LMFDB - Embedded newform 1003.2.a.g.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1003,2,Mod(1,1003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1003, 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("1003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1003 = 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1003.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:	$8.00899532273$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 10x^{8} + 34x^{7} + 28x^{6} - 129x^{5} - 3x^{4} + 178x^{3} - 56x^{2} - 56x + 15 $ x^10 - 3x^9 - 10x^8 + 34x^7 + 28x^6 - 129x^5 - 3x^4 + 178x^3 - 56x^2 - 56*x + 15
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.598829$ of defining polynomial
Character	$\chi$	$=$	1003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.441455 q^{2} -1.59883 q^{3} -1.80512 q^{4} -1.49805 q^{5} +0.705811 q^{6} -0.804687 q^{7} +1.67979 q^{8} -0.443745 q^{9} +O(q^{10})$	\(q-0.441455 q^{2} -1.59883 q^{3} -1.80512 q^{4} -1.49805 q^{5} +0.705811 q^{6} -0.804687 q^{7} +1.67979 q^{8} -0.443745 q^{9} +0.661322 q^{10} +5.43186 q^{11} +2.88608 q^{12} +3.66056 q^{13} +0.355233 q^{14} +2.39513 q^{15} +2.86869 q^{16} -1.00000 q^{17} +0.195893 q^{18} +1.59861 q^{19} +2.70416 q^{20} +1.28656 q^{21} -2.39792 q^{22} -7.99749 q^{23} -2.68569 q^{24} -2.75584 q^{25} -1.61597 q^{26} +5.50596 q^{27} +1.45255 q^{28} +8.81434 q^{29} -1.05734 q^{30} -1.91478 q^{31} -4.62597 q^{32} -8.68461 q^{33} +0.441455 q^{34} +1.20546 q^{35} +0.801012 q^{36} -6.23291 q^{37} -0.705716 q^{38} -5.85261 q^{39} -2.51641 q^{40} -8.52355 q^{41} -0.567956 q^{42} +0.104899 q^{43} -9.80514 q^{44} +0.664753 q^{45} +3.53053 q^{46} -7.54961 q^{47} -4.58654 q^{48} -6.35248 q^{49} +1.21658 q^{50} +1.59883 q^{51} -6.60775 q^{52} +7.27334 q^{53} -2.43063 q^{54} -8.13721 q^{55} -1.35170 q^{56} -2.55591 q^{57} -3.89113 q^{58} -1.00000 q^{59} -4.32349 q^{60} +13.9063 q^{61} +0.845288 q^{62} +0.357075 q^{63} -3.69522 q^{64} -5.48371 q^{65} +3.83386 q^{66} -10.0065 q^{67} +1.80512 q^{68} +12.7866 q^{69} -0.532157 q^{70} +7.57712 q^{71} -0.745397 q^{72} +6.24871 q^{73} +2.75155 q^{74} +4.40611 q^{75} -2.88569 q^{76} -4.37094 q^{77} +2.58366 q^{78} -4.70222 q^{79} -4.29744 q^{80} -7.47186 q^{81} +3.76276 q^{82} -1.71792 q^{83} -2.32239 q^{84} +1.49805 q^{85} -0.0463082 q^{86} -14.0926 q^{87} +9.12436 q^{88} +0.392183 q^{89} -0.293458 q^{90} -2.94561 q^{91} +14.4364 q^{92} +3.06140 q^{93} +3.33281 q^{94} -2.39481 q^{95} +7.39613 q^{96} -8.37840 q^{97} +2.80433 q^{98} -2.41036 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9}+O(q^{10}) $ 10 * q - q^2 - 7 * q^3 + 15 * q^4 - 12 * q^5 + 5 * q^6 - 9 * q^7 - 12 * q^8 + 3 * q^9	\( 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9} + 4 q^{10} + 12 q^{11} - 24 q^{12} - 11 q^{13} - 12 q^{14} + 9 q^{15} - 3 q^{16} - 10 q^{17} - 22 q^{18} - 5 q^{19} - 36 q^{20} - 10 q^{21} + 6 q^{22} - 7 q^{23} + 35 q^{24} + 2 q^{25} + q^{26} - 31 q^{27} - 4 q^{28} + 10 q^{29} - 9 q^{30} + 13 q^{31} - 15 q^{32} - 9 q^{33} + q^{34} - 8 q^{35} + 40 q^{36} + 12 q^{37} - 50 q^{38} + 24 q^{39} + 5 q^{40} - 29 q^{41} - 17 q^{42} - 18 q^{43} - 6 q^{44} - 14 q^{45} + 11 q^{46} - 18 q^{47} - 43 q^{48} - 9 q^{49} - 31 q^{50} + 7 q^{51} - 68 q^{52} + 19 q^{54} - 27 q^{55} - 7 q^{56} + 20 q^{57} + 23 q^{58} - 10 q^{59} + 38 q^{60} + 8 q^{61} - 46 q^{62} + 39 q^{63} - 20 q^{64} + 58 q^{65} - 34 q^{66} - 6 q^{67} - 15 q^{68} + 6 q^{69} + 73 q^{70} + 8 q^{71} - 70 q^{72} - 41 q^{73} - 10 q^{74} + 10 q^{75} + 12 q^{76} - 22 q^{77} - 43 q^{78} + 3 q^{79} - 15 q^{80} + 26 q^{81} + 8 q^{82} - 22 q^{84} + 12 q^{85} - 29 q^{86} - 28 q^{87} + 33 q^{88} - 45 q^{89} + 56 q^{90} - 14 q^{91} + 36 q^{92} - 19 q^{93} + 15 q^{94} - 17 q^{95} + 90 q^{96} - 5 q^{97} + 30 q^{98} + 14 q^{99}+O(q^{100}) \) 10 * q - q^2 - 7 * q^3 + 15 * q^4 - 12 * q^5 + 5 * q^6 - 9 * q^7 - 12 * q^8 + 3 * q^9 + 4 * q^10 + 12 * q^11 - 24 * q^12 - 11 * q^13 - 12 * q^14 + 9 * q^15 - 3 * q^16 - 10 * q^17 - 22 * q^18 - 5 * q^19 - 36 * q^20 - 10 * q^21 + 6 * q^22 - 7 * q^23 + 35 * q^24 + 2 * q^25 + q^26 - 31 * q^27 - 4 * q^28 + 10 * q^29 - 9 * q^30 + 13 * q^31 - 15 * q^32 - 9 * q^33 + q^34 - 8 * q^35 + 40 * q^36 + 12 * q^37 - 50 * q^38 + 24 * q^39 + 5 * q^40 - 29 * q^41 - 17 * q^42 - 18 * q^43 - 6 * q^44 - 14 * q^45 + 11 * q^46 - 18 * q^47 - 43 * q^48 - 9 * q^49 - 31 * q^50 + 7 * q^51 - 68 * q^52 + 19 * q^54 - 27 * q^55 - 7 * q^56 + 20 * q^57 + 23 * q^58 - 10 * q^59 + 38 * q^60 + 8 * q^61 - 46 * q^62 + 39 * q^63 - 20 * q^64 + 58 * q^65 - 34 * q^66 - 6 * q^67 - 15 * q^68 + 6 * q^69 + 73 * q^70 + 8 * q^71 - 70 * q^72 - 41 * q^73 - 10 * q^74 + 10 * q^75 + 12 * q^76 - 22 * q^77 - 43 * q^78 + 3 * q^79 - 15 * q^80 + 26 * q^81 + 8 * q^82 - 22 * q^84 + 12 * q^85 - 29 * q^86 - 28 * q^87 + 33 * q^88 - 45 * q^89 + 56 * q^90 - 14 * q^91 + 36 * q^92 - 19 * q^93 + 15 * q^94 - 17 * q^95 + 90 * q^96 - 5 * q^97 + 30 * q^98 + 14 * 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 $

$2$	−0.441455	−0.312156	−0.156078	−	0.987745i	$-0.549885\pi$
$2$	−0.441455	−0.312156	−0.156078	+	0.987745i	$0.549885\pi$
$3$	−1.59883	−0.923085	−0.461542	−	0.887118i	$-0.652704\pi$
$3$	−1.59883	−0.923085	−0.461542	+	0.887118i	$0.652704\pi$
$4$	−1.80512	−0.902559
$5$	−1.49805	−0.669950	−0.334975	−	0.942227i	$-0.608728\pi$
$5$	−1.49805	−0.669950	−0.334975	+	0.942227i	$0.608728\pi$
$6$	0.705811	0.288146
$7$	−0.804687	−0.304143	−0.152071	−	0.988369i	$-0.548594\pi$
$7$	−0.804687	−0.304143	−0.152071	+	0.988369i	$0.548594\pi$
$8$	1.67979	0.593894
$9$	−0.443745	−0.147915
$10$	0.661322	0.209128
$11$	5.43186	1.63777	0.818883	−	0.573960i	$-0.194594\pi$
$11$	5.43186	1.63777	0.818883	+	0.573960i	$0.194594\pi$
$12$	2.88608	0.833138
$13$	3.66056	1.01526	0.507629	−	0.861576i	$-0.330522\pi$
$13$	3.66056	1.01526	0.507629	+	0.861576i	$0.330522\pi$
$14$	0.355233	0.0949399
$15$	2.39513	0.618420
$16$	2.86869	0.717171
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.195893	0.0461725
$19$	1.59861	0.366747	0.183374	−	0.983043i	$-0.441298\pi$
$19$	1.59861	0.366747	0.183374	+	0.983043i	$0.441298\pi$
$20$	2.70416	0.604669
$21$	1.28656	0.280750
$22$	−2.39792	−0.511238
$23$	−7.99749	−1.66759	−0.833796	−	0.552072i	$-0.813837\pi$
$23$	−7.99749	−1.66759	−0.833796	+	0.552072i	$0.813837\pi$
