LMFDB - Embedded newform 2001.2.a.n.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,2,Mod(1,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, 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("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2001.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:	$15.9780654445$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} - 28 x^{14} + 27 x^{13} + 316 x^{12} - 295 x^{11} - 1835 x^{10} + 1665 x^{9} + \cdots - 192 $ x^16 - x^15 - 28x^14 + 27x^13 + 316x^12 - 295x^11 - 1835x^10 + 1665x^9 + 5778x^8 - 5124x^7 - 9405x^6 + 8288x^5 + 6405x^4 - 6032x^3 - 400x^2 + 1088x - 192
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Root			$-2.65986$ of defining polynomial
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.65986 q^{2} +1.00000 q^{3} +5.07484 q^{4} -2.26251 q^{5} +2.65986 q^{6} +3.13860 q^{7} +8.17864 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.65986 q^{2} +1.00000 q^{3} +5.07484 q^{4} -2.26251 q^{5} +2.65986 q^{6} +3.13860 q^{7} +8.17864 q^{8} +1.00000 q^{9} -6.01796 q^{10} +2.75152 q^{11} +5.07484 q^{12} -4.39658 q^{13} +8.34822 q^{14} -2.26251 q^{15} +11.6043 q^{16} -5.15020 q^{17} +2.65986 q^{18} +6.77659 q^{19} -11.4819 q^{20} +3.13860 q^{21} +7.31866 q^{22} -1.00000 q^{23} +8.17864 q^{24} +0.118961 q^{25} -11.6943 q^{26} +1.00000 q^{27} +15.9279 q^{28} -1.00000 q^{29} -6.01796 q^{30} +2.65285 q^{31} +14.5086 q^{32} +2.75152 q^{33} -13.6988 q^{34} -7.10112 q^{35} +5.07484 q^{36} +0.716519 q^{37} +18.0248 q^{38} -4.39658 q^{39} -18.5043 q^{40} -4.09771 q^{41} +8.34822 q^{42} +9.18604 q^{43} +13.9635 q^{44} -2.26251 q^{45} -2.65986 q^{46} -9.21938 q^{47} +11.6043 q^{48} +2.85080 q^{49} +0.316421 q^{50} -5.15020 q^{51} -22.3120 q^{52} +7.55372 q^{53} +2.65986 q^{54} -6.22536 q^{55} +25.6695 q^{56} +6.77659 q^{57} -2.65986 q^{58} -6.47205 q^{59} -11.4819 q^{60} -1.02808 q^{61} +7.05619 q^{62} +3.13860 q^{63} +15.3821 q^{64} +9.94733 q^{65} +7.31866 q^{66} -8.08875 q^{67} -26.1365 q^{68} -1.00000 q^{69} -18.8880 q^{70} +4.92645 q^{71} +8.17864 q^{72} -7.67814 q^{73} +1.90584 q^{74} +0.118961 q^{75} +34.3901 q^{76} +8.63593 q^{77} -11.6943 q^{78} -14.3627 q^{79} -26.2549 q^{80} +1.00000 q^{81} -10.8993 q^{82} -9.71872 q^{83} +15.9279 q^{84} +11.6524 q^{85} +24.4336 q^{86} -1.00000 q^{87} +22.5037 q^{88} +4.23269 q^{89} -6.01796 q^{90} -13.7991 q^{91} -5.07484 q^{92} +2.65285 q^{93} -24.5222 q^{94} -15.3321 q^{95} +14.5086 q^{96} +8.66126 q^{97} +7.58272 q^{98} +2.75152 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9}+O(q^{10}) $ 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9	\( 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9} + 11 q^{10} + 8 q^{11} + 25 q^{12} + 19 q^{13} + 16 q^{14} + 3 q^{15} + 31 q^{16} - 4 q^{17} - q^{18} + 19 q^{19} + 16 q^{20} + 13 q^{21} + 6 q^{22} - 16 q^{23} + 23 q^{25} - 15 q^{26} + 16 q^{27} + 18 q^{28} - 16 q^{29} + 11 q^{30} + 24 q^{31} - 21 q^{32} + 8 q^{33} - 9 q^{34} - 13 q^{35} + 25 q^{36} + 26 q^{37} + 19 q^{39} - 22 q^{40} - 15 q^{41} + 16 q^{42} + 33 q^{43} + 6 q^{44} + 3 q^{45} + q^{46} + 13 q^{47} + 31 q^{48} + 41 q^{49} + 13 q^{50} - 4 q^{51} - 26 q^{52} + 5 q^{53} - q^{54} + 9 q^{55} + 40 q^{56} + 19 q^{57} + q^{58} + 2 q^{59} + 16 q^{60} + 29 q^{61} - 32 q^{62} + 13 q^{63} + 28 q^{64} + 18 q^{65} + 6 q^{66} + 32 q^{67} - 26 q^{68} - 16 q^{69} + 18 q^{70} + 29 q^{71} + 19 q^{73} - 16 q^{74} + 23 q^{75} + 64 q^{76} - 21 q^{77} - 15 q^{78} + 56 q^{79} + 16 q^{81} + 14 q^{82} + 5 q^{83} + 18 q^{84} + 16 q^{85} - 20 q^{86} - 16 q^{87} + q^{88} + 7 q^{89} + 11 q^{90} - 6 q^{91} - 25 q^{92} + 24 q^{93} - 11 q^{94} + 39 q^{95} - 21 q^{96} + 35 q^{97} - 109 q^{98} + 8 q^{99}+O(q^{100}) \) 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9 + 11 * q^10 + 8 * q^11 + 25 * q^12 + 19 * q^13 + 16 * q^14 + 3 * q^15 + 31 * q^16 - 4 * q^17 - q^18 + 19 * q^19 + 16 * q^20 + 13 * q^21 + 6 * q^22 - 16 * q^23 + 23 * q^25 - 15 * q^26 + 16 * q^27 + 18 * q^28 - 16 * q^29 + 11 * q^30 + 24 * q^31 - 21 * q^32 + 8 * q^33 - 9 * q^34 - 13 * q^35 + 25 * q^36 + 26 * q^37 + 19 * q^39 - 22 * q^40 - 15 * q^41 + 16 * q^42 + 33 * q^43 + 6 * q^44 + 3 * q^45 + q^46 + 13 * q^47 + 31 * q^48 + 41 * q^49 + 13 * q^50 - 4 * q^51 - 26 * q^52 + 5 * q^53 - q^54 + 9 * q^55 + 40 * q^56 + 19 * q^57 + q^58 + 2 * q^59 + 16 * q^60 + 29 * q^61 - 32 * q^62 + 13 * q^63 + 28 * q^64 + 18 * q^65 + 6 * q^66 + 32 * q^67 - 26 * q^68 - 16 * q^69 + 18 * q^70 + 29 * q^71 + 19 * q^73 - 16 * q^74 + 23 * q^75 + 64 * q^76 - 21 * q^77 - 15 * q^78 + 56 * q^79 + 16 * q^81 + 14 * q^82 + 5 * q^83 + 18 * q^84 + 16 * q^85 - 20 * q^86 - 16 * q^87 + q^88 + 7 * q^89 + 11 * q^90 - 6 * q^91 - 25 * q^92 + 24 * q^93 - 11 * q^94 + 39 * q^95 - 21 * q^96 + 35 * q^97 - 109 * q^98 + 8 * 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 $

$2$	2.65986	1.88080	0.940402	−	0.340066i	$-0.110449\pi$
$2$	2.65986	1.88080	0.940402	+	0.340066i	$0.110449\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.07484	2.53742
$5$	−2.26251	−1.01183	−0.505913	−	0.862584i	$-0.668844\pi$
$5$	−2.26251	−1.01183	−0.505913	+	0.862584i	$0.668844\pi$
$6$	2.65986	1.08588
$7$	3.13860	1.18628	0.593139	−	0.805100i	$-0.297888\pi$
$7$	3.13860	1.18628	0.593139	+	0.805100i	$0.297888\pi$
$8$	8.17864	2.89158
$9$	1.00000	0.333333
$10$	−6.01796	−1.90305
$11$	2.75152	0.829616	0.414808	−	0.909909i	$-0.363849\pi$
$11$	2.75152	0.829616	0.414808	+	0.909909i	$0.363849\pi$
$12$	5.07484	1.46498
$13$	−4.39658	−1.21939	−0.609697	−	0.792635i	$-0.708709\pi$
$13$	−4.39658	−1.21939	−0.609697	+	0.792635i	$0.708709\pi$
$14$	8.34822	2.23116
$15$	−2.26251	−0.584178
$16$	11.6043	2.90108
$17$	−5.15020	−1.24911	−0.624554	−	0.780982i	$-0.714719\pi$
$17$	−5.15020	−1.24911	−0.624554	+	0.780982i	$0.714719\pi$
$18$	2.65986	0.626934
$19$	6.77659	1.55466	0.777328	−	0.629095i	$-0.216574\pi$
$19$	6.77659	1.55466	0.777328	+	0.629095i	$0.216574\pi$
$20$	−11.4819	−2.56743
$21$	3.13860	0.684898
$22$	7.31866	1.56034
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	8.17864	1.66946
$25$	0.118961	0.0237923
$26$	−11.6943	−2.29344
$27$	1.00000	0.192450
