292078	−	0.956394i	$-0.405653\pi$
$383$	11.4322	0.584156	0.292078	+	0.956394i	$0.405653\pi$
$384$	−2.66978	−0.136242
$385$	−2.97835	−0.151791
$386$	48.3302	2.45994
$387$	−3.03190	−0.154120
$388$	−16.2536	−0.825151
$389$	12.5237	0.634978	0.317489	−	0.948262i	$-0.397160\pi$
$389$	12.5237	0.634978	0.317489	+	0.948262i	$0.397160\pi$
$390$	−11.3698	−0.575730
$391$	0.151235	0.00764829
$392$	0.450216	0.0227394
$393$	1.60065	0.0807420
$394$	−13.5479	−0.682534
$395$	8.89241	0.447426
$396$	1.23034	0.0618270
$397$	11.7504	0.589734	0.294867	−	0.955538i	$-0.404725\pi$
$397$	11.7504	0.589734	0.294867	+	0.955538i	$0.404725\pi$
$398$	6.38602	0.320102
$399$	0	0
$400$	−3.81856	−0.190928
$401$	14.6418	0.731178	0.365589	−	0.930776i	$-0.380868\pi$
$401$	14.6418	0.731178	0.365589	+	0.930776i	$0.380868\pi$
$402$	−35.9198	−1.79152
$403$	27.7510	1.38237
$404$	−6.35187	−0.316017
$405$	10.4616	0.519841
$406$	58.3101	2.89388
$407$	1.07626	0.0533482
$408$	0.0130148	0.000644330 0
$409$	−12.7478	−0.630338	−0.315169	−	0.949035i	$-0.602061\pi$
$409$	−12.7478	−0.630338	−0.315169	+	0.949035i	$0.602061\pi$
$410$	24.4104	1.20554
$411$	−9.64298	−0.475653
$412$	0.685713	0.0337827
$413$	−8.57972	−0.422180
$414$	4.80302	0.236056
$415$	9.60447	0.471465
$416$	−23.8842	−1.17102
$417$	5.18923	0.254118
$418$	0	0
$419$	2.84601	0.139037	0.0695184	−	0.997581i	$-0.477854\pi$
$419$	2.84601	0.139037	0.0695184	+	0.997581i	$0.477854\pi$
$420$	−12.2646	−0.598450
$421$	−11.1505	−0.543442	−0.271721	−	0.962376i	$-0.587593\pi$
$421$	−11.1505	−0.543442	−0.271721	+	0.962376i	$0.587593\pi$
$422$	23.1637	1.12759
$423$	4.90613	0.238544
$424$	−1.06507	−0.0517242
$425$	0.0389621	0.00188994
$426$	−48.3707	−2.34357
$427$	−31.0152	−1.50093
$428$	26.6864	1.28993
$429$	5.41705	0.261538
$430$	10.0140	0.482920
$431$	14.9363	0.719455	0.359727	−	0.933057i	$-0.382870\pi$
$431$	14.9363	0.719455	0.359727	+	0.933057i	$0.382870\pi$
$432$	17.3300	0.833791
$433$	38.7567	1.86253	0.931265	−	0.364343i	$-0.118706\pi$
$433$	38.7567	1.86253	0.931265	+	0.364343i	$0.118706\pi$
$434$	58.6230	2.81399
$435$	−17.7280	−0.849991
$436$	31.8074	1.52330
$437$	0	0
$438$	3.44688	0.164698
$439$	31.4285	1.50000	0.749999	−	0.661438i	$-0.230054\pi$
$439$	31.4285	1.50000	0.749999	+	0.661438i	$0.230054\pi$
$440$	−0.169289	−0.00807055
$441$	1.56786	0.0746600
$442$	0.233085	0.0110867
$443$	10.6508	0.506036	0.253018	−	0.967462i	$-0.418577\pi$
$443$	10.6508	0.506036	0.253018	+	0.967462i	$0.418577\pi$
$444$	4.43194	0.210331
$445$	−8.74675	−0.414636
$446$	15.1909	0.719309
$447$	−12.6304	−0.597398
$448$	−26.8393	−1.26804
$449$	−4.10400	−0.193680	−0.0968399	−	0.995300i	$-0.530873\pi$
$449$	−4.10400	−0.193680	−0.0968399	+	0.995300i	$0.530873\pi$
$450$	1.23738	0.0583307
$451$	−11.6302	−0.547644
$452$	−5.35049	−0.251666
$453$	9.86495	0.463496
$454$	8.49452	0.398668
$455$	−9.15035	−0.428975
$456$	0	0
$457$	9.25947	0.433140	0.216570	−	0.976267i	$-0.430513\pi$
$457$	9.25947	0.433140	0.216570	+	0.976267i	$0.430513\pi$
$458$	45.6397	2.13260
$459$	−0.176824	−0.00825343
$460$	−8.10067	−0.377696
$461$	6.64611	0.309540	0.154770	−	0.987951i	$-0.450536\pi$
$461$	6.64611	0.309540	0.154770	+	0.987951i	$0.450536\pi$
$462$	11.4433	0.532392
$463$	22.2948	1.03613	0.518064	−	0.855342i	$-0.326653\pi$
$463$	22.2948	1.03613	0.518064	+	0.855342i	$0.326653\pi$
$464$	−35.6189	−1.65357
$465$	−17.8231	−0.826526
$466$	−22.1951	−1.02817
$467$	−15.4739	−0.716048	−0.358024	−	0.933712i	$-0.616549\pi$
$467$	−15.4739	−0.716048	−0.358024	+	0.933712i	$0.616549\pi$
$468$	3.77997	0.174729
$469$	−28.9082	−1.33486
