LMFDB - Embedded newform 6034.2.a.n.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.685916 q^{3} +1.00000 q^{4} +1.44966 q^{5} -0.685916 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.52952 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.685916 q^{3} +1.00000 q^{4} +1.44966 q^{5} -0.685916 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.52952 q^{9} -1.44966 q^{10} -0.0308170 q^{11} +0.685916 q^{12} +6.22014 q^{13} +1.00000 q^{14} +0.994342 q^{15} +1.00000 q^{16} -5.48560 q^{17} +2.52952 q^{18} +1.99267 q^{19} +1.44966 q^{20} -0.685916 q^{21} +0.0308170 q^{22} +8.11388 q^{23} -0.685916 q^{24} -2.89850 q^{25} -6.22014 q^{26} -3.79278 q^{27} -1.00000 q^{28} +2.29482 q^{29} -0.994342 q^{30} +3.66210 q^{31} -1.00000 q^{32} -0.0211379 q^{33} +5.48560 q^{34} -1.44966 q^{35} -2.52952 q^{36} +6.75121 q^{37} -1.99267 q^{38} +4.26649 q^{39} -1.44966 q^{40} +5.26102 q^{41} +0.685916 q^{42} -5.40770 q^{43} -0.0308170 q^{44} -3.66693 q^{45} -8.11388 q^{46} -3.31714 q^{47} +0.685916 q^{48} +1.00000 q^{49} +2.89850 q^{50} -3.76266 q^{51} +6.22014 q^{52} -2.40729 q^{53} +3.79278 q^{54} -0.0446741 q^{55} +1.00000 q^{56} +1.36680 q^{57} -2.29482 q^{58} +4.54061 q^{59} +0.994342 q^{60} -6.20443 q^{61} -3.66210 q^{62} +2.52952 q^{63} +1.00000 q^{64} +9.01707 q^{65} +0.0211379 q^{66} -0.636232 q^{67} -5.48560 q^{68} +5.56544 q^{69} +1.44966 q^{70} +1.56907 q^{71} +2.52952 q^{72} -8.94194 q^{73} -6.75121 q^{74} -1.98812 q^{75} +1.99267 q^{76} +0.0308170 q^{77} -4.26649 q^{78} -7.94777 q^{79} +1.44966 q^{80} +4.98703 q^{81} -5.26102 q^{82} -3.11054 q^{83} -0.685916 q^{84} -7.95223 q^{85} +5.40770 q^{86} +1.57405 q^{87} +0.0308170 q^{88} +9.22104 q^{89} +3.66693 q^{90} -6.22014 q^{91} +8.11388 q^{92} +2.51190 q^{93} +3.31714 q^{94} +2.88868 q^{95} -0.685916 q^{96} +18.0193 q^{97} -1.00000 q^{98} +0.0779523 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9} - 8 q^{10} + 15 q^{11} + 7 q^{12} - 7 q^{13} + 24 q^{14} + 13 q^{15} + 24 q^{16} - 5 q^{17} - 19 q^{18} + 6 q^{19} + 8 q^{20} - 7 q^{21} - 15 q^{22} + 3 q^{23} - 7 q^{24} + 12 q^{25} + 7 q^{26} + 22 q^{27} - 24 q^{28} + 5 q^{29} - 13 q^{30} + 13 q^{31} - 24 q^{32} - 8 q^{33} + 5 q^{34} - 8 q^{35} + 19 q^{36} + 2 q^{37} - 6 q^{38} + 7 q^{39} - 8 q^{40} + 25 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 41 q^{45} - 3 q^{46} + 35 q^{47} + 7 q^{48} + 24 q^{49} - 12 q^{50} + 31 q^{51} - 7 q^{52} + 2 q^{53} - 22 q^{54} + 14 q^{55} + 24 q^{56} - 13 q^{57} - 5 q^{58} + 35 q^{59} + 13 q^{60} - 7 q^{61} - 13 q^{62} - 19 q^{63} + 24 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} - 5 q^{68} + 6 q^{69} + 8 q^{70} + 58 q^{71} - 19 q^{72} + 9 q^{73} - 2 q^{74} + 7 q^{75} + 6 q^{76} - 15 q^{77} - 7 q^{78} + 31 q^{79} + 8 q^{80} + 16 q^{81} - 25 q^{82} - q^{83} - 7 q^{84} - 4 q^{85} + 15 q^{86} + 30 q^{87} - 15 q^{88} + 45 q^{89} - 41 q^{90} + 7 q^{91} + 3 q^{92} + 25 q^{93} - 35 q^{94} - 10 q^{95} - 7 q^{96} - 9 q^{97} - 24 q^{98} + 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9 - 8 * q^10 + 15 * q^11 + 7 * q^12 - 7 * q^13 + 24 * q^14 + 13 * q^15 + 24 * q^16 - 5 * q^17 - 19 * q^18 + 6 * q^19 + 8 * q^20 - 7 * q^21 - 15 * q^22 + 3 * q^23 - 7 * q^24 + 12 * q^25 + 7 * q^26 + 22 * q^27 - 24 * q^28 + 5 * q^29 - 13 * q^30 + 13 * q^31 - 24 * q^32 - 8 * q^33 + 5 * q^34 - 8 * q^35 + 19 * q^36 + 2 * q^37 - 6 * q^38 + 7 * q^39 - 8 * q^40 + 25 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 41 * q^45 - 3 * q^46 + 35 * q^47 + 7 * q^48 + 24 * q^49 - 12 * q^50 + 31 * q^51 - 7 * q^52 + 2 * q^53 - 22 * q^54 + 14 * q^55 + 24 * q^56 - 13 * q^57 - 5 * q^58 + 35 * q^59 + 13 * q^60 - 7 * q^61 - 13 * q^62 - 19 * q^63 + 24 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 - 5 * q^68 + 6 * q^69 + 8 * q^70 + 58 * q^71 - 19 * q^72 + 9 * q^73 - 2 * q^74 + 7 * q^75 + 6 * q^76 - 15 * q^77 - 7 * q^78 + 31 * q^79 + 8 * q^80 + 16 * q^81 - 25 * q^82 - q^83 - 7 * q^84 - 4 * q^85 + 15 * q^86 + 30 * q^87 - 15 * q^88 + 45 * q^89 - 41 * q^90 + 7 * q^91 + 3 * q^92 + 25 * q^93 - 35 * q^94 - 10 * q^95 - 7 * q^96 - 9 * q^97 - 24 * q^98 + 64 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.685916	0.396014	0.198007	−	0.980201i	$-0.436553\pi$