$24$	−2.68569	−0.548215
$25$	−2.75584	−0.551168
$26$	−1.61597	−0.316918
$27$	5.50596	1.05962
$28$	1.45255	0.274507
$29$	8.81434	1.63678	0.818391	−	0.574662i	$-0.194867\pi$
$29$	8.81434	1.63678	0.818391	+	0.574662i	$0.194867\pi$
$30$	−1.05734	−0.193043
$31$	−1.91478	−0.343904	−0.171952	−	0.985105i	$-0.555007\pi$
$31$	−1.91478	−0.343904	−0.171952	+	0.985105i	$0.555007\pi$
$32$	−4.62597	−0.817763
$33$	−8.68461	−1.51180
$34$	0.441455	0.0757088
$35$	1.20546	0.203760
$36$	0.801012	0.133502
$37$	−6.23291	−1.02468	−0.512342	−	0.858782i	$-0.671222\pi$
$37$	−6.23291	−1.02468	−0.512342	+	0.858782i	$0.671222\pi$
$38$	−0.705716	−0.114482
$39$	−5.85261	−0.937168
$40$	−2.51641	−0.397879
$41$	−8.52355	−1.33116	−0.665578	−	0.746329i	$-0.731815\pi$
$41$	−8.52355	−1.33116	−0.665578	+	0.746329i	$0.731815\pi$
$42$	−0.567956	−0.0876376
$43$	0.104899	0.0159970	0.00799848	−	0.999968i	$-0.497454\pi$
$43$	0.104899	0.0159970	0.00799848	+	0.999968i	$0.497454\pi$
$44$	−9.80514	−1.47818
$45$	0.664753	0.0990955
$46$	3.53053	0.520548
$47$	−7.54961	−1.10122	−0.550612	−	0.834761i	$-0.685606\pi$
$47$	−7.54961	−1.10122	−0.550612	+	0.834761i	$0.685606\pi$
$48$	−4.58654	−0.662010
$49$	−6.35248	−0.907497
$50$	1.21658	0.172050
$51$	1.59883	0.223881
$52$	−6.60775	−0.916329
$53$	7.27334	0.999071	0.499535	−	0.866294i	$-0.333504\pi$
$53$	7.27334	0.999071	0.499535	+	0.866294i	$0.333504\pi$
$54$	−2.43063	−0.330767
$55$	−8.13721	−1.09722
$56$	−1.35170	−0.180629
$57$	−2.55591	−0.338539
$58$	−3.89113	−0.510930
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−4.32349	−0.558161
$61$	13.9063	1.78052	0.890260	−	0.455452i	$-0.150522\pi$
$61$	13.9063	1.78052	0.890260	+	0.455452i	$0.150522\pi$
$62$	0.845288	0.107352
$63$	0.357075	0.0449873
$64$	−3.69522	−0.461902
$65$	−5.48371	−0.680171
$66$	3.83386	0.471916
$67$	−10.0065	−1.22249	−0.611245	−	0.791442i	$-0.709331\pi$
$67$	−10.0065	−1.22249	−0.611245	+	0.791442i	$0.709331\pi$
$68$	1.80512	0.218903
$69$	12.7866	1.53933
$70$	−0.532157	−0.0636050
$71$	7.57712	0.899239	0.449620	−	0.893220i	$-0.351560\pi$
$71$	7.57712	0.899239	0.449620	+	0.893220i	$0.351560\pi$
$72$	−0.745397	−0.0878458
$73$	6.24871	0.731356	0.365678	−	0.930741i	$-0.380837\pi$
$73$	6.24871	0.731356	0.365678	+	0.930741i	$0.380837\pi$
$74$	2.75155	0.319861
$75$	4.40611	0.508774
$76$	−2.88569	−0.331011
$77$	−4.37094	−0.498115
$78$	2.58366	0.292542
$79$	−4.70222	−0.529041	−0.264521	−	0.964380i	$-0.585214\pi$
$79$	−4.70222	−0.529041	−0.264521	+	0.964380i	$0.585214\pi$
$80$	−4.29744	−0.480469
$81$	−7.47186	−0.830206
$82$	3.76276	0.415528
$83$	−1.71792	−0.188567	−0.0942833	−	0.995545i	$-0.530056\pi$
$83$	−1.71792	−0.188567	−0.0942833	+	0.995545i	$0.530056\pi$
$84$	−2.32239	−0.253393
$85$	1.49805	0.162487
$86$	−0.0463082	−0.00499354
$87$	−14.0926	−1.51089
$88$	9.12436	0.972660
$89$	0.392183	0.0415713	0.0207856	−	0.999784i	$-0.493383\pi$
$89$	0.392183	0.0415713	0.0207856	+	0.999784i	$0.493383\pi$
$90$	−0.293458	−0.0309332
$91$	−2.94561	−0.308783
$92$	14.4364	1.50510
$93$	3.06140	0.317453
$94$	3.33281	0.343753
$95$	−2.39481	−0.245702
$96$	7.39613	0.754865
$97$	−8.37840	−0.850698	−0.425349	−	0.905030i	$-0.639849\pi$
$97$	−8.37840	−0.850698	−0.425349	+	0.905030i	$0.639849\pi$
$98$	2.80433	0.283280
$99$	−2.41036	−0.242250
$100$	4.97461	0.497461
$101$	−18.3890	−1.82978	−0.914889	−	0.403705i	$-0.867722\pi$
$101$	−18.3890	−1.82978	−0.914889	+	0.403705i	$0.867722\pi$
$102$	−0.705811	−0.0698857
$103$	−3.92490	−0.386732	−0.193366	−	0.981127i	$-0.561941\pi$
$103$	−3.92490	−0.386732	−0.193366	+	0.981127i	$0.561941\pi$
$104$	6.14896	0.602956
$105$	−1.92733	−0.188088
$106$	−3.21085	−0.311865
$107$	8.57203	0.828689	0.414345	−	0.910120i	$-0.364011\pi$
$107$	8.57203	0.828689	0.414345	+	0.910120i	$0.364011\pi$
$108$	−9.93891	−0.956372
$109$	−16.3224	−1.56340	−0.781700	−	0.623654i	$-0.785647\pi$
$109$	−16.3224	−1.56340	−0.781700	+	0.623654i	$0.785647\pi$
$110$	3.59221	0.342504
$111$	9.96536	0.945870
$112$	−2.30839	−0.218123
$113$	−17.3274	−1.63003	−0.815014	−	0.579441i	$-0.803271\pi$
$113$	−17.3274	−1.63003	−0.815014	+	0.579441i	$0.803271\pi$
$114$	1.12832	0.105677
$115$	11.9807	1.11720
$116$	−15.9109	−1.47729
$117$	−1.62436	−0.150172
$118$	0.441455	0.0406392
$119$	0.804687	0.0737655
$120$	4.02331	0.367276
$121$	18.5051	1.68228
$122$	−6.13900	−0.555799
$123$	13.6277	1.22877
$124$	3.45640	0.310394
$125$	11.6187	1.03920
$126$	−0.157633	−0.0140430
$127$	21.1251	1.87455	0.937274	−	0.348593i	$-0.113340\pi$
$127$	21.1251	1.87455	0.937274	+	0.348593i	$0.113340\pi$
$128$	10.8832	0.961949
$129$	−0.167716	−0.0147665
$130$	2.42081	0.212319
$131$	−1.17418	−0.102589	−0.0512945	−	0.998684i	$-0.516335\pi$
$131$	−1.17418	−0.102589	−0.0512945	+	0.998684i	$0.516335\pi$
$132$	15.6767	1.36449
$133$	−1.28638	−0.111544
$134$	4.41742	0.381607
$135$	−8.24822	−0.709894
$136$	−1.67979	−0.144041
$137$	−12.2856	−1.04963	−0.524815	−	0.851216i	$-0.675865\pi$
$137$	−12.2856	−1.04963	−0.524815	+	0.851216i	$0.675865\pi$
$138$	−5.64472	−0.480510
$139$	−9.51231	−0.806824	−0.403412	−	0.915019i	$-0.632176\pi$
$139$	−9.51231	−0.806824	−0.403412	+	0.915019i	$0.632176\pi$
$140$	−2.17600	−0.183906
$141$	12.0705	1.01652
$142$	−3.34496	−0.280703
$143$	19.8836	1.66275
$144$	−1.27296	−0.106080
$145$	−13.2043	−1.09656
$146$	−2.75852	−0.228297
$147$	10.1565	0.837697
$148$	11.2511	0.924838
$149$	−19.9486	−1.63425	−0.817125	−	0.576460i	$-0.804434\pi$
$149$	−19.9486	−1.63425	−0.817125	+	0.576460i	$0.804434\pi$
$150$	−1.94510	−0.158817
$151$	−1.38923	−0.113054	−0.0565272	−	0.998401i	$-0.518003\pi$
$151$	−1.38923	−0.113054	−0.0565272	+	0.998401i	$0.518003\pi$
$152$	2.68533	0.217809
$153$	0.443745	0.0358746
$154$	1.92957	0.155489
$155$	2.86844	0.230399
$156$	10.5647	0.845850
$157$	−4.38818	−0.350215	−0.175107	−	0.984549i	$-0.556027\pi$
$157$	−4.38818	−0.350215	−0.175107	+	0.984549i	$0.556027\pi$
$158$	2.07582	0.165143
$159$	−11.6288	−0.922227
$160$	6.92994	0.547860
$161$	6.43548	0.507187
$162$	3.29849	0.259154
$163$	7.74332	0.606504	0.303252	−	0.952910i	$-0.401928\pi$
$163$	7.74332	0.606504	0.303252	+	0.952910i	$0.401928\pi$
$164$	15.3860	1.20145
$165$	13.0100	1.01283
$166$	0.758385	0.0588621
$167$	−23.1720	−1.79310	−0.896550	−	0.442942i	$-0.853935\pi$