$470$	−16.2044	−0.747454
$471$	22.1372	1.02003
$472$	−0.487671	−0.0224469
$473$	−4.77113	−0.219377
$474$	−34.1662	−1.56931
$475$	0	0
$476$	0.251429	0.0115242
$477$	−3.70906	−0.169826
$478$	−5.51011	−0.252026
$479$	32.2057	1.47152	0.735758	−	0.677245i	$-0.236826\pi$
$479$	32.2057	1.47152	0.735758	+	0.677245i	$0.236826\pi$
$480$	15.3397	0.700157
$481$	3.30658	0.150767
$482$	−22.5491	−1.02709
$483$	22.8115	1.03796
$484$	−21.0202	−0.955465
$485$	7.78824	0.353646
$486$	−12.6708	−0.574759
$487$	3.65139	0.165460	0.0827301	−	0.996572i	$-0.473636\pi$
$487$	3.65139	0.165460	0.0827301	+	0.996572i	$0.473636\pi$
$488$	−1.76291	−0.0798030
$489$	−1.05822	−0.0478542
$490$	−5.17848	−0.233940
$491$	4.54862	0.205276	0.102638	−	0.994719i	$-0.467272\pi$
$491$	4.54862	0.205276	0.102638	+	0.994719i	$0.467272\pi$
$492$	−47.8921	−2.15914
$493$	0.363431	0.0163681
$494$	0	0
$495$	−0.589543	−0.0264980
$496$	−35.8100	−1.60792
$497$	−38.9286	−1.74619
$498$	−36.9021	−1.65362
$499$	−21.8234	−0.976950	−0.488475	−	0.872578i	$-0.662447\pi$
$499$	−21.8234	−0.976950	−0.488475	+	0.872578i	$0.662447\pi$
$500$	−2.08694	−0.0933308
$501$	−42.1091	−1.88130
$502$	−55.3283	−2.46942
$503$	−24.7388	−1.10305	−0.551524	−	0.834159i	$-0.685954\pi$
$503$	−24.7388	−1.10305	−0.551524	+	0.834159i	$0.685954\pi$
$504$	0.332650	0.0148174
$505$	3.04363	0.135440
$506$	7.55825	0.336005
$507$	−8.06433	−0.358149
$508$	32.2977	1.43298
$509$	17.3491	0.768987	0.384494	−	0.923128i	$-0.374376\pi$
$509$	17.3491	0.768987	0.384494	+	0.923128i	$0.374376\pi$
$510$	−0.149699	−0.00662879
$511$	2.77404	0.122716
$512$	32.1626	1.42140
$513$	0	0
$514$	40.9637	1.80683
$515$	−0.328573	−0.0144787
$516$	−19.6471	−0.864916
$517$	7.72050	0.339547
$518$	6.98504	0.306905
$519$	21.7729	0.955725
$520$	−0.520106	−0.0228082
$521$	−0.456675	−0.0200073	−0.0100036	−	0.999950i	$-0.503184\pi$
$521$	−0.456675	−0.0200073	−0.0100036	+	0.999950i	$0.503184\pi$
$522$	11.5421	0.505183
$523$	37.7965	1.65273	0.826363	−	0.563138i	$-0.190406\pi$
$523$	37.7965	1.65273	0.826363	+	0.563138i	$0.190406\pi$
$524$	1.75763	0.0767824
$525$	5.87682	0.256486
$526$	19.3314	0.842890
$527$	0.365381	0.0159163
$528$	−6.99019	−0.304209
$529$	−7.93318	−0.344921
$530$	12.2506	0.532133
$531$	−1.69830	−0.0736998
$532$	0	0
$533$	−35.7313	−1.54769
$534$	33.6066	1.45430
$535$	−12.7873	−0.552844
$536$	−1.64314	−0.0709729
$537$	−11.3389	−0.489309
$538$	−9.24800	−0.398710
$539$	2.46726	0.106272
$540$	9.47129	0.407579
$541$	−21.1299	−0.908444	−0.454222	−	0.890889i	$-0.650083\pi$
$541$	−21.1299	−0.908444	−0.454222	+	0.890889i	$0.650083\pi$
$542$	−44.7503	−1.92219
$543$	11.7413	0.503866
$544$	−0.314470	−0.0134828
$545$	−15.2412	−0.652859
$546$	35.1573	1.50459
$547$	12.5424	0.536276	0.268138	−	0.963381i	$-0.413592\pi$
$547$	12.5424	0.536276	0.268138	+	0.963381i	$0.413592\pi$
$548$	−10.5887	−0.452327
$549$	−6.13925	−0.262017
$550$	1.94720	0.0830288
$551$	0	0
$552$	1.29660	0.0551872
$553$	−27.4969	−1.16929
$554$	47.6175	2.02308
$555$	−2.12366	−0.0901442
$556$	5.69816	0.241656
$557$	−32.0252	−1.35695	−0.678475	−	0.734623i	$-0.737359\pi$
$557$	−32.0252	−1.35695	−0.678475	+	0.734623i	$0.737359\pi$
$558$	11.6040	0.491237
$559$	−14.6583	−0.619981
$560$	11.8077	0.498965
$561$	0.0713233	0.00301127
$562$	−20.8690	−0.880307
$563$	−19.5807	−0.825228	−0.412614	−	0.910906i	$-0.635384\pi$
$563$	−19.5807	−0.825228	−0.412614	+	0.910906i	$0.635384\pi$
$564$	31.7923	1.33870
$565$	2.56380	0.107860
$566$	−62.4132	−2.62342
$567$	−32.3491	−1.35853
$568$	−2.21270	−0.0928430
$569$	18.6525	0.781953	0.390977	−	0.920401i	$-0.372137\pi$