$28$	15.9279	3.01009
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−6.01796	−1.09872
$31$	2.65285	0.476465	0.238233	−	0.971208i	$-0.423432\pi$
$31$	2.65285	0.476465	0.238233	+	0.971208i	$0.423432\pi$
$32$	14.5086	2.56478
$33$	2.75152	0.478979
$34$	−13.6988	−2.34933
$35$	−7.10112	−1.20031
$36$	5.07484	0.845807
$37$	0.716519	0.117795	0.0588975	−	0.998264i	$-0.481241\pi$
$37$	0.716519	0.117795	0.0588975	+	0.998264i	$0.481241\pi$
$38$	18.0248	2.92400
$39$	−4.39658	−0.704017
$40$	−18.5043	−2.92578
$41$	−4.09771	−0.639955	−0.319977	−	0.947425i	$-0.603675\pi$
$41$	−4.09771	−0.639955	−0.319977	+	0.947425i	$0.603675\pi$
$42$	8.34822	1.28816
$43$	9.18604	1.40086	0.700429	−	0.713722i	$-0.252992\pi$
$43$	9.18604	1.40086	0.700429	+	0.713722i	$0.252992\pi$
$44$	13.9635	2.10508
$45$	−2.26251	−0.337275
$46$	−2.65986	−0.392175
$47$	−9.21938	−1.34478	−0.672392	−	0.740195i	$-0.734733\pi$
$47$	−9.21938	−1.34478	−0.672392	+	0.740195i	$0.734733\pi$
$48$	11.6043	1.67494
$49$	2.85080	0.407257
$50$	0.316421	0.0447486
$51$	−5.15020	−0.721173
$52$	−22.3120	−3.09411
$53$	7.55372	1.03758	0.518791	−	0.854901i	$-0.326382\pi$
$53$	7.55372	1.03758	0.518791	+	0.854901i	$0.326382\pi$
$54$	2.65986	0.361961
$55$	−6.22536	−0.839427
$56$	25.6695	3.43023
$57$	6.77659	0.897581
$58$	−2.65986	−0.349256
$59$	−6.47205	−0.842590	−0.421295	−	0.906924i	$-0.638424\pi$
$59$	−6.47205	−0.842590	−0.421295	+	0.906924i	$0.638424\pi$
$60$	−11.4819	−1.48231
$61$	−1.02808	−0.131632	−0.0658158	−	0.997832i	$-0.520965\pi$
$61$	−1.02808	−0.131632	−0.0658158	+	0.997832i	$0.520965\pi$
$62$	7.05619	0.896137
$63$	3.13860	0.395426
$64$	15.3821	1.92276
$65$	9.94733	1.23381
$66$	7.31866	0.900865
$67$	−8.08875	−0.988198	−0.494099	−	0.869406i	$-0.664502\pi$
$67$	−8.08875	−0.988198	−0.494099	+	0.869406i	$0.664502\pi$
$68$	−26.1365	−3.16951
$69$	−1.00000	−0.120386
$70$	−18.8880	−2.25754
$71$	4.92645	0.584662	0.292331	−	0.956317i	$-0.405569\pi$
$71$	4.92645	0.584662	0.292331	+	0.956317i	$0.405569\pi$
$72$	8.17864	0.963862
$73$	−7.67814	−0.898658	−0.449329	−	0.893366i	$-0.648337\pi$
$73$	−7.67814	−0.898658	−0.449329	+	0.893366i	$0.648337\pi$
$74$	1.90584	0.221549
$75$	0.118961	0.0137365
$76$	34.3901	3.94482
$77$	8.63593	0.984155
$78$	−11.6943	−1.32412
$79$	−14.3627	−1.61593	−0.807964	−	0.589232i	$-0.799430\pi$
$79$	−14.3627	−1.61593	−0.807964	+	0.589232i	$0.799430\pi$
$80$	−26.2549	−2.93539
$81$	1.00000	0.111111
$82$	−10.8993	−1.20363
$83$	−9.71872	−1.06677	−0.533384	−	0.845873i	$-0.679080\pi$
$83$	−9.71872	−1.06677	−0.533384	+	0.845873i	$0.679080\pi$
$84$	15.9279	1.73787
$85$	11.6524	1.26388
$86$	24.4336	2.63474
$87$	−1.00000	−0.107211
$88$	22.5037	2.39890
$89$	4.23269	0.448665	0.224332	−	0.974513i	$-0.427980\pi$
$89$	4.23269	0.448665	0.224332	+	0.974513i	$0.427980\pi$
$90$	−6.01796	−0.634349
$91$	−13.7991	−1.44654
$92$	−5.07484	−0.529089
$93$	2.65285	0.275087
$94$	−24.5222	−2.52927
$95$	−15.3321	−1.57304
$96$	14.5086	1.48078
$97$	8.66126	0.879418	0.439709	−	0.898140i	$-0.355082\pi$
$97$	8.66126	0.879418	0.439709	+	0.898140i	$0.355082\pi$
$98$	7.58272	0.765971
$99$	2.75152	0.276539
$100$	0.603710	0.0603710
$101$	2.93514	0.292057	0.146029	−	0.989280i	$-0.453351\pi$
$101$	2.93514	0.292057	0.146029	+	0.989280i	$0.453351\pi$
$102$	−13.6988	−1.35638
$103$	−1.16031	−0.114328	−0.0571642	−	0.998365i	$-0.518206\pi$
$103$	−1.16031	−0.114328	−0.0571642	+	0.998365i	$0.518206\pi$
$104$	−35.9581	−3.52598
$105$	−7.10112	−0.692998
$106$	20.0918	1.95149
$107$	−3.72708	−0.360311	−0.180155	−	0.983638i	$-0.557660\pi$
$107$	−3.72708	−0.360311	−0.180155	+	0.983638i	$0.557660\pi$
$108$	5.07484	0.488327
$109$	11.9328	1.14295	0.571477	−	0.820618i	$-0.306371\pi$
$109$	11.9328	1.14295	0.571477	+	0.820618i	$0.306371\pi$
$110$	−16.5586	−1.57880
$111$	0.716519	0.0680089
$112$	36.4213	3.44149
$113$	−1.96344	−0.184705	−0.0923527	−	0.995726i	$-0.529439\pi$
$113$	−1.96344	−0.184705	−0.0923527	+	0.995726i	$0.529439\pi$
$114$	18.0248	1.68817
$115$	2.26251	0.210980
$116$	−5.07484	−0.471187
$117$	−4.39658	−0.406464
$118$	−17.2147	−1.58474
$119$	−16.1644	−1.48179
$120$	−18.5043	−1.68920
$121$	−3.42912	−0.311738
$122$	−2.73453	−0.247573
$123$	−4.09771	−0.369478
$124$	13.4628	1.20899
$125$	11.0434	0.987753
$126$	8.34822	0.743719
$127$	14.4525	1.28245	0.641224	−	0.767354i	$-0.278427\pi$
$127$	14.4525	1.28245	0.641224	+	0.767354i	$0.278427\pi$
$128$	11.8970	1.05156
$129$	9.18604	0.808786
$130$	26.4585	2.32056
$131$	−10.1767	−0.889146	−0.444573	−	0.895743i	$-0.646645\pi$
$131$	−10.1767	−0.889146	−0.444573	+	0.895743i	$0.646645\pi$
$132$	13.9635	1.21537
$133$	21.2690	1.84426
$134$	−21.5149	−1.85861
$135$	−2.26251	−0.194726
$136$	−42.1216	−3.61190
$137$	−15.4872	−1.32316	−0.661579	−	0.749876i	$-0.730113\pi$
$137$	−15.4872	−1.32316	−0.661579	+	0.749876i	$0.730113\pi$
$138$	−2.65986	−0.226422
$139$	−6.85193	−0.581173	−0.290587	−	0.956849i	$-0.593850\pi$
$139$	−6.85193	−0.581173	−0.290587	+	0.956849i	$0.593850\pi$
$140$	−36.0370	−3.04569
$141$	−9.21938	−0.776412
$142$	13.1037	1.09963
$143$	−12.0973	−1.01163
$144$	11.6043	0.967027
$145$	2.26251	0.187891
$146$	−20.4227	−1.69020
$147$	2.85080	0.235130
$148$	3.63622	0.298895
$149$	−0.508794	−0.0416820	−0.0208410	−	0.999783i	$-0.506634\pi$
$149$	−0.508794	−0.0416820	−0.0208410	+	0.999783i	$0.506634\pi$
$150$	0.316421	0.0258356
$151$	0.0598146	0.00486764	0.00243382	−	0.999997i	$-0.499225\pi$
$151$	0.0598146	0.00486764	0.00243382	+	0.999997i	$0.499225\pi$
$152$	55.4233	4.49542
$153$	−5.15020	−0.416369
$154$	22.9703	1.85100
$155$	−6.00210	−0.482100
$156$	−22.3120	−1.78639
$157$	22.2381	1.77480	0.887398	−	0.461003i	$-0.152510\pi$
$157$	22.2381	1.77480	0.887398	+	0.461003i	$0.152510\pi$
$158$	−38.2027	−3.03924
$159$	7.55372	0.599049
$160$	−32.8258	−2.59511
$161$	−3.13860	−0.247356
$162$	2.65986	0.208978
$163$	13.8763	1.08687	0.543437	−	0.839450i	$-0.317123\pi$
$163$	13.8763	1.08687	0.543437	+	0.839450i	$0.317123\pi$
$164$	−20.7952	−1.62383
$165$	−6.22536	−0.484643
$166$	−25.8504	−2.00638
$167$	15.8394	1.22569	0.612843	−	0.790204i	$-0.290026\pi$
$167$	15.8394	1.22569	0.612843	+	0.790204i	$0.290026\pi$
$168$	25.6695	1.98044
