LMFDB - Embedded newform 1045.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,2,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1045.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:	$8.34436701122$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 10x^{5} + 8x^{4} + 27x^{3} - 16x^{2} - 18x + 11 $ x^7 - x^6 - 10x^5 + 8x^4 + 27x^3 - 16x^2 - 18*x + 11
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.40300$ of defining polynomial
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.40300 q^{2} -1.17935 q^{3} +3.77440 q^{4} -1.00000 q^{5} +2.83397 q^{6} -2.15598 q^{7} -4.26389 q^{8} -1.60914 q^{9} +O(q^{10})$	\(q-2.40300 q^{2} -1.17935 q^{3} +3.77440 q^{4} -1.00000 q^{5} +2.83397 q^{6} -2.15598 q^{7} -4.26389 q^{8} -1.60914 q^{9} +2.40300 q^{10} +1.00000 q^{11} -4.45134 q^{12} -3.54733 q^{13} +5.18083 q^{14} +1.17935 q^{15} +2.69732 q^{16} -0.622194 q^{17} +3.86675 q^{18} -1.00000 q^{19} -3.77440 q^{20} +2.54266 q^{21} -2.40300 q^{22} -5.67863 q^{23} +5.02862 q^{24} +1.00000 q^{25} +8.52423 q^{26} +5.43578 q^{27} -8.13756 q^{28} +7.32397 q^{29} -2.83397 q^{30} -7.89640 q^{31} +2.04612 q^{32} -1.17935 q^{33} +1.49513 q^{34} +2.15598 q^{35} -6.07353 q^{36} -9.19792 q^{37} +2.40300 q^{38} +4.18354 q^{39} +4.26389 q^{40} +2.29509 q^{41} -6.11000 q^{42} +0.194427 q^{43} +3.77440 q^{44} +1.60914 q^{45} +13.6457 q^{46} +0.340863 q^{47} -3.18108 q^{48} -2.35173 q^{49} -2.40300 q^{50} +0.733784 q^{51} -13.3891 q^{52} -6.94545 q^{53} -13.0622 q^{54} -1.00000 q^{55} +9.19289 q^{56} +1.17935 q^{57} -17.5995 q^{58} +8.99709 q^{59} +4.45134 q^{60} -13.7381 q^{61} +18.9750 q^{62} +3.46927 q^{63} -10.3115 q^{64} +3.54733 q^{65} +2.83397 q^{66} -0.226658 q^{67} -2.34841 q^{68} +6.69709 q^{69} -5.18083 q^{70} +0.343554 q^{71} +6.86119 q^{72} +9.18704 q^{73} +22.1026 q^{74} -1.17935 q^{75} -3.77440 q^{76} -2.15598 q^{77} -10.0530 q^{78} +14.4980 q^{79} -2.69732 q^{80} -1.58327 q^{81} -5.51510 q^{82} +3.15514 q^{83} +9.59702 q^{84} +0.622194 q^{85} -0.467207 q^{86} -8.63752 q^{87} -4.26389 q^{88} +5.44854 q^{89} -3.86675 q^{90} +7.64799 q^{91} -21.4335 q^{92} +9.31261 q^{93} -0.819094 q^{94} +1.00000 q^{95} -2.41309 q^{96} +13.7041 q^{97} +5.65121 q^{98} -1.60914 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + q^{2} + 3 q^{3} + 7 q^{4} - 7 q^{5} + 8 q^{6} - q^{7} + 3 q^{8} + 2 q^{9}+O(q^{10}) $ 7 * q + q^2 + 3 * q^3 + 7 * q^4 - 7 * q^5 + 8 * q^6 - q^7 + 3 * q^8 + 2 * q^9	\( 7 q + q^{2} + 3 q^{3} + 7 q^{4} - 7 q^{5} + 8 q^{6} - q^{7} + 3 q^{8} + 2 q^{9} - q^{10} + 7 q^{11} + 13 q^{12} + q^{13} + 12 q^{14} - 3 q^{15} + 3 q^{16} + q^{17} + 7 q^{18} - 7 q^{19} - 7 q^{20} + 5 q^{21} + q^{22} - 8 q^{23} + 25 q^{24} + 7 q^{25} + 12 q^{27} + 4 q^{28} + 11 q^{29} - 8 q^{30} + 7 q^{31} + 12 q^{32} + 3 q^{33} - 14 q^{34} + q^{35} + 7 q^{36} - 17 q^{37} - q^{38} + 30 q^{39} - 3 q^{40} + 17 q^{41} + 33 q^{42} - 3 q^{43} + 7 q^{44} - 2 q^{45} + 18 q^{46} + 14 q^{47} - 12 q^{48} + 6 q^{49} + q^{50} + 8 q^{51} - 17 q^{52} + 7 q^{53} - 27 q^{54} - 7 q^{55} + 36 q^{56} - 3 q^{57} - 15 q^{58} + 35 q^{59} - 13 q^{60} + 17 q^{61} + 46 q^{62} - 22 q^{63} + 5 q^{64} - q^{65} + 8 q^{66} + 4 q^{67} - 35 q^{68} - 4 q^{69} - 12 q^{70} + 10 q^{71} + 12 q^{72} + 22 q^{73} - 11 q^{74} + 3 q^{75} - 7 q^{76} - q^{77} - 41 q^{78} + 11 q^{79} - 3 q^{80} - 21 q^{81} - 14 q^{82} + 39 q^{83} + 21 q^{84} - q^{85} - 24 q^{86} - 2 q^{87} + 3 q^{88} + 18 q^{89} - 7 q^{90} - 22 q^{91} - 51 q^{92} + 10 q^{93} + 14 q^{94} + 7 q^{95} - 11 q^{96} - 4 q^{97} - 26 q^{98} + 2 q^{99}+O(q^{100}) \) 7 * q + q^2 + 3 * q^3 + 7 * q^4 - 7 * q^5 + 8 * q^6 - q^7 + 3 * q^8 + 2 * q^9 - q^10 + 7 * q^11 + 13 * q^12 + q^13 + 12 * q^14 - 3 * q^15 + 3 * q^16 + q^17 + 7 * q^18 - 7 * q^19 - 7 * q^20 + 5 * q^21 + q^22 - 8 * q^23 + 25 * q^24 + 7 * q^25 + 12 * q^27 + 4 * q^28 + 11 * q^29 - 8 * q^30 + 7 * q^31 + 12 * q^32 + 3 * q^33 - 14 * q^34 + q^35 + 7 * q^36 - 17 * q^37 - q^38 + 30 * q^39 - 3 * q^40 + 17 * q^41 + 33 * q^42 - 3 * q^43 + 7 * q^44 - 2 * q^45 + 18 * q^46 + 14 * q^47 - 12 * q^48 + 6 * q^49 + q^50 + 8 * q^51 - 17 * q^52 + 7 * q^53 - 27 * q^54 - 7 * q^55 + 36 * q^56 - 3 * q^57 - 15 * q^58 + 35 * q^59 - 13 * q^60 + 17 * q^61 + 46 * q^62 - 22 * q^63 + 5 * q^64 - q^65 + 8 * q^66 + 4 * q^67 - 35 * q^68 - 4 * q^69 - 12 * q^70 + 10 * q^71 + 12 * q^72 + 22 * q^73 - 11 * q^74 + 3 * q^75 - 7 * q^76 - q^77 - 41 * q^78 + 11 * q^79 - 3 * q^80 - 21 * q^81 - 14 * q^82 + 39 * q^83 + 21 * q^84 - q^85 - 24 * q^86 - 2 * q^87 + 3 * q^88 + 18 * q^89 - 7 * q^90 - 22 * q^91 - 51 * q^92 + 10 * q^93 + 14 * q^94 + 7 * q^95 - 11 * q^96 - 4 * q^97 - 26 * q^98 + 2 * 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 $

$2$	−2.40300	−1.69918	−0.849589	−	0.527446i	$-0.823150\pi$
$2$	−2.40300	−1.69918	−0.849589	+	0.527446i	$0.823150\pi$
$3$	−1.17935	−0.680897	−0.340449	−	0.940263i	$-0.610579\pi$
$3$	−1.17935	−0.680897	−0.340449	+	0.940263i	$0.610579\pi$
$4$	3.77440	1.88720
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.83397	1.15697
$7$	−2.15598	−0.814885	−0.407443	−	0.913231i	$-0.633579\pi$
$7$	−2.15598	−0.814885	−0.407443	+	0.913231i	$0.633579\pi$
$8$	−4.26389	−1.50751
$9$	−1.60914	−0.536379
$10$	2.40300	0.759895
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−4.45134	−1.28499
$13$	−3.54733	−0.983852	−0.491926	−	0.870637i	$-0.663707\pi$
$13$	−3.54733	−0.983852	−0.491926	+	0.870637i	$0.663707\pi$
$14$	5.18083	1.38463
$15$	1.17935	0.304507
$16$	2.69732	0.674331
$17$	−0.622194	−0.150904	−0.0754521	−	0.997149i	$-0.524040\pi$
$17$	−0.622194	−0.150904	−0.0754521	+	0.997149i	$0.524040\pi$
$18$	3.86675	0.911403
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−3.77440	−0.843983
$21$	2.54266	0.554853
$22$	−2.40300	−0.512321
$23$	−5.67863	−1.18408	−0.592038	−	0.805910i	$-0.701677\pi$
$23$	−5.67863	−1.18408	−0.592038	+	0.805910i	$0.701677\pi$
$24$	5.02862	1.02646
$25$	1.00000	0.200000
$26$	8.52423	1.67174
$27$	5.43578	1.04612
$28$	−8.13756	−1.53785
$29$	7.32397	1.36003	0.680014	−	0.733199i	$-0.261974\pi$
$29$	7.32397	1.36003	0.680014	+	0.733199i	$0.261974\pi$
$30$	−2.83397	−0.517410
$31$	−7.89640	−1.41824	−0.709118	−	0.705090i	$-0.750907\pi$