$569$	18.6525	0.781953	0.390977	+	0.920401i	$0.372137\pi$
$570$	0	0
$571$	−0.460181	−0.0192580	−0.00962899	−	0.999954i	$-0.503065\pi$
$571$	−0.460181	−0.0192580	−0.00962899	+	0.999954i	$0.503065\pi$
$572$	5.94832	0.248712
$573$	−35.4716	−1.48185
$574$	−75.4812	−3.15052
$575$	3.88160	0.161874
$576$	−5.31265	−0.221361
$577$	11.7478	0.489069	0.244534	−	0.969641i	$-0.421365\pi$
$577$	11.7478	0.489069	0.244534	+	0.969641i	$0.421365\pi$
$578$	−34.3644	−1.42937
$579$	45.4358	1.88825
$580$	−19.4666	−0.808307
$581$	−29.6987	−1.23211
$582$	−29.9238	−1.24038
$583$	−5.83673	−0.241733
$584$	0.157676	0.00652470
$585$	−1.81125	−0.0748859
$586$	−12.8596	−0.531224
$587$	−4.90039	−0.202261	−0.101130	−	0.994873i	$-0.532246\pi$
$587$	−4.90039	−0.202261	−0.101130	+	0.994873i	$0.532246\pi$
$588$	10.1599	0.418989
$589$	0	0
$590$	5.60929	0.230931
$591$	−12.7365	−0.523911
$592$	−4.26683	−0.175366
$593$	−18.4976	−0.759606	−0.379803	−	0.925067i	$-0.624008\pi$
$593$	−18.4976	−0.759606	−0.379803	+	0.925067i	$0.624008\pi$
$594$	−8.83709	−0.362590
$595$	−0.120478	−0.00493910
$596$	−13.8691	−0.568101
$597$	6.00357	0.245710
$598$	23.2211	0.949583
$599$	21.4258	0.875433	0.437717	−	0.899113i	$-0.355787\pi$
$599$	21.4258	0.875433	0.437717	+	0.899113i	$0.355787\pi$
$600$	0.334039	0.0136371
$601$	−30.0390	−1.22532	−0.612659	−	0.790348i	$-0.709900\pi$
$601$	−30.0390	−1.22532	−0.612659	+	0.790348i	$0.709900\pi$
$602$	−30.9652	−1.26205
$603$	−5.72217	−0.233025
$604$	10.8324	0.440766
$605$	10.0723	0.409496
$606$	−11.6942	−0.475043
$607$	−29.3882	−1.19283	−0.596415	−	0.802676i	$-0.703409\pi$
$607$	−29.3882	−1.19283	−0.596415	+	0.802676i	$0.703409\pi$
$608$	0	0
$609$	54.8180	2.22134
$610$	20.2773	0.821003
$611$	23.7196	0.959593
$612$	0.0497687	0.00201178
$613$	−5.51121	−0.222596	−0.111298	−	0.993787i	$-0.535501\pi$
$613$	−5.51121	−0.222596	−0.111298	+	0.993787i	$0.535501\pi$
$614$	11.9002	0.480251
$615$	22.9485	0.925371
$616$	0.523472	0.0210913
$617$	45.9066	1.84813	0.924065	−	0.382234i	$-0.124845\pi$
$617$	45.9066	1.84813	0.924065	+	0.382234i	$0.124845\pi$
$618$	1.26244	0.0507827
$619$	−0.478605	−0.0192368	−0.00961839	−	0.999954i	$-0.503062\pi$
$619$	−0.478605	−0.0192368	−0.00961839	+	0.999954i	$0.503062\pi$
$620$	−19.5711	−0.785993
$621$	−17.6161	−0.706910
$622$	−51.3258	−2.05798
$623$	27.0465	1.08359
$624$	−21.4759	−0.859725
$625$	1.00000	0.0400000
$626$	12.2075	0.487912
$627$	0	0
$628$	24.3083	0.970008
$629$	0.0435359	0.00173589
$630$	−3.82620	−0.152440
$631$	16.8542	0.670954	0.335477	−	0.942048i	$-0.391103\pi$
$631$	16.8542	0.670954	0.335477	+	0.942048i	$0.391103\pi$
$632$	−1.56292	−0.0621698
$633$	21.7765	0.865536
$634$	−32.0947	−1.27464
$635$	−15.4761	−0.614150
$636$	−24.0352	−0.953056
$637$	7.58013	0.300336
$638$	18.1631	0.719085
$639$	−7.70566	−0.304831
$640$	1.40475	0.0555275
$641$	−22.9012	−0.904542	−0.452271	−	0.891880i	$-0.649386\pi$
$641$	−22.9012	−0.904542	−0.452271	+	0.891880i	$0.649386\pi$
$642$	49.1312	1.93905
$643$	−8.58168	−0.338429	−0.169214	−	0.985579i	$-0.554123\pi$
$643$	−8.58168	−0.338429	−0.169214	+	0.985579i	$0.554123\pi$
$644$	25.0487	0.987057
$645$	9.41432	0.370688
$646$	0	0
$647$	−27.2647	−1.07188	−0.535942	−	0.844255i	$-0.680043\pi$
$647$	−27.2647	−1.07188	−0.535942	+	0.844255i	$0.680043\pi$
$648$	−1.83872	−0.0722318
$649$	−2.67251	−0.104905
$650$	5.98236	0.234648
$651$	55.1121	2.16001
$652$	−1.16200	−0.0455074
$653$	−26.2598	−1.02763	−0.513813	−	0.857902i	$-0.671767\pi$
$653$	−26.2598	−1.02763	−0.513813	+	0.857902i	$0.671767\pi$
$654$	58.5592	2.28985
$655$	−0.842204	−0.0329076
