LMFDB - Embedded newform 4017.2.a.g.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.73242 q^{2} -1.00000 q^{3} +1.00128 q^{4} +0.756937 q^{5} -1.73242 q^{6} -4.14115 q^{7} -1.73020 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.73242 q^{2} -1.00000 q^{3} +1.00128 q^{4} +0.756937 q^{5} -1.73242 q^{6} -4.14115 q^{7} -1.73020 q^{8} +1.00000 q^{9} +1.31133 q^{10} +4.78184 q^{11} -1.00128 q^{12} -1.00000 q^{13} -7.17422 q^{14} -0.756937 q^{15} -5.00000 q^{16} -2.70653 q^{17} +1.73242 q^{18} -3.73356 q^{19} +0.757907 q^{20} +4.14115 q^{21} +8.28416 q^{22} +7.59322 q^{23} +1.73020 q^{24} -4.42705 q^{25} -1.73242 q^{26} -1.00000 q^{27} -4.14646 q^{28} +2.16012 q^{29} -1.31133 q^{30} +3.70110 q^{31} -5.20170 q^{32} -4.78184 q^{33} -4.68885 q^{34} -3.13459 q^{35} +1.00128 q^{36} +6.95627 q^{37} -6.46810 q^{38} +1.00000 q^{39} -1.30965 q^{40} +2.96686 q^{41} +7.17422 q^{42} +10.7454 q^{43} +4.78797 q^{44} +0.756937 q^{45} +13.1547 q^{46} -6.31238 q^{47} +5.00000 q^{48} +10.1492 q^{49} -7.66951 q^{50} +2.70653 q^{51} -1.00128 q^{52} +10.6779 q^{53} -1.73242 q^{54} +3.61955 q^{55} +7.16503 q^{56} +3.73356 q^{57} +3.74224 q^{58} -5.11496 q^{59} -0.757907 q^{60} +2.23914 q^{61} +6.41186 q^{62} -4.14115 q^{63} +0.988466 q^{64} -0.756937 q^{65} -8.28416 q^{66} +11.9667 q^{67} -2.71000 q^{68} -7.59322 q^{69} -5.43043 q^{70} -16.4400 q^{71} -1.73020 q^{72} +1.90555 q^{73} +12.0512 q^{74} +4.42705 q^{75} -3.73834 q^{76} -19.8023 q^{77} +1.73242 q^{78} +10.4074 q^{79} -3.78468 q^{80} +1.00000 q^{81} +5.13986 q^{82} +4.41105 q^{83} +4.14646 q^{84} -2.04867 q^{85} +18.6156 q^{86} -2.16012 q^{87} -8.27354 q^{88} +0.167906 q^{89} +1.31133 q^{90} +4.14115 q^{91} +7.60295 q^{92} -3.70110 q^{93} -10.9357 q^{94} -2.82607 q^{95} +5.20170 q^{96} -14.4656 q^{97} +17.5826 q^{98} +4.78184 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9} - 2 q^{10} + 7 q^{11} - 25 q^{12} - 24 q^{13} + 8 q^{14} - 3 q^{15} + 23 q^{16} + 4 q^{17} + 3 q^{18} - 20 q^{19} + 8 q^{20} - 11 q^{21} + 5 q^{22} + 41 q^{23} - 6 q^{24} + 23 q^{25} - 3 q^{26} - 24 q^{27} + 16 q^{28} + 12 q^{29} + 2 q^{30} + 2 q^{31} + 25 q^{32} - 7 q^{33} - 11 q^{34} + 36 q^{35} + 25 q^{36} + 18 q^{37} + 10 q^{38} + 24 q^{39} + 14 q^{40} - 9 q^{41} - 8 q^{42} + 23 q^{43} + 41 q^{44} + 3 q^{45} + 7 q^{46} + 32 q^{47} - 23 q^{48} + 11 q^{49} + 26 q^{50} - 4 q^{51} - 25 q^{52} + 46 q^{53} - 3 q^{54} + 18 q^{55} + 26 q^{56} + 20 q^{57} + 37 q^{58} - 12 q^{59} - 8 q^{60} - q^{61} + 53 q^{62} + 11 q^{63} + 26 q^{64} - 3 q^{65} - 5 q^{66} + 8 q^{67} + 6 q^{68} - 41 q^{69} + 19 q^{70} + 20 q^{71} + 6 q^{72} + 12 q^{73} + 86 q^{74} - 23 q^{75} - 28 q^{76} + 23 q^{77} + 3 q^{78} + 27 q^{79} + 6 q^{80} + 24 q^{81} - 28 q^{82} + 33 q^{83} - 16 q^{84} - 13 q^{85} + 63 q^{86} - 12 q^{87} + 11 q^{88} - 2 q^{90} - 11 q^{91} + 79 q^{92} - 2 q^{93} - 12 q^{94} + 37 q^{95} - 25 q^{96} - 14 q^{97} + 20 q^{98} + 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9 - 2 * q^10 + 7 * q^11 - 25 * q^12 - 24 * q^13 + 8 * q^14 - 3 * q^15 + 23 * q^16 + 4 * q^17 + 3 * q^18 - 20 * q^19 + 8 * q^20 - 11 * q^21 + 5 * q^22 + 41 * q^23 - 6 * q^24 + 23 * q^25 - 3 * q^26 - 24 * q^27 + 16 * q^28 + 12 * q^29 + 2 * q^30 + 2 * q^31 + 25 * q^32 - 7 * q^33 - 11 * q^34 + 36 * q^35 + 25 * q^36 + 18 * q^37 + 10 * q^38 + 24 * q^39 + 14 * q^40 - 9 * q^41 - 8 * q^42 + 23 * q^43 + 41 * q^44 + 3 * q^45 + 7 * q^46 + 32 * q^47 - 23 * q^48 + 11 * q^49 + 26 * q^50 - 4 * q^51 - 25 * q^52 + 46 * q^53 - 3 * q^54 + 18 * q^55 + 26 * q^56 + 20 * q^57 + 37 * q^58 - 12 * q^59 - 8 * q^60 - q^61 + 53 * q^62 + 11 * q^63 + 26 * q^64 - 3 * q^65 - 5 * q^66 + 8 * q^67 + 6 * q^68 - 41 * q^69 + 19 * q^70 + 20 * q^71 + 6 * q^72 + 12 * q^73 + 86 * q^74 - 23 * q^75 - 28 * q^76 + 23 * q^77 + 3 * q^78 + 27 * q^79 + 6 * q^80 + 24 * q^81 - 28 * q^82 + 33 * q^83 - 16 * q^84 - 13 * q^85 + 63 * q^86 - 12 * q^87 + 11 * q^88 - 2 * q^90 - 11 * q^91 + 79 * q^92 - 2 * q^93 - 12 * q^94 + 37 * q^95 - 25 * q^96 - 14 * q^97 + 20 * q^98 + 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.73242	1.22501	0.612503	−	0.790468i	$-0.290163\pi$
$2$	1.73242	1.22501	0.612503	+	0.790468i	$0.290163\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00128	0.500641
$5$	0.756937	0.338512	0.169256	−	0.985572i	$-0.445863\pi$
$5$	0.756937	0.338512	0.169256	+	0.985572i	$0.445863\pi$
$6$	−1.73242	−0.707258
$7$	−4.14115	−1.56521	−0.782605	−	0.622519i	$-0.786109\pi$
$7$	−4.14115	−1.56521	−0.782605	+	0.622519i	$0.786109\pi$
$8$	−1.73020	−0.611718
$9$	1.00000	0.333333
$10$	1.31133	0.414680
$11$	4.78184	1.44178	0.720889	−	0.693050i	$-0.243734\pi$
$11$	4.78184	1.44178	0.720889	+	0.693050i	$0.243734\pi$
$12$	−1.00128	−0.289045
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−7.17422	−1.91739
$15$	−0.756937	−0.195440
$16$	−5.00000	−1.25000
$17$	−2.70653	−0.656431	−0.328215	−	0.944603i	$-0.606447\pi$
$17$	−2.70653	−0.656431	−0.328215	+	0.944603i	$0.606447\pi$
$18$	1.73242	0.408335
$19$	−3.73356	−0.856537	−0.428269	−	0.903651i	$-0.640876\pi$
$19$	−3.73356	−0.856537	−0.428269	+	0.903651i	$0.640876\pi$
$20$	0.757907	0.169473
$21$	4.14115	0.903674
$22$	8.28416	1.76619
$23$	7.59322	1.58330	0.791648	−	0.610977i	$-0.209223\pi$
$23$	7.59322	1.58330	0.791648	+	0.610977i	$0.209223\pi$
$24$	1.73020	0.353176
$25$	−4.42705	−0.885409
$26$	−1.73242	−0.339756
$27$	−1.00000	−0.192450
$28$	−4.14646	−0.783607
$29$	2.16012	0.401125	0.200562	−	0.979681i	$-0.435723\pi$
$29$	2.16012	0.401125	0.200562	+	0.979681i	$0.435723\pi$
$30$	−1.31133	−0.239416
$31$	3.70110	0.664737	0.332368	−	0.943150i	$-0.392152\pi$
$31$	3.70110	0.664737	0.332368	+	0.943150i	$0.392152\pi$
$32$	−5.20170	−0.919539
$33$	−4.78184	−0.832411
$34$	−4.68885	−0.804132
$35$	−3.13459	−0.529843
$36$	1.00128	0.166880
$37$	6.95627	1.14360	0.571801	−	0.820392i	$-0.306245\pi$
$37$	6.95627	1.14360	0.571801	+	0.820392i	$0.306245\pi$
$38$	−6.46810	−1.04926
$39$	1.00000	0.160128
$40$	−1.30965	−0.207074
$41$	2.96686	0.463346	0.231673	−	0.972794i	$-0.425580\pi$
$41$	2.96686	0.463346	0.231673	+	0.972794i	$0.425580\pi$