$167$	−23.1720	−1.79310	−0.896550	+	0.442942i	$0.853935\pi$
$168$	2.16114	0.166736
$169$	0.399714	0.0307472
$170$	−0.661322	−0.0507211
$171$	−0.709377	−0.0542474
$172$	−0.189355	−0.0144382
$173$	−19.8143	−1.50645	−0.753227	−	0.657761i	$-0.771504\pi$
$173$	−19.8143	−1.50645	−0.753227	+	0.657761i	$0.771504\pi$
$174$	6.22125	0.471632
$175$	2.21759	0.167634
$176$	15.5823	1.17456
$177$	1.59883	0.120175
$178$	−0.173131	−0.0129767
$179$	9.10115	0.680252	0.340126	−	0.940380i	$-0.389530\pi$
$179$	9.10115	0.680252	0.340126	+	0.940380i	$0.389530\pi$
$180$	−1.19996	−0.0894396
$181$	16.4692	1.22415	0.612073	−	0.790801i	$-0.290336\pi$
$181$	16.4692	1.22415	0.612073	+	0.790801i	$0.290336\pi$
$182$	1.30035	0.0963884
$183$	−22.2338	−1.64357
$184$	−13.4341	−0.990374
$185$	9.33723	0.686487
$186$	−1.35147	−0.0990947
$187$	−5.43186	−0.397217
$188$	13.6279	0.993919
$189$	−4.43057	−0.322277
$190$	1.05720	0.0766973
$191$	−8.71942	−0.630915	−0.315457	−	0.948940i	$-0.602158\pi$
$191$	−8.71942	−0.630915	−0.315457	+	0.948940i	$0.602158\pi$
$192$	5.90802	0.426375
$193$	−7.57631	−0.545355	−0.272677	−	0.962106i	$-0.587909\pi$
$193$	−7.57631	−0.545355	−0.272677	+	0.962106i	$0.587909\pi$
$194$	3.69868	0.265550
$195$	8.76752	0.627855
$196$	11.4670	0.819070
$197$	−2.70930	−0.193030	−0.0965150	−	0.995332i	$-0.530770\pi$
$197$	−2.70930	−0.193030	−0.0965150	+	0.995332i	$0.530770\pi$
$198$	1.06406	0.0756197
$199$	3.54327	0.251176	0.125588	−	0.992082i	$-0.459918\pi$
$199$	3.54327	0.251176	0.125588	+	0.992082i	$0.459918\pi$
$200$	−4.62922	−0.327335
$201$	15.9987	1.12846
$202$	8.11793	0.571175
$203$	−7.09278	−0.497816
$204$	−2.88608	−0.202066
$205$	12.7687	0.891807
$206$	1.73267	0.120721
$207$	3.54885	0.246662
$208$	10.5010	0.728114
$209$	8.68345	0.600647
$210$	0.850829	0.0587128
$211$	26.0731	1.79495	0.897475	−	0.441066i	$-0.145400\pi$
$211$	26.0731	1.79495	0.897475	+	0.441066i	$0.145400\pi$
$212$	−13.1292	−0.901720
$213$	−12.1145	−0.830074
$214$	−3.78416	−0.258680
$215$	−0.157144	−0.0107172
$216$	9.24884	0.629304
$217$	1.54080	0.104596
$218$	7.20559	0.488024
$219$	−9.99062	−0.675104
$220$	14.6886	0.990307
$221$	−3.66056	−0.246236
$222$	−4.39925	−0.295259
$223$	−8.63161	−0.578015	−0.289008	−	0.957327i	$-0.593325\pi$
$223$	−8.63161	−0.578015	−0.289008	+	0.957327i	$0.593325\pi$
$224$	3.72246	0.248717
$225$	1.22289	0.0815259
$226$	7.64928	0.508823
$227$	−7.46487	−0.495461	−0.247730	−	0.968829i	$-0.579685\pi$
$227$	−7.46487	−0.495461	−0.247730	+	0.968829i	$0.579685\pi$
$228$	4.61372	0.305551
$229$	−9.56800	−0.632271	−0.316136	−	0.948714i	$-0.602385\pi$
$229$	−9.56800	−0.632271	−0.316136	+	0.948714i	$0.602385\pi$
$230$	−5.28892	−0.348741
$231$	6.98839	0.459802
$232$	14.8062	0.972075
$233$	−5.56859	−0.364810	−0.182405	−	0.983223i	$-0.558388\pi$
$233$	−5.56859	−0.364810	−0.182405	+	0.983223i	$0.558388\pi$
$234$	0.717079	0.0468769
$235$	11.3097	0.737764
$236$	1.80512	0.117503
$237$	7.51805	0.488350
$238$	−0.355233	−0.0230263
$239$	−15.8361	−1.02435	−0.512176	−	0.858880i	$-0.671161\pi$
$239$	−15.8361	−1.02435	−0.512176	+	0.858880i	$0.671161\pi$
$240$	6.87088	0.443513
$241$	7.69809	0.495877	0.247939	−	0.968776i	$-0.420247\pi$
$241$	7.69809	0.495877	0.247939	+	0.968776i	$0.420247\pi$
$242$	−8.16915	−0.525133
$243$	−4.57166	−0.293272
$244$	−25.1025	−1.60702
$245$	9.51635	0.607977
$246$	−6.01601	−0.383567
$247$	5.85183	0.372343
$248$	−3.21642	−0.204243
$249$	2.74667	0.174063
$250$	−5.12911	−0.324393
$251$	−9.04406	−0.570856	−0.285428	−	0.958400i	$-0.592136\pi$
$251$	−9.04406	−0.570856	−0.285428	+	0.958400i	$0.592136\pi$
$252$	−0.644563	−0.0406037
$253$	−43.4412	−2.73113
$254$	−9.32577	−0.585151
$255$	−2.39513	−0.149989
$256$	2.58599	0.161624
$257$	−16.9344	−1.05634	−0.528170	−	0.849139i	$-0.677121\pi$
$257$	−16.9344	−1.05634	−0.528170	+	0.849139i	$0.677121\pi$
$258$	0.0740388	0.00460946
$259$	5.01554	0.311650
$260$	9.89875	0.613895
$261$	−3.91132	−0.242104
$262$	0.518349	0.0320237
$263$	27.2043	1.67749	0.838743	−	0.544527i	$-0.183291\pi$
$263$	27.2043	1.67749	0.838743	+	0.544527i	$0.183291\pi$
$264$	−14.5883	−0.897848
$265$	−10.8959	−0.669327
$266$	0.567880	0.0348190
$267$	−0.627033	−0.0383738
$268$	18.0629	1.10337
$269$	−20.1258	−1.22709	−0.613546	−	0.789659i	$-0.710257\pi$
$269$	−20.1258	−1.22709	−0.613546	+	0.789659i	$0.710257\pi$
$270$	3.64121	0.221597
$271$	−9.76941	−0.593450	−0.296725	−	0.954963i	$-0.595894\pi$
$271$	−9.76941	−0.593450	−0.296725	+	0.954963i	$0.595894\pi$
$272$	−2.86869	−0.173940
$273$	4.70952	0.285033
$274$	5.42354	0.327648
$275$	−14.9693	−0.902684
$276$	−23.0814	−1.38933
$277$	17.7821	1.06842	0.534212	−	0.845350i	$-0.320608\pi$
$277$	17.7821	1.06842	0.534212	+	0.845350i	$0.320608\pi$
$278$	4.19925	0.251854
$279$	0.849673	0.0508686
$280$	2.02492	0.121012
$281$	21.8008	1.30053	0.650263	−	0.759709i	$-0.274659\pi$
$281$	21.8008	1.30053	0.650263	+	0.759709i	$0.274659\pi$
$282$	−5.32859	−0.317313
$283$	26.6717	1.58547	0.792733	−	0.609569i	$-0.208658\pi$
$283$	26.6717	1.58547	0.792733	+	0.609569i	$0.208658\pi$
$284$	−13.6776	−0.811616
$285$	3.82889	0.226804
$286$	−8.77773	−0.519038
$287$	6.85879	0.404862
$288$	2.05275	0.120959
$289$	1.00000	0.0588235
$290$	5.82912	0.342298
$291$	13.3956	0.785266
$292$	−11.2797	−0.660092
$293$	−16.4212	−0.959340	−0.479670	−	0.877449i	$-0.659244\pi$
$293$	−16.4212	−0.959340	−0.479670	+	0.877449i	$0.659244\pi$
$294$	−4.48365	−0.261492
$295$	1.49805	0.0872200
$296$	−10.4700	−0.608554
$297$	29.9076	1.73541
$298$	8.80639	0.510140
$299$	−29.2753	−1.69304
$300$	−7.95356	−0.459199
$301$	−0.0844109	−0.00486536
$302$	0.613284	0.0352905
$303$	29.4009	1.68904
$304$	4.58592	0.263021
$305$	−20.8324	−1.19286
$306$	−0.195893	−0.0111985
$307$	−3.43606	−0.196107	−0.0980533	−	0.995181i	$-0.531262\pi$
$307$	−3.43606	−0.196107	−0.0980533	+	0.995181i	$0.531262\pi$
$308$	7.89007	0.449578
$309$	6.27525	0.356987
$310$	−1.26629	−0.0719202
$311$	27.4877	1.55868	0.779342	−	0.626599i	$-0.215554\pi$
$311$	27.4877	1.55868	0.779342	+	0.626599i	$0.215554\pi$
$312$	−9.83114	−0.556579
$313$	18.1720	1.02714	0.513571	−	0.858047i	$-0.328322\pi$
$313$	18.1720	1.02714	0.513571	+	0.858047i	$0.328322\pi$
$314$	1.93718	0.109322
$315$	−0.534918	−0.0301392
$316$	8.48807	0.477491