$3$	0.685916	0.396014	0.198007	+	0.980201i	$0.436553\pi$
$4$	1.00000	0.500000
$5$	1.44966	0.648306	0.324153	−	0.946005i	$-0.394921\pi$
$5$	1.44966	0.648306	0.324153	+	0.946005i	$0.394921\pi$
$6$	−0.685916	−0.280024
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−2.52952	−0.843173
$10$	−1.44966	−0.458421
$11$	−0.0308170	−0.00929169	−0.00464584	−	0.999989i	$-0.501479\pi$
$11$	−0.0308170	−0.00929169	−0.00464584	+	0.999989i	$0.501479\pi$
$12$	0.685916	0.198007
$13$	6.22014	1.72516	0.862579	−	0.505923i	$-0.168848\pi$
$13$	6.22014	1.72516	0.862579	+	0.505923i	$0.168848\pi$
$14$	1.00000	0.267261
$15$	0.994342	0.256738
$16$	1.00000	0.250000
$17$	−5.48560	−1.33045	−0.665226	−	0.746642i	$-0.731665\pi$
$17$	−5.48560	−1.33045	−0.665226	+	0.746642i	$0.731665\pi$
$18$	2.52952	0.596213
$19$	1.99267	0.457150	0.228575	−	0.973526i	$-0.426593\pi$
$19$	1.99267	0.457150	0.228575	+	0.973526i	$0.426593\pi$
$20$	1.44966	0.324153
$21$	−0.685916	−0.149679
$22$	0.0308170	0.00657021
$23$	8.11388	1.69186	0.845931	−	0.533292i	$-0.179045\pi$
$23$	8.11388	1.69186	0.845931	+	0.533292i	$0.179045\pi$
$24$	−0.685916	−0.140012
$25$	−2.89850	−0.579699
$26$	−6.22014	−1.21987
$27$	−3.79278	−0.729922
$28$	−1.00000	−0.188982
$29$	2.29482	0.426138	0.213069	−	0.977037i	$-0.431654\pi$
$29$	2.29482	0.426138	0.213069	+	0.977037i	$0.431654\pi$
$30$	−0.994342	−0.181541
$31$	3.66210	0.657733	0.328867	−	0.944376i	$-0.393333\pi$
$31$	3.66210	0.657733	0.328867	+	0.944376i	$0.393333\pi$
$32$	−1.00000	−0.176777
$33$	−0.0211379	−0.00367963
$34$	5.48560	0.940772
$35$	−1.44966	−0.245037
$36$	−2.52952	−0.421587
$37$	6.75121	1.10989	0.554946	−	0.831886i	$-0.312739\pi$
$37$	6.75121	1.10989	0.554946	+	0.831886i	$0.312739\pi$
$38$	−1.99267	−0.323254
$39$	4.26649	0.683186
$40$	−1.44966	−0.229211
$41$	5.26102	0.821633	0.410817	−	0.911718i	$-0.365244\pi$
$41$	5.26102	0.821633	0.410817	+	0.911718i	$0.365244\pi$
$42$	0.685916	0.105839
$43$	−5.40770	−0.824667	−0.412333	−	0.911033i	$-0.635286\pi$
$43$	−5.40770	−0.824667	−0.412333	+	0.911033i	$0.635286\pi$
$44$	−0.0308170	−0.00464584
$45$	−3.66693	−0.546634
$46$	−8.11388	−1.19633
$47$	−3.31714	−0.483855	−0.241927	−	0.970294i	$-0.577780\pi$
$47$	−3.31714	−0.483855	−0.241927	+	0.970294i	$0.577780\pi$
$48$	0.685916	0.0990034
$49$	1.00000	0.142857
$50$	2.89850	0.409909
$51$	−3.76266	−0.526877
$52$	6.22014	0.862579
$53$	−2.40729	−0.330666	−0.165333	−	0.986238i	$-0.552870\pi$
$53$	−2.40729	−0.330666	−0.165333	+	0.986238i	$0.552870\pi$
$54$	3.79278	0.516133
$55$	−0.0446741	−0.00602386
$56$	1.00000	0.133631
$57$	1.36680	0.181037
$58$	−2.29482	−0.301325
$59$	4.54061	0.591137	0.295568	−	0.955322i	$-0.404491\pi$
$59$	4.54061	0.591137	0.295568	+	0.955322i	$0.404491\pi$
$60$	0.994342	0.128369
$61$	−6.20443	−0.794396	−0.397198	−	0.917733i	$-0.630017\pi$
$61$	−6.20443	−0.794396	−0.397198	+	0.917733i	$0.630017\pi$
$62$	−3.66210	−0.465088
$63$	2.52952	0.318690
$64$	1.00000	0.125000
$65$	9.01707	1.11843
$66$	0.0211379	0.00260189
$67$	−0.636232	−0.0777281	−0.0388640	−	0.999245i	$-0.512374\pi$
$67$	−0.636232	−0.0777281	−0.0388640	+	0.999245i	$0.512374\pi$
$68$	−5.48560	−0.665226
$69$	5.56544	0.670000
$70$	1.44966	0.173267
$71$	1.56907	0.186214	0.0931072	−	0.995656i	$-0.470320\pi$
$71$	1.56907	0.186214	0.0931072	+	0.995656i	$0.470320\pi$
$72$	2.52952	0.298107
$73$	−8.94194	−1.04658	−0.523288	−	0.852156i	$-0.675295\pi$