$42$	7.17422	1.10701
$43$	10.7454	1.63866	0.819331	−	0.573321i	$-0.194345\pi$
$43$	10.7454	1.63866	0.819331	+	0.573321i	$0.194345\pi$
$44$	4.78797	0.721813
$45$	0.756937	0.112837
$46$	13.1547	1.93955
$47$	−6.31238	−0.920755	−0.460377	−	0.887723i	$-0.652286\pi$
$47$	−6.31238	−0.920755	−0.460377	+	0.887723i	$0.652286\pi$
$48$	5.00000	0.721688
$49$	10.1492	1.44988
$50$	−7.66951	−1.08463
$51$	2.70653	0.378991
$52$	−1.00128	−0.138853
$53$	10.6779	1.46673	0.733363	−	0.679837i	$-0.237950\pi$
$53$	10.6779	1.46673	0.733363	+	0.679837i	$0.237950\pi$
$54$	−1.73242	−0.235753
$55$	3.61955	0.488060
$56$	7.16503	0.957467
$57$	3.73356	0.494522
$58$	3.74224	0.491380
$59$	−5.11496	−0.665911	−0.332955	−	0.942943i	$-0.608046\pi$
$59$	−5.11496	−0.665911	−0.332955	+	0.942943i	$0.608046\pi$
$60$	−0.757907	−0.0978453
$61$	2.23914	0.286693	0.143346	−	0.989673i	$-0.454214\pi$
$61$	2.23914	0.286693	0.143346	+	0.989673i	$0.454214\pi$
$62$	6.41186	0.814307
$63$	−4.14115	−0.521736
$64$	0.988466	0.123558
$65$	−0.756937	−0.0938865
$66$	−8.28416	−1.01971
$67$	11.9667	1.46196	0.730982	−	0.682397i	$-0.239062\pi$
$67$	11.9667	1.46196	0.730982	+	0.682397i	$0.239062\pi$
$68$	−2.71000	−0.328636
$69$	−7.59322	−0.914117
$70$	−5.43043	−0.649061
$71$	−16.4400	−1.95107	−0.975533	−	0.219853i	$-0.929442\pi$
$71$	−16.4400	−1.95107	−0.975533	+	0.219853i	$0.929442\pi$
$72$	−1.73020	−0.203906
$73$	1.90555	0.223027	0.111514	−	0.993763i	$-0.464430\pi$
$73$	1.90555	0.223027	0.111514	+	0.993763i	$0.464430\pi$
$74$	12.0512	1.40092
$75$	4.42705	0.511191
$76$	−3.73834	−0.428817
$77$	−19.8023	−2.25669
$78$	1.73242	0.196158
$79$	10.4074	1.17093	0.585463	−	0.810699i	$-0.300913\pi$
$79$	10.4074	1.17093	0.585463	+	0.810699i	$0.300913\pi$
$80$	−3.78468	−0.423140
$81$	1.00000	0.111111
$82$	5.13986	0.567602
$83$	4.41105	0.484176	0.242088	−	0.970254i	$-0.422168\pi$
$83$	4.41105	0.484176	0.242088	+	0.970254i	$0.422168\pi$
$84$	4.14646	0.452416
$85$	−2.04867	−0.222210
$86$	18.6156	2.00737
$87$	−2.16012	−0.231590
$88$	−8.27354	−0.881962
$89$	0.167906	0.0177980	0.00889902	−	0.999960i	$-0.497167\pi$
$89$	0.167906	0.0177980	0.00889902	+	0.999960i	$0.497167\pi$
$90$	1.31133	0.138227
$91$	4.14115	0.434111
$92$	7.60295	0.792663
$93$	−3.70110	−0.383786
$94$	−10.9357	−1.12793
$95$	−2.82607	−0.289949
$96$	5.20170	0.530896
$97$	−14.4656	−1.46876	−0.734379	−	0.678739i	$-0.762527\pi$
$97$	−14.4656	−1.46876	−0.734379	+	0.678739i	$0.762527\pi$
$98$	17.5826	1.77611
$99$	4.78184	0.480593
$100$	−4.43272	−0.443272
$101$	2.43786	0.242576	0.121288	−	0.992617i	$-0.461298\pi$
$101$	2.43786	0.242576	0.121288	+	0.992617i	$0.461298\pi$
$102$	4.68885	0.464266
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.73020	0.169660
$105$	3.13459	0.305905
$106$	18.4987	1.79675
$107$	4.81911	0.465881	0.232941	−	0.972491i	$-0.425165\pi$
$107$	4.81911	0.465881	0.232941	+	0.972491i	$0.425165\pi$
$108$	−1.00128	−0.0963483
$109$	1.80775	0.173151	0.0865755	−	0.996245i	$-0.472408\pi$
$109$	1.80775	0.173151	0.0865755	+	0.996245i	$0.472408\pi$
$110$	6.27058	0.597877
$111$	−6.95627	−0.660259
$112$	20.7058	1.95651
$113$	14.8014	1.39240	0.696199	−	0.717849i	$-0.254873\pi$
$113$	14.8014	1.39240	0.696199	+	0.717849i	$0.254873\pi$
$114$	6.46810	0.605793
$115$	5.74759	0.535965
$116$	2.16289	0.200819
$117$	−1.00000	−0.0924500
$118$	−8.86126	−0.815745
$119$	11.2082	1.02745
$120$	1.30965	0.119554
$121$	11.8660	1.07873
$122$	3.87913	0.351200
$123$	−2.96686	−0.267513
$124$	3.70584	0.332794
$125$	−7.13568	−0.638235
$126$	−7.17422	−0.639130
$127$	12.7921	1.13512	0.567559	−	0.823333i	$-0.307888\pi$
$127$	12.7921	1.13512	0.567559	+	0.823333i	$0.307888\pi$
$128$	12.1158	1.07090
$129$	−10.7454	−0.946082
$130$	−1.31133	−0.115012
$131$	3.37725	0.295071	0.147536	−	0.989057i	$-0.452866\pi$
$131$	3.37725	0.295071	0.147536	+	0.989057i	$0.452866\pi$
$132$	−4.78797	−0.416739
$133$	15.4612	1.34066
$134$	20.7313	1.79092
$135$	−0.756937	−0.0651467
$136$	4.68285	0.401551
$137$	−1.35573	−0.115828	−0.0579138	−	0.998322i	$-0.518445\pi$
$137$	−1.35573	−0.115828	−0.0579138	+	0.998322i	$0.518445\pi$
$138$	−13.1547	−1.11980
$139$	−2.70787	−0.229678	−0.114839	−	0.993384i	$-0.536635\pi$
$139$	−2.70787	−0.229678	−0.114839	+	0.993384i	$0.536635\pi$
$140$	−3.13861	−0.265261
$141$	6.31238	0.531598
$142$	−28.4810	−2.39007
$143$	−4.78184	−0.399877
$144$	−5.00000	−0.416667
$145$	1.63508	0.135786
$146$	3.30121	0.273210
$147$	−10.1492	−0.837088
$148$	6.96518	0.572534
$149$	−6.88720	−0.564222	−0.282111	−	0.959382i	$-0.591035\pi$
$149$	−6.88720	−0.564222	−0.282111	+	0.959382i	$0.591035\pi$
$150$	7.66951	0.626213
$151$	−5.36916	−0.436936	−0.218468	−	0.975844i	$-0.570106\pi$
$151$	−5.36916	−0.436936	−0.218468	+	0.975844i	$0.570106\pi$
$152$	6.45981	0.523960
$153$	−2.70653	−0.218810
$154$	−34.3060	−2.76445
$155$	2.80150	0.225022
$156$	1.00128	0.0801667
$157$	16.1695	1.29047	0.645235	−	0.763984i	$-0.276760\pi$
$157$	16.1695	1.29047	0.645235	+	0.763984i	$0.276760\pi$
$158$	18.0300	1.43439
$159$	−10.6779	−0.846814
$160$	−3.93736	−0.311275
$161$	−31.4447	−2.47819
$162$	1.73242	0.136112
$163$	11.1057	0.869869	0.434934	−	0.900462i	$-0.356772\pi$
$163$	11.1057	0.869869	0.434934	+	0.900462i	$0.356772\pi$
$164$	2.97067	0.231970
$165$	−3.61955	−0.281782
$166$	7.64180	0.593119
$167$	19.5782	1.51501	0.757505	−	0.652830i	$-0.226418\pi$
$167$	19.5782	1.51501	0.757505	+	0.652830i	$0.226418\pi$
$168$	−7.16503	−0.552794
$169$	1.00000	0.0769231
$170$	−3.54917	−0.272209
$171$	−3.73356	−0.285512
$172$	10.7592	0.820381
$173$	2.95042	0.224316	0.112158	−	0.993690i	$-0.464224\pi$
$173$	2.95042	0.224316	0.112158	+	0.993690i	$0.464224\pi$
$174$	−3.74224	−0.283699
$175$	18.3331	1.38585
$176$	−23.9092	−1.80222
$177$	5.11496	0.384464
$178$	0.290885	0.0218027
$179$	16.0009	1.19596	0.597982	−	0.801510i	$-0.295969\pi$
$179$	16.0009	1.19596	0.597982	+	0.801510i	$0.295969\pi$
$180$	0.757907	0.0564910
$181$	4.43789	0.329866	0.164933	−	0.986305i	$-0.447259\pi$
$181$	4.43789	0.329866	0.164933	+	0.986305i	$0.447259\pi$
$182$	7.17422	0.531789
$183$	−2.23914	−0.165522