$31$	−7.89640	−1.41824	−0.709118	+	0.705090i	$0.750907\pi$
$32$	2.04612	0.361707
$33$	−1.17935	−0.205298
$34$	1.49513	0.256413
$35$	2.15598	0.364428
$36$	−6.07353	−1.01226
$37$	−9.19792	−1.51213	−0.756065	−	0.654497i	$-0.772881\pi$
$37$	−9.19792	−1.51213	−0.756065	+	0.654497i	$0.772881\pi$
$38$	2.40300	0.389818
$39$	4.18354	0.669902
$40$	4.26389	0.674181
$41$	2.29509	0.358433	0.179216	−	0.983810i	$-0.442644\pi$
$41$	2.29509	0.358433	0.179216	+	0.983810i	$0.442644\pi$
$42$	−6.11000	−0.942794
$43$	0.194427	0.0296498	0.0148249	−	0.999890i	$-0.495281\pi$
$43$	0.194427	0.0296498	0.0148249	+	0.999890i	$0.495281\pi$
$44$	3.77440	0.569013
$45$	1.60914	0.239876
$46$	13.6457	2.01196
$47$	0.340863	0.0497200	0.0248600	−	0.999691i	$-0.492086\pi$
$47$	0.340863	0.0497200	0.0248600	+	0.999691i	$0.492086\pi$
$48$	−3.18108	−0.459150
$49$	−2.35173	−0.335962
$50$	−2.40300	−0.339835
$51$	0.733784	0.102750
$52$	−13.3891	−1.85673
$53$	−6.94545	−0.954031	−0.477015	−	0.878895i	$-0.658281\pi$
$53$	−6.94545	−0.954031	−0.477015	+	0.878895i	$0.658281\pi$
$54$	−13.0622	−1.77754
$55$	−1.00000	−0.134840
$56$	9.19289	1.22845
$57$	1.17935	0.156209
$58$	−17.5995	−2.31093
$59$	8.99709	1.17132	0.585660	−	0.810557i	$-0.300835\pi$
$59$	8.99709	1.17132	0.585660	+	0.810557i	$0.300835\pi$
$60$	4.45134	0.574665
$61$	−13.7381	−1.75899	−0.879494	−	0.475910i	$-0.842119\pi$
$61$	−13.7381	−1.75899	−0.879494	+	0.475910i	$0.842119\pi$
$62$	18.9750	2.40983
$63$	3.46927	0.437087
$64$	−10.3115	−1.28893
$65$	3.54733	0.439992
$66$	2.83397	0.348838
$67$	−0.226658	−0.0276907	−0.0138453	−	0.999904i	$-0.504407\pi$
$67$	−0.226658	−0.0276907	−0.0138453	+	0.999904i	$0.504407\pi$
$68$	−2.34841	−0.284787
$69$	6.69709	0.806234
$70$	−5.18083	−0.619227
$71$	0.343554	0.0407724	0.0203862	−	0.999792i	$-0.493510\pi$
$71$	0.343554	0.0407724	0.0203862	+	0.999792i	$0.493510\pi$
$72$	6.86119	0.808599
$73$	9.18704	1.07526	0.537631	−	0.843180i	$-0.319319\pi$
$73$	9.18704	1.07526	0.537631	+	0.843180i	$0.319319\pi$
$74$	22.1026	2.56938
$75$	−1.17935	−0.136179
$76$	−3.77440	−0.432954
$77$	−2.15598	−0.245697
$78$	−10.0530	−1.13828
$79$	14.4980	1.63115	0.815574	−	0.578653i	$-0.196422\pi$
$79$	14.4980	1.63115	0.815574	+	0.578653i	$0.196422\pi$
$80$	−2.69732	−0.301570
$81$	−1.58327	−0.175919
$82$	−5.51510	−0.609041
$83$	3.15514	0.346321	0.173161	−	0.984894i	$-0.444602\pi$
$83$	3.15514	0.346321	0.173161	+	0.984894i	$0.444602\pi$
$84$	9.59702	1.04712
$85$	0.622194	0.0674864
$86$	−0.467207	−0.0503802
$87$	−8.63752	−0.926039
$88$	−4.26389	−0.454533
$89$	5.44854	0.577544	0.288772	−	0.957398i	$-0.406753\pi$
$89$	5.44854	0.577544	0.288772	+	0.957398i	$0.406753\pi$
$90$	−3.86675	−0.407592
$91$	7.64799	0.801727
$92$	−21.4335	−2.23459
$93$	9.31261	0.965673
$94$	−0.819094	−0.0844831
$95$	1.00000	0.102598
$96$	−2.41309	−0.246285
$97$	13.7041	1.39144	0.695722	−	0.718311i	$-0.255084\pi$
$97$	13.7041	1.39144	0.695722	+	0.718311i	$0.255084\pi$
$98$	5.65121	0.570858
$99$	−1.60914	−0.161724
$100$	3.77440	0.377440
$101$	−4.70463	−0.468128	−0.234064	−	0.972221i	$-0.575203\pi$
$101$	−4.70463	−0.468128	−0.234064	+	0.972221i	$0.575203\pi$
$102$	−1.76328	−0.174591
$103$	13.3333	1.31377	0.656885	−	0.753991i	$-0.271874\pi$
$103$	13.3333	1.31377	0.656885	+	0.753991i	$0.271874\pi$
$104$	15.1254	1.48317
$105$	−2.54266	−0.248138
$106$	16.6899	1.62107
$107$	−7.07306	−0.683779	−0.341889	−	0.939740i	$-0.611067\pi$
$107$	−7.07306	−0.683779	−0.341889	+	0.939740i	$0.611067\pi$
$108$	20.5168	1.97423
$109$	8.93287	0.855614	0.427807	−	0.903870i	$-0.359286\pi$
$109$	8.93287	0.855614	0.427807	+	0.903870i	$0.359286\pi$
$110$	2.40300	0.229117
$111$	10.8476	1.02960
$112$	−5.81539	−0.549502
$113$	8.90054	0.837293	0.418646	−	0.908149i	$-0.362505\pi$
$113$	8.90054	0.837293	0.418646	+	0.908149i	$0.362505\pi$
$114$	−2.83397	−0.265426
$115$	5.67863	0.529535
$116$	27.6436	2.56665
$117$	5.70814	0.527718
$118$	−21.6200	−1.99028
$119$	1.34144	0.122970
$120$	−5.02862	−0.459048
$121$	1.00000	0.0909091
$122$	33.0127	2.98883
$123$	−2.70671	−0.244056
$124$	−29.8042	−2.67650
$125$	−1.00000	−0.0894427
$126$	−8.33666	−0.742689
$127$	14.9809	1.32934	0.664672	−	0.747135i	$-0.268571\pi$
$127$	14.9809	1.32934	0.664672	+	0.747135i	$0.268571\pi$
$128$	20.6862	1.82842
$129$	−0.229297	−0.0201885
$130$	−8.52423	−0.747625
$131$	7.81438	0.682746	0.341373	−	0.939928i	$-0.389108\pi$
$131$	7.81438	0.682746	0.341373	+	0.939928i	$0.389108\pi$
$132$	−4.45134	−0.387439
$133$	2.15598	0.186948
$134$	0.544659	0.0470513
$135$	−5.43578	−0.467837
$136$	2.65297	0.227490
$137$	14.1390	1.20798	0.603988	−	0.796994i	$-0.293578\pi$
$137$	14.1390	1.20798	0.603988	+	0.796994i	$0.293578\pi$
$138$	−16.0931	−1.36994
$139$	12.5953	1.06832	0.534158	−	0.845385i	$-0.320629\pi$
$139$	12.5953	1.06832	0.534158	+	0.845385i	$0.320629\pi$
$140$	8.13756	0.687749
$141$	−0.401997	−0.0338542
$142$	−0.825561	−0.0692795
$143$	−3.54733	−0.296643
$144$	−4.34036	−0.361697
$145$	−7.32397	−0.608223
$146$	−22.0764	−1.82706
$147$	2.77351	0.228755
$148$	−34.7167	−2.85369
$149$	4.77915	0.391523	0.195761	−	0.980652i	$-0.437282\pi$
$149$	4.77915	0.391523	0.195761	+	0.980652i	$0.437282\pi$
$150$	2.83397	0.231393
$151$	−24.0449	−1.95674	−0.978371	−	0.206856i	$-0.933677\pi$
$151$	−24.0449	−1.95674	−0.978371	+	0.206856i	$0.933677\pi$
$152$	4.26389	0.345847
$153$	1.00119	0.0809418
$154$	5.18083	0.417483
$155$	7.89640	0.634254
$156$	15.7904	1.26424
$157$	−12.9931	−1.03696	−0.518481	−	0.855089i	$-0.673502\pi$
$157$	−12.9931	−1.03696	−0.518481	+	0.855089i	$0.673502\pi$
$158$	−34.8386	−2.77161
$159$	8.19110	0.649597
$160$	−2.04612	−0.161760
$161$	12.2430	0.964887
$162$	3.80459	0.298917
$163$	−19.7251	−1.54499	−0.772495	−	0.635021i	$-0.780992\pi$
$163$	−19.7251	−1.54499	−0.772495	+	0.635021i	$0.780992\pi$
$164$	8.66260	0.676435
$165$	1.17935	0.0918122
$166$	−7.58180	−0.588461
$167$	9.91934	0.767582	0.383791	−	0.923420i	$-0.374618\pi$
$167$	9.91934	0.767582	0.383791	+	0.923420i	$0.374618\pi$
$168$	−10.8416	−0.836449
$169$	−0.416450	−0.0320346
$170$	−1.49513	−0.114671
$171$	1.60914	0.123054
$172$	0.733845	0.0559552
$173$	10.7461	0.817009	0.408504	−	0.912756i	$-0.366050\pi$
$173$	10.7461	0.817009	0.408504	+	0.912756i	$0.366050\pi$