$169$	6.32995	0.486919
$170$	30.9937	2.37711
$171$	6.77659	0.518219
$172$	46.6177	3.55457
$173$	2.50875	0.190737	0.0953683	−	0.995442i	$-0.469597\pi$
$173$	2.50875	0.190737	0.0953683	+	0.995442i	$0.469597\pi$
$174$	−2.65986	−0.201643
$175$	0.373372	0.0282243
$176$	31.9296	2.40678
$177$	−6.47205	−0.486469
$178$	11.2584	0.843850
$179$	−2.55613	−0.191054	−0.0955269	−	0.995427i	$-0.530454\pi$
$179$	−2.55613	−0.191054	−0.0955269	+	0.995427i	$0.530454\pi$
$180$	−11.4819	−0.855809
$181$	−22.3089	−1.65821	−0.829104	−	0.559095i	$-0.811149\pi$
$181$	−22.3089	−1.65821	−0.829104	+	0.559095i	$0.811149\pi$
$182$	−36.7037	−2.72066
$183$	−1.02808	−0.0759975
$184$	−8.17864	−0.602937
$185$	−1.62113	−0.119188
$186$	7.05619	0.517385
$187$	−14.1709	−1.03628
$188$	−46.7869	−3.41228
$189$	3.13860	0.228299
$190$	−40.7812	−2.95858
$191$	23.8617	1.72657	0.863287	−	0.504713i	$-0.168402\pi$
$191$	23.8617	1.72657	0.863287	+	0.504713i	$0.168402\pi$
$192$	15.3821	1.11011
$193$	−22.3709	−1.61029	−0.805147	−	0.593076i	$-0.797914\pi$
$193$	−22.3709	−1.61029	−0.805147	+	0.593076i	$0.797914\pi$
$194$	23.0377	1.65401
$195$	9.94733	0.712343
$196$	14.4674	1.03338
$197$	−10.5354	−0.750619	−0.375309	−	0.926900i	$-0.622464\pi$
$197$	−10.5354	−0.750619	−0.375309	+	0.926900i	$0.622464\pi$
$198$	7.31866	0.520115
$199$	27.9193	1.97915	0.989575	−	0.144020i	$-0.0460029\pi$
$199$	27.9193	1.97915	0.989575	+	0.144020i	$0.0460029\pi$
$200$	0.972943	0.0687974
$201$	−8.08875	−0.570536
$202$	7.80706	0.549303
$203$	−3.13860	−0.220286
$204$	−26.1365	−1.82992
$205$	9.27112	0.647523
$206$	−3.08625	−0.215029
$207$	−1.00000	−0.0695048
$208$	−51.0194	−3.53756
$209$	18.6460	1.28977
$210$	−18.8880	−1.30339
$211$	−22.0925	−1.52091	−0.760456	−	0.649389i	$-0.775025\pi$
$211$	−22.0925	−1.52091	−0.760456	+	0.649389i	$0.775025\pi$
$212$	38.3339	2.63278
$213$	4.92645	0.337555
$214$	−9.91351	−0.677674
$215$	−20.7835	−1.41743
$216$	8.17864	0.556486
$217$	8.32622	0.565221
$218$	31.7395	2.14967
$219$	−7.67814	−0.518840
$220$	−31.5927	−2.12998
$221$	22.6433	1.52315
$222$	1.90584	0.127911
$223$	2.05410	0.137553	0.0687763	−	0.997632i	$-0.478091\pi$
$223$	2.05410	0.137553	0.0687763	+	0.997632i	$0.478091\pi$
$224$	45.5366	3.04254
$225$	0.118961	0.00793076
$226$	−5.22248	−0.347394
$227$	−4.41425	−0.292984	−0.146492	−	0.989212i	$-0.546798\pi$
$227$	−4.41425	−0.292984	−0.146492	+	0.989212i	$0.546798\pi$
$228$	34.3901	2.27754
$229$	−15.6794	−1.03612	−0.518062	−	0.855343i	$-0.673346\pi$
$229$	−15.6794	−1.03612	−0.518062	+	0.855343i	$0.673346\pi$
$230$	6.01796	0.396812
$231$	8.63593	0.568202
$232$	−8.17864	−0.536954
$233$	11.0992	0.727133	0.363567	−	0.931568i	$-0.381559\pi$
$233$	11.0992	0.727133	0.363567	+	0.931568i	$0.381559\pi$
$234$	−11.6943	−0.764479
$235$	20.8590	1.36069
$236$	−32.8446	−2.13800
$237$	−14.3627	−0.932956
$238$	−42.9950	−2.78696
$239$	−26.8994	−1.73997	−0.869987	−	0.493074i	$-0.835873\pi$
$239$	−26.8994	−1.73997	−0.869987	+	0.493074i	$0.835873\pi$
$240$	−26.2549	−1.69475
$241$	18.6629	1.20218	0.601090	−	0.799181i	$-0.294733\pi$
$241$	18.6629	1.20218	0.601090	+	0.799181i	$0.294733\pi$
$242$	−9.12096	−0.586317
$243$	1.00000	0.0641500
$244$	−5.21732	−0.334005
$245$	−6.44997	−0.412073
$246$	−10.8993	−0.694915
$247$	−29.7939	−1.89574
$248$	21.6967	1.37774
$249$	−9.71872	−0.615899
$250$	29.3739	1.85777
$251$	−26.5817	−1.67782	−0.838909	−	0.544271i	$-0.816806\pi$
$251$	−26.5817	−1.67782	−0.838909	+	0.544271i	$0.816806\pi$
$252$	15.9279	1.00336
$253$	−2.75152	−0.172987
$254$	38.4415	2.41203
$255$	11.6524	0.729701
$256$	0.880170	0.0550106
$257$	−17.3122	−1.07991	−0.539953	−	0.841695i	$-0.681558\pi$
$257$	−17.3122	−1.07991	−0.539953	+	0.841695i	$0.681558\pi$
$258$	24.4336	1.52117
$259$	2.24886	0.139738
$260$	50.4811	3.13070
$261$	−1.00000	−0.0618984
$262$	−27.0687	−1.67231
$263$	−12.5229	−0.772197	−0.386099	−	0.922458i	$-0.626178\pi$
$263$	−12.5229	−0.772197	−0.386099	+	0.922458i	$0.626178\pi$
$264$	22.5037	1.38501
$265$	−17.0904	−1.04985
$266$	56.5725	3.46868
$267$	4.23269	0.259037
$268$	−41.0491	−2.50747
$269$	−14.9810	−0.913410	−0.456705	−	0.889618i	$-0.650970\pi$
$269$	−14.9810	−0.913410	−0.456705	+	0.889618i	$0.650970\pi$
$270$	−6.01796	−0.366241
$271$	7.41476	0.450414	0.225207	−	0.974311i	$-0.427694\pi$
$271$	7.41476	0.450414	0.225207	+	0.974311i	$0.427694\pi$
$272$	−59.7646	−3.62376
$273$	−13.7991	−0.835160
$274$	−41.1936	−2.48860
$275$	0.327325	0.0197385
$276$	−5.07484	−0.305470
$277$	9.25490	0.556073	0.278037	−	0.960570i	$-0.410316\pi$
$277$	9.25490	0.556073	0.278037	+	0.960570i	$0.410316\pi$
$278$	−18.2252	−1.09307
$279$	2.65285	0.158822
$280$	−58.0775	−3.47079
$281$	15.6501	0.933607	0.466803	−	0.884361i	$-0.345406\pi$
$281$	15.6501	0.933607	0.466803	+	0.884361i	$0.345406\pi$
$282$	−24.5222	−1.46028
$283$	−27.7066	−1.64699	−0.823493	−	0.567326i	$-0.807978\pi$
$283$	−27.7066	−1.64699	−0.823493	+	0.567326i	$0.807978\pi$
$284$	25.0010	1.48353
$285$	−15.3321	−0.908196
$286$	−32.1771	−1.90267
$287$	−12.8611	−0.759164
$288$	14.5086	0.854926
$289$	9.52459	0.560270
$290$	6.01796	0.353387
$291$	8.66126	0.507732
$292$	−38.9653	−2.28027
$293$	13.6958	0.800115	0.400057	−	0.916490i	$-0.368990\pi$
$293$	13.6958	0.800115	0.400057	+	0.916490i	$0.368990\pi$
$294$	7.58272	0.442233
$295$	14.6431	0.852554
$296$	5.86015	0.340614
$297$	2.75152	0.159660
$298$	−1.35332	−0.0783957
$299$	4.39658	0.254261
$300$	0.603710	0.0348552
$301$	28.8313	1.66181
$302$	0.159098	0.00915508
$303$	2.93514	0.168619
$304$	78.6378	4.51019
$305$	2.32603	0.133188
$306$	−13.6988	−0.783109
$307$	−20.1645	−1.15085	−0.575424	−	0.817855i	$-0.695163\pi$
$307$	−20.1645	−1.15085	−0.575424	+	0.817855i	$0.695163\pi$
$308$	43.8260	2.49722
$309$	−1.16031	−0.0660075
$310$	−15.9647	−0.906735
$311$	15.6566	0.887804	0.443902	−	0.896075i	$-0.353594\pi$
$311$	15.6566	0.887804	0.443902	+	0.896075i	$0.353594\pi$
$312$	−35.9581	−2.03572
$313$	−16.9031	−0.955417	−0.477709	−	0.878518i	$-0.658533\pi$
$313$	−16.9031	−0.955417	−0.477709	+	0.878518i	$0.658533\pi$
$314$	59.1503	3.33804
$315$	−7.10112	−0.400103
$316$	−72.8883	−4.10029
$317$	−15.6646	−0.879811	−0.439905	−	0.898044i	$-0.644988\pi$