$73$	−8.94194	−1.04658	−0.523288	+	0.852156i	$0.675295\pi$
$74$	−6.75121	−0.784812
$75$	−1.98812	−0.229569
$76$	1.99267	0.228575
$77$	0.0308170	0.00351193
$78$	−4.26649	−0.483085
$79$	−7.94777	−0.894194	−0.447097	−	0.894486i	$-0.647542\pi$
$79$	−7.94777	−0.894194	−0.447097	+	0.894486i	$0.647542\pi$
$80$	1.44966	0.162076
$81$	4.98703	0.554114
$82$	−5.26102	−0.580982
$83$	−3.11054	−0.341426	−0.170713	−	0.985321i	$-0.554607\pi$
$83$	−3.11054	−0.341426	−0.170713	+	0.985321i	$0.554607\pi$
$84$	−0.685916	−0.0748395
$85$	−7.95223	−0.862540
$86$	5.40770	0.583127
$87$	1.57405	0.168756
$88$	0.0308170	0.00328511
$89$	9.22104	0.977428	0.488714	−	0.872444i	$-0.337466\pi$
$89$	9.22104	0.977428	0.488714	+	0.872444i	$0.337466\pi$
$90$	3.66693	0.386529
$91$	−6.22014	−0.652048
$92$	8.11388	0.845931
$93$	2.51190	0.260471
$94$	3.31714	0.342137
$95$	2.88868	0.296373
$96$	−0.685916	−0.0700060
$97$	18.0193	1.82958	0.914792	−	0.403926i	$-0.132355\pi$
$97$	18.0193	1.82958	0.914792	+	0.403926i	$0.132355\pi$
$98$	−1.00000	−0.101015
$99$	0.0779523	0.00783450
$100$	−2.89850	−0.289850
$101$	6.47759	0.644545	0.322272	−	0.946647i	$-0.395553\pi$
$101$	6.47759	0.644545	0.322272	+	0.946647i	$0.395553\pi$
$102$	3.76266	0.372559
$103$	13.5189	1.33206	0.666028	−	0.745927i	$-0.267993\pi$
$103$	13.5189	1.33206	0.666028	+	0.745927i	$0.267993\pi$
$104$	−6.22014	−0.609935
$105$	−0.994342	−0.0970378
$106$	2.40729	0.233816
$107$	0.845463	0.0817340	0.0408670	−	0.999165i	$-0.486988\pi$
$107$	0.845463	0.0817340	0.0408670	+	0.999165i	$0.486988\pi$
$108$	−3.79278	−0.364961
$109$	−17.5845	−1.68429	−0.842145	−	0.539251i	$-0.818707\pi$
$109$	−17.5845	−1.68429	−0.842145	+	0.539251i	$0.818707\pi$
$110$	0.0446741	0.00425951
$111$	4.63076	0.439532
$112$	−1.00000	−0.0944911
$113$	13.1439	1.23647	0.618235	−	0.785993i	$-0.287848\pi$
$113$	13.1439	1.23647	0.618235	+	0.785993i	$0.287848\pi$
$114$	−1.36680	−0.128013
$115$	11.7623	1.09684
$116$	2.29482	0.213069
$117$	−15.7340	−1.45461
$118$	−4.54061	−0.417997
$119$	5.48560	0.502864
$120$	−0.994342	−0.0907706
$121$	−10.9991	−0.999914
$122$	6.20443	0.561723
$123$	3.60862	0.325378
$124$	3.66210	0.328867
$125$	−11.4501	−1.02413
$126$	−2.52952	−0.225348
$127$	1.40559	0.124726	0.0623629	−	0.998054i	$-0.480136\pi$
$127$	1.40559	0.124726	0.0623629	+	0.998054i	$0.480136\pi$
$128$	−1.00000	−0.0883883
$129$	−3.70923	−0.326579
$130$	−9.01707	−0.790849
$131$	13.9716	1.22071	0.610353	−	0.792129i	$-0.291027\pi$
$131$	13.9716	1.22071	0.610353	+	0.792129i	$0.291027\pi$
$132$	−0.0211379	−0.00183982
$133$	−1.99267	−0.172786
$134$	0.636232	0.0549621
$135$	−5.49823	−0.473213
$136$	5.48560	0.470386
$137$	2.12475	0.181529	0.0907646	−	0.995872i	$-0.471069\pi$
$137$	2.12475	0.181529	0.0907646	+	0.995872i	$0.471069\pi$
$138$	−5.56544	−0.473762
$139$	−12.8453	−1.08952	−0.544760	−	0.838592i	$-0.683379\pi$
$139$	−12.8453	−1.08952	−0.544760	+	0.838592i	$0.683379\pi$
$140$	−1.44966	−0.122518
$141$	−2.27528	−0.191613
$142$	−1.56907	−0.131673
$143$	−0.191686	−0.0160296
$144$	−2.52952	−0.210793
$145$	3.32670	0.276268
$146$	8.94194	0.740041
$147$	0.685916	0.0565734
$148$	6.75121	0.554946
$149$	19.0524	1.56084	0.780418	−	0.625259i	$-0.215007\pi$
$149$	19.0524	1.56084	0.780418	+	0.625259i	$0.215007\pi$
$150$	1.98812	0.162330
$151$	−14.7131	−1.19733	−0.598667	−	0.800998i	$-0.704303\pi$
$151$	−14.7131	−1.19733	−0.598667	+	0.800998i	$0.704303\pi$
$152$	−1.99267	−0.161627
$153$	13.8759	1.12180
$154$	−0.0308170	−0.00248331
$155$	5.30879	0.426412
$156$	4.26649	0.341593
$157$	−5.26211	−0.419962	−0.209981	−	0.977705i	$-0.567340\pi$
$157$	−5.26211	−0.419962	−0.209981	+	0.977705i	$0.567340\pi$
$158$	7.94777	0.632290
$159$	−1.65120	−0.130948
$160$	−1.44966	−0.114605
$161$	−8.11388	−0.639464
$162$	−4.98703	−0.391818
$163$	11.7413	0.919649	0.459824	−	0.888010i	$-0.347912\pi$