$174$	20.7559	1.57350
$175$	−2.15598	−0.162977
$176$	2.69732	0.203318
$177$	−10.6107	−0.797549
$178$	−13.0928	−0.981350
$179$	9.08355	0.678936	0.339468	−	0.940618i	$-0.389753\pi$
$179$	9.08355	0.678936	0.339468	+	0.940618i	$0.389753\pi$
$180$	6.07353	0.452694
$181$	−6.00048	−0.446012	−0.223006	−	0.974817i	$-0.571587\pi$
$181$	−6.00048	−0.446012	−0.223006	+	0.974817i	$0.571587\pi$
$182$	−18.3781	−1.36228
$183$	16.2020	1.19769
$184$	24.2131	1.78501
$185$	9.19792	0.676245
$186$	−22.3782	−1.64085
$187$	−0.622194	−0.0454993
$188$	1.28656	0.0938318
$189$	−11.7195	−0.852465
$190$	−2.40300	−0.174332
$191$	−12.6793	−0.917443	−0.458721	−	0.888580i	$-0.651692\pi$
$191$	−12.6793	−0.917443	−0.458721	+	0.888580i	$0.651692\pi$
$192$	12.1608	0.877632
$193$	14.5221	1.04533	0.522664	−	0.852539i	$-0.324938\pi$
$193$	14.5221	1.04533	0.522664	+	0.852539i	$0.324938\pi$
$194$	−32.9310	−2.36431
$195$	−4.18354	−0.299589
$196$	−8.87639	−0.634028
$197$	−1.83384	−0.130656	−0.0653278	−	0.997864i	$-0.520809\pi$
$197$	−1.83384	−0.130656	−0.0653278	+	0.997864i	$0.520809\pi$
$198$	3.86675	0.274798
$199$	−12.9881	−0.920701	−0.460350	−	0.887737i	$-0.652276\pi$
$199$	−12.9881	−0.920701	−0.460350	+	0.887737i	$0.652276\pi$
$200$	−4.26389	−0.301503
$201$	0.267309	0.0188545
$202$	11.3052	0.795433
$203$	−15.7904	−1.10827
$204$	2.76960	0.193911
$205$	−2.29509	−0.160296
$206$	−32.0399	−2.23233
$207$	9.13769	0.635114
$208$	−9.56830	−0.663442
$209$	−1.00000	−0.0691714
$210$	6.11000	0.421630
$211$	9.51881	0.655302	0.327651	−	0.944799i	$-0.393743\pi$
$211$	9.51881	0.655302	0.327651	+	0.944799i	$0.393743\pi$
$212$	−26.2149	−1.80045
$213$	−0.405170	−0.0277618
$214$	16.9966	1.16186
$215$	−0.194427	−0.0132598
$216$	−23.1776	−1.57703
$217$	17.0245	1.15570
$218$	−21.4657	−1.45384
$219$	−10.8347	−0.732143
$220$	−3.77440	−0.254470
$221$	2.20713	0.148467
$222$	−26.0667	−1.74948
$223$	0.494807	0.0331348	0.0165674	−	0.999863i	$-0.494726\pi$
$223$	0.494807	0.0331348	0.0165674	+	0.999863i	$0.494726\pi$
$224$	−4.41141	−0.294750
$225$	−1.60914	−0.107276
$226$	−21.3880	−1.42271
$227$	27.7697	1.84314	0.921571	−	0.388210i	$-0.126906\pi$
$227$	27.7697	1.84314	0.921571	+	0.388210i	$0.126906\pi$
$228$	4.45134	0.294797
$229$	−2.65545	−0.175477	−0.0877386	−	0.996144i	$-0.527964\pi$
$229$	−2.65545	−0.175477	−0.0877386	+	0.996144i	$0.527964\pi$
$230$	−13.6457	−0.899774
$231$	2.54266	0.167295
$232$	−31.2286	−2.05026
$233$	−19.8348	−1.29942	−0.649711	−	0.760182i	$-0.725110\pi$
$233$	−19.8348	−1.29942	−0.649711	+	0.760182i	$0.725110\pi$
$234$	−13.7167	−0.896686
$235$	−0.340863	−0.0222355
$236$	33.9586	2.21052
$237$	−17.0981	−1.11064
$238$	−3.22348	−0.208947
$239$	9.34316	0.604359	0.302179	−	0.953251i	$-0.402286\pi$
$239$	9.34316	0.604359	0.302179	+	0.953251i	$0.402286\pi$
$240$	3.18108	0.205338
$241$	−14.6621	−0.944470	−0.472235	−	0.881473i	$-0.656553\pi$
$241$	−14.6621	−0.944470	−0.472235	+	0.881473i	$0.656553\pi$
$242$	−2.40300	−0.154471
$243$	−14.4401	−0.926334
$244$	−51.8533	−3.31957
$245$	2.35173	0.150247
$246$	6.50422	0.414694
$247$	3.54733	0.225711
$248$	33.6694	2.13801
$249$	−3.72101	−0.235809
$250$	2.40300	0.151979
$251$	18.0162	1.13717	0.568586	−	0.822624i	$-0.307491\pi$
$251$	18.0162	1.13717	0.568586	+	0.822624i	$0.307491\pi$
$252$	13.0944	0.824872
$253$	−5.67863	−0.357013
$254$	−35.9992	−2.25879
$255$	−0.733784	−0.0459513
$256$	−29.0860	−1.81788
$257$	−17.0567	−1.06397	−0.531984	−	0.846754i	$-0.678554\pi$
$257$	−17.0567	−1.06397	−0.531984	+	0.846754i	$0.678554\pi$
$258$	0.551000	0.0343038
$259$	19.8306	1.23221
$260$	13.3891	0.830354
$261$	−11.7853	−0.729490
$262$	−18.7780	−1.16011
$263$	2.21160	0.136373	0.0681866	−	0.997673i	$-0.478279\pi$
$263$	2.21160	0.136373	0.0681866	+	0.997673i	$0.478279\pi$
$264$	5.02862	0.309490
$265$	6.94545	0.426655
$266$	−5.18083	−0.317657
$267$	−6.42573	−0.393248
$268$	−0.855498	−0.0522579
$269$	−27.1402	−1.65477	−0.827384	−	0.561637i	$-0.810172\pi$
$269$	−27.1402	−1.65477	−0.827384	+	0.561637i	$0.810172\pi$
$270$	13.0622	0.794939
$271$	21.4161	1.30094	0.650468	−	0.759534i	$-0.274573\pi$
$271$	21.4161	1.30094	0.650468	+	0.759534i	$0.274573\pi$
$272$	−1.67826	−0.101759
$273$	−9.01964	−0.545894
$274$	−33.9760	−2.05256
$275$	1.00000	0.0603023
$276$	25.2775	1.52153
$277$	11.4909	0.690424	0.345212	−	0.938525i	$-0.387807\pi$
$277$	11.4909	0.690424	0.345212	+	0.938525i	$0.387807\pi$
$278$	−30.2664	−1.81526
$279$	12.7064	0.760712
$280$	−9.19289	−0.549380
$281$	−27.5824	−1.64543	−0.822715	−	0.568454i	$-0.807542\pi$
$281$	−27.5824	−1.64543	−0.822715	+	0.568454i	$0.807542\pi$
$282$	0.965998	0.0575243
$283$	−14.5401	−0.864318	−0.432159	−	0.901797i	$-0.642248\pi$
$283$	−14.5401	−0.864318	−0.432159	+	0.901797i	$0.642248\pi$
$284$	1.29671	0.0769457
$285$	−1.17935	−0.0698586
$286$	8.52423	0.504048
$287$	−4.94818	−0.292082
$288$	−3.29249	−0.194012
$289$	−16.6129	−0.977228
$290$	17.5995	1.03348
$291$	−16.1620	−0.947431
$292$	34.6756	2.02924
$293$	15.1038	0.882373	0.441186	−	0.897416i	$-0.354558\pi$
$293$	15.1038	0.882373	0.441186	+	0.897416i	$0.354558\pi$
$294$	−6.66475	−0.388696
$295$	−8.99709	−0.523831
$296$	39.2190	2.27956
$297$	5.43578	0.315416
$298$	−11.4843	−0.665267
$299$	20.1440	1.16496
$300$	−4.45134	−0.256998
$301$	−0.419181	−0.0241612
$302$	57.7798	3.32485
$303$	5.54840	0.318747
$304$	−2.69732	−0.154702
$305$	13.7381	0.786643
$306$	−2.40587	−0.137534
$307$	14.1979	0.810318	0.405159	−	0.914246i	$-0.367216\pi$
$307$	14.1979	0.810318	0.405159	+	0.914246i	$0.367216\pi$
$308$	−8.13756	−0.463680
$309$	−15.7246	−0.894543
$310$	−18.9750	−1.07771
$311$	11.4136	0.647203	0.323602	−	0.946193i	$-0.395106\pi$
$311$	11.4136	0.647203	0.323602	+	0.946193i	$0.395106\pi$
$312$	−17.8382	−1.00989
$313$	−17.5462	−0.991773	−0.495886	−	0.868387i	$-0.665157\pi$
$313$	−17.5462	−0.991773	−0.495886	+	0.868387i	$0.665157\pi$
$314$	31.2224	1.76198
$315$	−3.46927	−0.195471
$316$	54.7211	3.07830
$317$	9.50403	0.533800	0.266900	−	0.963724i	$-0.414001\pi$
$317$	9.50403	0.533800	0.266900	+	0.963724i	$0.414001\pi$
$318$	−19.6832	−1.10378
$319$	7.32397	0.410064
$320$	10.3115	0.576429
$321$	8.34160	0.465583
$322$	−29.4200	−1.63951