$656$	46.1079	1.80021
$657$	0.549102	0.0214225
$658$	50.1069	1.95337
$659$	23.0115	0.896399	0.448200	−	0.893934i	$-0.352065\pi$
$659$	23.0115	0.896399	0.448200	+	0.893934i	$0.352065\pi$
$660$	−3.82032	−0.148706
$661$	−30.5998	−1.19019	−0.595097	−	0.803654i	$-0.702886\pi$
$661$	−30.5998	−1.19019	−0.595097	+	0.803654i	$0.702886\pi$
$662$	28.6454	1.11334
$663$	0.219126	0.00851015
$664$	−1.68807	−0.0655100
$665$	0	0
$666$	1.38264	0.0535763
$667$	36.2069	1.40194
$668$	−46.2389	−1.78904
$669$	14.2811	0.552140
$670$	18.8997	0.730160
$671$	−9.66099	−0.372959
$672$	−47.4330	−1.82977
$673$	37.8667	1.45966	0.729828	−	0.683631i	$-0.239600\pi$
$673$	37.8667	1.45966	0.729828	+	0.683631i	$0.239600\pi$
$674$	4.34634	0.167415
$675$	−4.53836	−0.174682
$676$	−8.85523	−0.340586
$677$	43.6943	1.67931	0.839654	−	0.543122i	$-0.182758\pi$
$677$	43.6943	1.67931	0.839654	+	0.543122i	$0.182758\pi$
$678$	−9.85056	−0.378309
$679$	−24.0826	−0.924206
$680$	−0.00684795	−0.000262607 0
$681$	7.98579	0.306016
$682$	18.2606	0.699234
$683$	−15.0878	−0.577320	−0.288660	−	0.957432i	$-0.593210\pi$
$683$	−15.0878	−0.577320	−0.288660	+	0.957432i	$0.593210\pi$
$684$	0	0
$685$	5.07379	0.193860
$686$	−27.7456	−1.05933
$687$	42.9064	1.63698
$688$	18.9152	0.721134
$689$	−17.9322	−0.683161
$690$	−14.9138	−0.567759
$691$	10.7207	0.407834	0.203917	−	0.978988i	$-0.434633\pi$
$691$	10.7207	0.407834	0.203917	+	0.978988i	$0.434633\pi$
$692$	23.9083	0.908856
$693$	1.82297	0.0692489
$694$	−22.3439	−0.848164
$695$	−2.73039	−0.103570
$696$	3.11585	0.118106
$697$	−0.470454	−0.0178197
$698$	71.4542	2.70458
$699$	−20.8659	−0.789220
$700$	6.45319	0.243907
$701$	24.5411	0.926904	0.463452	−	0.886122i	$-0.346611\pi$
$701$	24.5411	0.926904	0.463452	+	0.886122i	$0.346611\pi$
$702$	−27.1501	−1.02472
$703$	0	0
$704$	−8.36023	−0.315088
$705$	−15.2340	−0.573744
$706$	44.8605	1.68835
$707$	−9.41144	−0.353954
$708$	−11.0052	−0.413600
$709$	−42.8046	−1.60756	−0.803781	−	0.594925i	$-0.797182\pi$
$709$	−42.8046	−1.60756	−0.803781	+	0.594925i	$0.797182\pi$
$710$	25.4510	0.955158
$711$	−5.44282	−0.204122
$712$	1.53732	0.0576136
$713$	36.4012	1.36323
$714$	0.462896	0.0173235
$715$	−2.85026	−0.106594
$716$	−12.4509	−0.465313
$717$	−5.18011	−0.193455
$718$	−19.2228	−0.717388
$719$	21.2712	0.793283	0.396641	−	0.917974i	$-0.370176\pi$
$719$	21.2712	0.793283	0.396641	+	0.917974i	$0.370176\pi$
$720$	2.33725	0.0871040
$721$	1.01601	0.0378381
$722$	0	0
$723$	−21.1987	−0.788388
$724$	12.8928	0.479156
$725$	9.32783	0.346427
$726$	−38.6995	−1.43627
$727$	−10.5343	−0.390696	−0.195348	−	0.980734i	$-0.562584\pi$
$727$	−10.5343	−0.390696	−0.195348	+	0.980734i	$0.562584\pi$
$728$	1.60826	0.0596061
$729$	19.4728	0.721215
$730$	−1.81363	−0.0671253
$731$	−0.192998	−0.00713828
$732$	−39.7831	−1.47043
$733$	−25.0892	−0.926692	−0.463346	−	0.886178i	$-0.653351\pi$
$733$	−25.0892	−0.926692	−0.463346	+	0.886178i	$0.653351\pi$
$734$	−4.41362	−0.162910
$735$	−4.86835	−0.179572
$736$	−31.3291	−1.15481
$737$	−9.00466	−0.331691
$738$	−14.9410	−0.549985
$739$	28.4679	1.04721	0.523604	−	0.851962i	$-0.324587\pi$
$739$	28.4679	1.04721	0.523604	+	0.851962i	$0.324587\pi$
$740$	−2.33193	−0.0857235
$741$	0	0
$742$	−37.8811	−1.39066
$743$	10.1611	0.372774	0.186387	−	0.982476i	$-0.440322\pi$
$743$	10.1611	0.372774	0.186387	+	0.982476i	$0.440322\pi$
$744$	3.13257	0.114846
$745$	6.64567	0.243479
$746$	24.9482	0.913417
$747$	−5.87865	−0.215089
$748$	0.0783182	0.00286360
$749$	39.5407	1.44478
$750$	−3.84218	−0.140297
$751$	25.6900	0.937440	0.468720	−	0.883347i	$-0.344715\pi$