$317$	−15.6646	−0.879811	−0.439905	+	0.898044i	$0.644988\pi$
$318$	20.0918	1.12669
$319$	−2.75152	−0.154056
$320$	−34.8022	−1.94550
$321$	−3.72708	−0.208026
$322$	−8.34822	−0.465228
$323$	−34.9008	−1.94193
$324$	5.07484	0.281936
$325$	−0.523024	−0.0290122
$326$	36.9089	2.04420
$327$	11.9328	0.659885
$328$	−33.5137	−1.85048
$329$	−28.9359	−1.59529
$330$	−16.5586	−0.911519
$331$	16.9341	0.930783	0.465392	−	0.885105i	$-0.345913\pi$
$331$	16.9341	0.930783	0.465392	+	0.885105i	$0.345913\pi$
$332$	−49.3209	−2.70684
$333$	0.716519	0.0392650
$334$	42.1304	2.30527
$335$	18.3009	0.999885
$336$	36.4213	1.98695
$337$	−7.35219	−0.400499	−0.200250	−	0.979745i	$-0.564175\pi$
$337$	−7.35219	−0.400499	−0.200250	+	0.979745i	$0.564175\pi$
$338$	16.8368	0.915800
$339$	−1.96344	−0.106640
$340$	59.1341	3.20699
$341$	7.29937	0.395283
$342$	18.0248	0.974668
$343$	−13.0227	−0.703158
$344$	75.1293	4.05070
$345$	2.26251	0.121810
$346$	6.67291	0.358738
$347$	25.9400	1.39253	0.696267	−	0.717783i	$-0.254843\pi$
$347$	25.9400	1.39253	0.696267	+	0.717783i	$0.254843\pi$
$348$	−5.07484	−0.272040
$349$	27.9065	1.49380	0.746901	−	0.664935i	$-0.231541\pi$
$349$	27.9065	1.49380	0.746901	+	0.664935i	$0.231541\pi$
$350$	0.993117	0.0530843
$351$	−4.39658	−0.234672
$352$	39.9207	2.12778
$353$	1.17625	0.0626056	0.0313028	−	0.999510i	$-0.490034\pi$
$353$	1.17625	0.0626056	0.0313028	+	0.999510i	$0.490034\pi$
$354$	−17.2147	−0.914953
$355$	−11.1462	−0.591576
$356$	21.4802	1.13845
$357$	−16.1644	−0.855512
$358$	−6.79893	−0.359335
$359$	22.1702	1.17010	0.585049	−	0.810998i	$-0.301075\pi$
$359$	22.1702	1.17010	0.585049	+	0.810998i	$0.301075\pi$
$360$	−18.5043	−0.975260
$361$	26.9222	1.41696
$362$	−59.3385	−3.11876
$363$	−3.42912	−0.179982
$364$	−70.0283	−3.67048
$365$	17.3719	0.909286
$366$	−2.73453	−0.142936
$367$	13.8124	0.721001	0.360501	−	0.932759i	$-0.382606\pi$
$367$	13.8124	0.721001	0.360501	+	0.932759i	$0.382606\pi$
$368$	−11.6043	−0.604917
$369$	−4.09771	−0.213318
$370$	−4.31198	−0.224169
$371$	23.7081	1.23086
$372$	13.4628	0.698012
$373$	24.7713	1.28261	0.641306	−	0.767286i	$-0.278393\pi$
$373$	24.7713	1.28261	0.641306	+	0.767286i	$0.278393\pi$
$374$	−37.6926	−1.94904
$375$	11.0434	0.570279
$376$	−75.4019	−3.88856
$377$	4.39658	0.226436
$378$	8.34822	0.429386
$379$	33.4991	1.72073	0.860367	−	0.509675i	$-0.170234\pi$
$379$	33.4991	1.72073	0.860367	+	0.509675i	$0.170234\pi$
$380$	−77.8081	−3.99147
$381$	14.4525	0.740422
$382$	63.4688	3.24735
$383$	−15.4759	−0.790781	−0.395390	−	0.918513i	$-0.629391\pi$
$383$	−15.4759	−0.790781	−0.395390	+	0.918513i	$0.629391\pi$
$384$	11.8970	0.607117
$385$	−19.5389	−0.995794
$386$	−59.5034	−3.02865
$387$	9.18604	0.466953
$388$	43.9545	2.23145
$389$	−1.64191	−0.0832484	−0.0416242	−	0.999133i	$-0.513253\pi$
$389$	−1.64191	−0.0832484	−0.0416242	+	0.999133i	$0.513253\pi$
$390$	26.4585	1.33978
$391$	5.15020	0.260457
$392$	23.3157	1.17762
$393$	−10.1767	−0.513349
$394$	−28.0228	−1.41177
$395$	32.4957	1.63504
$396$	13.9635	0.701695
$397$	36.6980	1.84182	0.920911	−	0.389773i	$-0.127447\pi$
$397$	36.6980	1.84182	0.920911	+	0.389773i	$0.127447\pi$
$398$	74.2615	3.72239
$399$	21.2690	1.06478
$400$	1.38047	0.0690234
$401$	−1.23031	−0.0614389	−0.0307194	−	0.999528i	$-0.509780\pi$
$401$	−1.23031	−0.0614389	−0.0307194	+	0.999528i	$0.509780\pi$
$402$	−21.5149	−1.07307
$403$	−11.6635	−0.580999
$404$	14.8954	0.741073
$405$	−2.26251	−0.112425
$406$	−8.34822	−0.414315
$407$	1.97152	0.0977245
$408$	−42.1216	−2.08533
$409$	20.5385	1.01556	0.507781	−	0.861486i	$-0.330466\pi$
$409$	20.5385	1.01556	0.507781	+	0.861486i	$0.330466\pi$
$410$	24.6598	1.21786
$411$	−15.4872	−0.763925
$412$	−5.88837	−0.290099
$413$	−20.3132	−0.999546
$414$	−2.65986	−0.130725
$415$	21.9887	1.07938
$416$	−63.7882	−3.12747
$417$	−6.85193	−0.335541
$418$	49.5956	2.42580
$419$	2.61132	0.127571	0.0637857	−	0.997964i	$-0.479683\pi$
$419$	2.61132	0.127571	0.0637857	+	0.997964i	$0.479683\pi$
$420$	−36.0370	−1.75843
$421$	−1.79880	−0.0876680	−0.0438340	−	0.999039i	$-0.513957\pi$
$421$	−1.79880	−0.0876680	−0.0438340	+	0.999039i	$0.513957\pi$
$422$	−58.7630	−2.86054
$423$	−9.21938	−0.448261
$424$	61.7791	3.00026
$425$	−0.612676	−0.0297191
$426$	13.1037	0.634874
$427$	−3.22672	−0.156152
$428$	−18.9144	−0.914260
$429$	−12.0973	−0.584064
$430$	−55.2812	−2.66590
$431$	33.3744	1.60759	0.803794	−	0.594908i	$-0.202812\pi$
$431$	33.3744	1.60759	0.803794	+	0.594908i	$0.202812\pi$
$432$	11.6043	0.558313
$433$	10.1052	0.485627	0.242813	−	0.970073i	$-0.421930\pi$
$433$	10.1052	0.485627	0.242813	+	0.970073i	$0.421930\pi$
$434$	22.1466	1.06307
$435$	2.26251	0.108479
$436$	60.5570	2.90015
$437$	−6.77659	−0.324168
$438$	−20.4227	−0.975837
$439$	27.6169	1.31808	0.659042	−	0.752106i	$-0.270962\pi$
$439$	27.6169	1.31808	0.659042	+	0.752106i	$0.270962\pi$
$440$	−50.9149	−2.42727
$441$	2.85080	0.135752
$442$	60.2280	2.86475
$443$	−16.2505	−0.772085	−0.386042	−	0.922481i	$-0.626158\pi$
$443$	−16.2505	−0.772085	−0.386042	+	0.922481i	$0.626158\pi$
$444$	3.63622	0.172567
$445$	−9.57652	−0.453971
$446$	5.46361	0.258710
$447$	−0.508794	−0.0240651
$448$	48.2782	2.28093
$449$	−1.13164	−0.0534055	−0.0267028	−	0.999643i	$-0.508501\pi$
$449$	−1.13164	−0.0534055	−0.0267028	+	0.999643i	$0.508501\pi$
$450$	0.316421	0.0149162
$451$	−11.2749	−0.530916
$452$	−9.96417	−0.468675
$453$	0.0598146	0.00281033
$454$	−11.7413	−0.551045
$455$	31.2207	1.46365
$456$	55.4233	2.59543
$457$	25.6079	1.19788	0.598942	−	0.800792i	$-0.295588\pi$
$457$	25.6079	1.19788	0.598942	+	0.800792i	$0.295588\pi$
$458$	−41.7050	−1.94875
$459$	−5.15020	−0.240391
$460$	11.4819	0.535346
$461$	−5.01815	−0.233718	−0.116859	−	0.993148i	$-0.537283\pi$
$461$	−5.01815	−0.233718	−0.116859	+	0.993148i	$0.537283\pi$
$462$	22.9703	1.06868
$463$	−23.3885	−1.08696	−0.543479	−	0.839423i	$-0.682893\pi$
$463$	−23.3885	−1.08696	−0.543479	+	0.839423i	$0.682893\pi$
$464$	−11.6043	−0.538717
$465$	−6.00210	−0.278341
$466$	29.5223	1.36759
$467$	33.4940	1.54992	0.774959	−	0.632011i	$-0.217770\pi$
$467$	33.4940	1.54992	0.774959	+	0.632011i	$0.217770\pi$
$468$	−22.3120	−1.03137
$469$	−25.3873	−1.17228