$317$	−23.2596	−1.30639	−0.653194	−	0.757190i	$-0.726572\pi$
$317$	−23.2596	−1.30639	−0.653194	+	0.757190i	$0.726572\pi$
$318$	5.13360	0.287878
$319$	47.8782	2.68067
$320$	5.53563	0.309451
$321$	−13.7052	−0.764950
$322$	−2.84097	−0.158321
$323$	−1.59861	−0.0889493
$324$	13.4876	0.749310
$325$	−10.0879	−0.559577
$326$	−3.41833	−0.189324
$327$	26.0967	1.44315
$328$	−14.3178	−0.790566
$329$	6.07507	0.334929
$330$	−5.74333	−0.316160
$331$	8.63850	0.474815	0.237408	−	0.971410i	$-0.423702\pi$
$331$	8.63850	0.474815	0.237408	+	0.971410i	$0.423702\pi$
$332$	3.10105	0.170192
$333$	2.76582	0.151566
$334$	10.2294	0.559726
$335$	14.9903	0.819006
$336$	3.69073	0.201346
$337$	2.17923	0.118710	0.0593550	−	0.998237i	$-0.481096\pi$
$337$	2.17923	0.118710	0.0593550	+	0.998237i	$0.481096\pi$
$338$	−0.176455	−0.00959791
$339$	27.7036	1.50465
$340$	−2.70416	−0.146654
$341$	−10.4008	−0.563235
$342$	0.313158	0.0169336
$343$	10.7446	0.580152
$344$	0.176208	0.00950050
$345$	−19.1550	−1.03127
$346$	8.74712	0.470248
$347$	−29.3952	−1.57802	−0.789009	−	0.614381i	$-0.789406\pi$
$347$	−29.3952	−1.57802	−0.789009	+	0.614381i	$0.789406\pi$
$348$	25.4388	1.36367
$349$	9.34657	0.500310	0.250155	−	0.968206i	$-0.419518\pi$
$349$	9.34657	0.500310	0.250155	+	0.968206i	$0.419518\pi$
$350$	−0.978964	−0.0523278
$351$	20.1549	1.07579
$352$	−25.1276	−1.33931
$353$	−0.896291	−0.0477048	−0.0238524	−	0.999715i	$-0.507593\pi$
$353$	−0.896291	−0.0477048	−0.0238524	+	0.999715i	$0.507593\pi$
$354$	−0.705811	−0.0375134
$355$	−11.3509	−0.602445
$356$	−0.707936	−0.0375205
$357$	−1.28656	−0.0680918
$358$	−4.01775	−0.212344
$359$	−17.2908	−0.912574	−0.456287	−	0.889833i	$-0.650821\pi$
$359$	−17.2908	−0.912574	−0.456287	+	0.889833i	$0.650821\pi$
$360$	1.11664	0.0588523
$361$	−16.4444	−0.865496
$362$	−7.27041	−0.382124
$363$	−29.5865	−1.55289
$364$	5.31716	0.278695
$365$	−9.36090	−0.489972
$366$	9.81522	0.513050
$367$	−30.1833	−1.57556	−0.787778	−	0.615959i	$-0.788769\pi$
$367$	−30.1833	−1.57556	−0.787778	+	0.615959i	$0.788769\pi$
$368$	−22.9423	−1.19595
$369$	3.78228	0.196898
$370$	−4.12196	−0.214291
$371$	−5.85276	−0.303860
$372$	−5.52620	−0.286520
$373$	−19.6233	−1.01605	−0.508027	−	0.861341i	$-0.669625\pi$
$373$	−19.6233	−1.01605	−0.508027	+	0.861341i	$0.669625\pi$
$374$	2.39792	0.123993
$375$	−18.5762	−0.959273
$376$	−12.6817	−0.654010
$377$	32.2654	1.66175
$378$	1.95590	0.100600
$379$	27.4951	1.41233	0.706164	−	0.708048i	$-0.250424\pi$
$379$	27.4951	1.41233	0.706164	+	0.708048i	$0.250424\pi$
$380$	4.32291	0.221761
$381$	−33.7754	−1.73037
$382$	3.84923	0.196944
$383$	1.61196	0.0823676	0.0411838	−	0.999152i	$-0.486887\pi$
$383$	1.61196	0.0823676	0.0411838	+	0.999152i	$0.486887\pi$
$384$	−17.4004	−0.887960
$385$	6.54790	0.333712
$386$	3.34460	0.170235
$387$	−0.0465484	−0.00236619
$388$	15.1240	0.767805
$389$	−3.23104	−0.163820	−0.0819102	−	0.996640i	$-0.526102\pi$
$389$	−3.23104	−0.163820	−0.0819102	+	0.996640i	$0.526102\pi$
$390$	−3.87046	−0.195989
$391$	7.99749	0.404451
$392$	−10.6708	−0.538957
$393$	1.87732	0.0946983
$394$	1.19603	0.0602554
$395$	7.04418	0.354431
$396$	4.35098	0.218645
$397$	5.10362	0.256143	0.128072	−	0.991765i	$-0.459121\pi$
$397$	5.10362	0.256143	0.128072	+	0.991765i	$0.459121\pi$
$398$	−1.56419	−0.0784059
$399$	2.05671	0.102964
$400$	−7.90563	−0.395282
$401$	−34.2802	−1.71187	−0.855937	−	0.517081i	$-0.827019\pi$
$401$	−34.2802	−1.71187	−0.855937	+	0.517081i	$0.827019\pi$
$402$	−7.06270	−0.352255
$403$	−7.00917	−0.349151
$404$	33.1944	1.65148
$405$	11.1932	0.556196
$406$	3.13114	0.155396
$407$	−33.8563	−1.67819
$408$	2.68569	0.132962
$409$	−11.9443	−0.590610	−0.295305	−	0.955403i	$-0.595421\pi$
$409$	−11.9443	−0.590610	−0.295305	+	0.955403i	$0.595421\pi$
$410$	−5.63682	−0.278383
$411$	19.6426	0.968897
$412$	7.08492	0.349049
$413$	0.804687	0.0395960
$414$	−1.56665	−0.0769968
$415$	2.57354	0.126330
$416$	−16.9336	−0.830240
$417$	15.2086	0.744766
$418$	−3.83335	−0.187495
$419$	39.6966	1.93931	0.969653	−	0.244485i	$-0.0786188\pi$
$419$	39.6966	1.93931	0.969653	+	0.244485i	$0.0786188\pi$
$420$	3.47906	0.169761
$421$	−26.5898	−1.29591	−0.647954	−	0.761680i	$-0.724375\pi$
$421$	−26.5898	−1.29591	−0.647954	+	0.761680i	$0.724375\pi$
$422$	−11.5101	−0.560303
$423$	3.35010	0.162887
$424$	12.2177	0.593342
$425$	2.75584	0.133678
$426$	5.34802	0.259112
$427$	−11.1902	−0.541533
$428$	−15.4735	−0.747941
$429$	−31.7906	−1.53486
$430$	0.0693721	0.00334542
$431$	24.8114	1.19512	0.597561	−	0.801824i	$-0.296137\pi$
$431$	24.8114	1.19512	0.597561	+	0.801824i	$0.296137\pi$
$432$	15.7949	0.759931
$433$	−23.3868	−1.12390	−0.561950	−	0.827171i	$-0.689949\pi$
$433$	−23.3868	−1.12390	−0.561950	+	0.827171i	$0.689949\pi$
$434$	−0.680192	−0.0326503
$435$	21.1115	1.01222
$436$	29.4638	1.41106
$437$	−12.7849	−0.611585
$438$	4.41041	0.210737
$439$	−0.245545	−0.0117192	−0.00585962	−	0.999983i	$-0.501865\pi$
$439$	−0.245545	−0.0117192	−0.00585962	+	0.999983i	$0.501865\pi$
$440$	−13.6688	−0.651633
$441$	2.81888	0.134232
$442$	1.61597	0.0768639
$443$	14.1917	0.674267	0.337133	−	0.941457i	$-0.390543\pi$
$443$	14.1917	0.674267	0.337133	+	0.941457i	$0.390543\pi$
$444$	−17.9886	−0.853703
$445$	−0.587510	−0.0278507
$446$	3.81046	0.180431
$447$	31.8944	1.50855
$448$	2.97349	0.140484
$449$	19.0076	0.897025	0.448513	−	0.893776i	$-0.351954\pi$
$449$	19.0076	0.897025	0.448513	+	0.893776i	$0.351954\pi$
$450$	−0.539850	−0.0254488
$451$	−46.2987	−2.18012
$452$	31.2781	1.47120
$453$	2.22115	0.104359
$454$	3.29540	0.154661
$455$	4.41267	0.206869
$456$	−4.29339	−0.201056
$457$	1.77315	0.0829443	0.0414721	−	0.999140i	$-0.486795\pi$
$457$	1.77315	0.0829443	0.0414721	+	0.999140i	$0.486795\pi$
$458$	4.22384	0.197367
$459$	−5.50596	−0.256996
$460$	−21.6265	−1.00834
$461$	−31.5903	−1.47131	−0.735653	−	0.677359i	$-0.763125\pi$
$461$	−31.5903	−1.47131	−0.735653	+	0.677359i	$0.763125\pi$
$462$	−3.08506	−0.143530
$463$	−8.46593	−0.393445	−0.196722	−	0.980459i	$-0.563030\pi$
$463$	−8.46593	−0.393445	−0.196722	+	0.980459i	$0.563030\pi$
$464$	25.2856	1.17385
$465$	−4.58615	−0.212677
$466$	2.45828	0.113878
$467$	−19.9678	−0.923999	−0.462000	−	0.886880i	$-0.652868\pi$
$467$	−19.9678	−0.923999	−0.462000	+	0.886880i	$0.652868\pi$
$468$	2.93215	0.135539
$469$	8.05210	0.371811