$163$	11.7413	0.919649	0.459824	+	0.888010i	$0.347912\pi$
$164$	5.26102	0.410817
$165$	−0.0306427	−0.00238553
$166$	3.11054	0.241425
$167$	−9.95291	−0.770180	−0.385090	−	0.922879i	$-0.625830\pi$
$167$	−9.95291	−0.770180	−0.385090	+	0.922879i	$0.625830\pi$
$168$	0.685916	0.0529195
$169$	25.6902	1.97617
$170$	7.95223	0.609908
$171$	−5.04049	−0.385456
$172$	−5.40770	−0.412333
$173$	15.1987	1.15553	0.577767	−	0.816202i	$-0.303924\pi$
$173$	15.1987	1.15553	0.577767	+	0.816202i	$0.303924\pi$
$174$	−1.57405	−0.119329
$175$	2.89850	0.219106
$176$	−0.0308170	−0.00232292
$177$	3.11447	0.234098
$178$	−9.22104	−0.691146
$179$	23.3175	1.74284	0.871418	−	0.490542i	$-0.163201\pi$
$179$	23.3175	1.74284	0.871418	+	0.490542i	$0.163201\pi$
$180$	−3.66693	−0.273317
$181$	10.4772	0.778768	0.389384	−	0.921076i	$-0.372688\pi$
$181$	10.4772	0.778768	0.389384	+	0.921076i	$0.372688\pi$
$182$	6.22014	0.461068
$183$	−4.25572	−0.314592
$184$	−8.11388	−0.598164
$185$	9.78693	0.719549
$186$	−2.51190	−0.184181
$187$	0.169050	0.0123622
$188$	−3.31714	−0.241927
$189$	3.79278	0.275884
$190$	−2.88868	−0.209567
$191$	10.2549	0.742020	0.371010	−	0.928629i	$-0.379012\pi$
$191$	10.2549	0.742020	0.371010	+	0.928629i	$0.379012\pi$
$192$	0.685916	0.0495017
$193$	9.26826	0.667144	0.333572	−	0.942725i	$-0.391746\pi$
$193$	9.26826	0.667144	0.333572	+	0.942725i	$0.391746\pi$
$194$	−18.0193	−1.29371
$195$	6.18495	0.442913
$196$	1.00000	0.0714286
$197$	10.5984	0.755108	0.377554	−	0.925988i	$-0.376765\pi$
$197$	10.5984	0.755108	0.377554	+	0.925988i	$0.376765\pi$
$198$	−0.0779523	−0.00553983
$199$	19.5234	1.38397	0.691987	−	0.721910i	$-0.256735\pi$
$199$	19.5234	1.38397	0.691987	+	0.721910i	$0.256735\pi$
$200$	2.89850	0.204955
$201$	−0.436401	−0.0307814
$202$	−6.47759	−0.455762
$203$	−2.29482	−0.161065
$204$	−3.76266	−0.263439
$205$	7.62667	0.532670
$206$	−13.5189	−0.941906
$207$	−20.5242	−1.42653
$208$	6.22014	0.431289
$209$	−0.0614081	−0.00424769
$210$	0.994342	0.0686161
$211$	21.5412	1.48296	0.741478	−	0.670977i	$-0.234125\pi$
$211$	21.5412	1.48296	0.741478	+	0.670977i	$0.234125\pi$
$212$	−2.40729	−0.165333
$213$	1.07625	0.0737434
$214$	−0.845463	−0.0577947
$215$	−7.83931	−0.534636
$216$	3.79278	0.258066
$217$	−3.66210	−0.248600
$218$	17.5845	1.19097
$219$	−6.13342	−0.414458
$220$	−0.0446741	−0.00301193
$221$	−34.1212	−2.29524
$222$	−4.63076	−0.310796
$223$	−16.5991	−1.11156	−0.555779	−	0.831330i	$-0.687580\pi$
$223$	−16.5991	−1.11156	−0.555779	+	0.831330i	$0.687580\pi$
$224$	1.00000	0.0668153
$225$	7.33181	0.488787
$226$	−13.1439	−0.874317
$227$	2.51733	0.167081	0.0835404	−	0.996504i	$-0.473377\pi$
$227$	2.51733	0.167081	0.0835404	+	0.996504i	$0.473377\pi$
$228$	1.36680	0.0905187
$229$	9.48297	0.626652	0.313326	−	0.949646i	$-0.398557\pi$
$229$	9.48297	0.626652	0.313326	+	0.949646i	$0.398557\pi$
$230$	−11.7623	−0.775586
$231$	0.0211379	0.00139077
$232$	−2.29482	−0.150662
$233$	6.67919	0.437568	0.218784	−	0.975773i	$-0.429791\pi$
$233$	6.67919	0.437568	0.218784	+	0.975773i	$0.429791\pi$
$234$	15.7340	1.02856
$235$	−4.80871	−0.313686
$236$	4.54061	0.295568
$237$	−5.45150	−0.354113
$238$	−5.48560	−0.355578
$239$	−8.65865	−0.560082	−0.280041	−	0.959988i	$-0.590348\pi$
$239$	−8.65865	−0.560082	−0.280041	+	0.959988i	$0.590348\pi$
$240$	0.994342	0.0641845
$241$	30.2892	1.95110	0.975549	−	0.219781i	$-0.0705342\pi$
$241$	30.2892	1.95110	0.975549	+	0.219781i	$0.0705342\pi$
$242$	10.9991	0.707046
$243$	14.7990	0.949359
$244$	−6.20443	−0.397198
$245$	1.44966	0.0926151
$246$	−3.60862	−0.230077
$247$	12.3947	0.788655
$248$	−3.66210	−0.232544
$249$	−2.13357	−0.135209
$250$	11.4501	0.724168
$251$	−27.4516	−1.73273	−0.866363	−	0.499414i	$-0.833549\pi$
$251$	−27.4516	−1.73273	−0.866363	+	0.499414i	$0.833549\pi$
$252$	2.52952	0.159345