$184$	−13.1378	−0.968531
$185$	5.26545	0.387124
$186$	−6.41186	−0.470140
$187$	−12.9422	−0.946428
$188$	−6.32046	−0.460967
$189$	4.14115	0.301225
$190$	−4.89594	−0.355189
$191$	−15.3484	−1.11057	−0.555284	−	0.831661i	$-0.687390\pi$
$191$	−15.3484	−1.11057	−0.555284	+	0.831661i	$0.687390\pi$
$192$	−0.988466	−0.0713364
$193$	−1.73927	−0.125196	−0.0625979	−	0.998039i	$-0.519939\pi$
$193$	−1.73927	−0.125196	−0.0625979	+	0.998039i	$0.519939\pi$
$194$	−25.0605	−1.79924
$195$	0.756937	0.0542054
$196$	10.1622	0.725869
$197$	−3.80243	−0.270912	−0.135456	−	0.990783i	$-0.543250\pi$
$197$	−3.80243	−0.270912	−0.135456	+	0.990783i	$0.543250\pi$
$198$	8.28416	0.588729
$199$	−22.5269	−1.59689	−0.798444	−	0.602069i	$-0.794343\pi$
$199$	−22.5269	−1.59689	−0.798444	+	0.602069i	$0.794343\pi$
$200$	7.65968	0.541621
$201$	−11.9667	−0.844066
$202$	4.22339	0.297157
$203$	−8.94540	−0.627844
$204$	2.71000	0.189738
$205$	2.24573	0.156848
$206$	1.73242	0.120703
$207$	7.59322	0.527765
$208$	5.00000	0.346688
$209$	−17.8533	−1.23494
$210$	5.43043	0.374735
$211$	11.0984	0.764045	0.382022	−	0.924153i	$-0.375228\pi$
$211$	11.0984	0.764045	0.382022	+	0.924153i	$0.375228\pi$
$212$	10.6916	0.734303
$213$	16.4400	1.12645
$214$	8.34873	0.570707
$215$	8.13361	0.554707
$216$	1.73020	0.117725
$217$	−15.3268	−1.04045
$218$	3.13178	0.212111
$219$	−1.90555	−0.128765
$220$	3.62419	0.244343
$221$	2.70653	0.182061
$222$	−12.0512	−0.808822
$223$	−11.3880	−0.762599	−0.381299	−	0.924452i	$-0.624523\pi$
$223$	−11.3880	−0.762599	−0.381299	+	0.924452i	$0.624523\pi$
$224$	21.5410	1.43927
$225$	−4.42705	−0.295136
$226$	25.6422	1.70570
$227$	−9.05460	−0.600975	−0.300487	−	0.953786i	$-0.597149\pi$
$227$	−9.05460	−0.600975	−0.300487	+	0.953786i	$0.597149\pi$
$228$	3.73834	0.247578
$229$	25.7355	1.70065	0.850325	−	0.526258i	$-0.176405\pi$
$229$	25.7355	1.70065	0.850325	+	0.526258i	$0.176405\pi$
$230$	9.95724	0.656561
$231$	19.8023	1.30290
$232$	−3.73745	−0.245375
$233$	−15.2443	−0.998685	−0.499342	−	0.866405i	$-0.666425\pi$
$233$	−15.2443	−0.998685	−0.499342	+	0.866405i	$0.666425\pi$
$234$	−1.73242	−0.113252
$235$	−4.77807	−0.311687
$236$	−5.12151	−0.333382
$237$	−10.4074	−0.676034
$238$	19.4173	1.25863
$239$	14.2021	0.918661	0.459330	−	0.888266i	$-0.348089\pi$
$239$	14.2021	0.918661	0.459330	+	0.888266i	$0.348089\pi$
$240$	3.78468	0.244300
$241$	7.69026	0.495373	0.247686	−	0.968840i	$-0.420330\pi$
$241$	7.69026	0.495373	0.247686	+	0.968840i	$0.420330\pi$
$242$	20.5569	1.32145
$243$	−1.00000	−0.0641500
$244$	2.24201	0.143530
$245$	7.68227	0.490802
$246$	−5.13986	−0.327705
$247$	3.73356	0.237561
$248$	−6.40364	−0.406632
$249$	−4.41105	−0.279539
$250$	−12.3620	−0.781841
$251$	23.0092	1.45233	0.726164	−	0.687522i	$-0.241301\pi$
$251$	23.0092	1.45233	0.726164	+	0.687522i	$0.241301\pi$
$252$	−4.14646	−0.261202
$253$	36.3096	2.28276
$254$	22.1613	1.39053
$255$	2.04867	0.128293
$256$	19.0128	1.18830
$257$	−6.25276	−0.390036	−0.195018	−	0.980800i	$-0.562477\pi$
$257$	−6.25276	−0.390036	−0.195018	+	0.980800i	$0.562477\pi$
$258$	−18.6156	−1.15896
$259$	−28.8070	−1.78998
$260$	−0.757907	−0.0470034
$261$	2.16012	0.133708
$262$	5.85081	0.361464
$263$	11.5689	0.713371	0.356685	−	0.934225i	$-0.383907\pi$
$263$	11.5689	0.713371	0.356685	+	0.934225i	$0.383907\pi$
$264$	8.27354	0.509201
$265$	8.08251	0.496505
$266$	26.7854	1.64232
$267$	−0.167906	−0.0102757
$268$	11.9820	0.731919
$269$	−0.985227	−0.0600704	−0.0300352	−	0.999549i	$-0.509562\pi$
$269$	−0.985227	−0.0600704	−0.0300352	+	0.999549i	$0.509562\pi$
$270$	−1.31133	−0.0798052
$271$	25.2251	1.53231	0.766157	−	0.642653i	$-0.222166\pi$
$271$	25.2251	1.53231	0.766157	+	0.642653i	$0.222166\pi$
$272$	13.5327	0.820538
$273$	−4.14115	−0.250634
$274$	−2.34869	−0.141889
$275$	−21.1694	−1.27656
$276$	−7.60295	−0.457644
$277$	−22.7823	−1.36886	−0.684428	−	0.729080i	$-0.739948\pi$
$277$	−22.7823	−1.36886	−0.684428	+	0.729080i	$0.739948\pi$
$278$	−4.69117	−0.281357
$279$	3.70110	0.221579
$280$	5.42347	0.324115
$281$	16.8803	1.00700	0.503498	−	0.863996i	$-0.332046\pi$
$281$	16.8803	1.00700	0.503498	+	0.863996i	$0.332046\pi$
$282$	10.9357	0.651211
$283$	8.40458	0.499600	0.249800	−	0.968297i	$-0.419635\pi$
$283$	8.40458	0.499600	0.249800	+	0.968297i	$0.419635\pi$
$284$	−16.4610	−0.976783
$285$	2.82607	0.167402
$286$	−8.28416	−0.489852
$287$	−12.2862	−0.725234
$288$	−5.20170	−0.306513
$289$	−9.67468	−0.569099
$290$	2.83264	0.166338
$291$	14.4656	0.847988
$292$	1.90799	0.111657
$293$	−18.7229	−1.09380	−0.546902	−	0.837196i	$-0.684193\pi$
$293$	−18.7229	−1.09380	−0.546902	+	0.837196i	$0.684193\pi$
$294$	−17.5826	−1.02544
$295$	−3.87170	−0.225419
$296$	−12.0357	−0.699563
$297$	−4.78184	−0.277470
$298$	−11.9315	−0.691175
$299$	−7.59322	−0.439127
$300$	4.43272	0.255923
$301$	−44.4984	−2.56485
$302$	−9.30164	−0.535249
$303$	−2.43786	−0.140051
$304$	18.6678	1.07067
$305$	1.69489	0.0970490
$306$	−4.68885	−0.268044
$307$	3.29304	0.187944	0.0939719	−	0.995575i	$-0.470044\pi$
$307$	3.29304	0.187944	0.0939719	+	0.995575i	$0.470044\pi$
$308$	−19.8277	−1.12979
$309$	−1.00000	−0.0568880
$310$	4.85337	0.275653
$311$	−22.0976	−1.25304	−0.626519	−	0.779406i	$-0.715521\pi$
$311$	−22.0976	−1.25304	−0.626519	+	0.779406i	$0.715521\pi$
$312$	−1.73020	−0.0979533
$313$	7.58516	0.428739	0.214369	−	0.976753i	$-0.431230\pi$
$313$	7.58516	0.428739	0.214369	+	0.976753i	$0.431230\pi$
$314$	28.0124	1.58083
$315$	−3.13459	−0.176614
$316$	10.4207	0.586213
$317$	14.7854	0.830430	0.415215	−	0.909723i	$-0.363706\pi$
$317$	14.7854	0.830430	0.415215	+	0.909723i	$0.363706\pi$
$318$	−18.4987	−1.03735
$319$	10.3294	0.578333
$320$	0.748206	0.0418260
$321$	−4.81911	−0.268977
$322$	−54.4755	−3.03580
$323$	10.1050	0.562257
$324$	1.00128	0.0556267
$325$	4.42705	0.245568
$326$	19.2398	1.06559
$327$	−1.80775	−0.0999687
$328$	−5.13327	−0.283437
$329$	26.1405	1.44117
$330$	−6.27058	−0.345184
$331$	−4.68459	−0.257489	−0.128744	−	0.991678i	$-0.541095\pi$
$331$	−4.68459	−0.257489	−0.128744	+	0.991678i	$0.541095\pi$
$332$	4.41670	0.242398
$333$	6.95627	0.381201
$334$	33.9177	1.85590