$323$	0.622194	0.0346198
$324$	−5.97590	−0.331994
$325$	−3.54733	−0.196770
$326$	47.3994	2.62521
$327$	−10.5350	−0.582585
$328$	−9.78602	−0.540343
$329$	−0.734896	−0.0405161
$330$	−2.83397	−0.156005
$331$	18.8296	1.03497	0.517483	−	0.855693i	$-0.326869\pi$
$331$	18.8296	1.03497	0.517483	+	0.855693i	$0.326869\pi$
$332$	11.9088	0.653579
$333$	14.8007	0.811074
$334$	−23.8362	−1.30426
$335$	0.226658	0.0123836
$336$	6.85837	0.374155
$337$	−3.44511	−0.187667	−0.0938336	−	0.995588i	$-0.529912\pi$
$337$	−3.44511	−0.187667	−0.0938336	+	0.995588i	$0.529912\pi$
$338$	1.00073	0.0544324
$339$	−10.4968	−0.570110
$340$	2.34841	0.127361
$341$	−7.89640	−0.427614
$342$	−3.86675	−0.209090
$343$	20.1622	1.08866
$344$	−0.829015	−0.0446975
$345$	−6.69709	−0.360559
$346$	−25.8228	−1.38824
$347$	13.2512	0.711361	0.355681	−	0.934608i	$-0.384249\pi$
$347$	13.2512	0.711361	0.355681	+	0.934608i	$0.384249\pi$
$348$	−32.6015	−1.74762
$349$	14.8843	0.796737	0.398369	−	0.917225i	$-0.369576\pi$
$349$	14.8843	0.796737	0.398369	+	0.917225i	$0.369576\pi$
$350$	5.18083	0.276927
$351$	−19.2825	−1.02922
$352$	2.04612	0.109059
$353$	−26.2048	−1.39474	−0.697371	−	0.716710i	$-0.745647\pi$
$353$	−26.2048	−1.39474	−0.697371	+	0.716710i	$0.745647\pi$
$354$	25.4975	1.35518
$355$	−0.343554	−0.0182340
$356$	20.5650	1.08994
$357$	−1.58203	−0.0837297
$358$	−21.8278	−1.15363
$359$	−24.3560	−1.28546	−0.642731	−	0.766092i	$-0.722199\pi$
$359$	−24.3560	−1.28546	−0.642731	+	0.766092i	$0.722199\pi$
$360$	−6.86119	−0.361616
$361$	1.00000	0.0526316
$362$	14.4191	0.757854
$363$	−1.17935	−0.0618998
$364$	28.8666	1.51302
$365$	−9.18704	−0.480871
$366$	−38.9335	−2.03509
$367$	27.2556	1.42273	0.711365	−	0.702823i	$-0.248077\pi$
$367$	27.2556	1.42273	0.711365	+	0.702823i	$0.248077\pi$
$368$	−15.3171	−0.798459
$369$	−3.69311	−0.192256
$370$	−22.1026	−1.14906
$371$	14.9743	0.777426
$372$	35.1496	1.82242
$373$	−28.9149	−1.49716	−0.748579	−	0.663045i	$-0.769264\pi$
$373$	−28.9149	−1.49716	−0.748579	+	0.663045i	$0.769264\pi$
$374$	1.49513	0.0773114
$375$	1.17935	0.0609013
$376$	−1.45341	−0.0749537
$377$	−25.9805	−1.33807
$378$	28.1618	1.44849
$379$	−31.0010	−1.59241	−0.796207	−	0.605025i	$-0.793163\pi$
$379$	−31.0010	−1.59241	−0.796207	+	0.605025i	$0.793163\pi$
$380$	3.77440	0.193623
$381$	−17.6678	−0.905147
$382$	30.4684	1.55890
$383$	23.3273	1.19197	0.595985	−	0.802996i	$-0.296762\pi$
$383$	23.3273	1.19197	0.595985	+	0.802996i	$0.296762\pi$
$384$	−24.3963	−1.24497
$385$	2.15598	0.109879
$386$	−34.8967	−1.77620
$387$	−0.312859	−0.0159035
$388$	51.7250	2.62594
$389$	13.0462	0.661468	0.330734	−	0.943724i	$-0.392704\pi$
$389$	13.0462	0.661468	0.330734	+	0.943724i	$0.392704\pi$
$390$	10.0530	0.509056
$391$	3.53321	0.178682
$392$	10.0275	0.506467
$393$	−9.21588	−0.464880
$394$	4.40671	0.222007
$395$	−14.4980	−0.729471
$396$	−6.07353	−0.305207
$397$	19.3816	0.972733	0.486366	−	0.873755i	$-0.338322\pi$
$397$	19.3816	0.972733	0.486366	+	0.873755i	$0.338322\pi$
$398$	31.2104	1.56443
$399$	−2.54266	−0.127292
$400$	2.69732	0.134866
$401$	−17.1713	−0.857496	−0.428748	−	0.903424i	$-0.641045\pi$
$401$	−17.1713	−0.857496	−0.428748	+	0.903424i	$0.641045\pi$
$402$	−0.642342	−0.0320371
$403$	28.0111	1.39533
$404$	−17.7572	−0.883453
$405$	1.58327	0.0786733
$406$	37.9442	1.88314
$407$	−9.19792	−0.455924
$408$	−3.12877	−0.154897
$409$	32.5084	1.60744	0.803718	−	0.595011i	$-0.202852\pi$
$409$	32.5084	1.60744	0.803718	+	0.595011i	$0.202852\pi$
$410$	5.51510	0.272371
$411$	−16.6748	−0.822507
$412$	50.3253	2.47935
$413$	−19.3976	−0.954492
$414$	−21.9579	−1.07917
$415$	−3.15514	−0.154880
$416$	−7.25827	−0.355866
$417$	−14.8542	−0.727414
$418$	2.40300	0.117535
$419$	0.917867	0.0448407	0.0224204	−	0.999749i	$-0.492863\pi$
$419$	0.917867	0.0448407	0.0224204	+	0.999749i	$0.492863\pi$
$420$	−9.59702	−0.468287
$421$	14.2065	0.692382	0.346191	−	0.938164i	$-0.387475\pi$
$421$	14.2065	0.692382	0.346191	+	0.938164i	$0.387475\pi$
$422$	−22.8737	−1.11347
$423$	−0.548496	−0.0266688
$424$	29.6147	1.43821
$425$	−0.622194	−0.0301808
$426$	0.973624	0.0471722
$427$	29.6192	1.43337
$428$	−26.6966	−1.29043
$429$	4.18354	0.201983
$430$	0.467207	0.0225307
$431$	−24.3672	−1.17373	−0.586863	−	0.809687i	$-0.699637\pi$
$431$	−24.3672	−1.17373	−0.586863	+	0.809687i	$0.699637\pi$
$432$	14.6621	0.705428
$433$	−34.1956	−1.64333	−0.821667	−	0.569967i	$-0.806956\pi$
$433$	−34.1956	−1.64333	−0.821667	+	0.569967i	$0.806956\pi$
$434$	−40.9099	−1.96374
$435$	8.63752	0.414137
$436$	33.7163	1.61472
$437$	5.67863	0.271646
$438$	26.0358	1.24404
$439$	−14.2883	−0.681942	−0.340971	−	0.940074i	$-0.610756\pi$
$439$	−14.2883	−0.681942	−0.340971	+	0.940074i	$0.610756\pi$
$440$	4.26389	0.203273
$441$	3.78426	0.180203
$442$	−5.30372	−0.252272
$443$	26.4567	1.25700	0.628498	−	0.777812i	$-0.283670\pi$
$443$	26.4567	1.25700	0.628498	+	0.777812i	$0.283670\pi$
$444$	40.9431	1.94307
$445$	−5.44854	−0.258286
$446$	−1.18902	−0.0563018
$447$	−5.63628	−0.266587
$448$	22.2314	1.05033
$449$	−9.81985	−0.463428	−0.231714	−	0.972784i	$-0.574433\pi$
$449$	−9.81985	−0.463428	−0.231714	+	0.972784i	$0.574433\pi$
$450$	3.86675	0.182281
$451$	2.29509	0.108072
$452$	33.5942	1.58014
$453$	28.3573	1.33234
$454$	−66.7307	−3.13182
$455$	−7.64799	−0.358543
$456$	−5.02862	−0.235487
$457$	−8.44589	−0.395082	−0.197541	−	0.980295i	$-0.563296\pi$
$457$	−8.44589	−0.395082	−0.197541	+	0.980295i	$0.563296\pi$
$458$	6.38105	0.298167
$459$	−3.38211	−0.157863
$460$	21.4335	0.999340
$461$	−25.0196	−1.16528	−0.582639	−	0.812731i	$-0.697980\pi$
$461$	−25.0196	−1.16528	−0.582639	+	0.812731i	$0.697980\pi$
$462$	−6.11000	−0.284263
$463$	−5.25947	−0.244428	−0.122214	−	0.992504i	$-0.538999\pi$
$463$	−5.25947	−0.244428	−0.122214	+	0.992504i	$0.538999\pi$
$464$	19.7551	0.917108
$465$	−9.31261	−0.431862
$466$	47.6630	2.20795
$467$	16.4456	0.761013	0.380507	−	0.924778i	$-0.375750\pi$
$467$	16.4456	0.761013	0.380507	+	0.924778i	$0.375750\pi$
$468$	21.5448	0.995910
$469$	0.488671	0.0225647
$470$	0.819094	0.0377820
$471$	15.3234	0.706065
$472$	−38.3626	−1.76578
$473$	0.194427	0.00893975
$474$	41.0868	1.88718
$475$	−1.00000	−0.0458831
$476$	5.06314	0.232069
$477$	11.1762	0.511722