$253$	−0.250046	−0.0157203
$254$	−1.40559	−0.0881944
$255$	−5.45456	−0.341578
$256$	1.00000	0.0625000
$257$	−17.6464	−1.10075	−0.550377	−	0.834916i	$-0.685516\pi$
$257$	−17.6464	−1.10075	−0.550377	+	0.834916i	$0.685516\pi$
$258$	3.70923	0.230926
$259$	−6.75121	−0.419500
$260$	9.01707	0.559215
$261$	−5.80480	−0.359308
$262$	−13.9716	−0.863170
$263$	31.6063	1.94893	0.974465	−	0.224540i	$-0.0720878\pi$
$263$	31.6063	1.94893	0.974465	+	0.224540i	$0.0720878\pi$
$264$	0.0211379	0.00130095
$265$	−3.48974	−0.214373
$266$	1.99267	0.122178
$267$	6.32486	0.387075
$268$	−0.636232	−0.0388640
$269$	8.76947	0.534684	0.267342	−	0.963602i	$-0.413855\pi$
$269$	8.76947	0.534684	0.267342	+	0.963602i	$0.413855\pi$
$270$	5.49823	0.334612
$271$	3.46805	0.210669	0.105334	−	0.994437i	$-0.466409\pi$
$271$	3.46805	0.210669	0.105334	+	0.994437i	$0.466409\pi$
$272$	−5.48560	−0.332613
$273$	−4.26649	−0.258220
$274$	−2.12475	−0.128361
$275$	0.0893231	0.00538639
$276$	5.56544	0.335000
$277$	−7.15105	−0.429665	−0.214832	−	0.976651i	$-0.568921\pi$
$277$	−7.15105	−0.429665	−0.214832	+	0.976651i	$0.568921\pi$
$278$	12.8453	0.770407
$279$	−9.26337	−0.554583
$280$	1.44966	0.0866335
$281$	−1.72925	−0.103158	−0.0515792	−	0.998669i	$-0.516425\pi$
$281$	−1.72925	−0.103158	−0.0515792	+	0.998669i	$0.516425\pi$
$282$	2.27528	0.135491
$283$	−6.18264	−0.367520	−0.183760	−	0.982971i	$-0.558827\pi$
$283$	−6.18264	−0.367520	−0.183760	+	0.982971i	$0.558827\pi$
$284$	1.56907	0.0931072
$285$	1.98139	0.117368
$286$	0.191686	0.0113347
$287$	−5.26102	−0.310548
$288$	2.52952	0.149053
$289$	13.0918	0.770105
$290$	−3.32670	−0.195351
$291$	12.3597	0.724540
$292$	−8.94194	−0.523288
$293$	−12.7021	−0.742063	−0.371032	−	0.928620i	$-0.620996\pi$
$293$	−12.7021	−0.742063	−0.371032	+	0.928620i	$0.620996\pi$
$294$	−0.685916	−0.0400034
$295$	6.58232	0.383237
$296$	−6.75121	−0.392406
$297$	0.116882	0.00678220
$298$	−19.0524	−1.10368
$299$	50.4695	2.91873
$300$	−1.98812	−0.114784
$301$	5.40770	0.311695
$302$	14.7131	0.846643
$303$	4.44308	0.255249
$304$	1.99267	0.114287
$305$	−8.99429	−0.515011
$306$	−13.8759	−0.793234
$307$	11.3220	0.646181	0.323090	−	0.946368i	$-0.395278\pi$
$307$	11.3220	0.646181	0.323090	+	0.946368i	$0.395278\pi$
$308$	0.0308170	0.00175596
$309$	9.27282	0.527512
$310$	−5.30879	−0.301519
$311$	−27.8624	−1.57993	−0.789966	−	0.613150i	$-0.789902\pi$
$311$	−27.8624	−1.57993	−0.789966	+	0.613150i	$0.789902\pi$
$312$	−4.26649	−0.241543
$313$	−2.64490	−0.149499	−0.0747494	−	0.997202i	$-0.523816\pi$
$313$	−2.64490	−0.149499	−0.0747494	+	0.997202i	$0.523816\pi$
$314$	5.26211	0.296958
$315$	3.66693	0.206608
$316$	−7.94777	−0.447097
$317$	21.6517	1.21608	0.608042	−	0.793905i	$-0.291955\pi$
$317$	21.6517	1.21608	0.608042	+	0.793905i	$0.291955\pi$
$318$	1.65120	0.0925945
$319$	−0.0707196	−0.00395954
$320$	1.44966	0.0810382
$321$	0.579917	0.0323678
$322$	8.11388	0.452169
$323$	−10.9310	−0.608216
$324$	4.98703	0.277057
$325$	−18.0291	−1.00007
$326$	−11.7413	−0.650290
$327$	−12.0615	−0.667002
$328$	−5.26102	−0.290491
$329$	3.31714	0.182880
$330$	0.0306427	0.00168682
$331$	8.21795	0.451699	0.225850	−	0.974162i	$-0.427484\pi$
$331$	8.21795	0.451699	0.225850	+	0.974162i	$0.427484\pi$
$332$	−3.11054	−0.170713
$333$	−17.0773	−0.935831
$334$	9.95291	0.544599
$335$	−0.922317	−0.0503916
$336$	−0.685916	−0.0374198
$337$	0.122451	0.00667033	0.00333517	−	0.999994i	$-0.498938\pi$
$337$	0.122451	0.00667033	0.00333517	+	0.999994i	$0.498938\pi$
$338$	−25.6902	−1.39736
$339$	9.01558	0.489659
$340$	−7.95223	−0.431270
$341$	−0.112855	−0.00611145
$342$	5.04049	0.272559
$343$	−1.00000	−0.0539949
$344$	5.40770	0.291564
$345$	8.06798	0.434365
$346$	−15.1987	−0.817086
$347$	15.9204	0.854650	0.427325	−	0.904098i	$-0.359456\pi$
$347$	15.9204	0.854650	0.427325	+	0.904098i	$0.359456\pi$