$335$	9.05803	0.494893
$336$	−20.7058	−1.12959
$337$	−29.5734	−1.61096	−0.805482	−	0.592620i	$-0.798094\pi$
$337$	−29.5734	−1.61096	−0.805482	+	0.592620i	$0.798094\pi$
$338$	1.73242	0.0942313
$339$	−14.8014	−0.803901
$340$	−2.05130	−0.111247
$341$	17.6981	0.958403
$342$	−6.46810	−0.349755
$343$	−13.0411	−0.704155
$344$	−18.5917	−1.00240
$345$	−5.74759	−0.309440
$346$	5.11137	0.274789
$347$	−28.9755	−1.55549	−0.777743	−	0.628583i	$-0.783635\pi$
$347$	−28.9755	−1.55549	−0.777743	+	0.628583i	$0.783635\pi$
$348$	−2.16289	−0.115943
$349$	−28.8804	−1.54593	−0.772967	−	0.634446i	$-0.781228\pi$
$349$	−28.8804	−1.54593	−0.772967	+	0.634446i	$0.781228\pi$
$350$	31.7606	1.69768
$351$	1.00000	0.0533761
$352$	−24.8737	−1.32577
$353$	−23.4040	−1.24567	−0.622836	−	0.782353i	$-0.714019\pi$
$353$	−23.4040	−1.24567	−0.622836	+	0.782353i	$0.714019\pi$
$354$	8.86126	0.470971
$355$	−12.4440	−0.660460
$356$	0.168122	0.00891043
$357$	−11.2082	−0.593199
$358$	27.7203	1.46506
$359$	−33.4391	−1.76485	−0.882423	−	0.470457i	$-0.844089\pi$
$359$	−33.4391	−1.76485	−0.882423	+	0.470457i	$0.844089\pi$
$360$	−1.30965	−0.0690248
$361$	−5.06053	−0.266344
$362$	7.68829	0.404087
$363$	−11.8660	−0.622803
$364$	4.14646	0.217334
$365$	1.44238	0.0754975
$366$	−3.87913	−0.202766
$367$	1.29458	0.0675763	0.0337882	−	0.999429i	$-0.489243\pi$
$367$	1.29458	0.0675763	0.0337882	+	0.999429i	$0.489243\pi$
$368$	−37.9661	−1.97912
$369$	2.96686	0.154449
$370$	9.12198	0.474229
$371$	−44.2189	−2.29573
$372$	−3.70584	−0.192139
$373$	15.3238	0.793436	0.396718	−	0.917941i	$-0.370149\pi$
$373$	15.3238	0.793436	0.396718	+	0.917941i	$0.370149\pi$
$374$	−22.4213	−1.15938
$375$	7.13568	0.368485
$376$	10.9217	0.563242
$377$	−2.16012	−0.111252
$378$	7.17422	0.369002
$379$	10.2801	0.528053	0.264026	−	0.964515i	$-0.414949\pi$
$379$	10.2801	0.528053	0.264026	+	0.964515i	$0.414949\pi$
$380$	−2.82969	−0.145160
$381$	−12.7921	−0.655360
$382$	−26.5898	−1.36045
$383$	13.2605	0.677578	0.338789	−	0.940862i	$-0.389983\pi$
$383$	13.2605	0.677578	0.338789	+	0.940862i	$0.389983\pi$
$384$	−12.1158	−0.618284
$385$	−14.9891	−0.763916
$386$	−3.01316	−0.153366
$387$	10.7454	0.546221
$388$	−14.4841	−0.735320
$389$	−10.6004	−0.537460	−0.268730	−	0.963215i	$-0.586604\pi$
$389$	−10.6004	−0.537460	−0.268730	+	0.963215i	$0.586604\pi$
$390$	1.31133	0.0664019
$391$	−20.5513	−1.03932
$392$	−17.5601	−0.886918
$393$	−3.37725	−0.170360
$394$	−6.58741	−0.331869
$395$	7.87775	0.396373
$396$	4.78797	0.240604
$397$	−17.7614	−0.891420	−0.445710	−	0.895177i	$-0.647049\pi$
$397$	−17.7614	−0.891420	−0.445710	+	0.895177i	$0.647049\pi$
$398$	−39.0260	−1.95620
$399$	−15.4612	−0.774030
$400$	22.1352	1.10676
$401$	−5.68109	−0.283700	−0.141850	−	0.989888i	$-0.545305\pi$
$401$	−5.68109	−0.283700	−0.141850	+	0.989888i	$0.545305\pi$
$402$	−20.7313	−1.03399
$403$	−3.70110	−0.184365
$404$	2.44098	0.121443
$405$	0.756937	0.0376125
$406$	−15.4972	−0.769113
$407$	33.2637	1.64882
$408$	−4.68285	−0.231835
$409$	36.4098	1.80035	0.900173	−	0.435532i	$-0.143440\pi$
$409$	36.4098	1.80035	0.900173	+	0.435532i	$0.143440\pi$
$410$	3.89055	0.192140
$411$	1.35573	0.0668731
$412$	1.00128	0.0493296
$413$	21.1818	1.04229
$414$	13.1547	0.646516
$415$	3.33889	0.163900
$416$	5.20170	0.255034
$417$	2.70787	0.132605
$418$	−30.9294	−1.51281
$419$	8.57241	0.418790	0.209395	−	0.977831i	$-0.432851\pi$
$419$	8.57241	0.418790	0.209395	+	0.977831i	$0.432851\pi$
$420$	3.13861	0.153148
$421$	−34.3220	−1.67275	−0.836376	−	0.548157i	$-0.815330\pi$
$421$	−34.3220	−1.67275	−0.836376	+	0.548157i	$0.815330\pi$
$422$	19.2271	0.935960
$423$	−6.31238	−0.306918
$424$	−18.4750	−0.897223
$425$	11.9820	0.581210
$426$	28.4810	1.37991
$427$	−9.27263	−0.448734
$428$	4.82529	0.233239
$429$	4.78184	0.230869
$430$	14.0908	0.679520
$431$	−0.197512	−0.00951380	−0.00475690	−	0.999989i	$-0.501514\pi$
$431$	−0.197512	−0.00951380	−0.00475690	+	0.999989i	$0.501514\pi$
$432$	5.00000	0.240563
$433$	−30.3547	−1.45875	−0.729377	−	0.684112i	$-0.760190\pi$
$433$	−30.3547	−1.45875	−0.729377	+	0.684112i	$0.760190\pi$
$434$	−26.5525	−1.27456
$435$	−1.63508	−0.0783959
$436$	1.81007	0.0866864
$437$	−28.3497	−1.35615
$438$	−3.30121	−0.157738
$439$	−29.4772	−1.40687	−0.703436	−	0.710759i	$-0.748352\pi$
$439$	−29.4772	−1.40687	−0.703436	+	0.710759i	$0.748352\pi$
$440$	−6.26255	−0.298555
$441$	10.1492	0.483293
$442$	4.68885	0.223026
$443$	19.3127	0.917576	0.458788	−	0.888546i	$-0.348284\pi$
$443$	19.3127	0.917576	0.458788	+	0.888546i	$0.348284\pi$
$444$	−6.96518	−0.330553
$445$	0.127095	0.00602486
$446$	−19.7289	−0.934188
$447$	6.88720	0.325753
$448$	−4.09339	−0.193394
$449$	−17.5266	−0.827131	−0.413566	−	0.910474i	$-0.635717\pi$
$449$	−17.5266	−0.827131	−0.413566	+	0.910474i	$0.635717\pi$
$450$	−7.66951	−0.361544
$451$	14.1871	0.668043
$452$	14.8204	0.697091
$453$	5.36916	0.252265
$454$	−15.6864	−0.736198
$455$	3.13459	0.146952
$456$	−6.45981	−0.302508
$457$	−13.1253	−0.613977	−0.306988	−	0.951713i	$-0.599321\pi$
$457$	−13.1253	−0.613977	−0.306988	+	0.951713i	$0.599321\pi$
$458$	44.5847	2.08331
$459$	2.70653	0.126330
$460$	5.75495	0.268326
$461$	0.0177301	0.000825772 0	0.000412886	−	1.00000i	$-0.499869\pi$
$461$	0.0177301	0.000825772 0	0.000412886		1.00000i	$0.499869\pi$
$462$	34.3060	1.59606
$463$	−18.7584	−0.871779	−0.435889	−	0.900000i	$-0.643566\pi$
$463$	−18.7584	−0.871779	−0.435889	+	0.900000i	$0.643566\pi$
$464$	−10.8006	−0.501406
$465$	−2.80150	−0.129916
$466$	−26.4095	−1.22340
$467$	24.9177	1.15305	0.576526	−	0.817079i	$-0.304408\pi$
$467$	24.9177	1.15305	0.576526	+	0.817079i	$0.304408\pi$
$468$	−1.00128	−0.0462842
$469$	−49.5559	−2.28828
$470$	−8.27763	−0.381818
$471$	−16.1695	−0.745053
$472$	8.84990	0.407350
$473$	51.3829	2.36259
$474$	−18.0300	−0.828146
$475$	16.5286	0.758386
$476$	11.2225	0.514384
$477$	10.6779	0.488909
$478$	24.6041	1.12537
$479$	−13.1143	−0.599206	−0.299603	−	0.954064i	$-0.596854\pi$
$479$	−13.1143	−0.599206	−0.299603	+	0.954064i	$0.596854\pi$
$480$	3.93736	0.179715
$481$	−6.95627	−0.317178
$482$	13.3228	0.606835
$483$	31.4447	1.43078