$470$	55.4818	2.55919
$471$	22.2381	1.02468
$472$	−52.9326	−2.43642
$473$	25.2756	1.16217
$474$	−38.2027	−1.75471
$475$	0.806153	0.0369888
$476$	−82.0319	−3.75992
$477$	7.55372	0.345861
$478$	−71.5484	−3.27255
$479$	4.25385	0.194364	0.0971818	−	0.995267i	$-0.469017\pi$
$479$	4.25385	0.194364	0.0971818	+	0.995267i	$0.469017\pi$
$480$	−32.8258	−1.49829
$481$	−3.15023	−0.143638
$482$	49.6406	2.26107
$483$	−3.13860	−0.142811
$484$	−17.4022	−0.791010
$485$	−19.5962	−0.889818
$486$	2.65986	0.120654
$487$	9.76671	0.442572	0.221286	−	0.975209i	$-0.428975\pi$
$487$	9.76671	0.442572	0.221286	+	0.975209i	$0.428975\pi$
$488$	−8.40826	−0.380624
$489$	13.8763	0.627507
$490$	−17.1560	−0.775029
$491$	17.6398	0.796074	0.398037	−	0.917369i	$-0.369692\pi$
$491$	17.6398	0.796074	0.398037	+	0.917369i	$0.369692\pi$
$492$	−20.7952	−0.937521
$493$	5.15020	0.231953
$494$	−79.2474	−3.56551
$495$	−6.22536	−0.279809
$496$	30.7845	1.38226
$497$	15.4621	0.693572
$498$	−25.8504	−1.15838
$499$	28.2525	1.26476	0.632379	−	0.774659i	$-0.282079\pi$
$499$	28.2525	1.26476	0.632379	+	0.774659i	$0.282079\pi$
$500$	56.0435	2.50634
$501$	15.8394	0.707650
$502$	−70.7034	−3.15565
$503$	−27.9559	−1.24649	−0.623246	−	0.782026i	$-0.714186\pi$
$503$	−27.9559	−1.24649	−0.623246	+	0.782026i	$0.714186\pi$
$504$	25.6695	1.14341
$505$	−6.64079	−0.295511
$506$	−7.31866	−0.325354
$507$	6.32995	0.281123
$508$	73.3439	3.25411
$509$	43.0991	1.91033	0.955166	−	0.296069i	$-0.0956759\pi$
$509$	43.0991	1.91033	0.955166	+	0.296069i	$0.0956759\pi$
$510$	30.9937	1.37242
$511$	−24.0986	−1.06606
$512$	−21.4529	−0.948093
$513$	6.77659	0.299194
$514$	−46.0480	−2.03109
$515$	2.62521	0.115680
$516$	46.6177	2.05223
$517$	−25.3673	−1.11565
$518$	5.98166	0.262819
$519$	2.50875	0.110122
$520$	81.3556	3.56768
$521$	28.7125	1.25792	0.628959	−	0.777439i	$-0.283481\pi$
$521$	28.7125	1.25792	0.628959	+	0.777439i	$0.283481\pi$
$522$	−2.65986	−0.116419
$523$	−22.2348	−0.972259	−0.486130	−	0.873887i	$-0.661592\pi$
$523$	−22.2348	−0.972259	−0.486130	+	0.873887i	$0.661592\pi$
$524$	−51.6453	−2.25614
$525$	0.373372	0.0162953
$526$	−33.3092	−1.45235
$527$	−13.6627	−0.595157
$528$	31.9296	1.38956
$529$	1.00000	0.0434783
$530$	−45.4580	−1.97457
$531$	−6.47205	−0.280863
$532$	107.937	4.67965
$533$	18.0159	0.780356
$534$	11.2584	0.487197
$535$	8.43257	0.364572
$536$	−66.1550	−2.85746
$537$	−2.55613	−0.110305
$538$	−39.8474	−1.71794
$539$	7.84405	0.337867
$540$	−11.4819	−0.494102
$541$	−11.0404	−0.474662	−0.237331	−	0.971429i	$-0.576273\pi$
$541$	−11.0404	−0.474662	−0.237331	+	0.971429i	$0.576273\pi$
$542$	19.7222	0.847141
$543$	−22.3089	−0.957366
$544$	−74.7221	−3.20368
$545$	−26.9981	−1.15647
$546$	−36.7037	−1.57077
$547$	26.4815	1.13227	0.566133	−	0.824314i	$-0.308439\pi$
$547$	26.4815	1.13227	0.566133	+	0.824314i	$0.308439\pi$
$548$	−78.5949	−3.35741
$549$	−1.02808	−0.0438772
$550$	0.870639	0.0371242
$551$	−6.77659	−0.288692
$552$	−8.17864	−0.348106
$553$	−45.0787	−1.91694
$554$	24.6167	1.04586
$555$	−1.62113	−0.0688132
$556$	−34.7725	−1.47468
$557$	−42.2594	−1.79059	−0.895293	−	0.445478i	$-0.853034\pi$
$557$	−42.2594	−1.79059	−0.895293	+	0.445478i	$0.853034\pi$
$558$	7.05619	0.298712
$559$	−40.3872	−1.70820
$560$	−82.4037	−3.48219
$561$	−14.1709	−0.598296
$562$	41.6270	1.75593
$563$	−17.9672	−0.757226	−0.378613	−	0.925555i	$-0.623599\pi$
$563$	−17.9672	−0.757226	−0.378613	+	0.925555i	$0.623599\pi$
$564$	−46.7869	−1.97008
$565$	4.44232	0.186890
$566$	−73.6956	−3.09766
$567$	3.13860	0.131809
$568$	40.2916	1.69060
$569$	−27.4987	−1.15281	−0.576403	−	0.817165i	$-0.695544\pi$
$569$	−27.4987	−1.15281	−0.576403	+	0.817165i	$0.695544\pi$
$570$	−40.7812	−1.70814
$571$	11.2951	0.472685	0.236342	−	0.971670i	$-0.424051\pi$
$571$	11.2951	0.472685	0.236342	+	0.971670i	$0.424051\pi$
$572$	−61.3919	−2.56692
$573$	23.8617	0.996838
$574$	−34.2086	−1.42784
$575$	−0.118961	−0.00496104
$576$	15.3821	0.640920
$577$	15.5449	0.647142	0.323571	−	0.946204i	$-0.395117\pi$
$577$	15.5449	0.647142	0.323571	+	0.946204i	$0.395117\pi$
$578$	25.3341	1.05376
$579$	−22.3709	−0.929703
$580$	11.4819	0.476759
$581$	−30.5032	−1.26548
$582$	23.0377	0.954944
$583$	20.7842	0.860795
$584$	−62.7967	−2.59855
$585$	9.94733	0.411271
$586$	36.4288	1.50486
$587$	45.1478	1.86345	0.931725	−	0.363165i	$-0.118304\pi$
$587$	45.1478	1.86345	0.931725	+	0.363165i	$0.118304\pi$
$588$	14.4674	0.596624
$589$	17.9773	0.740740
$590$	38.9486	1.60349
$591$	−10.5354	−0.433370
$592$	8.31472	0.341733
$593$	41.3729	1.69898	0.849490	−	0.527605i	$-0.176910\pi$
$593$	41.3729	1.69898	0.849490	+	0.527605i	$0.176910\pi$
$594$	7.31866	0.300288
$595$	36.5722	1.49931
$596$	−2.58205	−0.105765
$597$	27.9193	1.14266
$598$	11.6943	0.478215
$599$	8.78420	0.358913	0.179456	−	0.983766i	$-0.442566\pi$
$599$	8.78420	0.358913	0.179456	+	0.983766i	$0.442566\pi$
$600$	0.972943	0.0397202
$601$	35.7677	1.45899	0.729497	−	0.683984i	$-0.239754\pi$
$601$	35.7677	1.45899	0.729497	+	0.683984i	$0.239754\pi$
$602$	76.6871	3.12553
$603$	−8.08875	−0.329399
$604$	0.303550	0.0123513
$605$	7.75842	0.315424
$606$	7.80706	0.317140
$607$	−25.2442	−1.02463	−0.512316	−	0.858797i	$-0.671212\pi$
$607$	−25.2442	−1.02463	−0.512316	+	0.858797i	$0.671212\pi$
$608$	98.3187	3.98735
$609$	−3.13860	−0.127182
$610$	6.18692	0.250501
$611$	40.5338	1.63982
$612$	−26.1365	−1.05650
$613$	18.8034	0.759461	0.379730	−	0.925097i	$-0.376017\pi$
$613$	18.8034	0.759461	0.379730	+	0.925097i	$0.376017\pi$
$614$	−53.6346	−2.16452
$615$	9.27112	0.373847
$616$	70.6301	2.84577
$617$	9.10900	0.366715	0.183357	−	0.983046i	$-0.441303\pi$
$617$	9.10900	0.366715	0.183357	+	0.983046i	$0.441303\pi$
$618$	−3.08625	−0.124147
$619$	−2.64073	−0.106140	−0.0530699	−	0.998591i	$-0.516901\pi$
$619$	−2.64073	−0.106140	−0.0530699	+	0.998591i	$0.516901\pi$
$620$	−30.4597	−1.22329
$621$	−1.00000	−0.0401286
$622$	41.6443	1.66979
$623$	13.2847	0.532241
$624$	−51.0194	−2.04241
$625$	−25.5807	−1.02323
$626$	−44.9597	−1.79695
$627$	18.6460	0.744648
$628$	112.855	4.50341
$629$	−3.69022	−0.147139
$630$	−18.8880	−0.752514
$631$	40.0674	1.59506	0.797529	−	0.603281i	$-0.206140\pi$