$348$	1.57405	0.0843782
$349$	−15.4343	−0.826180	−0.413090	−	0.910690i	$-0.635551\pi$
$349$	−15.4343	−0.826180	−0.413090	+	0.910690i	$0.635551\pi$
$350$	−2.89850	−0.154931
$351$	−23.5917	−1.25923
$352$	0.0308170	0.00164255
$353$	−12.2792	−0.653555	−0.326777	−	0.945101i	$-0.605963\pi$
$353$	−12.2792	−0.653555	−0.326777	+	0.945101i	$0.605963\pi$
$354$	−3.11447	−0.165532
$355$	2.27461	0.120724
$356$	9.22104	0.488714
$357$	3.76266	0.199141
$358$	−23.3175	−1.23237
$359$	8.69460	0.458883	0.229442	−	0.973322i	$-0.426310\pi$
$359$	8.69460	0.458883	0.229442	+	0.973322i	$0.426310\pi$
$360$	3.66693	0.193264
$361$	−15.0293	−0.791014
$362$	−10.4772	−0.550672
$363$	−7.54442	−0.395979
$364$	−6.22014	−0.326024
$365$	−12.9627	−0.678501
$366$	4.25572	0.222450
$367$	19.3936	1.01234	0.506169	−	0.862434i	$-0.331061\pi$
$367$	19.3936	1.01234	0.506169	+	0.862434i	$0.331061\pi$
$368$	8.11388	0.422965
$369$	−13.3079	−0.692779
$370$	−9.78693	−0.508798
$371$	2.40729	0.124980
$372$	2.51190	0.130236
$373$	−10.3958	−0.538276	−0.269138	−	0.963102i	$-0.586739\pi$
$373$	−10.3958	−0.538276	−0.269138	+	0.963102i	$0.586739\pi$
$374$	−0.169050	−0.00874136
$375$	−7.85381	−0.405569
$376$	3.31714	0.171068
$377$	14.2741	0.735155
$378$	−3.79278	−0.195080
$379$	12.1040	0.621740	0.310870	−	0.950452i	$-0.399380\pi$
$379$	12.1040	0.621740	0.310870	+	0.950452i	$0.399380\pi$
$380$	2.88868	0.148186
$381$	0.964115	0.0493931
$382$	−10.2549	−0.524687
$383$	−24.9672	−1.27577	−0.637883	−	0.770134i	$-0.720190\pi$
$383$	−24.9672	−1.27577	−0.637883	+	0.770134i	$0.720190\pi$
$384$	−0.685916	−0.0350030
$385$	0.0446741	0.00227680
$386$	−9.26826	−0.471742
$387$	13.6789	0.695337
$388$	18.0193	0.914792
$389$	−7.59387	−0.385025	−0.192512	−	0.981295i	$-0.561664\pi$
$389$	−7.59387	−0.385025	−0.192512	+	0.981295i	$0.561664\pi$
$390$	−6.18495	−0.313187
$391$	−44.5095	−2.25094
$392$	−1.00000	−0.0505076
$393$	9.58336	0.483416
$394$	−10.5984	−0.533942
$395$	−11.5215	−0.579711
$396$	0.0779523	0.00391725
$397$	−27.8996	−1.40024	−0.700120	−	0.714025i	$-0.746870\pi$
$397$	−27.8996	−1.40024	−0.700120	+	0.714025i	$0.746870\pi$
$398$	−19.5234	−0.978618
$399$	−1.36680	−0.0684257
$400$	−2.89850	−0.144925
$401$	−29.8254	−1.48941	−0.744704	−	0.667395i	$-0.767409\pi$
$401$	−29.8254	−1.48941	−0.744704	+	0.667395i	$0.767409\pi$
$402$	0.436401	0.0217657
$403$	22.7788	1.13469
$404$	6.47759	0.322272
$405$	7.22948	0.359236
$406$	2.29482	0.113890
$407$	−0.208052	−0.0103128
$408$	3.76266	0.186279
$409$	−20.0637	−0.992085	−0.496043	−	0.868298i	$-0.665214\pi$
$409$	−20.0637	−0.992085	−0.496043	+	0.868298i	$0.665214\pi$
$410$	−7.62667	−0.376654
$411$	1.45740	0.0718880
$412$	13.5189	0.666028
$413$	−4.54061	−0.223429
$414$	20.5242	1.00871
$415$	−4.50921	−0.221348
$416$	−6.22014	−0.304968
$417$	−8.81076	−0.431465
$418$	0.0614081	0.00300357
$419$	35.1960	1.71944	0.859718	−	0.510769i	$-0.170639\pi$
$419$	35.1960	1.71944	0.859718	+	0.510769i	$0.170639\pi$
$420$	−0.994342	−0.0485189
$421$	−22.9700	−1.11949	−0.559746	−	0.828664i	$-0.689101\pi$
$421$	−22.9700	−1.11949	−0.559746	+	0.828664i	$0.689101\pi$
$422$	−21.5412	−1.04861
$423$	8.39077	0.407973
$424$	2.40729	0.116908
$425$	15.9000	0.771263
$426$	−1.07625	−0.0521445
$427$	6.20443	0.300253
$428$	0.845463	0.0408670
$429$	−0.131481	−0.00634795
$430$	7.83931	0.378045
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−3.79278	−0.182480
$433$	−30.5862	−1.46988	−0.734941	−	0.678131i	$-0.762790\pi$
$433$	−30.5862	−1.46988	−0.734941	+	0.678131i	$0.762790\pi$
$434$	3.66210	0.175787
$435$	2.28184	0.109406
$436$	−17.5845	−0.842145
$437$	16.1683	0.773434
$438$	6.13342	0.293066
$439$	21.7019	1.03578	0.517888	−	0.855448i	$-0.326718\pi$
$439$	21.7019	1.03578	0.517888	+	0.855448i	$0.326718\pi$
$440$	0.0446741	0.00212975