$484$	11.8812	0.540054
$485$	−10.9495	−0.497193
$486$	−1.73242	−0.0785842
$487$	35.9326	1.62826	0.814130	−	0.580683i	$-0.197214\pi$
$487$	35.9326	1.62826	0.814130	+	0.580683i	$0.197214\pi$
$488$	−3.87416	−0.175375
$489$	−11.1057	−0.502219
$490$	13.3089	0.601236
$491$	−0.487049	−0.0219802	−0.0109901	−	0.999940i	$-0.503498\pi$
$491$	−0.487049	−0.0219802	−0.0109901	+	0.999940i	$0.503498\pi$
$492$	−2.97067	−0.133928
$493$	−5.84645	−0.263311
$494$	6.46810	0.291013
$495$	3.61955	0.162687
$496$	−18.5055	−0.830921
$497$	68.0805	3.05383
$498$	−7.64180	−0.342437
$499$	37.2841	1.66907	0.834533	−	0.550957i	$-0.185737\pi$
$499$	37.2841	1.66907	0.834533	+	0.550957i	$0.185737\pi$
$500$	−7.14482	−0.319526
$501$	−19.5782	−0.874691
$502$	39.8616	1.77911
$503$	−1.77941	−0.0793401	−0.0396701	−	0.999213i	$-0.512631\pi$
$503$	−1.77941	−0.0793401	−0.0396701	+	0.999213i	$0.512631\pi$
$504$	7.16503	0.319156
$505$	1.84530	0.0821150
$506$	62.9034	2.79640
$507$	−1.00000	−0.0444116
$508$	12.8085	0.568286
$509$	24.3607	1.07977	0.539885	−	0.841738i	$-0.318468\pi$
$509$	24.3607	1.07977	0.539885	+	0.841738i	$0.318468\pi$
$510$	3.54917	0.157160
$511$	−7.89116	−0.349084
$512$	8.70649	0.384776
$513$	3.73356	0.164841
$514$	−10.8324	−0.477797
$515$	0.756937	0.0333546
$516$	−10.7592	−0.473647
$517$	−30.1848	−1.32752
$518$	−49.9058	−2.19273
$519$	−2.95042	−0.129509
$520$	1.30965	0.0574321
$521$	35.1163	1.53847	0.769237	−	0.638963i	$-0.220637\pi$
$521$	35.1163	1.53847	0.769237	+	0.638963i	$0.220637\pi$
$522$	3.74224	0.163793
$523$	33.7496	1.47577	0.737884	−	0.674928i	$-0.235825\pi$
$523$	33.7496	1.47577	0.737884	+	0.674928i	$0.235825\pi$
$524$	3.38158	0.147725
$525$	−18.3331	−0.800121
$526$	20.0423	0.873884
$527$	−10.0171	−0.436354
$528$	23.9092	1.04051
$529$	34.6570	1.50683
$530$	14.0023	0.608222
$531$	−5.11496	−0.221970
$532$	15.4811	0.671189
$533$	−2.96686	−0.128509
$534$	−0.290885	−0.0125878
$535$	3.64776	0.157707
$536$	−20.7048	−0.894310
$537$	−16.0009	−0.690490
$538$	−1.70683	−0.0735866
$539$	48.5316	2.09041
$540$	−0.757907	−0.0326151
$541$	−11.7486	−0.505110	−0.252555	−	0.967583i	$-0.581271\pi$
$541$	−11.7486	−0.505110	−0.252555	+	0.967583i	$0.581271\pi$
$542$	43.7005	1.87710
$543$	−4.43789	−0.190448
$544$	14.0786	0.603614
$545$	1.36835	0.0586137
$546$	−7.17422	−0.307028
$547$	−8.37690	−0.358170	−0.179085	−	0.983834i	$-0.557314\pi$
$547$	−8.37690	−0.358170	−0.179085	+	0.983834i	$0.557314\pi$
$548$	−1.35746	−0.0579880
$549$	2.23914	0.0955642
$550$	−36.6743	−1.56380
$551$	−8.06495	−0.343578
$552$	13.1378	0.559182
$553$	−43.0987	−1.83274
$554$	−39.4685	−1.67686
$555$	−5.26545	−0.223506
$556$	−2.71134	−0.114986
$557$	7.62739	0.323183	0.161591	−	0.986858i	$-0.448337\pi$
$557$	7.62739	0.323183	0.161591	+	0.986858i	$0.448337\pi$
$558$	6.41186	0.271436
$559$	−10.7454	−0.454483
$560$	15.6730	0.662303
$561$	12.9422	0.546420
$562$	29.2438	1.23358
$563$	1.14001	0.0480458	0.0240229	−	0.999711i	$-0.492353\pi$
$563$	1.14001	0.0480458	0.0240229	+	0.999711i	$0.492353\pi$
$564$	6.32046	0.266140
$565$	11.2037	0.471344
$566$	14.5603	0.612014
$567$	−4.14115	−0.173912
$568$	28.4445	1.19350
$569$	27.1473	1.13807	0.569037	−	0.822312i	$-0.307316\pi$
$569$	27.1473	1.13807	0.569037	+	0.822312i	$0.307316\pi$
$570$	4.89594	0.205068
$571$	20.6451	0.863969	0.431984	−	0.901881i	$-0.357814\pi$
$571$	20.6451	0.863969	0.431984	+	0.901881i	$0.357814\pi$
$572$	−4.78797	−0.200195
$573$	15.3484	0.641187
$574$	−21.2849	−0.888416
$575$	−33.6155	−1.40187
$576$	0.988466	0.0411861
$577$	−28.1384	−1.17142	−0.585708	−	0.810522i	$-0.699183\pi$
$577$	−28.1384	−1.17142	−0.585708	+	0.810522i	$0.699183\pi$
$578$	−16.7606	−0.697149
$579$	1.73927	0.0722818
$580$	1.63717	0.0679799
$581$	−18.2668	−0.757837
$582$	25.0605	1.03879
$583$	51.0601	2.11469
$584$	−3.29698	−0.136430
$585$	−0.756937	−0.0312955
$586$	−32.4360	−1.33992
$587$	18.2817	0.754565	0.377282	−	0.926098i	$-0.376859\pi$
$587$	18.2817	0.754565	0.377282	+	0.926098i	$0.376859\pi$
$588$	−10.1622	−0.419080
$589$	−13.8183	−0.569372
$590$	−6.70741	−0.276140
$591$	3.80243	0.156411
$592$	−34.7813	−1.42950
$593$	−6.93747	−0.284888	−0.142444	−	0.989803i	$-0.545496\pi$
$593$	−6.93747	−0.284888	−0.142444	+	0.989803i	$0.545496\pi$
$594$	−8.28416	−0.339903
$595$	8.48388	0.347805
$596$	−6.89603	−0.282472
$597$	22.5269	0.921964
$598$	−13.1547	−0.537934
$599$	−23.9735	−0.979530	−0.489765	−	0.871855i	$-0.662917\pi$
$599$	−23.9735	−0.979530	−0.489765	+	0.871855i	$0.662917\pi$
$600$	−7.65968	−0.312705
$601$	−36.7634	−1.49961	−0.749805	−	0.661659i	$-0.769853\pi$
$601$	−36.7634	−1.49961	−0.749805	+	0.661659i	$0.769853\pi$
$602$	−77.0900	−3.14196
$603$	11.9667	0.487321
$604$	−5.37604	−0.218748
$605$	8.98180	0.365162
$606$	−4.22339	−0.171564
$607$	34.0194	1.38080	0.690402	−	0.723426i	$-0.257434\pi$
$607$	34.0194	1.38080	0.690402	+	0.723426i	$0.257434\pi$
$608$	19.4209	0.787620
$609$	8.94540	0.362486
$610$	2.93626	0.118886
$611$	6.31238	0.255371
$612$	−2.71000	−0.109545
$613$	24.4054	0.985724	0.492862	−	0.870108i	$-0.335951\pi$
$613$	24.4054	0.985724	0.492862	+	0.870108i	$0.335951\pi$
$614$	5.70493	0.230232
$615$	−2.24573	−0.0905565
$616$	34.2620	1.38046
$617$	−45.4834	−1.83109	−0.915545	−	0.402215i	$-0.868241\pi$
$617$	−45.4834	−1.83109	−0.915545	+	0.402215i	$0.868241\pi$
$618$	−1.73242	−0.0696882
$619$	33.7848	1.35793	0.678963	−	0.734172i	$-0.262429\pi$
$619$	33.7848	1.35793	0.678963	+	0.734172i	$0.262429\pi$
$620$	2.80509	0.112655
$621$	−7.59322	−0.304706
$622$	−38.2823	−1.53498
$623$	−0.695326	−0.0278577
$624$	−5.00000	−0.200160
$625$	16.7340	0.669359
$626$	13.1407	0.525208
$627$	17.8533	0.712991
$628$	16.1903	0.646061
$629$	−18.8274	−0.750696
$630$	−5.43043	−0.216354
$631$	16.5720	0.659721	0.329860	−	0.944030i	$-0.392998\pi$
$631$	16.5720	0.659721	0.329860	+	0.944030i	$0.392998\pi$
$632$	−18.0069	−0.716276
$633$	−11.0984	−0.441122
$634$	25.6145	1.01728
$635$	9.68283	0.384251
$636$	−10.6916	−0.423950
$637$	−10.1492	−0.402124
$638$	17.8948	0.708462
$639$	−16.4400	−0.650355
$640$	9.17092	0.362513