$470$	−4.99272	−0.230297
$471$	7.01595	0.323278
$472$	−1.67979	−0.0773185
$473$	0.569797	0.0261993
$474$	−3.31888	−0.152441
$475$	−4.40552	−0.202139
$476$	−1.45255	−0.0665777
$477$	−3.22751	−0.147777
$478$	6.99092	0.319757
$479$	−26.2880	−1.20113	−0.600564	−	0.799576i	$-0.705057\pi$
$479$	−26.2880	−1.20113	−0.600564	+	0.799576i	$0.705057\pi$
$480$	−11.0798	−0.505721
$481$	−22.8160	−1.04032
$482$	−3.39836	−0.154791
$483$	−10.2892	−0.468176
$484$	−33.4038	−1.51836
$485$	12.5513	0.569924
$486$	2.01818	0.0915465
$487$	−22.1991	−1.00594	−0.502969	−	0.864305i	$-0.667759\pi$
$487$	−22.1991	−1.00594	−0.502969	+	0.864305i	$0.667759\pi$
$488$	23.3596	1.05744
$489$	−12.3803	−0.559854
$490$	−4.20104	−0.189783
$491$	7.24421	0.326926	0.163463	−	0.986549i	$-0.447733\pi$
$491$	7.24421	0.326926	0.163463	+	0.986549i	$0.447733\pi$
$492$	−24.5996	−1.10904
$493$	−8.81434	−0.396978
$494$	−2.58332	−0.116229
$495$	3.61084	0.162295
$496$	−5.49290	−0.246638
$497$	−6.09721	−0.273497
$498$	−1.21253	−0.0543347
$499$	27.5862	1.23493	0.617464	−	0.786599i	$-0.288160\pi$
$499$	27.5862	1.23493	0.617464	+	0.786599i	$0.288160\pi$
$500$	−20.9730	−0.937943
$501$	37.0480	1.65518
$502$	3.99254	0.178196
$503$	−1.14341	−0.0509822	−0.0254911	−	0.999675i	$-0.508115\pi$
$503$	−1.14341	−0.0509822	−0.0254911	+	0.999675i	$0.508115\pi$
$504$	0.599811	0.0267177
$505$	27.5478	1.22586
$506$	19.1773	0.852537
$507$	−0.639074	−0.0283823
$508$	−38.1333	−1.69189
$509$	7.75924	0.343922	0.171961	−	0.985104i	$-0.444990\pi$
$509$	7.75924	0.343922	0.171961	+	0.985104i	$0.444990\pi$
$510$	1.05734	0.0468199
$511$	−5.02826	−0.222437
$512$	−22.9080	−1.01240
$513$	8.80191	0.388614
$514$	7.47577	0.329742
$515$	5.87971	0.259091
$516$	0.302746	0.0133277
$517$	−41.0084	−1.80355
$518$	−2.21413	−0.0972834
$519$	31.6797	1.39058
$520$	−9.21147	−0.403950
$521$	−40.0957	−1.75662	−0.878312	−	0.478088i	$-0.841330\pi$
$521$	−40.0957	−1.75662	−0.878312	+	0.478088i	$0.841330\pi$
$522$	1.72667	0.0755742
$523$	−33.1850	−1.45108	−0.725539	−	0.688181i	$-0.758410\pi$
$523$	−33.1850	−1.45108	−0.725539	+	0.688181i	$0.758410\pi$
$524$	2.11954	0.0925926
$525$	−3.54554	−0.154740
$526$	−12.0094	−0.523637
$527$	1.91478	0.0834091
$528$	−24.9134	−1.08422
$529$	40.9599	1.78086
$530$	4.81002	0.208934
$531$	0.443745	0.0192569
$532$	2.32207	0.100675
$533$	−31.2010	−1.35147
$534$	0.276807	0.0119786
$535$	−12.8413	−0.555180
$536$	−16.8088	−0.726029
$537$	−14.5512	−0.627930
$538$	8.88462	0.383043
$539$	−34.5058	−1.48627
$540$	14.8890	0.640721
$541$	36.0577	1.55024	0.775120	−	0.631814i	$-0.217689\pi$
$541$	36.0577	1.55024	0.775120	+	0.631814i	$0.217689\pi$
$542$	4.31275	0.185249
$543$	−26.3314	−1.12999
$544$	4.62597	0.198337
$545$	24.4518	1.04740
$546$	−2.07904	−0.0889747
$547$	2.88845	0.123501	0.0617506	−	0.998092i	$-0.480332\pi$
$547$	2.88845	0.123501	0.0617506	+	0.998092i	$0.480332\pi$
$548$	22.1770	0.947353
$549$	−6.17085	−0.263366
$550$	6.60827	0.281778
$551$	14.0907	0.600285
$552$	21.4788	0.914199
$553$	3.78382	0.160904
$554$	−7.85000	−0.333515
$555$	−14.9286	−0.633685
$556$	17.1708	0.728206
$557$	9.89724	0.419359	0.209680	−	0.977770i	$-0.432758\pi$
$557$	9.89724	0.419359	0.209680	+	0.977770i	$0.432758\pi$
$558$	−0.375092	−0.0158789
$559$	0.383989	0.0162410
$560$	3.45810	0.146131
$561$	8.68461	0.366665
$562$	−9.62405	−0.405966
$563$	28.5042	1.20131	0.600654	−	0.799509i	$-0.294907\pi$
$563$	28.5042	1.20131	0.600654	+	0.799509i	$0.294907\pi$
$564$	−21.7887	−0.917471
$565$	25.9574	1.09204
$566$	−11.7743	−0.494912
$567$	6.01250	0.252501
$568$	12.7280	0.534053
$569$	−22.1395	−0.928137	−0.464069	−	0.885799i	$-0.653611\pi$
$569$	−22.1395	−0.928137	−0.464069	+	0.885799i	$0.653611\pi$
$570$	−1.69028	−0.0707981
$571$	32.6506	1.36639	0.683193	−	0.730237i	$-0.260591\pi$
$571$	32.6506	1.36639	0.683193	+	0.730237i	$0.260591\pi$
$572$	−35.8923	−1.50073
$573$	13.9409	0.582388
$574$	−3.02784	−0.126380
$575$	22.0398	0.919123
$576$	1.63973	0.0683222
$577$	2.42841	0.101096	0.0505480	−	0.998722i	$-0.483903\pi$
$577$	2.42841	0.101096	0.0505480	+	0.998722i	$0.483903\pi$
$578$	−0.441455	−0.0183621
$579$	12.1132	0.503408
$580$	23.8354	0.989711
$581$	1.38239	0.0573512
$582$	−5.91356	−0.245125
$583$	39.5078	1.63624
$584$	10.4965	0.434348
$585$	2.43337	0.100607
$586$	7.24924	0.299463
$587$	−11.9631	−0.493770	−0.246885	−	0.969045i	$-0.579407\pi$
$587$	−11.9631	−0.493770	−0.246885	+	0.969045i	$0.579407\pi$
$588$	−18.3337	−0.756070
$589$	−3.06099	−0.126126
$590$	−0.661322	−0.0272262
$591$	4.33172	0.178183
$592$	−17.8803	−0.734874
$593$	−40.4422	−1.66076	−0.830381	−	0.557196i	$-0.811877\pi$
$593$	−40.4422	−1.66076	−0.830381	+	0.557196i	$0.811877\pi$
$594$	−13.2028	−0.541719
$595$	−1.20546	−0.0494192
$596$	36.0095	1.47501
$597$	−5.66508	−0.231856
$598$	12.9237	0.528490
$599$	39.6848	1.62148	0.810738	−	0.585409i	$-0.199066\pi$
$599$	39.6848	1.62148	0.810738	+	0.585409i	$0.199066\pi$
$600$	7.40133	0.302158
$601$	−4.27528	−0.174392	−0.0871961	−	0.996191i	$-0.527791\pi$
$601$	−4.27528	−0.174392	−0.0871961	+	0.996191i	$0.527791\pi$
$602$	0.0372636	0.00151875
$603$	4.44033	0.180824
$604$	2.50773	0.102038
$605$	−27.7216	−1.12704
$606$	−12.9792	−0.527243
$607$	−25.1121	−1.01927	−0.509634	−	0.860391i	$-0.670219\pi$
$607$	−25.1121	−1.01927	−0.509634	+	0.860391i	$0.670219\pi$
$608$	−7.39514	−0.299913
$609$	11.3401	0.459526
$610$	9.19655	0.372358
$611$	−27.6358	−1.11803
$612$	−0.801012	−0.0323790
$613$	16.9977	0.686529	0.343264	−	0.939239i	$-0.388467\pi$
$613$	16.9977	0.686529	0.343264	+	0.939239i	$0.388467\pi$
$614$	1.51687	0.0612157
$615$	−20.4150	−0.823213
$616$	−7.34225	−0.295828
$617$	42.6753	1.71804	0.859022	−	0.511938i	$-0.171072\pi$
$617$	42.6753	1.71804	0.859022	+	0.511938i	$0.171072\pi$
$618$	−2.77024	−0.111435
$619$	7.89614	0.317373	0.158686	−	0.987329i	$-0.449274\pi$
$619$	7.89614	0.317373	0.158686	+	0.987329i	$0.449274\pi$
$620$	−5.17787	−0.207948
$621$	−44.0339	−1.76702
$622$	−12.1346	−0.486552
$623$	−0.315584	−0.0126436
$624$	−16.7893	−0.672110
$625$	−3.62617	−0.145047
$626$	−8.02212	−0.320628
$627$	−13.8833	−0.554448
$628$	7.92118	0.316090
$629$	6.23291	0.248522
$630$	0.236142	0.00940812
$631$	−4.64853	−0.185055	−0.0925274	−	0.995710i	$-0.529495\pi$