$478$	−22.4516	−1.02691
$479$	−21.0736	−0.962876	−0.481438	−	0.876480i	$-0.659885\pi$
$479$	−21.0736	−0.962876	−0.481438	+	0.876480i	$0.659885\pi$
$480$	2.41309	0.110142
$481$	32.6281	1.48771
$482$	35.2330	1.60482
$483$	−14.4388	−0.656989
$484$	3.77440	0.171564
$485$	−13.7041	−0.622273
$486$	34.6996	1.57400
$487$	−19.2996	−0.874547	−0.437274	−	0.899329i	$-0.644056\pi$
$487$	−19.2996	−0.874547	−0.437274	+	0.899329i	$0.644056\pi$
$488$	58.5779	2.65170
$489$	23.2628	1.05198
$490$	−5.65121	−0.255296
$491$	0.412492	0.0186155	0.00930775	−	0.999957i	$-0.497037\pi$
$491$	0.412492	0.0186155	0.00930775	+	0.999957i	$0.497037\pi$
$492$	−10.2162	−0.460583
$493$	−4.55693	−0.205234
$494$	−8.52423	−0.383523
$495$	1.60914	0.0723253
$496$	−21.2991	−0.956360
$497$	−0.740698	−0.0332248
$498$	8.94158	0.400682
$499$	35.3500	1.58248	0.791241	−	0.611504i	$-0.209435\pi$
$499$	35.3500	1.58248	0.791241	+	0.611504i	$0.209435\pi$
$500$	−3.77440	−0.168797
$501$	−11.6984	−0.522644
$502$	−43.2929	−1.93226
$503$	9.66966	0.431149	0.215575	−	0.976487i	$-0.430838\pi$
$503$	9.66966	0.431149	0.215575	+	0.976487i	$0.430838\pi$
$504$	−14.7926	−0.658915
$505$	4.70463	0.209353
$506$	13.6457	0.606627
$507$	0.491139	0.0218123
$508$	56.5442	2.50874
$509$	32.5575	1.44308	0.721542	−	0.692370i	$-0.243434\pi$
$509$	32.5575	1.44308	0.721542	+	0.692370i	$0.243434\pi$
$510$	1.76328	0.0780794
$511$	−19.8071	−0.876215
$512$	28.5213	1.26047
$513$	−5.43578	−0.239996
$514$	40.9873	1.80787
$515$	−13.3333	−0.587536
$516$	−0.865459	−0.0380997
$517$	0.340863	0.0149912
$518$	−47.6529	−2.09375
$519$	−12.6734	−0.556299
$520$	−15.1254	−0.663294
$521$	13.0671	0.572482	0.286241	−	0.958158i	$-0.407594\pi$
$521$	13.0671	0.572482	0.286241	+	0.958158i	$0.407594\pi$
$522$	28.3200	1.23953
$523$	12.2092	0.533870	0.266935	−	0.963714i	$-0.413989\pi$
$523$	12.2092	0.533870	0.266935	+	0.963714i	$0.413989\pi$
$524$	29.4946	1.28848
$525$	2.54266	0.110971
$526$	−5.31448	−0.231722
$527$	4.91309	0.214018
$528$	−3.18108	−0.138439
$529$	9.24686	0.402037
$530$	−16.6899	−0.724963
$531$	−14.4775	−0.628272
$532$	8.13756	0.352808
$533$	−8.14144	−0.352645
$534$	15.4410	0.668198
$535$	7.07306	0.305795
$536$	0.966445	0.0417441
$537$	−10.7127	−0.462286
$538$	65.2179	2.81174
$539$	−2.35173	−0.101296
$540$	−20.5168	−0.882904
$541$	16.5139	0.709990	0.354995	−	0.934868i	$-0.384483\pi$
$541$	16.5139	0.709990	0.354995	+	0.934868i	$0.384483\pi$
$542$	−51.4629	−2.21052
$543$	7.07666	0.303689
$544$	−1.27308	−0.0545831
$545$	−8.93287	−0.382642
$546$	21.6742	0.927570
$547$	5.86659	0.250837	0.125419	−	0.992104i	$-0.459973\pi$
$547$	5.86659	0.250837	0.125419	+	0.992104i	$0.459973\pi$
$548$	53.3663	2.27969
$549$	22.1065	0.943484
$550$	−2.40300	−0.102464
$551$	−7.32397	−0.312012
$552$	−28.5557	−1.21541
$553$	−31.2574	−1.32920
$554$	−27.6127	−1.17315
$555$	−10.8476	−0.460453
$556$	47.5396	2.01613
$557$	−27.3711	−1.15975	−0.579875	−	0.814705i	$-0.696899\pi$
$557$	−27.3711	−1.15975	−0.579875	+	0.814705i	$0.696899\pi$
$558$	−30.5334	−1.29258
$559$	−0.689696	−0.0291710
$560$	5.81539	0.245745
$561$	0.733784	0.0309804
$562$	66.2806	2.79588
$563$	35.1477	1.48130	0.740649	−	0.671892i	$-0.234518\pi$
$563$	35.1477	1.48130	0.740649	+	0.671892i	$0.234518\pi$
$564$	−1.51730	−0.0638898
$565$	−8.90054	−0.374449
$566$	34.9398	1.46863
$567$	3.41350	0.143354
$568$	−1.46488	−0.0614649
$569$	−32.5565	−1.36484	−0.682420	−	0.730960i	$-0.739073\pi$
$569$	−32.5565	−1.36484	−0.682420	+	0.730960i	$0.739073\pi$
$570$	2.83397	0.118702
$571$	27.4850	1.15021	0.575106	−	0.818079i	$-0.304961\pi$
$571$	27.4850	1.15021	0.575106	+	0.818079i	$0.304961\pi$
$572$	−13.3891	−0.559825
$573$	14.9533	0.624684
$574$	11.8905	0.496299
$575$	−5.67863	−0.236815
$576$	16.5926	0.691357
$577$	−3.42422	−0.142552	−0.0712760	−	0.997457i	$-0.522707\pi$
$577$	−3.42422	−0.142552	−0.0712760	+	0.997457i	$0.522707\pi$
$578$	39.9207	1.66048
$579$	−17.1267	−0.711760
$580$	−27.6436	−1.14784
$581$	−6.80243	−0.282212
$582$	38.8372	1.60985
$583$	−6.94545	−0.287651
$584$	−39.1725	−1.62097
$585$	−5.70814	−0.236002
$586$	−36.2944	−1.49931
$587$	−18.7672	−0.774604	−0.387302	−	0.921953i	$-0.626593\pi$
$587$	−18.7672	−0.774604	−0.387302	+	0.921953i	$0.626593\pi$
$588$	10.4684	0.431708
$589$	7.89640	0.325366
$590$	21.6200	0.890081
$591$	2.16273	0.0889630
$592$	−24.8098	−1.01968
$593$	10.8009	0.443538	0.221769	−	0.975099i	$-0.428817\pi$
$593$	10.8009	0.443538	0.221769	+	0.975099i	$0.428817\pi$
$594$	−13.0622	−0.535947
$595$	−1.34144	−0.0549937
$596$	18.0384	0.738883
$597$	15.3175	0.626903
$598$	−48.4060	−1.97947
$599$	6.00417	0.245324	0.122662	−	0.992449i	$-0.460857\pi$
$599$	6.00417	0.245324	0.122662	+	0.992449i	$0.460857\pi$
$600$	5.02862	0.205292
$601$	−34.2605	−1.39751	−0.698757	−	0.715359i	$-0.746263\pi$
$601$	−34.2605	−1.39751	−0.698757	+	0.715359i	$0.746263\pi$
$602$	1.00729	0.0410541
$603$	0.364723	0.0148527
$604$	−90.7550	−3.69277
$605$	−1.00000	−0.0406558
$606$	−13.3328	−0.541608
$607$	−26.8024	−1.08788	−0.543938	−	0.839126i	$-0.683067\pi$
$607$	−26.8024	−1.08788	−0.543938	+	0.839126i	$0.683067\pi$
$608$	−2.04612	−0.0829812
$609$	18.6224	0.754616
$610$	−33.0127	−1.33665
$611$	−1.20915	−0.0489172
$612$	3.77892	0.152754
$613$	−20.7648	−0.838682	−0.419341	−	0.907829i	$-0.637739\pi$
$613$	−20.7648	−0.838682	−0.419341	+	0.907829i	$0.637739\pi$
$614$	−34.1176	−1.37687
$615$	2.70671	0.109145
$616$	9.19289	0.370392
$617$	−1.40456	−0.0565455	−0.0282728	−	0.999600i	$-0.509001\pi$
$617$	−1.40456	−0.0565455	−0.0282728	+	0.999600i	$0.509001\pi$
$618$	37.7863	1.51999
$619$	47.5216	1.91005	0.955027	−	0.296519i	$-0.0958258\pi$
$619$	47.5216	1.91005	0.955027	+	0.296519i	$0.0958258\pi$
$620$	29.8042	1.19697
$621$	−30.8678	−1.23868
$622$	−27.4268	−1.09971
$623$	−11.7470	−0.470632
$624$	11.2844	0.451736
$625$	1.00000	0.0400000
$626$	42.1636	1.68520
$627$	1.17935	0.0470987
$628$	−49.0412	−1.95696
$629$	5.72289	0.228187
$630$	8.33666	0.332141
$631$	−25.1060	−0.999454	−0.499727	−	0.866183i	$-0.666566\pi$
$631$	−25.1060	−0.999454	−0.499727	+	0.866183i	$0.666566\pi$
$632$	−61.8177	−2.45898
$633$	−11.2260	−0.446193
$634$	−22.8382	−0.907020
$635$	−14.9809	−0.594501