$641$	−27.4263	−1.08327	−0.541637	−	0.840612i	$-0.682195\pi$
$641$	−27.4263	−1.08327	−0.541637	+	0.840612i	$0.682195\pi$
$642$	−8.34873	−0.329498
$643$	39.8425	1.57124	0.785618	−	0.618712i	$-0.212345\pi$
$643$	39.8425	1.57124	0.785618	+	0.618712i	$0.212345\pi$
$644$	−31.4850	−1.24068
$645$	−8.13361	−0.320260
$646$	17.5061	0.688769
$647$	−19.3620	−0.761200	−0.380600	−	0.924740i	$-0.624282\pi$
$647$	−19.3620	−0.761200	−0.380600	+	0.924740i	$0.624282\pi$
$648$	−1.73020	−0.0679687
$649$	−24.4589	−0.960096
$650$	7.66951	0.300823
$651$	15.3268	0.600705
$652$	11.1200	0.435492
$653$	25.8702	1.01238	0.506190	−	0.862422i	$-0.331054\pi$
$653$	25.8702	1.01238	0.506190	+	0.862422i	$0.331054\pi$
$654$	−3.13178	−0.122462
$655$	2.55636	0.0998854
$656$	−14.8343	−0.579183
$657$	1.90555	0.0743424
$658$	45.2864	1.76545
$659$	39.5773	1.54171	0.770857	−	0.637008i	$-0.219828\pi$
$659$	39.5773	1.54171	0.770857	+	0.637008i	$0.219828\pi$
$660$	−3.62419	−0.141071
$661$	−9.24046	−0.359412	−0.179706	−	0.983720i	$-0.557515\pi$
$661$	−9.24046	−0.359412	−0.179706	+	0.983720i	$0.557515\pi$
$662$	−8.11569	−0.315425
$663$	−2.70653	−0.105113
$664$	−7.63201	−0.296179
$665$	11.7032	0.453830
$666$	12.0512	0.466974
$667$	16.4023	0.635099
$668$	19.6033	0.758475
$669$	11.3880	0.440287
$670$	15.6923	0.606247
$671$	10.7072	0.413347
$672$	−21.5410	−0.830964
$673$	−35.8981	−1.38377	−0.691885	−	0.722007i	$-0.743220\pi$
$673$	−35.8981	−1.38377	−0.691885	+	0.722007i	$0.743220\pi$
$674$	−51.2335	−1.97344
$675$	4.42705	0.170397
$676$	1.00128	0.0385108
$677$	−4.67036	−0.179496	−0.0897482	−	0.995964i	$-0.528606\pi$
$677$	−4.67036	−0.179496	−0.0897482	+	0.995964i	$0.528606\pi$
$678$	−25.6422	−0.984784
$679$	59.9043	2.29891
$680$	3.54462	0.135930
$681$	9.05460	0.346973
$682$	30.6605	1.17405
$683$	9.98461	0.382050	0.191025	−	0.981585i	$-0.438819\pi$
$683$	9.98461	0.382050	0.191025	+	0.981585i	$0.438819\pi$
$684$	−3.73834	−0.142939
$685$	−1.02620	−0.0392091
$686$	−22.5927	−0.862595
$687$	−25.7355	−0.981871
$688$	−53.7271	−2.04833
$689$	−10.6779	−0.406796
$690$	−9.95724	−0.379066
$691$	−12.8831	−0.490098	−0.245049	−	0.969511i	$-0.578804\pi$
$691$	−12.8831	−0.490098	−0.245049	+	0.969511i	$0.578804\pi$
$692$	2.95420	0.112302
$693$	−19.8023	−0.752228
$694$	−50.1977	−1.90548
$695$	−2.04968	−0.0777490
$696$	3.73745	0.141668
$697$	−8.02992	−0.304155
$698$	−50.0331	−1.89378
$699$	15.2443	0.576591
$700$	18.3566	0.693813
$701$	32.6949	1.23487	0.617435	−	0.786622i	$-0.288172\pi$
$701$	32.6949	1.23487	0.617435	+	0.786622i	$0.288172\pi$
$702$	1.73242	0.0653860
$703$	−25.9716	−0.979539
$704$	4.72668	0.178144
$705$	4.77807	0.179953
$706$	−40.5456	−1.52595
$707$	−10.0955	−0.379682
$708$	5.12151	0.192478
$709$	29.3581	1.10257	0.551283	−	0.834319i	$-0.314139\pi$
$709$	29.3581	1.10257	0.551283	+	0.834319i	$0.314139\pi$
$710$	−21.5583	−0.809068
$711$	10.4074	0.390308
$712$	−0.290512	−0.0108874
$713$	28.1033	1.05248
$714$	−19.4173	−0.726673
$715$	−3.61955	−0.135363
$716$	16.0214	0.598748
$717$	−14.2021	−0.530389
$718$	−57.9305	−2.16195
$719$	10.3674	0.386640	0.193320	−	0.981136i	$-0.438074\pi$
$719$	10.3674	0.386640	0.193320	+	0.981136i	$0.438074\pi$
$720$	−3.78468	−0.141047
$721$	−4.14115	−0.154225
$722$	−8.76697	−0.326273
$723$	−7.69026	−0.286004
$724$	4.44357	0.165144
$725$	−9.56297	−0.355160
$726$	−20.5569	−0.762937
$727$	44.4343	1.64798	0.823988	−	0.566608i	$-0.191745\pi$
$727$	44.4343	1.64798	0.823988	+	0.566608i	$0.191745\pi$
$728$	−7.16503	−0.265554
$729$	1.00000	0.0370370
$730$	2.49881	0.0924850
$731$	−29.0828	−1.07567
$732$	−2.24201	−0.0828671
$733$	−5.06457	−0.187064	−0.0935321	−	0.995616i	$-0.529816\pi$
$733$	−5.06457	−0.187064	−0.0935321	+	0.995616i	$0.529816\pi$
$734$	2.24275	0.0827814
$735$	−7.68227	−0.283365
$736$	−39.4977	−1.45590
$737$	57.2228	2.10783
$738$	5.13986	0.189201
$739$	−9.28069	−0.341396	−0.170698	−	0.985323i	$-0.554602\pi$
$739$	−9.28069	−0.341396	−0.170698	+	0.985323i	$0.554602\pi$
$740$	5.27220	0.193810
$741$	−3.73356	−0.137156
$742$	−76.6058	−2.81229
$743$	2.04314	0.0749555	0.0374778	−	0.999297i	$-0.488068\pi$
$743$	2.04314	0.0749555	0.0374778	+	0.999297i	$0.488068\pi$
$744$	6.40364	0.234769
$745$	−5.21318	−0.190996
$746$	26.5473	0.971964
$747$	4.41105	0.161392
$748$	−12.9588	−0.473820
$749$	−19.9567	−0.729201
$750$	12.3620	0.451396
$751$	−23.8193	−0.869178	−0.434589	−	0.900629i	$-0.643106\pi$
$751$	−23.8193	−0.869178	−0.434589	+	0.900629i	$0.643106\pi$
$752$	31.5619	1.15094
$753$	−23.0092	−0.838502
$754$	−3.74224	−0.136284
$755$	−4.06411	−0.147908
$756$	4.14646	0.150805
$757$	−1.06185	−0.0385937	−0.0192968	−	0.999814i	$-0.506143\pi$
$757$	−1.06185	−0.0385937	−0.0192968	+	0.999814i	$0.506143\pi$
$758$	17.8094	0.646868
$759$	−36.3096	−1.31795
$760$	4.88967	0.177367
$761$	−36.5734	−1.32579	−0.662893	−	0.748714i	$-0.730672\pi$
$761$	−36.5734	−1.32579	−0.662893	+	0.748714i	$0.730672\pi$
$762$	−22.1613	−0.802821
$763$	−7.48617	−0.271017
$764$	−15.3680	−0.555996
$765$	−2.04867	−0.0740700
$766$	22.9727	0.830037
$767$	5.11496	0.184690
$768$	−19.0128	−0.686065
$769$	−4.17759	−0.150648	−0.0753239	−	0.997159i	$-0.523999\pi$
$769$	−4.17759	−0.150648	−0.0753239	+	0.997159i	$0.523999\pi$
$770$	−25.9675	−0.935802
$771$	6.25276	0.225187
$772$	−1.74150	−0.0626781
$773$	−24.6930	−0.888145	−0.444072	−	0.895991i	$-0.646467\pi$
$773$	−24.6930	−0.888145	−0.444072	+	0.895991i	$0.646467\pi$
$774$	18.6156	0.669124
$775$	−16.3849	−0.588564
$776$	25.0284	0.898467
$777$	28.8070	1.03344
$778$	−18.3643	−0.658392
$779$	−11.0770	−0.396873
$780$	0.757907	0.0271374
$781$	−78.6133	−2.81301
$782$	−35.6035	−1.27318
$783$	−2.16012	−0.0771965
$784$	−50.7458	−1.81235
$785$	12.2393	0.436840
$786$	−5.85081	−0.208692
$787$	−0.285306	−0.0101701	−0.00508504	−	0.999987i	$-0.501619\pi$
$787$	−0.285306	−0.0101701	−0.00508504	+	0.999987i	$0.501619\pi$
$788$	−3.80730	−0.135630
$789$	−11.5689	−0.411865
$790$	13.6476	0.485559
$791$	−61.2949	−2.17939
$792$	−8.27354	−0.293987
$793$	−2.23914	−0.0795142
$794$	−30.7703	−1.09200
$795$	−8.08251	−0.286657
$796$	−22.5557	−0.799467