$441$	−2.52952	−0.120453
$442$	34.1212	1.62298
$443$	18.8299	0.894634	0.447317	−	0.894375i	$-0.352380\pi$
$443$	18.8299	0.894634	0.447317	+	0.894375i	$0.352380\pi$
$444$	4.63076	0.219766
$445$	13.3673	0.633672
$446$	16.5991	0.785990
$447$	13.0684	0.618112
$448$	−1.00000	−0.0472456
$449$	14.2002	0.670150	0.335075	−	0.942192i	$-0.391238\pi$
$449$	14.2002	0.670150	0.335075	+	0.942192i	$0.391238\pi$
$450$	−7.33181	−0.345625
$451$	−0.162129	−0.00763436
$452$	13.1439	0.618235
$453$	−10.0919	−0.474161
$454$	−2.51733	−0.118144
$455$	−9.01707	−0.422727
$456$	−1.36680	−0.0640064
$457$	−6.48130	−0.303182	−0.151591	−	0.988443i	$-0.548440\pi$
$457$	−6.48130	−0.303182	−0.151591	+	0.988443i	$0.548440\pi$
$458$	−9.48297	−0.443110
$459$	20.8057	0.971126
$460$	11.7623	0.548422
$461$	−36.2829	−1.68986	−0.844931	−	0.534875i	$-0.820359\pi$
$461$	−36.2829	−1.68986	−0.844931	+	0.534875i	$0.820359\pi$
$462$	−0.0211379	−0.000983424 0
$463$	21.2718	0.988584	0.494292	−	0.869296i	$-0.335427\pi$
$463$	21.2718	0.988584	0.494292	+	0.869296i	$0.335427\pi$
$464$	2.29482	0.106534
$465$	3.64138	0.168865
$466$	−6.67919	−0.309407
$467$	31.3240	1.44950	0.724750	−	0.689012i	$-0.241955\pi$
$467$	31.3240	1.44950	0.724750	+	0.689012i	$0.241955\pi$
$468$	−15.7340	−0.727303
$469$	0.636232	0.0293785
$470$	4.80871	0.221809
$471$	−3.60937	−0.166311
$472$	−4.54061	−0.208998
$473$	0.166649	0.00766254
$474$	5.45150	0.250396
$475$	−5.77574	−0.265009
$476$	5.48560	0.251432
$477$	6.08928	0.278809
$478$	8.65865	0.396038
$479$	13.2576	0.605756	0.302878	−	0.953029i	$-0.402053\pi$
$479$	13.2576	0.605756	0.302878	+	0.953029i	$0.402053\pi$
$480$	−0.994342	−0.0453853
$481$	41.9935	1.91474
$482$	−30.2892	−1.37964
$483$	−5.56544	−0.253236
$484$	−10.9991	−0.499957
$485$	26.1218	1.18613
$486$	−14.7990	−0.671298
$487$	−7.13345	−0.323247	−0.161624	−	0.986852i	$-0.551673\pi$
$487$	−7.13345	−0.323247	−0.161624	+	0.986852i	$0.551673\pi$
$488$	6.20443	0.280861
$489$	8.05354	0.364193
$490$	−1.44966	−0.0654888
$491$	2.55846	0.115462	0.0577309	−	0.998332i	$-0.481613\pi$
$491$	2.55846	0.115462	0.0577309	+	0.998332i	$0.481613\pi$
$492$	3.60862	0.162689
$493$	−12.5885	−0.566956
$494$	−12.3947	−0.557663
$495$	0.113004	0.00507915
$496$	3.66210	0.164433
$497$	−1.56907	−0.0703824
$498$	2.13357	0.0956074
$499$	25.5539	1.14395	0.571974	−	0.820272i	$-0.306178\pi$
$499$	25.5539	1.14395	0.571974	+	0.820272i	$0.306178\pi$
$500$	−11.4501	−0.512064
$501$	−6.82686	−0.305002
$502$	27.4516	1.22522
$503$	−19.9164	−0.888029	−0.444014	−	0.896020i	$-0.646446\pi$
$503$	−19.9164	−0.888029	−0.444014	+	0.896020i	$0.646446\pi$
$504$	−2.52952	−0.112674
$505$	9.39028	0.417862
$506$	0.250046	0.0111159
$507$	17.6213	0.782590
$508$	1.40559	0.0623629
$509$	−25.4468	−1.12791	−0.563955	−	0.825806i	$-0.690721\pi$
$509$	−25.4468	−1.12791	−0.563955	+	0.825806i	$0.690721\pi$
$510$	5.45456	0.241532
$511$	8.94194	0.395568
$512$	−1.00000	−0.0441942
$513$	−7.55776	−0.333683
$514$	17.6464	0.778351
$515$	19.5977	0.863580
$516$	−3.70923	−0.163290
$517$	0.102224	0.00449583
$518$	6.75121	0.296631
$519$	10.4250	0.457607
$520$	−9.01707	−0.395425
$521$	−12.9030	−0.565292	−0.282646	−	0.959224i	$-0.591212\pi$
$521$	−12.9030	−0.565292	−0.282646	+	0.959224i	$0.591212\pi$
$522$	5.80480	0.254069
$523$	2.69005	0.117628	0.0588138	−	0.998269i	$-0.481268\pi$
$523$	2.69005	0.117628	0.0588138	+	0.998269i	$0.481268\pi$
$524$	13.9716	0.610353
$525$	1.98812	0.0867689
$526$	−31.6063	−1.37810
$527$	−20.0888	−0.875083
$528$	−0.0211379	−0.000919909 0
$529$	42.8351	1.86240
$530$	3.48974	0.151585
$531$	−11.4856	−0.498431
$532$	−1.99267	−0.0863931
$533$	32.7243	1.41745
$534$	−6.32486	−0.273703
$535$	1.22563	0.0529887
$536$	0.636232	0.0274810
$537$	15.9939	0.690187
$538$	−8.76947	−0.378079
$539$	−0.0308170	−0.00132738