$636$	30.9165	1.22592
$637$	8.34237	0.330537
$638$	−17.5995	−0.696771
$639$	−0.552826	−0.0218694
$640$	−20.6862	−0.817695
$641$	21.3481	0.843199	0.421600	−	0.906782i	$-0.361469\pi$
$641$	21.3481	0.843199	0.421600	+	0.906782i	$0.361469\pi$
$642$	−20.0449	−0.791108
$643$	−14.5139	−0.572371	−0.286185	−	0.958174i	$-0.592387\pi$
$643$	−14.5139	−0.572371	−0.286185	+	0.958174i	$0.592387\pi$
$644$	46.2102	1.82094
$645$	0.229297	0.00902855
$646$	−1.49513	−0.0588252
$647$	−23.8976	−0.939511	−0.469755	−	0.882797i	$-0.655658\pi$
$647$	−23.8976	−0.939511	−0.469755	+	0.882797i	$0.655658\pi$
$648$	6.75089	0.265200
$649$	8.99709	0.353167
$650$	8.52423	0.334348
$651$	−20.0778	−0.786913
$652$	−74.4506	−2.91571
$653$	16.3847	0.641181	0.320591	−	0.947218i	$-0.396119\pi$
$653$	16.3847	0.641181	0.320591	+	0.947218i	$0.396119\pi$
$654$	25.3155	0.989916
$655$	−7.81438	−0.305333
$656$	6.19060	0.241702
$657$	−14.7832	−0.576747
$658$	1.76595	0.0688441
$659$	3.86889	0.150711	0.0753554	−	0.997157i	$-0.475991\pi$
$659$	3.86889	0.150711	0.0753554	+	0.997157i	$0.475991\pi$
$660$	4.45134	0.173268
$661$	4.57508	0.177950	0.0889749	−	0.996034i	$-0.471641\pi$
$661$	4.57508	0.177950	0.0889749	+	0.996034i	$0.471641\pi$
$662$	−45.2474	−1.75859
$663$	−2.60297	−0.101091
$664$	−13.4532	−0.522084
$665$	−2.15598	−0.0836055
$666$	−35.5661	−1.37816
$667$	−41.5901	−1.61038
$668$	37.4396	1.44858
$669$	−0.583550	−0.0225614
$670$	−0.544659	−0.0210420
$671$	−13.7381	−0.530355
$672$	5.20259	0.200694
$673$	22.2879	0.859135	0.429568	−	0.903035i	$-0.358666\pi$
$673$	22.2879	0.859135	0.429568	+	0.903035i	$0.358666\pi$
$674$	8.27860	0.318880
$675$	5.43578	0.209223
$676$	−1.57185	−0.0604557
$677$	−22.4962	−0.864600	−0.432300	−	0.901730i	$-0.642298\pi$
$677$	−22.4962	−0.864600	−0.432300	+	0.901730i	$0.642298\pi$
$678$	25.2239	0.968718
$679$	−29.5459	−1.13387
$680$	−2.65297	−0.101737
$681$	−32.7502	−1.25499
$682$	18.9750	0.726592
$683$	12.8458	0.491532	0.245766	−	0.969329i	$-0.420961\pi$
$683$	12.8458	0.491532	0.245766	+	0.969329i	$0.420961\pi$
$684$	6.07353	0.232227
$685$	−14.1390	−0.540223
$686$	−48.4497	−1.84982
$687$	3.13170	0.119482
$688$	0.524432	0.0199938
$689$	24.6378	0.938625
$690$	16.0931	0.612654
$691$	−24.2131	−0.921110	−0.460555	−	0.887631i	$-0.652350\pi$
$691$	−24.2131	−0.921110	−0.460555	+	0.887631i	$0.652350\pi$
$692$	40.5600	1.54186
$693$	3.46927	0.131787
$694$	−31.8426	−1.20873
$695$	−12.5953	−0.477766
$696$	36.8295	1.39602
$697$	−1.42799	−0.0540890
$698$	−35.7669	−1.35380
$699$	23.3922	0.884772
$700$	−8.13756	−0.307571
$701$	−36.6327	−1.38360	−0.691798	−	0.722091i	$-0.743181\pi$
$701$	−36.6327	−1.38360	−0.691798	+	0.722091i	$0.743181\pi$
$702$	46.3358	1.74883
$703$	9.19792	0.346906
$704$	−10.3115	−0.388628
$705$	0.401997	0.0151401
$706$	62.9702	2.36991
$707$	10.1431	0.381471
$708$	−40.0491	−1.50514
$709$	37.1353	1.39464	0.697322	−	0.716758i	$-0.254375\pi$
$709$	37.1353	1.39464	0.697322	+	0.716758i	$0.254375\pi$
$710$	0.825561	0.0309827
$711$	−23.3292	−0.874913
$712$	−23.2320	−0.870656
$713$	44.8408	1.67930
$714$	3.80161	0.142272
$715$	3.54733	0.132663
$716$	34.2850	1.28129
$717$	−11.0188	−0.411506
$718$	58.5275	2.18423
$719$	5.84694	0.218054	0.109027	−	0.994039i	$-0.465226\pi$
$719$	5.84694	0.218054	0.109027	+	0.994039i	$0.465226\pi$
$720$	4.34036	0.161756
$721$	−28.7464	−1.07057
$722$	−2.40300	−0.0894304
$723$	17.2917	0.643087
$724$	−22.6482	−0.841715
$725$	7.32397	0.272006
$726$	2.83397	0.105179
$727$	52.5801	1.95009	0.975044	−	0.222013i	$-0.0712627\pi$
$727$	52.5801	1.95009	0.975044	+	0.222013i	$0.0712627\pi$
$728$	−32.6102	−1.20861
$729$	21.7797	0.806657
$730$	22.0764	0.817086
$731$	−0.120971	−0.00447428
$732$	61.1531	2.26028
$733$	31.6350	1.16847	0.584233	−	0.811586i	$-0.301395\pi$
$733$	31.6350	1.16847	0.584233	+	0.811586i	$0.301395\pi$
$734$	−65.4951	−2.41747
$735$	−2.77351	−0.102303
$736$	−11.6192	−0.428288
$737$	−0.226658	−0.00834905
$738$	8.87455	0.326677
$739$	25.8243	0.949963	0.474982	−	0.879996i	$-0.342455\pi$
$739$	25.8243	0.949963	0.474982	+	0.879996i	$0.342455\pi$
$740$	34.7167	1.27621
$741$	−4.18354	−0.153686
$742$	−35.9832	−1.32098
$743$	−22.0227	−0.807933	−0.403967	−	0.914774i	$-0.632369\pi$
$743$	−22.0227	−0.807933	−0.403967	+	0.914774i	$0.632369\pi$
$744$	−39.7080	−1.45577
$745$	−4.77915	−0.175094
$746$	69.4826	2.54394
$747$	−5.07705	−0.185760
$748$	−2.34841	−0.0858664
$749$	15.2494	0.557201
$750$	−2.83397	−0.103482
$751$	25.1467	0.917618	0.458809	−	0.888535i	$-0.348276\pi$
$751$	25.1467	0.917618	0.458809	+	0.888535i	$0.348276\pi$
$752$	0.919419	0.0335277
$753$	−21.2474	−0.774297
$754$	62.4312	2.27361
$755$	24.0449	0.875082
$756$	−44.2340	−1.60877
$757$	−24.6908	−0.897403	−0.448702	−	0.893682i	$-0.648113\pi$
$757$	−24.6908	−0.897403	−0.448702	+	0.893682i	$0.648113\pi$
$758$	74.4953	2.70579
$759$	6.69709	0.243089
$760$	−4.26389	−0.154668
$761$	22.1274	0.802119	0.401059	−	0.916052i	$-0.368642\pi$
$761$	22.1274	0.802119	0.401059	+	0.916052i	$0.368642\pi$
$762$	42.4556	1.53800
$763$	−19.2591	−0.697227
$764$	−47.8568	−1.73140
$765$	−1.00119	−0.0361983
$766$	−56.0555	−2.02537
$767$	−31.9156	−1.15241
$768$	34.3026	1.23779
$769$	0.0310222	0.00111869	0.000559344	−	1.00000i	$-0.499822\pi$
$769$	0.0310222	0.00111869	0.000559344		1.00000i	$0.499822\pi$
$770$	−5.18083	−0.186704
$771$	20.1158	0.724454
$772$	54.8125	1.97274
$773$	42.3683	1.52388	0.761940	−	0.647647i	$-0.224247\pi$
$773$	42.3683	1.52388	0.761940	+	0.647647i	$0.224247\pi$
$774$	0.751800	0.0270229
$775$	−7.89640	−0.283647
$776$	−58.4330	−2.09762
$777$	−23.3872	−0.839010
$778$	−31.3500	−1.12395
$779$	−2.29509	−0.0822301
$780$	−15.7904	−0.565386
$781$	0.343554	0.0122933
$782$	−8.49030	−0.303612
$783$	39.8115	1.42275
$784$	−6.34338	−0.226549
$785$	12.9931	0.463744
$786$	22.1458	0.789913
$787$	−33.4522	−1.19244	−0.596222	−	0.802820i	$-0.703332\pi$
$787$	−33.4522	−1.19244	−0.596222	+	0.802820i	$0.703332\pi$
$788$	−6.92165	−0.246573
$789$	−2.60825	−0.0928562
$790$	34.8386	1.23950
$791$	−19.1894	−0.682298
$792$	6.86119	0.243802
$793$	48.7337	1.73058
$794$	−46.5739	−1.65285
$795$	−8.19110	−0.290509
$796$	−49.0223	−1.73755
$797$	−12.2471	−0.433816	−0.216908	−	0.976192i	$-0.569597\pi$