$631$	−4.64853	−0.185055	−0.0925274	+	0.995710i	$0.529495\pi$
$632$	−7.89873	−0.314195
$633$	−41.6865	−1.65689
$634$	10.2681	0.407797
$635$	−31.6465	−1.25585
$636$	20.9914	0.832364
$637$	−23.2536	−0.921343
$638$	−21.1361	−0.836785
$639$	−3.36231	−0.133011
$640$	−16.3036	−0.644457
$641$	25.3320	1.00055	0.500276	−	0.865866i	$-0.333232\pi$
$641$	25.3320	1.00055	0.500276	+	0.865866i	$0.333232\pi$
$642$	6.05023	0.238783
$643$	5.77396	0.227703	0.113851	−	0.993498i	$-0.463681\pi$
$643$	5.77396	0.227703	0.113851	+	0.993498i	$0.463681\pi$
$644$	−11.6168	−0.457766
$645$	0.251247	0.00989284
$646$	0.705716	0.0277660
$647$	−26.8756	−1.05659	−0.528294	−	0.849062i	$-0.677168\pi$
$647$	−26.8756	−1.05659	−0.528294	+	0.849062i	$0.677168\pi$
$648$	−12.5511	−0.493055
$649$	−5.43186	−0.213219
$650$	4.45336	0.174675
$651$	−2.46347	−0.0965510
$652$	−13.9776	−0.547406
$653$	21.3510	0.835530	0.417765	−	0.908555i	$-0.362814\pi$
$653$	21.3510	0.835530	0.417765	+	0.908555i	$0.362814\pi$
$654$	−11.5205	−0.450488
$655$	1.75899	0.0687295
$656$	−24.4514	−0.954667
$657$	−2.77283	−0.108179
$658$	−2.68187	−0.104550
$659$	−21.4975	−0.837425	−0.418712	−	0.908119i	$-0.637518\pi$
$659$	−21.4975	−0.837425	−0.418712	+	0.908119i	$0.637518\pi$
$660$	−23.4846	−0.914137
$661$	39.2272	1.52576	0.762880	−	0.646540i	$-0.223784\pi$
$661$	39.2272	1.52576	0.762880	+	0.646540i	$0.223784\pi$
$662$	−3.81351	−0.148216
$663$	5.85261	0.227297
$664$	−2.88574	−0.111989
$665$	1.92707	0.0747286
$666$	−1.22098	−0.0473122
$667$	−70.4926	−2.72948
$668$	41.8281	1.61838
$669$	13.8005	0.533557
$670$	−6.61752	−0.255657
$671$	75.5371	2.91608
$672$	−5.95157	−0.229587
$673$	13.7349	0.529443	0.264721	−	0.964325i	$-0.414720\pi$
$673$	13.7349	0.529443	0.264721	+	0.964325i	$0.414720\pi$
$674$	−0.962030	−0.0370560
$675$	−15.1735	−0.584030
$676$	−0.721530	−0.0277512
$677$	−5.54097	−0.212957	−0.106478	−	0.994315i	$-0.533958\pi$
$677$	−5.54097	−0.212957	−0.106478	+	0.994315i	$0.533958\pi$
$678$	−12.2299	−0.469686
$679$	6.74199	0.258734
$680$	2.51641	0.0964999
$681$	11.9350	0.457352
$682$	4.59148	0.175817
$683$	4.81058	0.184072	0.0920358	−	0.995756i	$-0.470663\pi$
$683$	4.81058	0.184072	0.0920358	+	0.995756i	$0.470663\pi$
$684$	1.28051	0.0489615
$685$	18.4045	0.703199
$686$	−4.74324	−0.181098
$687$	15.2976	0.583640
$688$	0.300922	0.0114726
$689$	26.6245	1.01431
$690$	8.45608	0.321917
$691$	51.7580	1.96897	0.984483	−	0.175478i	$-0.0561472\pi$
$691$	51.7580	1.96897	0.984483	+	0.175478i	$0.0561472\pi$
$692$	35.7672	1.35966
$693$	1.93958	0.0736787
$694$	12.9767	0.492587
$695$	14.2499	0.540531
$696$	−23.6726	−0.897308
$697$	8.52355	0.322853
$698$	−4.12609	−0.156175
$699$	8.90322	0.336751
$700$	−4.00300	−0.151299
$701$	−44.5166	−1.68137	−0.840685	−	0.541524i	$-0.817847\pi$
$701$	−44.5166	−1.68137	−0.840685	+	0.541524i	$0.817847\pi$
$702$	−8.89748	−0.335814
$703$	−9.96402	−0.375800
$704$	−20.0719	−0.756488
$705$	−18.0823	−0.681019
$706$	0.395672	0.0148913
$707$	14.7974	0.556514
$708$	−2.88608	−0.108465
$709$	25.9580	0.974875	0.487438	−	0.873158i	$-0.337932\pi$
$709$	25.9580	0.974875	0.487438	+	0.873158i	$0.337932\pi$
$710$	5.01092	0.188057
$711$	2.08659	0.0782531
$712$	0.658783	0.0246890
$713$	15.3134	0.573492
$714$	0.567956	0.0212552
$715$	−29.7868	−1.11396
$716$	−16.4286	−0.613967
$717$	25.3192	0.945564
$718$	7.63311	0.284865
$719$	−32.4878	−1.21159	−0.605795	−	0.795621i	$-0.707145\pi$
$719$	−32.4878	−1.21159	−0.605795	+	0.795621i	$0.707145\pi$
$720$	1.90697	0.0710685
$721$	3.15832	0.117622
$722$	7.25947	0.270170
$723$	−12.3079	−0.457737
$724$	−29.7289	−1.10486
$725$	−24.2909	−0.902141
$726$	13.0611	0.484742
$727$	−1.79369	−0.0665242	−0.0332621	−	0.999447i	$-0.510590\pi$
$727$	−1.79369	−0.0665242	−0.0332621	+	0.999447i	$0.510590\pi$
$728$	−4.94799	−0.183385
$729$	29.7249	1.10092
$730$	4.13241	0.152947
$731$	−0.104899	−0.00387983
$732$	40.1347	1.48342
$733$	−0.310310	−0.0114616	−0.00573078	−	0.999984i	$-0.501824\pi$
$733$	−0.310310	−0.0114616	−0.00573078	+	0.999984i	$0.501824\pi$
$734$	13.3246	0.491819
$735$	−15.2150	−0.561214
$736$	36.9961	1.36370
$737$	−54.3539	−2.00215
$738$	−1.66971	−0.0614627
$739$	−11.0572	−0.406747	−0.203374	−	0.979101i	$-0.565191\pi$
$739$	−11.0572	−0.406747	−0.203374	+	0.979101i	$0.565191\pi$
$740$	−16.8548	−0.619595
$741$	−9.35607	−0.343704
$742$	2.58373	0.0948517
$743$	−10.9534	−0.401842	−0.200921	−	0.979607i	$-0.564393\pi$
$743$	−10.9534	−0.401842	−0.200921	+	0.979607i	$0.564393\pi$
$744$	5.14251	0.188533
$745$	29.8840	1.09487
$746$	8.66279	0.317167
$747$	0.762319	0.0278918
$748$	9.80514	0.358511
$749$	−6.89779	−0.252040
$750$	8.20057	0.299442
$751$	−27.6096	−1.00749	−0.503745	−	0.863853i	$-0.668045\pi$
$751$	−27.6096	−1.00749	−0.503745	+	0.863853i	$0.668045\pi$
$752$	−21.6575	−0.789766
$753$	14.4599	0.526948
$754$	−14.2437	−0.518726
$755$	2.08115	0.0757407
$756$	7.99771	0.290874
$757$	−6.89010	−0.250425	−0.125213	−	0.992130i	$-0.539961\pi$
$757$	−6.89010	−0.250425	−0.125213	+	0.992130i	$0.539961\pi$
$758$	−12.1378	−0.440866
$759$	69.4551	2.52106
$760$	−4.02277	−0.145921
$761$	29.7584	1.07874	0.539370	−	0.842069i	$-0.318662\pi$
$761$	29.7584	1.07874	0.539370	+	0.842069i	$0.318662\pi$
$762$	14.9103	0.540144
$763$	13.1344	0.475497
$764$	15.7396	0.569438
$765$	−0.664753	−0.0240342
$766$	−0.711609	−0.0257115
$767$	−3.66056	−0.132175
$768$	−4.13456	−0.149193
$769$	−35.5246	−1.28105	−0.640525	−	0.767937i	$-0.721283\pi$
$769$	−35.5246	−1.28105	−0.640525	+	0.767937i	$0.721283\pi$
$770$	−2.89060	−0.104170
$771$	27.0752	0.975090
$772$	13.6761	0.492215
$773$	−21.2580	−0.764597	−0.382299	−	0.924039i	$-0.624867\pi$
$773$	−21.2580	−0.764597	−0.382299	+	0.924039i	$0.624867\pi$
$774$	0.0205490	0.000738619 0
$775$	5.27682	0.189549
$776$	−14.0739	−0.505224
$777$	−8.01899	−0.287680
$778$	1.42636	0.0511375
$779$	−13.6259	−0.488198
$780$	−15.8264	−0.566677
$781$	41.1579	1.47274
$782$	−3.53053	−0.126251
$783$	48.5314	1.73437
$784$	−18.2233	−0.650831
$785$	6.57372	0.234626
$786$	−0.828752	−0.0295606
$787$	0.245100	0.00873686	0.00436843	−	0.999990i	$-0.498609\pi$
$787$	0.245100	0.00873686	0.00436843	+	0.999990i	$0.498609\pi$
$788$	4.89061	0.174221
$789$	−43.4950	−1.54846
$790$	−3.10968	−0.110638
$791$	13.9432	0.495762
$792$	−4.04889	−0.143871
$793$	50.9049	1.80769