$751$	25.6900	0.937440	0.468720	+	0.883347i	$0.344715\pi$
$752$	−30.6079	−1.11616
$753$	−52.0148	−1.89552
$754$	55.8024	2.03221
$755$	−5.19059	−0.188905
$756$	−29.2869	−1.06515
$757$	−31.5781	−1.14773	−0.573863	−	0.818952i	$-0.694556\pi$
$757$	−31.5781	−1.14773	−0.573863	+	0.818952i	$0.694556\pi$
$758$	37.4027	1.35853
$759$	7.10559	0.257917
$760$	0	0
$761$	−3.42183	−0.124041	−0.0620207	−	0.998075i	$-0.519754\pi$
$761$	−3.42183	−0.124041	−0.0620207	+	0.998075i	$0.519754\pi$
$762$	59.4619	2.15408
$763$	47.1283	1.70616
$764$	−38.9504	−1.40918
$765$	−0.0238477	−0.000862215 0
$766$	23.1115	0.835052
$767$	−8.21074	−0.296473
$768$	27.5952	0.995757
$769$	−28.5086	−1.02805	−0.514024	−	0.857776i	$-0.671846\pi$
$769$	−28.5086	−1.02805	−0.514024	+	0.857776i	$0.671846\pi$
$770$	−6.02108	−0.216985
$771$	38.5104	1.38692
$772$	49.8919	1.79565
$773$	−1.42585	−0.0512844	−0.0256422	−	0.999671i	$-0.508163\pi$
$773$	−1.42585	−0.0512844	−0.0256422	+	0.999671i	$0.508163\pi$
$774$	−6.12934	−0.220315
$775$	9.37788	0.336863
$776$	−1.36886	−0.0491391
$777$	6.56672	0.235580
$778$	25.3182	0.907701
$779$	0	0
$780$	−11.7371	−0.420257
$781$	−12.1260	−0.433901
$782$	0.305740	0.0109332
$783$	−42.3331	−1.51286
$784$	−9.78144	−0.349337
$785$	−11.6478	−0.415729
$786$	3.23590	0.115421
$787$	−24.3199	−0.866912	−0.433456	−	0.901175i	$-0.642706\pi$
$787$	−24.3199	−0.866912	−0.433456	+	0.901175i	$0.642706\pi$
$788$	−13.9857	−0.498219
$789$	18.1737	0.647001
$790$	17.9771	0.639595
$791$	−7.92771	−0.281877
$792$	0.103618	0.00368189
$793$	−29.6814	−1.05402
$794$	23.7547	0.843024
$795$	11.5169	0.408464
$796$	6.59236	0.233660
$797$	−33.5714	−1.18916	−0.594580	−	0.804037i	$-0.702681\pi$
$797$	−33.5714	−1.18916	−0.594580	+	0.804037i	$0.702681\pi$
$798$	0	0
$799$	0.312303	0.0110485
$800$	−8.07119	−0.285360
$801$	5.35366	0.189162
$802$	29.6002	1.04522
$803$	0.864091	0.0304931
$804$	−37.0804	−1.30773
$805$	−12.0026	−0.423036
$806$	56.1019	1.97610
$807$	−8.69415	−0.306049
$808$	−0.534946	−0.0188193
$809$	18.2407	0.641311	0.320655	−	0.947196i	$-0.396097\pi$
$809$	18.2407	0.641311	0.320655	+	0.947196i	$0.396097\pi$
$810$	21.1493	0.743112
$811$	36.5439	1.28323	0.641615	−	0.767027i	$-0.278265\pi$
$811$	36.5439	1.28323	0.641615	+	0.767027i	$0.278265\pi$
$812$	60.1942	2.11240
$813$	−42.0703	−1.47547
$814$	2.17578	0.0762612
$815$	0.556796	0.0195037
$816$	−0.282761	−0.00989863
$817$	0	0
$818$	−25.7712	−0.901069
$819$	5.60070	0.195704
$820$	25.1991	0.879991
$821$	10.6240	0.370781	0.185390	−	0.982665i	$-0.440645\pi$
$821$	10.6240	0.370781	0.185390	+	0.982665i	$0.440645\pi$
$822$	−19.4944	−0.679946
$823$	−37.0620	−1.29190	−0.645950	−	0.763380i	$-0.723538\pi$
$823$	−37.0620	−1.29190	−0.645950	+	0.763380i	$0.723538\pi$
$824$	0.0577498	0.00201181
$825$	1.83058	0.0637327
$826$	−17.3449	−0.603507
$827$	−27.8197	−0.967385	−0.483693	−	0.875238i	$-0.660705\pi$
$827$	−27.8197	−0.967385	−0.483693	+	0.875238i	$0.660705\pi$
$828$	4.95821	0.172310
$829$	13.8198	0.479982	0.239991	−	0.970775i	$-0.422855\pi$
$829$	13.8198	0.479982	0.239991	+	0.970775i	$0.422855\pi$
$830$	19.4166	0.673959
$831$	44.7658	1.55291
$832$	−25.6851	−0.890469
$833$	0.0998033	0.00345798
$834$	10.4906	0.363261
$835$	22.1563	0.766751
$836$	0	0
$837$	−42.5602	−1.47110
$838$	5.75355	0.198753
$839$	6.42771	0.221909	0.110955	−	0.993825i	$-0.464609\pi$
$839$	6.42771	0.221909	0.110955	+	0.993825i	$0.464609\pi$
$840$	−1.03291	−0.0356386
$841$	58.0084	2.00029
$842$	−22.5421	−0.776850
$843$	−19.6192	−0.675721
$844$	23.9122	0.823090
$845$	4.24316	0.145969
$846$	9.91831	0.340999