$797$	−12.2471	−0.433816	−0.216908	+	0.976192i	$0.569597\pi$
$798$	6.11000	0.216292
$799$	−0.212083	−0.00750296
$800$	2.04612	0.0723413
$801$	−8.76745	−0.309783
$802$	41.2627	1.45704
$803$	9.18704	0.324203
$804$	1.00893	0.0355822
$805$	−12.2430	−0.431510
$806$	−67.3108	−2.37092
$807$	32.0078	1.12673
$808$	20.0601	0.705710
$809$	−25.7316	−0.904676	−0.452338	−	0.891846i	$-0.649410\pi$
$809$	−25.7316	−0.904676	−0.452338	+	0.891846i	$0.649410\pi$
$810$	−3.80459	−0.133680
$811$	−17.4658	−0.613309	−0.306654	−	0.951821i	$-0.599210\pi$
$811$	−17.4658	−0.613309	−0.306654	+	0.951821i	$0.599210\pi$
$812$	−59.5993	−2.09152
$813$	−25.2570	−0.885803
$814$	22.1026	0.774696
$815$	19.7251	0.690941
$816$	1.97925	0.0692877
$817$	−0.194427	−0.00680213
$818$	−78.1176	−2.73132
$819$	−12.3067	−0.430029
$820$	−8.66260	−0.302511
$821$	18.5642	0.647896	0.323948	−	0.946075i	$-0.394990\pi$
$821$	18.5642	0.647896	0.323948	+	0.946075i	$0.394990\pi$
$822$	40.0695	1.39758
$823$	−19.1102	−0.666139	−0.333069	−	0.942902i	$-0.608084\pi$
$823$	−19.1102	−0.666139	−0.333069	+	0.942902i	$0.608084\pi$
$824$	−56.8518	−1.98053
$825$	−1.17935	−0.0410597
$826$	46.6124	1.62185
$827$	38.2855	1.33132	0.665658	−	0.746257i	$-0.268151\pi$
$827$	38.2855	1.33132	0.665658	+	0.746257i	$0.268151\pi$
$828$	34.4894	1.19859
$829$	8.64603	0.300289	0.150144	−	0.988664i	$-0.452026\pi$
$829$	8.64603	0.300289	0.150144	+	0.988664i	$0.452026\pi$
$830$	7.58180	0.263168
$831$	−13.5518	−0.470108
$832$	36.5782	1.26812
$833$	1.46323	0.0506980
$834$	35.6946	1.23600
$835$	−9.91934	−0.343273
$836$	−3.77440	−0.130541
$837$	−42.9231	−1.48364
$838$	−2.20563	−0.0761924
$839$	24.7123	0.853165	0.426582	−	0.904449i	$-0.359717\pi$
$839$	24.7123	0.853165	0.426582	+	0.904449i	$0.359717\pi$
$840$	10.8416	0.374071
$841$	24.6406	0.849675
$842$	−34.1382	−1.17648
$843$	32.5293	1.12037
$844$	35.9279	1.23669
$845$	0.416450	0.0143263
$846$	1.31803	0.0453150
$847$	−2.15598	−0.0740805
$848$	−18.7341	−0.643332
$849$	17.1478	0.588512
$850$	1.49513	0.0512826
$851$	52.2316	1.79048
$852$	−1.52928	−0.0523921
$853$	7.26768	0.248841	0.124420	−	0.992230i	$-0.460293\pi$
$853$	7.26768	0.248841	0.124420	+	0.992230i	$0.460293\pi$
$854$	−71.1749	−2.43556
$855$	−1.60914	−0.0550313
$856$	30.1588	1.03081
$857$	−52.0192	−1.77694	−0.888471	−	0.458932i	$-0.848232\pi$
$857$	−52.0192	−1.77694	−0.888471	+	0.458932i	$0.848232\pi$
$858$	−10.0530	−0.343205
$859$	−33.3223	−1.13694	−0.568472	−	0.822703i	$-0.692465\pi$
$859$	−33.3223	−1.13694	−0.568472	+	0.822703i	$0.692465\pi$
$860$	−0.733845	−0.0250239
$861$	5.83563	0.198878
$862$	58.5543	1.99437
$863$	12.4776	0.424743	0.212371	−	0.977189i	$-0.431881\pi$
$863$	12.4776	0.424743	0.212371	+	0.977189i	$0.431881\pi$
$864$	11.1223	0.378387
$865$	−10.7461	−0.365377
$866$	82.1720	2.79232
$867$	19.5924	0.665392
$868$	64.2574	2.18104
$869$	14.4980	0.491809
$870$	−20.7559	−0.703693
$871$	0.804030	0.0272435
$872$	−38.0888	−1.28985
$873$	−22.0518	−0.746342
$874$	−13.6457	−0.461574
$875$	2.15598	0.0728856
$876$	−40.8946	−1.38170
$877$	1.06682	0.0360238	0.0180119	−	0.999838i	$-0.494266\pi$
$877$	1.06682	0.0360238	0.0180119	+	0.999838i	$0.494266\pi$
$878$	34.3347	1.15874
$879$	−17.8126	−0.600805
$880$	−2.69732	−0.0909267
$881$	−34.9901	−1.17885	−0.589423	−	0.807825i	$-0.700645\pi$
$881$	−34.9901	−1.17885	−0.589423	+	0.807825i	$0.700645\pi$
$882$	−9.09357	−0.306196
$883$	−48.3044	−1.62557	−0.812786	−	0.582562i	$-0.802050\pi$
$883$	−48.3044	−1.62557	−0.812786	+	0.582562i	$0.802050\pi$
$884$	8.33059	0.280188
$885$	10.6107	0.356675
$886$	−63.5754	−2.13586
$887$	8.74597	0.293661	0.146830	−	0.989162i	$-0.453093\pi$
$887$	8.74597	0.293661	0.146830	+	0.989162i	$0.453093\pi$
$888$	−46.2528	−1.55214
$889$	−32.2987	−1.08326
$890$	13.0928	0.438873
$891$	−1.58327	−0.0530415
$892$	1.86760	0.0625320
$893$	−0.340863	−0.0114066
$894$	13.5440	0.452978
$895$	−9.08355	−0.303629
$896$	−44.5992	−1.48995
$897$	−23.7568	−0.793216
$898$	23.5971	0.787445
$899$	−57.8330	−1.92884
$900$	−6.07353	−0.202451
$901$	4.32141	0.143967
$902$	−5.51510	−0.183633
$903$	0.494360	0.0164513
$904$	−37.9510	−1.26223
$905$	6.00048	0.199463
$906$	−68.1425	−2.26388
$907$	−25.8242	−0.857479	−0.428739	−	0.903428i	$-0.641042\pi$
$907$	−25.8242	−0.857479	−0.428739	+	0.903428i	$0.641042\pi$
$908$	104.814	3.47838
$909$	7.57040	0.251094
$910$	18.3781	0.609228
$911$	−11.3062	−0.374591	−0.187296	−	0.982304i	$-0.559972\pi$
$911$	−11.3062	−0.374591	−0.187296	+	0.982304i	$0.559972\pi$
$912$	3.18108	0.105336
$913$	3.15514	0.104420
$914$	20.2955	0.671315
$915$	−16.2020	−0.535623
$916$	−10.0228	−0.331161
$917$	−16.8477	−0.556360
$918$	8.12720	0.268238
$919$	−1.21432	−0.0400567	−0.0200284	−	0.999799i	$-0.506376\pi$
$919$	−1.21432	−0.0400567	−0.0200284	+	0.999799i	$0.506376\pi$
$920$	−24.2131	−0.798282
$921$	−16.7443	−0.551743
$922$	60.1220	1.98001
$923$	−1.21870	−0.0401140
$924$	9.59702	0.315719
$925$	−9.19792	−0.302426
$926$	12.6385	0.415327
$927$	−21.4551	−0.704679
$928$	14.9857	0.491931
$929$	−45.7356	−1.50054	−0.750269	−	0.661133i	$-0.770076\pi$
$929$	−45.7356	−1.50054	−0.750269	+	0.661133i	$0.770076\pi$
$930$	22.3782	0.733810
$931$	2.35173	0.0770749
$932$	−74.8646	−2.45227
$933$	−13.4606	−0.440679
$934$	−39.5188	−1.29310
$935$	0.622194	0.0203479
$936$	−24.3389	−0.795542
$937$	−30.7781	−1.00548	−0.502739	−	0.864438i	$-0.667674\pi$
$937$	−30.7781	−1.00548	−0.502739	+	0.864438i	$0.667674\pi$
$938$	−1.17428	−0.0383414
$939$	20.6931	0.675295
$940$	−1.28656	−0.0419628
$941$	31.6570	1.03199	0.515995	−	0.856592i	$-0.327422\pi$
$941$	31.6570	1.03199	0.515995	+	0.856592i	$0.327422\pi$
$942$	−36.8221	−1.19973
$943$	−13.0330	−0.424412
$944$	24.2680	0.789858
$945$	11.7195	0.381234
$946$	−0.467207	−0.0151902
$947$	50.8102	1.65111	0.825555	−	0.564321i	$-0.190862\pi$
$947$	50.8102	1.65111	0.825555	+	0.564321i	$0.190862\pi$
$948$	−64.5353	−2.09601
$949$	−32.5895	−1.05790
$950$	2.40300	0.0779636
$951$	−11.2086	−0.363463
$952$	−5.71976	−0.185378
$953$	26.6043	0.861799	0.430899	−	0.902400i	$-0.358196\pi$
$953$	26.6043	0.861799	0.430899	+	0.902400i	$0.358196\pi$
$954$	−26.8563	−0.869506
$955$	12.6793	0.410293
$956$	35.2649	1.14055