$794$	−2.25302	−0.0799566
$795$	17.4206	0.617845
$796$	−6.39602	−0.226701
$797$	27.2703	0.965962	0.482981	−	0.875631i	$-0.339554\pi$
$797$	27.2703	0.965962	0.482981	+	0.875631i	$0.339554\pi$
$798$	−0.907943	−0.0321408
$799$	7.54961	0.267086
$800$	12.7484	0.450725
$801$	−0.174029	−0.00614901
$802$	15.1332	0.534371
$803$	33.9421	1.19779
$804$	−28.8795	−1.01850
$805$	−9.64068	−0.339789
$806$	3.09423	0.108990
$807$	32.1777	1.13271
$808$	−30.8897	−1.08669
$809$	−5.42708	−0.190806	−0.0954029	−	0.995439i	$-0.530414\pi$
$809$	−5.42708	−0.190806	−0.0954029	+	0.995439i	$0.530414\pi$
$810$	−4.94131	−0.173620
$811$	27.3112	0.959027	0.479513	−	0.877535i	$-0.340813\pi$
$811$	27.3112	0.959027	0.479513	+	0.877535i	$0.340813\pi$
$812$	12.8033	0.449308
$813$	15.6196	0.547804
$814$	14.9460	0.523857
$815$	−11.5999	−0.406327
$816$	4.58654	0.160561
$817$	0.167693	0.00586684
$818$	5.27289	0.184362
$819$	1.30710	0.0456737
$820$	−23.0491	−0.804908
$821$	−10.9839	−0.383339	−0.191670	−	0.981459i	$-0.561390\pi$
$821$	−10.9839	−0.383339	−0.191670	+	0.981459i	$0.561390\pi$
$822$	−8.67131	−0.302447
$823$	−38.0202	−1.32530	−0.662651	−	0.748928i	$-0.730569\pi$
$823$	−38.0202	−1.32530	−0.662651	+	0.748928i	$0.730569\pi$
$824$	−6.59300	−0.229678
$825$	23.9334	0.833253
$826$	−0.355233	−0.0123601
$827$	24.5276	0.852908	0.426454	−	0.904509i	$-0.359763\pi$
$827$	24.5276	0.852908	0.426454	+	0.904509i	$0.359763\pi$
$828$	−6.40608	−0.222627
$829$	46.8701	1.62787	0.813933	−	0.580959i	$-0.197323\pi$
$829$	46.8701	1.62787	0.813933	+	0.580959i	$0.197323\pi$
$830$	−1.13610	−0.0394346
$831$	−28.4306	−0.986246
$832$	−13.5266	−0.468949
$833$	6.35248	0.220100
$834$	−6.71389	−0.232483
$835$	34.7128	1.20129
$836$	−15.6746	−0.542119
$837$	−10.5427	−0.364409
$838$	−17.5243	−0.605365
$839$	−2.03270	−0.0701766	−0.0350883	−	0.999384i	$-0.511171\pi$
$839$	−2.03270	−0.0701766	−0.0350883	+	0.999384i	$0.511171\pi$
$840$	−3.23750	−0.111704
$841$	48.6926	1.67905
$842$	11.7382	0.404525
$843$	−34.8557	−1.20049
$844$	−47.0651	−1.62005
$845$	−0.598792	−0.0205991
$846$	−1.47892	−0.0508462
$847$	−14.8908	−0.511653
$848$	20.8649	0.716505
$849$	−42.6434	−1.46352
$850$	−1.21658	−0.0417283
$851$	49.8476	1.70876
$852$	21.8682	0.749191
$853$	−28.9398	−0.990879	−0.495440	−	0.868642i	$-0.664993\pi$
$853$	−28.9398	−0.990879	−0.495440	+	0.868642i	$0.664993\pi$
$854$	4.93998	0.169042
$855$	1.06268	0.0363430
$856$	14.3992	0.492154
$857$	3.47320	0.118642	0.0593211	−	0.998239i	$-0.481106\pi$
$857$	3.47320	0.118642	0.0593211	+	0.998239i	$0.481106\pi$
$858$	14.0341	0.479116
$859$	36.1946	1.23495	0.617473	−	0.786592i	$-0.288157\pi$
$859$	36.1946	1.23495	0.617473	+	0.786592i	$0.288157\pi$
$860$	0.283664	0.00967286
$861$	−10.9660	−0.373721
$862$	−10.9531	−0.373064
$863$	13.7154	0.466878	0.233439	−	0.972371i	$-0.425002\pi$
$863$	13.7154	0.466878	0.233439	+	0.972371i	$0.425002\pi$
$864$	−25.4704	−0.866521
$865$	29.6829	1.00925
$866$	10.3242	0.350832
$867$	−1.59883	−0.0542991
$868$	−2.78132	−0.0944041
$869$	−25.5418	−0.866446
$870$	−9.31977	−0.315970
$871$	−36.6294	−1.24114
$872$	−27.4181	−0.928495
$873$	3.71787	0.125831
$874$	5.64396	0.190910
$875$	−9.34938	−0.316067
$876$	18.0343	0.609321
$877$	19.4373	0.656349	0.328175	−	0.944617i	$-0.393567\pi$
$877$	19.4373	0.656349	0.328175	+	0.944617i	$0.393567\pi$
$878$	0.108397	0.00365823
$879$	26.2548	0.885552
$880$	−23.3431	−0.786896
$881$	7.86272	0.264902	0.132451	−	0.991190i	$-0.457715\pi$
$881$	7.86272	0.264902	0.132451	+	0.991190i	$0.457715\pi$
$882$	−1.24441	−0.0419014
$883$	−3.07227	−0.103390	−0.0516950	−	0.998663i	$-0.516462\pi$
$883$	−3.07227	−0.103390	−0.0516950	+	0.998663i	$0.516462\pi$
$884$	6.60775	0.222243
$885$	−2.39513	−0.0805114
$886$	−6.26498	−0.210476
$887$	21.3277	0.716113	0.358057	−	0.933700i	$-0.383439\pi$
$887$	21.3277	0.716113	0.358057	+	0.933700i	$0.383439\pi$
$888$	16.7397	0.561747
$889$	−16.9991	−0.570131
$890$	0.259359	0.00869374
$891$	−40.5861	−1.35968
$892$	15.5811	0.521693
$893$	−12.0689	−0.403871
$894$	−14.0799	−0.470903
$895$	−13.6340	−0.455735
$896$	−8.75757	−0.292570
$897$	46.8062	1.56281
$898$	−8.39100	−0.280011
$899$	−16.8775	−0.562896
$900$	−2.20746	−0.0735819
$901$	−7.27334	−0.242310
$902$	20.4388	0.680537
$903$	0.134959	0.00449114
$904$	−29.1064	−0.968065
$905$	−24.6717	−0.820116
$906$	−0.980537	−0.0325762
$907$	−17.8805	−0.593712	−0.296856	−	0.954922i	$-0.595938\pi$
$907$	−17.8805	−0.593712	−0.296856	+	0.954922i	$0.595938\pi$
$908$	13.4750	0.447182
$909$	8.16004	0.270651
$910$	−1.94799	−0.0645754
$911$	33.3265	1.10416	0.552079	−	0.833792i	$-0.313835\pi$
$911$	33.3265	1.10416	0.552079	+	0.833792i	$0.313835\pi$
$912$	−7.33211	−0.242790
$913$	−9.33151	−0.308828
$914$	−0.782764	−0.0258915
$915$	33.3074	1.10111
$916$	17.2714	0.570662
$917$	0.944851	0.0312017
$918$	2.43063	0.0802228
$919$	−10.5795	−0.348984	−0.174492	−	0.984659i	$-0.555828\pi$
$919$	−10.5795	−0.348984	−0.174492	+	0.984659i	$0.555828\pi$
$920$	20.1250	0.663500
$921$	5.49368	0.181023
$922$	13.9457	0.459276
$923$	27.7365	0.912959
$924$	−12.6149	−0.414999
$925$	17.1769	0.564773
$926$	3.73732	0.122816
$927$	1.74166	0.0572035
$928$	−40.7749	−1.33850
$929$	−19.5524	−0.641492	−0.320746	−	0.947165i	$-0.603934\pi$
$929$	−19.5524	−0.641492	−0.320746	+	0.947165i	$0.603934\pi$
$930$	2.02457	0.0663884
$931$	−10.1552	−0.332822
$932$	10.0520	0.329263
$933$	−43.9481	−1.43880
$934$	8.81487	0.288432
$935$	8.13721	0.266115
$936$	−2.72857	−0.0891861
$937$	13.8156	0.451335	0.225668	−	0.974204i	$-0.427544\pi$
$937$	13.8156	0.451335	0.225668	+	0.974204i	$0.427544\pi$
$938$	−3.55464	−0.116063
$939$	−29.0539	−0.948139
$940$	−20.4154	−0.665876
$941$	−53.1456	−1.73250	−0.866249	−	0.499613i	$-0.833476\pi$
$941$	−53.1456	−1.73250	−0.866249	+	0.499613i	$0.833476\pi$
$942$	−3.09722	−0.100913
$943$	68.1671	2.21982
$944$	−2.86869	−0.0933678
$945$	6.63723	0.215909
$946$	−0.251539	−0.00817825
$947$	42.9586	1.39597	0.697983	−	0.716114i	$-0.254081\pi$
$947$	42.9586	1.39597	0.697983	+	0.716114i	$0.254081\pi$
$948$	−13.5710	−0.440765
$949$	22.8738	0.742515
$950$	1.94484	0.0630989
$951$	37.1881	1.20591
$952$	1.35170	0.0438089
$953$	3.92147	0.127029	0.0635144	−	0.997981i	$-0.479769\pi$
$953$	3.92147	0.127029	0.0635144	+	0.997981i	$0.479769\pi$