$847$	−31.1452	−1.07016
$848$	23.1397	0.794622
$849$	−58.6754	−2.01373
$850$	0.0787664	0.00270167
$851$	4.33727	0.148680
$852$	−49.9337	−1.71070
$853$	26.3952	0.903753	0.451876	−	0.892081i	$-0.350755\pi$
$853$	26.3952	0.903753	0.451876	+	0.892081i	$0.350755\pi$
$854$	−62.7009	−2.14558
$855$	0	0
$856$	2.24749	0.0768177
$857$	−17.0307	−0.581757	−0.290878	−	0.956760i	$-0.593947\pi$
$857$	−17.0307	−0.581757	−0.290878	+	0.956760i	$0.593947\pi$
$858$	10.9512	0.373868
$859$	24.7212	0.843476	0.421738	−	0.906718i	$-0.361420\pi$
$859$	24.7212	0.843476	0.421738	+	0.906718i	$0.361420\pi$
$860$	10.3376	0.352510
$861$	−70.9607	−2.41833
$862$	30.1954	1.02846
$863$	1.03890	0.0353646	0.0176823	−	0.999844i	$-0.494371\pi$
$863$	1.03890	0.0353646	0.0176823	+	0.999844i	$0.494371\pi$
$864$	36.6300	1.24618
$865$	−11.4561	−0.389521
$866$	78.3513	2.66249
$867$	−32.3064	−1.09718
$868$	60.5172	2.05409
$869$	−8.56506	−0.290550
$870$	−35.8392	−1.21506
$871$	−27.6650	−0.937391
$872$	2.67877	0.0907147
$873$	−4.76699	−0.161338
$874$	0	0
$875$	−3.09218	−0.104535
$876$	3.55825	0.120222
$877$	−21.2022	−0.715948	−0.357974	−	0.933732i	$-0.616532\pi$
$877$	−21.2022	−0.715948	−0.357974	+	0.933732i	$0.616532\pi$
$878$	63.5364	2.14425
$879$	−12.0894	−0.407767
$880$	3.67799	0.123985
$881$	15.6819	0.528338	0.264169	−	0.964476i	$-0.414902\pi$
$881$	15.6819	0.528338	0.264169	+	0.964476i	$0.414902\pi$
$882$	3.16962	0.106727
$883$	19.6406	0.660960	0.330480	−	0.943813i	$-0.392789\pi$
$883$	19.6406	0.660960	0.330480	+	0.943813i	$0.392789\pi$
$884$	0.240617	0.00809281
$885$	5.27336	0.177262
$886$	21.5319	0.723378
$887$	−24.7805	−0.832049	−0.416025	−	0.909353i	$-0.636577\pi$
$887$	−24.7805	−0.832049	−0.416025	+	0.909353i	$0.636577\pi$
$888$	0.373252	0.0125255
$889$	47.8548	1.60500
$890$	−17.6826	−0.592721
$891$	−10.0765	−0.337575
$892$	15.6817	0.525063
$893$	0	0
$894$	−25.5339	−0.853980
$895$	5.96612	0.199425
$896$	−4.34372	−0.145114
$897$	21.8305	0.728898
$898$	−8.29672	−0.276865
$899$	87.4752	2.91746
$900$	1.27736	0.0425788
$901$	−0.236103	−0.00786572
$902$	−23.5118	−0.782856
$903$	−29.1107	−0.968744
$904$	−0.450611	−0.0149871
$905$	−6.17784	−0.205358
$906$	19.9432	0.662567
$907$	21.3228	0.708010	0.354005	−	0.935243i	$-0.384819\pi$
$907$	21.3228	0.708010	0.354005	+	0.935243i	$0.384819\pi$
$908$	8.76899	0.291009
$909$	−1.86293	−0.0617895
$910$	−18.4985	−0.613220
$911$	34.0175	1.12705	0.563524	−	0.826100i	$-0.309445\pi$
$911$	34.0175	1.12705	0.563524	+	0.826100i	$0.309445\pi$
$912$	0	0
$913$	−9.25091	−0.306160
$914$	18.7191	0.619174
$915$	19.0629	0.630200
$916$	47.1144	1.55670
$917$	2.60424	0.0859997
$918$	−0.357470	−0.0117983
$919$	−41.7419	−1.37694	−0.688470	−	0.725265i	$-0.741717\pi$
$919$	−41.7419	−1.37694	−0.688470	+	0.725265i	$0.741717\pi$
$920$	−0.682227	−0.0224924
$921$	11.1875	0.368640
$922$	13.4359	0.442487
$923$	−37.2545	−1.22625
$924$	11.8131	0.388622
$925$	1.11739	0.0367396
$926$	45.0716	1.48114
$927$	0.201112	0.00660537
$928$	−75.2867	−2.47141
$929$	−22.9048	−0.751481	−0.375741	−	0.926725i	$-0.622612\pi$
$929$	−22.9048	−0.751481	−0.375741	+	0.926725i	$0.622612\pi$
$930$	−36.0315	−1.18152
$931$	0	0
$932$	−22.9123	−0.750517
$933$	−48.2520	−1.57970
$934$	−31.2824	−1.02359
$935$	−0.0375278	−0.00122729
$936$	0.318344	0.0104054
$937$	11.6675	0.381160	0.190580	−	0.981672i	$-0.438963\pi$
$937$	11.6675	0.381160	0.190580	+	0.981672i	$0.438963\pi$
$938$	−58.4413	−1.90818
$939$	11.4765	0.374520
$940$	−16.7280	−0.545607
$941$	−55.4401	−1.80730	−0.903648	−	0.428276i	$-0.859121\pi$
$941$	−55.4401	−1.80730	−0.903648	+	0.428276i	$0.859121\pi$