$631$	40.0674	1.59506	0.797529	+	0.603281i	$0.206140\pi$
$632$	−117.467	−4.67259
$633$	−22.0925	−0.878099
$634$	−41.6655	−1.65475
$635$	−32.6989	−1.29761
$636$	38.3339	1.52004
$637$	−12.5338	−0.496607
$638$	−7.31866	−0.289749
$639$	4.92645	0.194887
$640$	−26.9171	−1.06399
$641$	−4.01980	−0.158773	−0.0793863	−	0.996844i	$-0.525296\pi$
$641$	−4.01980	−0.158773	−0.0793863	+	0.996844i	$0.525296\pi$
$642$	−9.91351	−0.391255
$643$	−23.5020	−0.926827	−0.463414	−	0.886142i	$-0.653376\pi$
$643$	−23.5020	−0.926827	−0.463414	+	0.886142i	$0.653376\pi$
$644$	−15.9279	−0.627647
$645$	−20.7835	−0.818351
$646$	−92.8312	−3.65239
$647$	−46.8966	−1.84369	−0.921847	−	0.387554i	$-0.873320\pi$
$647$	−46.8966	−1.84369	−0.921847	+	0.387554i	$0.873320\pi$
$648$	8.17864	0.321287
$649$	−17.8080	−0.699026
$650$	−1.39117	−0.0545662
$651$	8.32622	0.326330
$652$	70.4199	2.75786
$653$	−5.27270	−0.206337	−0.103168	−	0.994664i	$-0.532898\pi$
$653$	−5.27270	−0.206337	−0.103168	+	0.994664i	$0.532898\pi$
$654$	31.7395	1.24111
$655$	23.0250	0.899661
$656$	−47.5511	−1.85656
$657$	−7.67814	−0.299553
$658$	−76.9654	−3.00042
$659$	1.95551	0.0761760	0.0380880	−	0.999274i	$-0.487873\pi$
$659$	1.95551	0.0761760	0.0380880	+	0.999274i	$0.487873\pi$
$660$	−31.5927	−1.22974
$661$	−16.2707	−0.632859	−0.316429	−	0.948616i	$-0.602484\pi$
$661$	−16.2707	−0.632859	−0.316429	+	0.948616i	$0.602484\pi$
$662$	45.0423	1.75062
$663$	22.6433	0.879393
$664$	−79.4859	−3.08465
$665$	−48.1214	−1.86607
$666$	1.90584	0.0738497
$667$	1.00000	0.0387202
$668$	80.3822	3.11008
$669$	2.05410	0.0794161
$670$	48.6778	1.88059
$671$	−2.82878	−0.109204
$672$	45.5366	1.75661
$673$	−15.0247	−0.579160	−0.289580	−	0.957154i	$-0.593516\pi$
$673$	−15.0247	−0.579160	−0.289580	+	0.957154i	$0.593516\pi$
$674$	−19.5558	−0.753261
$675$	0.118961	0.00457883
$676$	32.1235	1.23552
$677$	19.2334	0.739199	0.369599	−	0.929191i	$-0.379495\pi$
$677$	19.2334	0.739199	0.369599	+	0.929191i	$0.379495\pi$
$678$	−5.22248	−0.200568
$679$	27.1842	1.04323
$680$	95.3007	3.65462
$681$	−4.41425	−0.169154
$682$	19.4153	0.743450
$683$	−10.2414	−0.391878	−0.195939	−	0.980616i	$-0.562775\pi$
$683$	−10.2414	−0.391878	−0.195939	+	0.980616i	$0.562775\pi$
$684$	34.3901	1.31494
$685$	35.0399	1.33881
$686$	−34.6384	−1.32250
$687$	−15.6794	−0.598207
$688$	106.598	4.06400
$689$	−33.2106	−1.26522
$690$	6.01796	0.229100
$691$	−27.2229	−1.03561	−0.517804	−	0.855499i	$-0.673250\pi$
$691$	−27.2229	−1.03561	−0.517804	+	0.855499i	$0.673250\pi$
$692$	12.7315	0.483979
$693$	8.63593	0.328052
$694$	68.9968	2.61908
$695$	15.5026	0.588046
$696$	−8.17864	−0.310010
$697$	21.1040	0.799372
$698$	74.2274	2.80955
$699$	11.0992	0.419810
$700$	1.89480	0.0716169
$701$	−22.4181	−0.846719	−0.423360	−	0.905962i	$-0.639149\pi$
$701$	−22.4181	−0.846719	−0.423360	+	0.905962i	$0.639149\pi$
$702$	−11.6943	−0.441372
$703$	4.85555	0.183131
$704$	42.3242	1.59515
$705$	20.8590	0.785594
$706$	3.12866	0.117749
$707$	9.21223	0.346462
$708$	−32.8446	−1.23438
$709$	12.3777	0.464855	0.232427	−	0.972614i	$-0.425333\pi$
$709$	12.3777	0.464855	0.232427	+	0.972614i	$0.425333\pi$
$710$	−29.6472	−1.11264
$711$	−14.3627	−0.538642
$712$	34.6177	1.29735
$713$	−2.65285	−0.0993499
$714$	−42.9950	−1.60905
$715$	27.3703	1.02359
$716$	−12.9719	−0.484784
$717$	−26.8994	−1.00457
$718$	58.9696	2.20073
$719$	21.8368	0.814376	0.407188	−	0.913344i	$-0.366509\pi$
$719$	21.8368	0.814376	0.407188	+	0.913344i	$0.366509\pi$
$720$	−26.2549	−0.978463
$721$	−3.64173	−0.135625
$722$	71.6092	2.66502
$723$	18.6629	0.694079
$724$	−113.214	−4.20757
$725$	−0.118961	−0.00441812
$726$	−9.12096	−0.338510
$727$	21.5088	0.797717	0.398858	−	0.917013i	$-0.369407\pi$
$727$	21.5088	0.797717	0.398858	+	0.917013i	$0.369407\pi$
$728$	−112.858	−4.18279
$729$	1.00000	0.0370370
$730$	46.2067	1.71019
$731$	−47.3100	−1.74982
$732$	−5.21732	−0.192838
$733$	17.4284	0.643734	0.321867	−	0.946785i	$-0.395690\pi$
$733$	17.4284	0.643734	0.321867	+	0.946785i	$0.395690\pi$
$734$	36.7390	1.35606
$735$	−6.44997	−0.237911
$736$	−14.5086	−0.534793
$737$	−22.2564	−0.819825
$738$	−10.8993	−0.401209
$739$	−50.8593	−1.87089	−0.935445	−	0.353471i	$-0.885001\pi$
$739$	−50.8593	−1.87089	−0.935445	+	0.353471i	$0.885001\pi$
$740$	−8.22699	−0.302430
$741$	−29.7939	−1.09450
$742$	63.0601	2.31501
$743$	45.6613	1.67515	0.837575	−	0.546323i	$-0.183973\pi$
$743$	45.6613	1.67515	0.837575	+	0.546323i	$0.183973\pi$
$744$	21.6967	0.795439
$745$	1.15115	0.0421750
$746$	65.8882	2.41234
$747$	−9.71872	−0.355589
$748$	−71.9151	−2.62948
$749$	−11.6978	−0.427429
$750$	29.3739	1.07258
$751$	35.9889	1.31326	0.656628	−	0.754215i	$-0.271982\pi$
$751$	35.9889	1.31326	0.656628	+	0.754215i	$0.271982\pi$
$752$	−106.985	−3.90133
$753$	−26.5817	−0.968689
$754$	11.6943	0.425881
$755$	−0.135331	−0.00492521
$756$	15.9279	0.579292
$757$	26.0191	0.945679	0.472839	−	0.881149i	$-0.343229\pi$
$757$	26.0191	0.945679	0.472839	+	0.881149i	$0.343229\pi$
$758$	89.1029	3.23636
$759$	−2.75152	−0.0998740
$760$	−125.396	−4.54859
$761$	43.2239	1.56687	0.783433	−	0.621476i	$-0.213467\pi$
$761$	43.2239	1.56687	0.783433	+	0.621476i	$0.213467\pi$
$762$	38.4415	1.39259
$763$	37.4522	1.35586
$764$	121.094	4.38105
$765$	11.6524	0.421293
$766$	−41.1636	−1.48730
$767$	28.4549	1.02745
$768$	0.880170	0.0317604
$769$	−19.0024	−0.685243	−0.342621	−	0.939474i	$-0.611315\pi$
$769$	−19.0024	−0.685243	−0.342621	+	0.939474i	$0.611315\pi$
$770$	−51.9707	−1.87289
$771$	−17.3122	−0.623484
$772$	−113.529	−4.08599
$773$	−26.9762	−0.970266	−0.485133	−	0.874440i	$-0.661229\pi$
$773$	−26.9762	−0.970266	−0.485133	+	0.874440i	$0.661229\pi$
$774$	24.4336	0.878246
$775$	0.315587	0.0113362
$776$	70.8373	2.54291
$777$	2.24886	0.0806776
$778$	−4.36726	−0.156574
$779$	−27.7685	−0.994910
$780$	50.4811	1.80751
$781$	13.5552	0.485045
$782$	13.6988	0.489868
$783$	−1.00000	−0.0357371
$784$	33.0816	1.18149
$785$	−50.3141	−1.79579
$786$	−27.0687	−0.965508
$787$	22.8508	0.814544	0.407272	−	0.913307i	$-0.366480\pi$
$787$	22.8508	0.814544	0.407272	+	0.913307i	$0.366480\pi$
$788$	−53.4657	−1.90464
$789$	−12.5229	−0.445828
$790$	86.4340	3.07518
$791$	−6.16246	−0.219112
$792$	22.5037	0.799635