$797$	41.0585	1.45437	0.727184	−	0.686443i	$-0.240829\pi$
$797$	41.0585	1.45437	0.727184	+	0.686443i	$0.240829\pi$
$798$	−26.7854	−0.948192
$799$	17.0847	0.604412
$800$	23.0282	0.814169
$801$	0.167906	0.00593268
$802$	−9.84205	−0.347535
$803$	9.11202	0.321556
$804$	−11.9820	−0.422574
$805$	−23.8017	−0.838898
$806$	−6.41186	−0.225848
$807$	0.985227	0.0346816
$808$	−4.21798	−0.148388
$809$	−39.3262	−1.38264	−0.691318	−	0.722550i	$-0.742970\pi$
$809$	−39.3262	−1.38264	−0.691318	+	0.722550i	$0.742970\pi$
$810$	1.31133	0.0460755
$811$	−6.98719	−0.245353	−0.122677	−	0.992447i	$-0.539148\pi$
$811$	−6.98719	−0.245353	−0.122677	+	0.992447i	$0.539148\pi$
$812$	−8.95686	−0.314324
$813$	−25.2251	−0.884682
$814$	57.6268	2.01982
$815$	8.40634	0.294461
$816$	−13.5327	−0.473738
$817$	−40.1187	−1.40357
$818$	63.0770	2.20544
$819$	4.14115	0.144704
$820$	2.24861	0.0785247
$821$	−40.1511	−1.40128	−0.700641	−	0.713514i	$-0.747102\pi$
$821$	−40.1511	−1.40128	−0.700641	+	0.713514i	$0.747102\pi$
$822$	2.34869	0.0819199
$823$	16.2779	0.567412	0.283706	−	0.958911i	$-0.408436\pi$
$823$	16.2779	0.567412	0.283706	+	0.958911i	$0.408436\pi$
$824$	−1.73020	−0.0602744
$825$	21.1694	0.737025
$826$	36.6958	1.27681
$827$	−13.9813	−0.486178	−0.243089	−	0.970004i	$-0.578161\pi$
$827$	−13.9813	−0.486178	−0.243089	+	0.970004i	$0.578161\pi$
$828$	7.60295	0.264221
$829$	8.65424	0.300574	0.150287	−	0.988642i	$-0.451980\pi$
$829$	8.65424	0.300574	0.150287	+	0.988642i	$0.451980\pi$
$830$	5.78436	0.200778
$831$	22.7823	0.790309
$832$	−0.988466	−0.0342689
$833$	−27.4690	−0.951745
$834$	4.69117	0.162442
$835$	14.8195	0.512849
$836$	−17.8762	−0.618260
$837$	−3.70110	−0.127929
$838$	14.8510	0.513020
$839$	35.9353	1.24063	0.620313	−	0.784355i	$-0.287006\pi$
$839$	35.9353	1.24063	0.620313	+	0.784355i	$0.287006\pi$
$840$	−5.42347	−0.187128
$841$	−24.3339	−0.839099
$842$	−59.4601	−2.04913
$843$	−16.8803	−0.581389
$844$	11.1126	0.382512
$845$	0.756937	0.0260394
$846$	−10.9357	−0.375977
$847$	−49.1389	−1.68843
$848$	−53.3896	−1.83341
$849$	−8.40458	−0.288444
$850$	20.7578	0.711986
$851$	52.8205	1.81066
$852$	16.4610	0.563946
$853$	−11.2579	−0.385462	−0.192731	−	0.981252i	$-0.561735\pi$
$853$	−11.2579	−0.385462	−0.192731	+	0.981252i	$0.561735\pi$
$854$	−16.0641	−0.549702
$855$	−2.82607	−0.0966495
$856$	−8.33803	−0.284988
$857$	14.9990	0.512358	0.256179	−	0.966629i	$-0.417536\pi$
$857$	14.9990	0.512358	0.256179	+	0.966629i	$0.417536\pi$
$858$	8.28416	0.282816
$859$	5.12273	0.174785	0.0873927	−	0.996174i	$-0.472147\pi$
$859$	5.12273	0.174785	0.0873927	+	0.996174i	$0.472147\pi$
$860$	8.14403	0.277709
$861$	12.2862	0.418714
$862$	−0.342173	−0.0116545
$863$	45.4449	1.54696	0.773482	−	0.633819i	$-0.218513\pi$
$863$	45.4449	1.54696	0.773482	+	0.633819i	$0.218513\pi$
$864$	5.20170	0.176965
$865$	2.23328	0.0759338
$866$	−52.5871	−1.78698
$867$	9.67468	0.328569
$868$	−15.3465	−0.520893
$869$	49.7666	1.68822
$870$	−2.83264	−0.0960355
$871$	−11.9667	−0.405476
$872$	−3.12777	−0.105920
$873$	−14.4656	−0.489586
$874$	−49.1137	−1.66130
$875$	29.5499	0.998970
$876$	−1.90799	−0.0644649
$877$	4.19302	0.141588	0.0707942	−	0.997491i	$-0.477447\pi$
$877$	4.19302	0.141588	0.0707942	+	0.997491i	$0.477447\pi$
$878$	−51.0670	−1.72343
$879$	18.7229	0.631509
$880$	−18.0977	−0.610075
$881$	−14.9298	−0.502999	−0.251499	−	0.967857i	$-0.580924\pi$
$881$	−14.9298	−0.502999	−0.251499	+	0.967857i	$0.580924\pi$
$882$	17.5826	0.592037
$883$	−16.1457	−0.543346	−0.271673	−	0.962390i	$-0.587577\pi$
$883$	−16.1457	−0.543346	−0.271673	+	0.962390i	$0.587577\pi$
$884$	2.71000	0.0911472
$885$	3.87170	0.130146
$886$	33.4578	1.12404
$887$	35.6306	1.19636	0.598179	−	0.801363i	$-0.295891\pi$
$887$	35.6306	1.19636	0.598179	+	0.801363i	$0.295891\pi$
$888$	12.0357	0.403893
$889$	−52.9741	−1.77670
$890$	0.220181	0.00738049
$891$	4.78184	0.160198
$892$	−11.4026	−0.381788
$893$	23.5676	0.788661
$894$	11.9315	0.399050
$895$	12.1117	0.404849
$896$	−50.1735	−1.67618
$897$	7.59322	0.253530
$898$	−30.3634	−1.01324
$899$	7.99483	0.266642
$900$	−4.43272	−0.147757
$901$	−28.9002	−0.962804
$902$	24.5780	0.818357
$903$	44.4984	1.48082
$904$	−25.6094	−0.851755
$905$	3.35920	0.111664
$906$	9.30164	0.309026
$907$	57.1285	1.89692	0.948461	−	0.316895i	$-0.102640\pi$
$907$	57.1285	1.89692	0.948461	+	0.316895i	$0.102640\pi$
$908$	−9.06620	−0.300872
$909$	2.43786	0.0808586
$910$	5.43043	0.180017
$911$	38.9300	1.28981	0.644904	−	0.764264i	$-0.276897\pi$
$911$	38.9300	1.28981	0.644904	+	0.764264i	$0.276897\pi$
$912$	−18.6678	−0.618152
$913$	21.0929	0.698075
$914$	−22.7386	−0.752125
$915$	−1.69489	−0.0560313
$916$	25.7685	0.851415
$917$	−13.9857	−0.461849
$918$	4.68885	0.154755
$919$	−27.1685	−0.896207	−0.448104	−	0.893982i	$-0.647900\pi$
$919$	−27.1685	−0.896207	−0.448104	+	0.893982i	$0.647900\pi$
$920$	−9.94448	−0.327860
$921$	−3.29304	−0.108509
$922$	0.0307160	0.00101158
$923$	16.4400	0.541128
$924$	19.8277	0.652284
$925$	−30.7957	−1.01256
$926$	−32.4975	−1.06793
$927$	1.00000	0.0328443
$928$	−11.2363	−0.368850
$929$	−3.65305	−0.119853	−0.0599264	−	0.998203i	$-0.519087\pi$
$929$	−3.65305	−0.119853	−0.0599264	+	0.998203i	$0.519087\pi$
$930$	−4.85337	−0.159148
$931$	−37.8925	−1.24188
$932$	−15.2638	−0.499982
$933$	22.0976	0.723442
$934$	43.1679	1.41250
$935$	−9.79643	−0.320378
$936$	1.73020	0.0565534
$937$	53.8141	1.75803	0.879015	−	0.476795i	$-0.158201\pi$
$937$	53.8141	1.75803	0.879015	+	0.476795i	$0.158201\pi$
$938$	−85.8517	−2.80316
$939$	−7.58516	−0.247532
$940$	−4.78419	−0.156043
$941$	30.0384	0.979225	0.489613	−	0.871940i	$-0.337138\pi$
$941$	30.0384	0.979225	0.489613	+	0.871940i	$0.337138\pi$
$942$	−28.0124	−0.912694
$943$	22.5281	0.733614
$944$	25.5748	0.832388
$945$	3.13459	0.101968
$946$	89.0168	2.89418
$947$	10.5717	0.343534	0.171767	−	0.985138i	$-0.445052\pi$
$947$	10.5717	0.343534	0.171767	+	0.985138i	$0.445052\pi$
$948$	−10.4207	−0.338450
$949$	−1.90555	−0.0618567
$950$	28.6346	0.929028
$951$	−14.7854	−0.479449
$952$	−19.3924	−0.628511
$953$	−7.50997	−0.243272	−0.121636	−	0.992575i	$-0.538814\pi$