$942$	44.7530	1.45813
$943$	−46.8690	−1.52627
$944$	10.5952	0.344844
$945$	14.0334	0.456507
$946$	−9.64541	−0.313599
$947$	−9.30476	−0.302364	−0.151182	−	0.988506i	$-0.548308\pi$
$947$	−9.30476	−0.302364	−0.151182	+	0.988506i	$0.548308\pi$
$948$	−35.2702	−1.14552
$949$	2.65474	0.0861765
$950$	0	0
$951$	−30.1726	−0.978413
$952$	0.0211751	0.000686287 0
$953$	17.2460	0.558652	0.279326	−	0.960196i	$-0.409889\pi$
$953$	17.2460	0.558652	0.279326	+	0.960196i	$0.409889\pi$
$954$	−7.49829	−0.242766
$955$	18.6639	0.603949
$956$	−5.68815	−0.183968
$957$	17.0754	0.551968
$958$	65.1076	2.10353
$959$	−15.6891	−0.506626
$960$	16.4963	0.532414
$961$	56.9445	1.83692
$962$	6.68465	0.215522
$963$	7.82680	0.252215
$964$	−23.2777	−0.749726
$965$	−23.9067	−0.769584
$966$	46.1161	1.48376
$967$	3.68636	0.118545	0.0592727	−	0.998242i	$-0.481122\pi$
$967$	3.68636	0.118545	0.0592727	+	0.998242i	$0.481122\pi$
$968$	−1.77029	−0.0568994
$969$	0	0
$970$	15.7449	0.505537
$971$	22.7457	0.729944	0.364972	−	0.931019i	$-0.381079\pi$
$971$	22.7457	0.729944	0.364972	+	0.931019i	$0.381079\pi$
$972$	−13.0802	−0.419548
$973$	8.44285	0.270665
$974$	7.38171	0.236525
$975$	5.62409	0.180115
$976$	38.3010	1.22599
$977$	45.0177	1.44024	0.720122	−	0.693848i	$-0.244086\pi$
$977$	45.0177	1.44024	0.720122	+	0.693848i	$0.244086\pi$
$978$	−2.13931	−0.0684075
$979$	8.42476	0.269257
$980$	−5.34580	−0.170765
$981$	9.32873	0.297843
$982$	9.19557	0.293442
$983$	−42.3156	−1.34966	−0.674830	−	0.737974i	$-0.735783\pi$
$983$	−42.3156	−1.34966	−0.674830	+	0.737974i	$0.735783\pi$
$984$	−4.03341	−0.128580
$985$	6.70152	0.213528
$986$	0.734720	0.0233982
$987$	47.1061	1.49940
$988$	0	0
$989$	−19.2274	−0.611397
$990$	−1.19183	−0.0378789
$991$	−31.1589	−0.989796	−0.494898	−	0.868951i	$-0.664795\pi$
$991$	−31.1589	−0.989796	−0.494898	+	0.868951i	$0.664795\pi$
$992$	−75.6906	−2.40318
$993$	26.9299	0.854594
$994$	−78.6988	−2.49618
$995$	−3.15886	−0.100143
$996$	−38.0945	−1.20707
$997$	38.8905	1.23167	0.615837	−	0.787873i	$-0.288818\pi$
$997$	38.8905	1.23167	0.615837	+	0.787873i	$0.288818\pi$
$998$	−44.1186	−1.39655
$999$	−5.07113	−0.160444

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.u.1.9		9
5.4	even	2		9025.2.a.cd.1.1		9
19.2	odd	18		95.2.k.b.61.3	✓	18
19.10	odd	18		95.2.k.b.81.3	yes	18
19.18	odd	2		1805.2.a.t.1.1		9
57.2	even	18		855.2.bs.b.631.1		18
57.29	even	18		855.2.bs.b.271.1		18
95.2	even	36		475.2.u.c.99.1		36
95.29	odd	18		475.2.l.b.176.1		18
95.48	even	36		475.2.u.c.24.1		36
95.59	odd	18		475.2.l.b.251.1		18
95.67	even	36		475.2.u.c.24.6		36
95.78	even	36		475.2.u.c.99.6		36
95.94	odd	2		9025.2.a.ce.1.9		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.b.61.3	✓	18	19.2	odd	18
95.2.k.b.81.3	yes	18	19.10	odd	18
475.2.l.b.176.1		18	95.29	odd	18
475.2.l.b.251.1		18	95.59	odd	18
475.2.u.c.24.1		36	95.48	even	36
475.2.u.c.24.6		36	95.67	even	36
475.2.u.c.99.1		36	95.2	even	36
475.2.u.c.99.6		36	95.78	even	36
855.2.bs.b.271.1		18	57.29	even	18
855.2.bs.b.631.1		18	57.2	even	18
1805.2.a.t.1.1		9	19.18	odd	2
1805.2.a.u.1.9		9	1.1	even	1	trivial
9025.2.a.cd.1.1		9	5.4	even	2
9025.2.a.ce.1.9		9	95.94	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:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