$793$	4.52002	0.160511
$794$	97.6116	3.46410
$795$	−17.0904	−0.606133
$796$	141.686	5.02193
$797$	−48.5677	−1.72036	−0.860178	−	0.509993i	$-0.829648\pi$
$797$	−48.5677	−1.72036	−0.860178	+	0.509993i	$0.829648\pi$
$798$	56.5725	2.00264
$799$	47.4817	1.67978
$800$	1.72596	0.0610220
$801$	4.23269	0.149555
$802$	−3.27246	−0.115554
$803$	−21.1266	−0.745541
$804$	−41.0491	−1.44769
$805$	7.10112	0.250281
$806$	−31.0231	−1.09274
$807$	−14.9810	−0.527357
$808$	24.0055	0.844509
$809$	46.4906	1.63452	0.817261	−	0.576268i	$-0.195491\pi$
$809$	46.4906	1.63452	0.817261	+	0.576268i	$0.195491\pi$
$810$	−6.01796	−0.211450
$811$	−27.4842	−0.965099	−0.482550	−	0.875869i	$-0.660289\pi$
$811$	−27.4842	−0.965099	−0.482550	+	0.875869i	$0.660289\pi$
$812$	−15.9279	−0.558959
$813$	7.41476	0.260047
$814$	5.24396	0.183801
$815$	−31.3953	−1.09973
$816$	−59.7646	−2.09218
$817$	62.2500	2.17785
$818$	54.6294	1.91007
$819$	−13.7991	−0.482180
$820$	47.0494	1.64304
$821$	31.8446	1.11139	0.555693	−	0.831388i	$-0.312453\pi$
$821$	31.8446	1.11139	0.555693	+	0.831388i	$0.312453\pi$
$822$	−41.1936	−1.43679
$823$	−20.0814	−0.699993	−0.349996	−	0.936751i	$-0.613817\pi$
$823$	−20.0814	−0.699993	−0.349996	+	0.936751i	$0.613817\pi$
$824$	−9.48972	−0.330590
$825$	0.327325	0.0113960
$826$	−54.0301	−1.87995
$827$	−41.1649	−1.43145	−0.715723	−	0.698385i	$-0.753903\pi$
$827$	−41.1649	−1.43145	−0.715723	+	0.698385i	$0.753903\pi$
$828$	−5.07484	−0.176363
$829$	41.8877	1.45482	0.727410	−	0.686203i	$-0.240724\pi$
$829$	41.8877	1.45482	0.727410	+	0.686203i	$0.240724\pi$
$830$	58.4868	2.03011
$831$	9.25490	0.321049
$832$	−67.6287	−2.34460
$833$	−14.6822	−0.508708
$834$	−18.2252	−0.631086
$835$	−35.8367	−1.24018
$836$	94.6252	3.27268
$837$	2.65285	0.0916958
$838$	6.94574	0.239937
$839$	37.1691	1.28322	0.641609	−	0.767031i	$-0.278267\pi$
$839$	37.1691	1.28322	0.641609	+	0.767031i	$0.278267\pi$
$840$	−58.0775	−2.00386
$841$	1.00000	0.0344828
$842$	−4.78454	−0.164886
$843$	15.6501	0.539018
$844$	−112.116	−3.85919
$845$	−14.3216	−0.492678
$846$	−24.5222	−0.843091
$847$	−10.7626	−0.369808
$848$	87.6558	3.01011
$849$	−27.7066	−0.950888
$850$	−1.62963	−0.0558958
$851$	−0.716519	−0.0245619
$852$	25.0010	0.856518
$853$	−25.3088	−0.866558	−0.433279	−	0.901260i	$-0.642644\pi$
$853$	−25.3088	−0.866558	−0.433279	+	0.901260i	$0.642644\pi$
$854$	−8.58261	−0.293691
$855$	−15.3321	−0.524347
$856$	−30.4825	−1.04187
$857$	−22.6996	−0.775403	−0.387702	−	0.921785i	$-0.626731\pi$
$857$	−22.6996	−0.775403	−0.387702	+	0.921785i	$0.626731\pi$
$858$	−32.1771	−1.09851
$859$	−50.1959	−1.71266	−0.856331	−	0.516428i	$-0.827262\pi$
$859$	−50.1959	−1.71266	−0.856331	+	0.516428i	$0.827262\pi$
$860$	−105.473	−3.59660
$861$	−12.8611	−0.438304
$862$	88.7711	3.02355
$863$	22.0917	0.752009	0.376004	−	0.926618i	$-0.377298\pi$
$863$	22.0917	0.752009	0.376004	+	0.926618i	$0.377298\pi$
$864$	14.5086	0.493592
$865$	−5.67607	−0.192992
$866$	26.8785	0.913369
$867$	9.52459	0.323472
$868$	42.2542	1.43420
$869$	−39.5193	−1.34060
$870$	6.01796	0.204028
$871$	35.5629	1.20500
$872$	97.5939	3.30495
$873$	8.66126	0.293139
$874$	−18.0248	−0.609697
$875$	34.6608	1.17175
$876$	−38.9653	−1.31652
$877$	−7.93433	−0.267923	−0.133962	−	0.990987i	$-0.542770\pi$
$877$	−7.93433	−0.267923	−0.133962	+	0.990987i	$0.542770\pi$
$878$	73.4571	2.47906
$879$	13.6958	0.461947
$880$	−72.2411	−2.43525
$881$	42.9553	1.44720	0.723601	−	0.690219i	$-0.242486\pi$
$881$	42.9553	1.44720	0.723601	+	0.690219i	$0.242486\pi$
$882$	7.58272	0.255324
$883$	50.9072	1.71316	0.856581	−	0.516012i	$-0.172584\pi$
$883$	50.9072	1.71316	0.856581	+	0.516012i	$0.172584\pi$
$884$	114.911	3.86488
$885$	14.6431	0.492222
$886$	−43.2240	−1.45214
$887$	−12.4970	−0.419609	−0.209804	−	0.977743i	$-0.567283\pi$
$887$	−12.4970	−0.419609	−0.209804	+	0.977743i	$0.567283\pi$
$888$	5.86015	0.196654
$889$	45.3605	1.52134
$890$	−25.4722	−0.853829
$891$	2.75152	0.0921795
$892$	10.4242	0.349029
$893$	−62.4759	−2.09068
$894$	−1.35332	−0.0452618
$895$	5.78327	0.193313
$896$	37.3399	1.24744
$897$	4.39658	0.146798
$898$	−3.01001	−0.100445
$899$	−2.65285	−0.0884774
$900$	0.603710	0.0201237
$901$	−38.9032	−1.29605
$902$	−29.9897	−0.998549
$903$	28.8313	0.959445
$904$	−16.0583	−0.534091
$905$	50.4742	1.67782
$906$	0.159098	0.00528569
$907$	1.42754	0.0474008	0.0237004	−	0.999719i	$-0.492455\pi$
$907$	1.42754	0.0474008	0.0237004	+	0.999719i	$0.492455\pi$
$908$	−22.4016	−0.743423
$909$	2.93514	0.0973525
$910$	83.0425	2.75283
$911$	−3.43971	−0.113963	−0.0569813	−	0.998375i	$-0.518148\pi$
$911$	−3.43971	−0.113963	−0.0569813	+	0.998375i	$0.518148\pi$
$912$	78.6378	2.60396
$913$	−26.7413	−0.885007
$914$	68.1132	2.25299
$915$	2.32603	0.0768963
$916$	−79.5705	−2.62908
$917$	−31.9407	−1.05477
$918$	−13.6988	−0.452128
$919$	−57.5205	−1.89743	−0.948713	−	0.316140i	$-0.897613\pi$
$919$	−57.5205	−1.89743	−0.948713	+	0.316140i	$0.897613\pi$
$920$	18.5043	0.610068
$921$	−20.1645	−0.664442
$922$	−13.3476	−0.439578
$923$	−21.6596	−0.712933
$924$	43.8260	1.44177
$925$	0.0852381	0.00280261
$926$	−62.2102	−2.04435
$927$	−1.16031	−0.0381094
$928$	−14.5086	−0.476267
$929$	−27.5561	−0.904088	−0.452044	−	0.891996i	$-0.649305\pi$
$929$	−27.5561	−0.904088	−0.452044	+	0.891996i	$0.649305\pi$
$930$	−15.9647	−0.523504
$931$	19.3187	0.633145
$932$	56.3267	1.84504
$933$	15.6566	0.512574
$934$	89.0893	2.91509
$935$	32.0619	1.04853
$936$	−35.9581	−1.17533
$937$	47.8901	1.56450	0.782251	−	0.622963i	$-0.214071\pi$
$937$	47.8901	1.56450	0.782251	+	0.622963i	$0.214071\pi$
$938$	−67.5267	−2.20482
$939$	−16.9031	−0.551610
$940$	105.856	3.45264
$941$	−9.91312	−0.323158	−0.161579	−	0.986860i	$-0.551659\pi$
$941$	−9.91312	−0.323158	−0.161579	+	0.986860i	$0.551659\pi$
$942$	59.1503	1.92722
$943$	4.09771	0.133440
$944$	−75.1038	−2.44442
$945$	−7.10112	−0.230999
$946$	67.2295	2.18582
$947$	−7.68531	−0.249739	−0.124869	−	0.992173i	$-0.539851\pi$
$947$	−7.68531	−0.249739	−0.124869	+	0.992173i	$0.539851\pi$
$948$	−72.8883	−2.36730
$949$	33.7576	1.09582
$950$	2.14425	0.0695687
$951$	−15.6646	−0.507959
$952$	−132.203	−4.28472
$953$	−10.7790	−0.349166	−0.174583	−	0.984642i	$-0.555858\pi$