$953$	−7.50997	−0.243272	−0.121636	+	0.992575i	$0.538814\pi$
$954$	18.4987	0.598916
$955$	−11.6177	−0.375941
$956$	14.2203	0.459919
$957$	−10.3294	−0.333901
$958$	−22.7194	−0.734031
$959$	5.61427	0.181294
$960$	−0.748206	−0.0241482
$961$	−17.3019	−0.558125
$962$	−12.0512	−0.388546
$963$	4.81911	0.155294
$964$	7.70011	0.248004
$965$	−1.31652	−0.0423803
$966$	54.4755	1.75272
$967$	0.499711	0.0160696	0.00803481	−	0.999968i	$-0.497442\pi$
$967$	0.499711	0.0160696	0.00803481	+	0.999968i	$0.497442\pi$
$968$	−20.5305	−0.659876
$969$	−10.1050	−0.324620
$970$	−18.9692	−0.609065
$971$	−49.1914	−1.57863	−0.789313	−	0.613991i	$-0.789563\pi$
$971$	−49.1914	−1.57863	−0.789313	+	0.613991i	$0.789563\pi$
$972$	−1.00128	−0.0321161
$973$	11.2137	0.359495
$974$	62.2503	1.99463
$975$	−4.42705	−0.141779
$976$	−11.1957	−0.358366
$977$	−44.6106	−1.42722	−0.713610	−	0.700543i	$-0.752941\pi$
$977$	−44.6106	−1.42722	−0.713610	+	0.700543i	$0.752941\pi$
$978$	−19.2398	−0.615221
$979$	0.802901	0.0256608
$980$	7.69211	0.245716
$981$	1.80775	0.0577170
$982$	−0.843774	−0.0269259
$983$	33.2047	1.05907	0.529533	−	0.848289i	$-0.322367\pi$
$983$	33.2047	1.05907	0.529533	+	0.848289i	$0.322367\pi$
$984$	5.13327	0.163643
$985$	−2.87820	−0.0917070
$986$	−10.1285	−0.322557
$987$	−26.1405	−0.832062
$988$	3.73834	0.118933
$989$	81.5924	2.59449
$990$	6.27058	0.199292
$991$	−11.3555	−0.360719	−0.180360	−	0.983601i	$-0.557726\pi$
$991$	−11.3555	−0.360719	−0.180360	+	0.983601i	$0.557726\pi$
$992$	−19.2520	−0.611252
$993$	4.68459	0.148661
$994$	117.944	3.74096
$995$	−17.0514	−0.540566
$996$	−4.41670	−0.139949
$997$	37.5662	1.18974	0.594868	−	0.803824i	$-0.297205\pi$
$997$	37.5662	1.18974	0.594868	+	0.803824i	$0.297205\pi$
$998$	64.5918	2.04462
$999$	−6.95627	−0.220086

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.g.1.19	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.g.1.19	✓	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q+1.73242 q^{2} -1.00000 q^{3} +1.00128 q^{4} +0.756937 q^{5} -1.73242 q^{6} -4.14115 q^{7} -1.73020 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.73242 q^{2} -1.00000 q^{3} +1.00128 q^{4} +0.756937 q^{5} -1.73242 q^{6} -4.14115 q^{7} -1.73020 q^{8} +1.00000 q^{9} +1.31133 q^{10} +4.78184 q^{11} -1.00128 q^{12} -1.00000 q^{13} -7.17422 q^{14} -0.756937 q^{15} -5.00000 q^{16} -2.70653 q^{17} +1.73242 q^{18} -3.73356 q^{19} +0.757907 q^{20} +4.14115 q^{21} +8.28416 q^{22} +7.59322 q^{23} +1.73020 q^{24} -4.42705 q^{25} -1.73242 q^{26} -1.00000 q^{27} -4.14646 q^{28} +2.16012 q^{29} -1.31133 q^{30} +3.70110 q^{31} -5.20170 q^{32} -4.78184 q^{33} -4.68885 q^{34} -3.13459 q^{35} +1.00128 q^{36} +6.95627 q^{37} -6.46810 q^{38} +1.00000 q^{39} -1.30965 q^{40} +2.96686 q^{41} +7.17422 q^{42} +10.7454 q^{43} +4.78797 q^{44} +0.756937 q^{45} +13.1547 q^{46} -6.31238 q^{47} +5.00000 q^{48} +10.1492 q^{49} -7.66951 q^{50} +2.70653 q^{51} -1.00128 q^{52} +10.6779 q^{53} -1.73242 q^{54} +3.61955 q^{55} +7.16503 q^{56} +3.73356 q^{57} +3.74224 q^{58} -5.11496 q^{59} -0.757907 q^{60} +2.23914 q^{61} +6.41186 q^{62} -4.14115 q^{63} +0.988466 q^{64} -0.756937 q^{65} -8.28416 q^{66} +11.9667 q^{67} -2.71000 q^{68} -7.59322 q^{69} -5.43043 q^{70} -16.4400 q^{71} -1.73020 q^{72} +1.90555 q^{73} +12.0512 q^{74} +4.42705 q^{75} -3.73834 q^{76} -19.8023 q^{77} +1.73242 q^{78} +10.4074 q^{79} -3.78468 q^{80} +1.00000 q^{81} +5.13986 q^{82} +4.41105 q^{83} +4.14646 q^{84} -2.04867 q^{85} +18.6156 q^{86} -2.16012 q^{87} -8.27354 q^{88} +0.167906 q^{89} +1.31133 q^{90} +4.14115 q^{91} +7.60295 q^{92} -3.70110 q^{93} -10.9357 q^{94} -2.82607 q^{95} +5.20170 q^{96} -14.4656 q^{97} +17.5826 q^{98} +4.78184 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9	\( 24 q + 3 q^{2} - 24 q^{3} + 25 q^{4} + 3 q^{5} - 3 q^{6} + 11 q^{7} + 6 q^{8} + 24 q^{9} - 2 q^{10} + 7 q^{11} - 25 q^{12} - 24 q^{13} + 8 q^{14} - 3 q^{15} + 23 q^{16} + 4 q^{17} + 3 q^{18} - 20 q^{19} + 8 q^{20} - 11 q^{21} + 5 q^{22} + 41 q^{23} - 6 q^{24} + 23 q^{25} - 3 q^{26} - 24 q^{27} + 16 q^{28} + 12 q^{29} + 2 q^{30} + 2 q^{31} + 25 q^{32} - 7 q^{33} - 11 q^{34} + 36 q^{35} + 25 q^{36} + 18 q^{37} + 10 q^{38} + 24 q^{39} + 14 q^{40} - 9 q^{41} - 8 q^{42} + 23 q^{43} + 41 q^{44} + 3 q^{45} + 7 q^{46} + 32 q^{47} - 23 q^{48} + 11 q^{49} + 26 q^{50} - 4 q^{51} - 25 q^{52} + 46 q^{53} - 3 q^{54} + 18 q^{55} + 26 q^{56} + 20 q^{57} + 37 q^{58} - 12 q^{59} - 8 q^{60} - q^{61} + 53 q^{62} + 11 q^{63} + 26 q^{64} - 3 q^{65} - 5 q^{66} + 8 q^{67} + 6 q^{68} - 41 q^{69} + 19 q^{70} + 20 q^{71} + 6 q^{72} + 12 q^{73} + 86 q^{74} - 23 q^{75} - 28 q^{76} + 23 q^{77} + 3 q^{78} + 27 q^{79} + 6 q^{80} + 24 q^{81} - 28 q^{82} + 33 q^{83} - 16 q^{84} - 13 q^{85} + 63 q^{86} - 12 q^{87} + 11 q^{88} - 2 q^{90} - 11 q^{91} + 79 q^{92} - 2 q^{93} - 12 q^{94} + 37 q^{95} - 25 q^{96} - 14 q^{97} + 20 q^{98} + 7 q^{99}+O(q^{100}) \) 24 * q + 3 * q^2 - 24 * q^3 + 25 * q^4 + 3 * q^5 - 3 * q^6 + 11 * q^7 + 6 * q^8 + 24 * q^9 - 2 * q^10 + 7 * q^11 - 25 * q^12 - 24 * q^13 + 8 * q^14 - 3 * q^15 + 23 * q^16 + 4 * q^17 + 3 * q^18 - 20 * q^19 + 8 * q^20 - 11 * q^21 + 5 * q^22 + 41 * q^23 - 6 * q^24 + 23 * q^25 - 3 * q^26 - 24 * q^27 + 16 * q^28 + 12 * q^29 + 2 * q^30 + 2 * q^31 + 25 * q^32 - 7 * q^33 - 11 * q^34 + 36 * q^35 + 25 * q^36 + 18 * q^37 + 10 * q^38 + 24 * q^39 + 14 * q^40 - 9 * q^41 - 8 * q^42 + 23 * q^43 + 41 * q^44 + 3 * q^45 + 7 * q^46 + 32 * q^47 - 23 * q^48 + 11 * q^49 + 26 * q^50 - 4 * q^51 - 25 * q^52 + 46 * q^53 - 3 * q^54 + 18 * q^55 + 26 * q^56 + 20 * q^57 + 37 * q^58 - 12 * q^59 - 8 * q^60 - q^61 + 53 * q^62 + 11 * q^63 + 26 * q^64 - 3 * q^65 - 5 * q^66 + 8 * q^67 + 6 * q^68 - 41 * q^69 + 19 * q^70 + 20 * q^71 + 6 * q^72 + 12 * q^73 + 86 * q^74 - 23 * q^75 - 28 * q^76 + 23 * q^77 + 3 * q^78 + 27 * q^79 + 6 * q^80 + 24 * q^81 - 28 * q^82 + 33 * q^83 - 16 * q^84 - 13 * q^85 + 63 * q^86 - 12 * q^87 + 11 * q^88 - 2 * q^90 - 11 * q^91 + 79 * q^92 - 2 * q^93 - 12 * q^94 + 37 * q^95 - 25 * q^96 - 14 * q^97 + 20 * q^98 + 7 * q^99

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