\(f(q)\)	\(=\)	\(q+2.02162 q^{2} +1.90055 q^{3} +2.08694 q^{4} -1.00000 q^{5} +3.84218 q^{6} +3.09218 q^{7} +0.175759 q^{8} +0.612075 q^{9} +O(q^{10})\)	\(q+2.02162 q^{2} +1.90055 q^{3} +2.08694 q^{4} -1.00000 q^{5} +3.84218 q^{6} +3.09218 q^{7} +0.175759 q^{8} +0.612075 q^{9} -2.02162 q^{10} +0.963188 q^{11} +3.96633 q^{12} +2.95920 q^{13} +6.25120 q^{14} -1.90055 q^{15} -3.81856 q^{16} +0.0389621 q^{17} +1.23738 q^{18} -2.08694 q^{20} +5.87682 q^{21} +1.94720 q^{22} +3.88160 q^{23} +0.334039 q^{24} +1.00000 q^{25} +5.98236 q^{26} -4.53836 q^{27} +6.45319 q^{28} +9.32783 q^{29} -3.84218 q^{30} +9.37788 q^{31} -8.07119 q^{32} +1.83058 q^{33} +0.0787664 q^{34} -3.09218 q^{35} +1.27736 q^{36} +1.11739 q^{37} +5.62409 q^{39} -0.175759 q^{40} -12.0747 q^{41} +11.8807 q^{42} -4.95348 q^{43} +2.01012 q^{44} -0.612075 q^{45} +7.84711 q^{46} +8.01557 q^{47} -7.25735 q^{48} +2.56155 q^{49} +2.02162 q^{50} +0.0740492 q^{51} +6.17566 q^{52} -6.05981 q^{53} -9.17483 q^{54} -0.963188 q^{55} +0.543479 q^{56} +18.8573 q^{58} -2.77465 q^{59} -3.96633 q^{60} -10.0302 q^{61} +18.9585 q^{62} +1.89264 q^{63} -8.67975 q^{64} -2.95920 q^{65} +3.70074 q^{66} -9.34881 q^{67} +0.0813115 q^{68} +7.37716 q^{69} -6.25120 q^{70} -12.5894 q^{71} +0.107578 q^{72} +0.897116 q^{73} +2.25894 q^{74} +1.90055 q^{75} +2.97835 q^{77} +11.3698 q^{78} -8.89241 q^{79} +3.81856 q^{80} -10.4616 q^{81} -24.4104 q^{82} -9.60447 q^{83} +12.2646 q^{84} -0.0389621 q^{85} -10.0140 q^{86} +17.7280 q^{87} +0.169289 q^{88} +8.74675 q^{89} -1.23738 q^{90} +9.15035 q^{91} +8.10067 q^{92} +17.8231 q^{93} +16.2044 q^{94} -15.3397 q^{96} -7.78824 q^{97} +5.17848 q^{98} +0.589543 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 3 q^{3} + 6 q^{4} - 9 q^{5} - 12 q^{6} - 12 q^{8} + 6 q^{9}+O(q^{10}) \) 9 * q + 3 * q^3 + 6 * q^4 - 9 * q^5 - 12 * q^6 - 12 * q^8 + 6 * q^9	\( 9 q + 3 q^{3} + 6 q^{4} - 9 q^{5} - 12 q^{6} - 12 q^{8} + 6 q^{9} + 6 q^{12} - 3 q^{13} + 12 q^{14} - 3 q^{15} - 12 q^{16} - 9 q^{17} + 6 q^{18} - 6 q^{20} + 12 q^{21} + 12 q^{22} + 15 q^{24} + 9 q^{25} + 21 q^{26} + 6 q^{27} - 15 q^{28} + 15 q^{29} + 12 q^{30} + 30 q^{31} - 9 q^{32} + 9 q^{33} - 6 q^{36} + 30 q^{37} + 6 q^{39} + 12 q^{40} + 18 q^{41} + 36 q^{42} - 6 q^{43} - 24 q^{44} - 6 q^{45} + 21 q^{46} + 21 q^{47} + 15 q^{48} + 3 q^{49} + 18 q^{51} - 3 q^{52} - 9 q^{53} - 9 q^{54} + 36 q^{56} + 18 q^{58} + 27 q^{59} - 6 q^{60} + 12 q^{61} - 6 q^{62} - 15 q^{63} + 24 q^{64} + 3 q^{65} + 3 q^{66} + 36 q^{67} + 3 q^{68} + 27 q^{69} - 12 q^{70} - 6 q^{71} + 12 q^{72} - 9 q^{73} - 9 q^{74} + 3 q^{75} + 12 q^{77} + 54 q^{78} + 45 q^{79} + 12 q^{80} - 15 q^{81} - 48 q^{82} - 12 q^{84} + 9 q^{85} - 9 q^{86} + 45 q^{87} + 39 q^{88} - 9 q^{89} - 6 q^{90} + 51 q^{91} - 54 q^{92} + 9 q^{93} + 33 q^{94} - 9 q^{96} + 45 q^{97} + 33 q^{98} + 12 q^{99}+O(q^{100}) \) 9 * q + 3 * q^3 + 6 * q^4 - 9 * q^5 - 12 * q^6 - 12 * q^8 + 6 * q^9 + 6 * q^12 - 3 * q^13 + 12 * q^14 - 3 * q^15 - 12 * q^16 - 9 * q^17 + 6 * q^18 - 6 * q^20 + 12 * q^21 + 12 * q^22 + 15 * q^24 + 9 * q^25 + 21 * q^26 + 6 * q^27 - 15 * q^28 + 15 * q^29 + 12 * q^30 + 30 * q^31 - 9 * q^32 + 9 * q^33 - 6 * q^36 + 30 * q^37 + 6 * q^39 + 12 * q^40 + 18 * q^41 + 36 * q^42 - 6 * q^43 - 24 * q^44 - 6 * q^45 + 21 * q^46 + 21 * q^47 + 15 * q^48 + 3 * q^49 + 18 * q^51 - 3 * q^52 - 9 * q^53 - 9 * q^54 + 36 * q^56 + 18 * q^58 + 27 * q^59 - 6 * q^60 + 12 * q^61 - 6 * q^62 - 15 * q^63 + 24 * q^64 + 3 * q^65 + 3 * q^66 + 36 * q^67 + 3 * q^68 + 27 * q^69 - 12 * q^70 - 6 * q^71 + 12 * q^72 - 9 * q^73 - 9 * q^74 + 3 * q^75 + 12 * q^77 + 54 * q^78 + 45 * q^79 + 12 * q^80 - 15 * q^81 - 48 * q^82 - 12 * q^84 + 9 * q^85 - 9 * q^86 + 45 * q^87 + 39 * q^88 - 9 * q^89 - 6 * q^90 + 51 * q^91 - 54 * q^92 + 9 * q^93 + 33 * q^94 - 9 * q^96 + 45 * q^97 + 33 * q^98 + 12 * q^99

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