$953$	−10.7790	−0.349166	−0.174583	+	0.984642i	$0.555858\pi$
$954$	20.0918	0.650496
$955$	−53.9875	−1.74699
$956$	−136.510	−4.41505
$957$	−2.75152	−0.0889441
$958$	11.3146	0.365560
$959$	−48.6080	−1.56963
$960$	−34.8022	−1.12324
$961$	−23.9624	−0.772981
$962$	−8.37917	−0.270155
$963$	−3.72708	−0.120104
$964$	94.7111	3.05044
$965$	50.6145	1.62934
$966$	−8.34822	−0.268600
$967$	57.1901	1.83911	0.919555	−	0.392961i	$-0.128549\pi$
$967$	57.1901	1.83911	0.919555	+	0.392961i	$0.128549\pi$
$968$	−28.0455	−0.901416
$969$	−34.9008	−1.12118
$970$	−52.1231	−1.67357
$971$	2.44663	0.0785162	0.0392581	−	0.999229i	$-0.487501\pi$
$971$	2.44663	0.0785162	0.0392581	+	0.999229i	$0.487501\pi$
$972$	5.07484	0.162776
$973$	−21.5055	−0.689434
$974$	25.9781	0.832391
$975$	−0.523024	−0.0167502
$976$	−11.9301	−0.381874
$977$	−23.1260	−0.739868	−0.369934	−	0.929058i	$-0.620620\pi$
$977$	−23.1260	−0.739868	−0.369934	+	0.929058i	$0.620620\pi$
$978$	36.9089	1.18022
$979$	11.6464	0.372219
$980$	−32.7326	−1.04560
$981$	11.9328	0.380985
$982$	46.9194	1.49726
$983$	−52.2201	−1.66556	−0.832781	−	0.553603i	$-0.813253\pi$
$983$	−52.2201	−1.66556	−0.832781	+	0.553603i	$0.813253\pi$
$984$	−33.5137	−1.06838
$985$	23.8366	0.759496
$986$	13.6988	0.436259
$987$	−28.9359	−0.921041
$988$	−151.199	−4.81028
$989$	−9.18604	−0.292099
$990$	−16.5586	−0.526266
$991$	−44.7304	−1.42091	−0.710454	−	0.703744i	$-0.751510\pi$
$991$	−44.7304	−1.42091	−0.710454	+	0.703744i	$0.751510\pi$
$992$	38.4890	1.22203
$993$	16.9341	0.537388
$994$	41.1271	1.30447
$995$	−63.1679	−2.00256
$996$	−49.3209	−1.56279
$997$	−36.2007	−1.14649	−0.573244	−	0.819385i	$-0.694315\pi$
$997$	−36.2007	−1.14649	−0.573244	+	0.819385i	$0.694315\pi$
$998$	75.1477	2.37876
$999$	0.716519	0.0226696

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.n.1.16	✓	16
3.2	odd	2		6003.2.a.r.1.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.n.1.16	✓	16	1.1	even	1	trivial
6003.2.a.r.1.1		16	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:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q+2.65986 q^{2} +1.00000 q^{3} +5.07484 q^{4} -2.26251 q^{5} +2.65986 q^{6} +3.13860 q^{7} +8.17864 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.65986 q^{2} +1.00000 q^{3} +5.07484 q^{4} -2.26251 q^{5} +2.65986 q^{6} +3.13860 q^{7} +8.17864 q^{8} +1.00000 q^{9} -6.01796 q^{10} +2.75152 q^{11} +5.07484 q^{12} -4.39658 q^{13} +8.34822 q^{14} -2.26251 q^{15} +11.6043 q^{16} -5.15020 q^{17} +2.65986 q^{18} +6.77659 q^{19} -11.4819 q^{20} +3.13860 q^{21} +7.31866 q^{22} -1.00000 q^{23} +8.17864 q^{24} +0.118961 q^{25} -11.6943 q^{26} +1.00000 q^{27} +15.9279 q^{28} -1.00000 q^{29} -6.01796 q^{30} +2.65285 q^{31} +14.5086 q^{32} +2.75152 q^{33} -13.6988 q^{34} -7.10112 q^{35} +5.07484 q^{36} +0.716519 q^{37} +18.0248 q^{38} -4.39658 q^{39} -18.5043 q^{40} -4.09771 q^{41} +8.34822 q^{42} +9.18604 q^{43} +13.9635 q^{44} -2.26251 q^{45} -2.65986 q^{46} -9.21938 q^{47} +11.6043 q^{48} +2.85080 q^{49} +0.316421 q^{50} -5.15020 q^{51} -22.3120 q^{52} +7.55372 q^{53} +2.65986 q^{54} -6.22536 q^{55} +25.6695 q^{56} +6.77659 q^{57} -2.65986 q^{58} -6.47205 q^{59} -11.4819 q^{60} -1.02808 q^{61} +7.05619 q^{62} +3.13860 q^{63} +15.3821 q^{64} +9.94733 q^{65} +7.31866 q^{66} -8.08875 q^{67} -26.1365 q^{68} -1.00000 q^{69} -18.8880 q^{70} +4.92645 q^{71} +8.17864 q^{72} -7.67814 q^{73} +1.90584 q^{74} +0.118961 q^{75} +34.3901 q^{76} +8.63593 q^{77} -11.6943 q^{78} -14.3627 q^{79} -26.2549 q^{80} +1.00000 q^{81} -10.8993 q^{82} -9.71872 q^{83} +15.9279 q^{84} +11.6524 q^{85} +24.4336 q^{86} -1.00000 q^{87} +22.5037 q^{88} +4.23269 q^{89} -6.01796 q^{90} -13.7991 q^{91} -5.07484 q^{92} +2.65285 q^{93} -24.5222 q^{94} -15.3321 q^{95} +14.5086 q^{96} +8.66126 q^{97} +7.58272 q^{98} +2.75152 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9}+O(q^{10}) \) 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9	\( 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9} + 11 q^{10} + 8 q^{11} + 25 q^{12} + 19 q^{13} + 16 q^{14} + 3 q^{15} + 31 q^{16} - 4 q^{17} - q^{18} + 19 q^{19} + 16 q^{20} + 13 q^{21} + 6 q^{22} - 16 q^{23} + 23 q^{25} - 15 q^{26} + 16 q^{27} + 18 q^{28} - 16 q^{29} + 11 q^{30} + 24 q^{31} - 21 q^{32} + 8 q^{33} - 9 q^{34} - 13 q^{35} + 25 q^{36} + 26 q^{37} + 19 q^{39} - 22 q^{40} - 15 q^{41} + 16 q^{42} + 33 q^{43} + 6 q^{44} + 3 q^{45} + q^{46} + 13 q^{47} + 31 q^{48} + 41 q^{49} + 13 q^{50} - 4 q^{51} - 26 q^{52} + 5 q^{53} - q^{54} + 9 q^{55} + 40 q^{56} + 19 q^{57} + q^{58} + 2 q^{59} + 16 q^{60} + 29 q^{61} - 32 q^{62} + 13 q^{63} + 28 q^{64} + 18 q^{65} + 6 q^{66} + 32 q^{67} - 26 q^{68} - 16 q^{69} + 18 q^{70} + 29 q^{71} + 19 q^{73} - 16 q^{74} + 23 q^{75} + 64 q^{76} - 21 q^{77} - 15 q^{78} + 56 q^{79} + 16 q^{81} + 14 q^{82} + 5 q^{83} + 18 q^{84} + 16 q^{85} - 20 q^{86} - 16 q^{87} + q^{88} + 7 q^{89} + 11 q^{90} - 6 q^{91} - 25 q^{92} + 24 q^{93} - 11 q^{94} + 39 q^{95} - 21 q^{96} + 35 q^{97} - 109 q^{98} + 8 q^{99}+O(q^{100}) \) 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9 + 11 * q^10 + 8 * q^11 + 25 * q^12 + 19 * q^13 + 16 * q^14 + 3 * q^15 + 31 * q^16 - 4 * q^17 - q^18 + 19 * q^19 + 16 * q^20 + 13 * q^21 + 6 * q^22 - 16 * q^23 + 23 * q^25 - 15 * q^26 + 16 * q^27 + 18 * q^28 - 16 * q^29 + 11 * q^30 + 24 * q^31 - 21 * q^32 + 8 * q^33 - 9 * q^34 - 13 * q^35 + 25 * q^36 + 26 * q^37 + 19 * q^39 - 22 * q^40 - 15 * q^41 + 16 * q^42 + 33 * q^43 + 6 * q^44 + 3 * q^45 + q^46 + 13 * q^47 + 31 * q^48 + 41 * q^49 + 13 * q^50 - 4 * q^51 - 26 * q^52 + 5 * q^53 - q^54 + 9 * q^55 + 40 * q^56 + 19 * q^57 + q^58 + 2 * q^59 + 16 * q^60 + 29 * q^61 - 32 * q^62 + 13 * q^63 + 28 * q^64 + 18 * q^65 + 6 * q^66 + 32 * q^67 - 26 * q^68 - 16 * q^69 + 18 * q^70 + 29 * q^71 + 19 * q^73 - 16 * q^74 + 23 * q^75 + 64 * q^76 - 21 * q^77 - 15 * q^78 + 56 * q^79 + 16 * q^81 + 14 * q^82 + 5 * q^83 + 18 * q^84 + 16 * q^85 - 20 * q^86 - 16 * q^87 + q^88 + 7 * q^89 + 11 * q^90 - 6 * q^91 - 25 * q^92 + 24 * q^93 - 11 * q^94 + 39 * q^95 - 21 * q^96 + 35 * q^97 - 109 * q^98 + 8 * q^99

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