$957$	−8.63752	−0.279211
$958$	50.6398	1.63610
$959$	−30.4834	−0.984361
$960$	−12.1608	−0.392489
$961$	31.3532	1.01139
$962$	−78.4052	−2.52789
$963$	11.3815	0.366764
$964$	−55.3407	−1.78241
$965$	−14.5221	−0.467485
$966$	34.6965	1.11634
$967$	−24.6428	−0.792458	−0.396229	−	0.918152i	$-0.629681\pi$
$967$	−24.6428	−0.792458	−0.396229	+	0.918152i	$0.629681\pi$
$968$	−4.26389	−0.137047
$969$	−0.733784	−0.0235725
$970$	32.9310	1.05735
$971$	9.87139	0.316788	0.158394	−	0.987376i	$-0.449368\pi$
$971$	9.87139	0.316788	0.158394	+	0.987376i	$0.449368\pi$
$972$	−54.5028	−1.74818
$973$	−27.1552	−0.870555
$974$	46.3769	1.48601
$975$	4.18354	0.133980
$976$	−37.0562	−1.18614
$977$	15.0169	0.480434	0.240217	−	0.970719i	$-0.422781\pi$
$977$	15.0169	0.480434	0.240217	+	0.970719i	$0.422781\pi$
$978$	−55.9005	−1.78750
$979$	5.44854	0.174136
$980$	8.87639	0.283546
$981$	−14.3742	−0.458933
$982$	−0.991218	−0.0316310
$983$	−7.52621	−0.240049	−0.120024	−	0.992771i	$-0.538297\pi$
$983$	−7.52621	−0.240049	−0.120024	+	0.992771i	$0.538297\pi$
$984$	11.5411	0.367918
$985$	1.83384	0.0584309
$986$	10.9503	0.348729
$987$	0.866699	0.0275873
$988$	13.3891	0.425963
$989$	−1.10408	−0.0351076
$990$	−3.86675	−0.122894
$991$	49.1175	1.56027	0.780135	−	0.625611i	$-0.215150\pi$
$991$	49.1175	1.56027	0.780135	+	0.625611i	$0.215150\pi$
$992$	−16.1570	−0.512985
$993$	−22.2066	−0.704706
$994$	1.77990	0.0564549
$995$	12.9881	0.411750
$996$	−14.0446	−0.445020
$997$	26.7842	0.848263	0.424132	−	0.905601i	$-0.360579\pi$
$997$	26.7842	0.848263	0.424132	+	0.905601i	$0.360579\pi$
$998$	−84.9460	−2.68892
$999$	−49.9979	−1.58186

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.2.a.h.1.1	✓	7
3.2	odd	2		9405.2.a.bd.1.7		7
5.4	even	2		5225.2.a.m.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.2.a.h.1.1	✓	7	1.1	even	1	trivial
5225.2.a.m.1.7		7	5.4	even	2
9405.2.a.bd.1.7		7	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:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q-2.40300 q^{2} -1.17935 q^{3} +3.77440 q^{4} -1.00000 q^{5} +2.83397 q^{6} -2.15598 q^{7} -4.26389 q^{8} -1.60914 q^{9} +O(q^{10})\)	\(q-2.40300 q^{2} -1.17935 q^{3} +3.77440 q^{4} -1.00000 q^{5} +2.83397 q^{6} -2.15598 q^{7} -4.26389 q^{8} -1.60914 q^{9} +2.40300 q^{10} +1.00000 q^{11} -4.45134 q^{12} -3.54733 q^{13} +5.18083 q^{14} +1.17935 q^{15} +2.69732 q^{16} -0.622194 q^{17} +3.86675 q^{18} -1.00000 q^{19} -3.77440 q^{20} +2.54266 q^{21} -2.40300 q^{22} -5.67863 q^{23} +5.02862 q^{24} +1.00000 q^{25} +8.52423 q^{26} +5.43578 q^{27} -8.13756 q^{28} +7.32397 q^{29} -2.83397 q^{30} -7.89640 q^{31} +2.04612 q^{32} -1.17935 q^{33} +1.49513 q^{34} +2.15598 q^{35} -6.07353 q^{36} -9.19792 q^{37} +2.40300 q^{38} +4.18354 q^{39} +4.26389 q^{40} +2.29509 q^{41} -6.11000 q^{42} +0.194427 q^{43} +3.77440 q^{44} +1.60914 q^{45} +13.6457 q^{46} +0.340863 q^{47} -3.18108 q^{48} -2.35173 q^{49} -2.40300 q^{50} +0.733784 q^{51} -13.3891 q^{52} -6.94545 q^{53} -13.0622 q^{54} -1.00000 q^{55} +9.19289 q^{56} +1.17935 q^{57} -17.5995 q^{58} +8.99709 q^{59} +4.45134 q^{60} -13.7381 q^{61} +18.9750 q^{62} +3.46927 q^{63} -10.3115 q^{64} +3.54733 q^{65} +2.83397 q^{66} -0.226658 q^{67} -2.34841 q^{68} +6.69709 q^{69} -5.18083 q^{70} +0.343554 q^{71} +6.86119 q^{72} +9.18704 q^{73} +22.1026 q^{74} -1.17935 q^{75} -3.77440 q^{76} -2.15598 q^{77} -10.0530 q^{78} +14.4980 q^{79} -2.69732 q^{80} -1.58327 q^{81} -5.51510 q^{82} +3.15514 q^{83} +9.59702 q^{84} +0.622194 q^{85} -0.467207 q^{86} -8.63752 q^{87} -4.26389 q^{88} +5.44854 q^{89} -3.86675 q^{90} +7.64799 q^{91} -21.4335 q^{92} +9.31261 q^{93} -0.819094 q^{94} +1.00000 q^{95} -2.41309 q^{96} +13.7041 q^{97} +5.65121 q^{98} -1.60914 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + q^{2} + 3 q^{3} + 7 q^{4} - 7 q^{5} + 8 q^{6} - q^{7} + 3 q^{8} + 2 q^{9}+O(q^{10}) \) 7 * q + q^2 + 3 * q^3 + 7 * q^4 - 7 * q^5 + 8 * q^6 - q^7 + 3 * q^8 + 2 * q^9	\( 7 q + q^{2} + 3 q^{3} + 7 q^{4} - 7 q^{5} + 8 q^{6} - q^{7} + 3 q^{8} + 2 q^{9} - q^{10} + 7 q^{11} + 13 q^{12} + q^{13} + 12 q^{14} - 3 q^{15} + 3 q^{16} + q^{17} + 7 q^{18} - 7 q^{19} - 7 q^{20} + 5 q^{21} + q^{22} - 8 q^{23} + 25 q^{24} + 7 q^{25} + 12 q^{27} + 4 q^{28} + 11 q^{29} - 8 q^{30} + 7 q^{31} + 12 q^{32} + 3 q^{33} - 14 q^{34} + q^{35} + 7 q^{36} - 17 q^{37} - q^{38} + 30 q^{39} - 3 q^{40} + 17 q^{41} + 33 q^{42} - 3 q^{43} + 7 q^{44} - 2 q^{45} + 18 q^{46} + 14 q^{47} - 12 q^{48} + 6 q^{49} + q^{50} + 8 q^{51} - 17 q^{52} + 7 q^{53} - 27 q^{54} - 7 q^{55} + 36 q^{56} - 3 q^{57} - 15 q^{58} + 35 q^{59} - 13 q^{60} + 17 q^{61} + 46 q^{62} - 22 q^{63} + 5 q^{64} - q^{65} + 8 q^{66} + 4 q^{67} - 35 q^{68} - 4 q^{69} - 12 q^{70} + 10 q^{71} + 12 q^{72} + 22 q^{73} - 11 q^{74} + 3 q^{75} - 7 q^{76} - q^{77} - 41 q^{78} + 11 q^{79} - 3 q^{80} - 21 q^{81} - 14 q^{82} + 39 q^{83} + 21 q^{84} - q^{85} - 24 q^{86} - 2 q^{87} + 3 q^{88} + 18 q^{89} - 7 q^{90} - 22 q^{91} - 51 q^{92} + 10 q^{93} + 14 q^{94} + 7 q^{95} - 11 q^{96} - 4 q^{97} - 26 q^{98} + 2 q^{99}+O(q^{100}) \) 7 * q + q^2 + 3 * q^3 + 7 * q^4 - 7 * q^5 + 8 * q^6 - q^7 + 3 * q^8 + 2 * q^9 - q^10 + 7 * q^11 + 13 * q^12 + q^13 + 12 * q^14 - 3 * q^15 + 3 * q^16 + q^17 + 7 * q^18 - 7 * q^19 - 7 * q^20 + 5 * q^21 + q^22 - 8 * q^23 + 25 * q^24 + 7 * q^25 + 12 * q^27 + 4 * q^28 + 11 * q^29 - 8 * q^30 + 7 * q^31 + 12 * q^32 + 3 * q^33 - 14 * q^34 + q^35 + 7 * q^36 - 17 * q^37 - q^38 + 30 * q^39 - 3 * q^40 + 17 * q^41 + 33 * q^42 - 3 * q^43 + 7 * q^44 - 2 * q^45 + 18 * q^46 + 14 * q^47 - 12 * q^48 + 6 * q^49 + q^50 + 8 * q^51 - 17 * q^52 + 7 * q^53 - 27 * q^54 - 7 * q^55 + 36 * q^56 - 3 * q^57 - 15 * q^58 + 35 * q^59 - 13 * q^60 + 17 * q^61 + 46 * q^62 - 22 * q^63 + 5 * q^64 - q^65 + 8 * q^66 + 4 * q^67 - 35 * q^68 - 4 * q^69 - 12 * q^70 + 10 * q^71 + 12 * q^72 + 22 * q^73 - 11 * q^74 + 3 * q^75 - 7 * q^76 - q^77 - 41 * q^78 + 11 * q^79 - 3 * q^80 - 21 * q^81 - 14 * q^82 + 39 * q^83 + 21 * q^84 - q^85 - 24 * q^86 - 2 * q^87 + 3 * q^88 + 18 * q^89 - 7 * q^90 - 22 * q^91 - 51 * q^92 + 10 * q^93 + 14 * q^94 + 7 * q^95 - 11 * q^96 - 4 * q^97 - 26 * q^98 + 2 * q^99

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