$954$	1.42480	0.0461295
$955$	13.0621	0.422681
$956$	28.5860	0.924539
$957$	−76.5491	−2.47448
$958$	11.6050	0.374939
$959$	9.88606	0.319238
$960$	−8.85053	−0.285650
$961$	−27.3336	−0.881730
$962$	10.0722	0.324741
$963$	−3.80379	−0.122575
$964$	−13.8960	−0.447558
$965$	11.3497	0.365360
$966$	4.54223	0.146144
$967$	33.9957	1.09323	0.546614	−	0.837384i	$-0.315916\pi$
$967$	33.9957	1.09323	0.546614	+	0.837384i	$0.315916\pi$
$968$	31.0846	0.999096
$969$	2.55591	0.0821077
$970$	−5.54082	−0.177905
$971$	−21.8262	−0.700436	−0.350218	−	0.936668i	$-0.613892\pi$
$971$	−21.8262	−0.700436	−0.350218	+	0.936668i	$0.613892\pi$
$972$	8.25238	0.264695
$973$	7.65443	0.245390
$974$	9.79990	0.314009
$975$	16.1289	0.516537
$976$	39.8928	1.27694
$977$	−59.1305	−1.89175	−0.945876	−	0.324530i	$-0.894794\pi$
$977$	−59.1305	−1.89175	−0.945876	+	0.324530i	$0.894794\pi$
$978$	5.46532	0.174762
$979$	2.13028	0.0680841
$980$	−17.1781	−0.548735
$981$	7.24297	0.231250
$982$	−3.19799	−0.102052
$983$	−28.3551	−0.904388	−0.452194	−	0.891920i	$-0.649358\pi$
$983$	−28.3551	−0.904388	−0.452194	+	0.891920i	$0.649358\pi$
$984$	22.8916	0.729759
$985$	4.05868	0.129320
$986$	3.89113	0.123919
$987$	−9.71300	−0.309168
$988$	−10.5632	−0.336061
$989$	−0.838929	−0.0266764
$990$	−1.59402	−0.0506614
$991$	30.5662	0.970967	0.485483	−	0.874246i	$-0.338644\pi$
$991$	30.5662	0.970967	0.485483	+	0.874246i	$0.338644\pi$
$992$	8.85771	0.281232
$993$	−13.8115	−0.438294
$994$	2.69164	0.0853737
$995$	−5.30801	−0.168275
$996$	−4.95806	−0.157102
$997$	11.6491	0.368930	0.184465	−	0.982839i	$-0.440945\pi$
$997$	11.6491	0.368930	0.184465	+	0.982839i	$0.440945\pi$
$998$	−12.1781	−0.385490
$999$	−34.3182	−1.08578

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.g.1.5	✓	10
3.2	odd	2		9027.2.a.j.1.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.g.1.5	✓	10	1.1	even	1	trivial
9027.2.a.j.1.6		10	3.2	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:	\( N \)	\(=\)	\( 1003 = 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1003.a (trivial)

\(f(q)\)	\(=\)	\(q-0.441455 q^{2} -1.59883 q^{3} -1.80512 q^{4} -1.49805 q^{5} +0.705811 q^{6} -0.804687 q^{7} +1.67979 q^{8} -0.443745 q^{9} +O(q^{10})\)	\(q-0.441455 q^{2} -1.59883 q^{3} -1.80512 q^{4} -1.49805 q^{5} +0.705811 q^{6} -0.804687 q^{7} +1.67979 q^{8} -0.443745 q^{9} +0.661322 q^{10} +5.43186 q^{11} +2.88608 q^{12} +3.66056 q^{13} +0.355233 q^{14} +2.39513 q^{15} +2.86869 q^{16} -1.00000 q^{17} +0.195893 q^{18} +1.59861 q^{19} +2.70416 q^{20} +1.28656 q^{21} -2.39792 q^{22} -7.99749 q^{23} -2.68569 q^{24} -2.75584 q^{25} -1.61597 q^{26} +5.50596 q^{27} +1.45255 q^{28} +8.81434 q^{29} -1.05734 q^{30} -1.91478 q^{31} -4.62597 q^{32} -8.68461 q^{33} +0.441455 q^{34} +1.20546 q^{35} +0.801012 q^{36} -6.23291 q^{37} -0.705716 q^{38} -5.85261 q^{39} -2.51641 q^{40} -8.52355 q^{41} -0.567956 q^{42} +0.104899 q^{43} -9.80514 q^{44} +0.664753 q^{45} +3.53053 q^{46} -7.54961 q^{47} -4.58654 q^{48} -6.35248 q^{49} +1.21658 q^{50} +1.59883 q^{51} -6.60775 q^{52} +7.27334 q^{53} -2.43063 q^{54} -8.13721 q^{55} -1.35170 q^{56} -2.55591 q^{57} -3.89113 q^{58} -1.00000 q^{59} -4.32349 q^{60} +13.9063 q^{61} +0.845288 q^{62} +0.357075 q^{63} -3.69522 q^{64} -5.48371 q^{65} +3.83386 q^{66} -10.0065 q^{67} +1.80512 q^{68} +12.7866 q^{69} -0.532157 q^{70} +7.57712 q^{71} -0.745397 q^{72} +6.24871 q^{73} +2.75155 q^{74} +4.40611 q^{75} -2.88569 q^{76} -4.37094 q^{77} +2.58366 q^{78} -4.70222 q^{79} -4.29744 q^{80} -7.47186 q^{81} +3.76276 q^{82} -1.71792 q^{83} -2.32239 q^{84} +1.49805 q^{85} -0.0463082 q^{86} -14.0926 q^{87} +9.12436 q^{88} +0.392183 q^{89} -0.293458 q^{90} -2.94561 q^{91} +14.4364 q^{92} +3.06140 q^{93} +3.33281 q^{94} -2.39481 q^{95} +7.39613 q^{96} -8.37840 q^{97} +2.80433 q^{98} -2.41036 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9}+O(q^{10}) \) 10 * q - q^2 - 7 * q^3 + 15 * q^4 - 12 * q^5 + 5 * q^6 - 9 * q^7 - 12 * q^8 + 3 * q^9	\( 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9} + 4 q^{10} + 12 q^{11} - 24 q^{12} - 11 q^{13} - 12 q^{14} + 9 q^{15} - 3 q^{16} - 10 q^{17} - 22 q^{18} - 5 q^{19} - 36 q^{20} - 10 q^{21} + 6 q^{22} - 7 q^{23} + 35 q^{24} + 2 q^{25} + q^{26} - 31 q^{27} - 4 q^{28} + 10 q^{29} - 9 q^{30} + 13 q^{31} - 15 q^{32} - 9 q^{33} + q^{34} - 8 q^{35} + 40 q^{36} + 12 q^{37} - 50 q^{38} + 24 q^{39} + 5 q^{40} - 29 q^{41} - 17 q^{42} - 18 q^{43} - 6 q^{44} - 14 q^{45} + 11 q^{46} - 18 q^{47} - 43 q^{48} - 9 q^{49} - 31 q^{50} + 7 q^{51} - 68 q^{52} + 19 q^{54} - 27 q^{55} - 7 q^{56} + 20 q^{57} + 23 q^{58} - 10 q^{59} + 38 q^{60} + 8 q^{61} - 46 q^{62} + 39 q^{63} - 20 q^{64} + 58 q^{65} - 34 q^{66} - 6 q^{67} - 15 q^{68} + 6 q^{69} + 73 q^{70} + 8 q^{71} - 70 q^{72} - 41 q^{73} - 10 q^{74} + 10 q^{75} + 12 q^{76} - 22 q^{77} - 43 q^{78} + 3 q^{79} - 15 q^{80} + 26 q^{81} + 8 q^{82} - 22 q^{84} + 12 q^{85} - 29 q^{86} - 28 q^{87} + 33 q^{88} - 45 q^{89} + 56 q^{90} - 14 q^{91} + 36 q^{92} - 19 q^{93} + 15 q^{94} - 17 q^{95} + 90 q^{96} - 5 q^{97} + 30 q^{98} + 14 q^{99}+O(q^{100}) \) 10 * q - q^2 - 7 * q^3 + 15 * q^4 - 12 * q^5 + 5 * q^6 - 9 * q^7 - 12 * q^8 + 3 * q^9 + 4 * q^10 + 12 * q^11 - 24 * q^12 - 11 * q^13 - 12 * q^14 + 9 * q^15 - 3 * q^16 - 10 * q^17 - 22 * q^18 - 5 * q^19 - 36 * q^20 - 10 * q^21 + 6 * q^22 - 7 * q^23 + 35 * q^24 + 2 * q^25 + q^26 - 31 * q^27 - 4 * q^28 + 10 * q^29 - 9 * q^30 + 13 * q^31 - 15 * q^32 - 9 * q^33 + q^34 - 8 * q^35 + 40 * q^36 + 12 * q^37 - 50 * q^38 + 24 * q^39 + 5 * q^40 - 29 * q^41 - 17 * q^42 - 18 * q^43 - 6 * q^44 - 14 * q^45 + 11 * q^46 - 18 * q^47 - 43 * q^48 - 9 * q^49 - 31 * q^50 + 7 * q^51 - 68 * q^52 + 19 * q^54 - 27 * q^55 - 7 * q^56 + 20 * q^57 + 23 * q^58 - 10 * q^59 + 38 * q^60 + 8 * q^61 - 46 * q^62 + 39 * q^63 - 20 * q^64 + 58 * q^65 - 34 * q^66 - 6 * q^67 - 15 * q^68 + 6 * q^69 + 73 * q^70 + 8 * q^71 - 70 * q^72 - 41 * q^73 - 10 * q^74 + 10 * q^75 + 12 * q^76 - 22 * q^77 - 43 * q^78 + 3 * q^79 - 15 * q^80 + 26 * q^81 + 8 * q^82 - 22 * q^84 + 12 * q^85 - 29 * q^86 - 28 * q^87 + 33 * q^88 - 45 * q^89 + 56 * q^90 - 14 * q^91 + 36 * q^92 - 19 * q^93 + 15 * q^94 - 17 * q^95 + 90 * q^96 - 5 * q^97 + 30 * q^98 + 14 * q^99

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