$540$	−5.49823	−0.236606
$541$	39.4037	1.69410	0.847049	−	0.531514i	$-0.178377\pi$
$541$	39.4037	1.69410	0.847049	+	0.531514i	$0.178377\pi$
$542$	−3.46805	−0.148965
$543$	7.18651	0.308403
$544$	5.48560	0.235193
$545$	−25.4915	−1.09194
$546$	4.26649	0.182589
$547$	−22.0756	−0.943886	−0.471943	−	0.881629i	$-0.656447\pi$
$547$	−22.0756	−0.943886	−0.471943	+	0.881629i	$0.656447\pi$
$548$	2.12475	0.0907646
$549$	15.6942	0.669813
$550$	−0.0893231	−0.00380875
$551$	4.57282	0.194809
$552$	−5.56544	−0.236881
$553$	7.94777	0.337973
$554$	7.15105	0.303819
$555$	6.71301	0.284951
$556$	−12.8453	−0.544760
$557$	41.5496	1.76051	0.880257	−	0.474498i	$-0.157370\pi$
$557$	41.5496	1.76051	0.880257	+	0.474498i	$0.157370\pi$
$558$	9.26337	0.392150
$559$	−33.6367	−1.42268
$560$	−1.44966	−0.0612591
$561$	0.115954	0.00489558
$562$	1.72925	0.0729439
$563$	−0.0444233	−0.00187222	−0.000936109	−	1.00000i	$-0.500298\pi$
$563$	−0.0444233	−0.00187222	−0.000936109		1.00000i	$0.500298\pi$
$564$	−2.27528	−0.0958065
$565$	19.0541	0.801611
$566$	6.18264	0.259876
$567$	−4.98703	−0.209436
$568$	−1.56907	−0.0658367
$569$	5.30329	0.222325	0.111163	−	0.993802i	$-0.464543\pi$
$569$	5.30329	0.222325	0.111163	+	0.993802i	$0.464543\pi$
$570$	−1.98139	−0.0829915
$571$	4.51455	0.188928	0.0944641	−	0.995528i	$-0.469886\pi$
$571$	4.51455	0.188928	0.0944641	+	0.995528i	$0.469886\pi$
$572$	−0.191686	−0.00801481
$573$	7.03401	0.293850
$574$	5.26102	0.219591
$575$	−23.5181	−0.980771
$576$	−2.52952	−0.105397
$577$	−44.9834	−1.87268	−0.936341	−	0.351092i	$-0.885810\pi$
$577$	−44.9834	−1.87268	−0.936341	+	0.351092i	$0.885810\pi$
$578$	−13.0918	−0.544546
$579$	6.35725	0.264198
$580$	3.32670	0.138134
$581$	3.11054	0.129047
$582$	−12.3597	−0.512327
$583$	0.0741855	0.00307245
$584$	8.94194	0.370020
$585$	−22.8089	−0.943030
$586$	12.7021	0.524718
$587$	25.7132	1.06130	0.530649	−	0.847592i	$-0.321948\pi$
$587$	25.7132	1.06130	0.530649	+	0.847592i	$0.321948\pi$
$588$	0.685916	0.0282867
$589$	7.29736	0.300683
$590$	−6.58232	−0.270990
$591$	7.26964	0.299033
$592$	6.75121	0.277473
$593$	16.9784	0.697220	0.348610	−	0.937268i	$-0.386654\pi$
$593$	16.9784	0.697220	0.348610	+	0.937268i	$0.386654\pi$
$594$	−0.116882	−0.00479574
$595$	7.95223	0.326010
$596$	19.0524	0.780418
$597$	13.3914	0.548073
$598$	−50.4695	−2.06385
$599$	4.67359	0.190958	0.0954789	−	0.995431i	$-0.469562\pi$
$599$	4.67359	0.190958	0.0954789	+	0.995431i	$0.469562\pi$
$600$	1.98812	0.0811649
$601$	−28.1126	−1.14674	−0.573368	−	0.819298i	$-0.694363\pi$
$601$	−28.1126	−1.14674	−0.573368	+	0.819298i	$0.694363\pi$
$602$	−5.40770	−0.220401
$603$	1.60936	0.0655383
$604$	−14.7131	−0.598667
$605$	−15.9448	−0.648250
$606$	−4.44308	−0.180488
$607$	16.3675	0.664335	0.332168	−	0.943220i	$-0.392220\pi$
$607$	16.3675	0.664335	0.332168	+	0.943220i	$0.392220\pi$
$608$	−1.99267	−0.0808134
$609$	−1.57405	−0.0637839
$610$	8.99429	0.364168
$611$	−20.6331	−0.834725
$612$	13.8759	0.560901
$613$	24.0957	0.973218	0.486609	−	0.873620i	$-0.338234\pi$
$613$	24.0957	0.973218	0.486609	+	0.873620i	$0.338234\pi$
$614$	−11.3220	−0.456919
$615$	5.23125	0.210944
$616$	−0.0308170	−0.00124165
$617$	20.1151	0.809802	0.404901	−	0.914361i	$-0.367306\pi$
$617$	20.1151	0.809802	0.404901	+	0.914361i	$0.367306\pi$
$618$	−9.27282	−0.373008
$619$	15.6598	0.629419	0.314709	−	0.949188i	$-0.398093\pi$
$619$	15.6598	0.629419	0.314709	+	0.949188i	$0.398093\pi$
$620$	5.30879	0.213206
$621$	−30.7742	−1.23493
$622$	27.8624	1.11718
$623$	−9.22104	−0.369433
$624$	4.26649	0.170796
$625$	−2.10623	−0.0842490
$626$	2.64490	0.105712
$627$	−0.0421208	−0.00168214
$628$	−5.26211	−0.209981
$629$	−37.0344	−1.47666
$630$	−3.66693	−0.146094
$631$	−6.11162	−0.243300	−0.121650	−	0.992573i	$-0.538818\pi$
$631$	−6.11162	−0.243300	−0.121650	+	0.992573i	$0.538818\pi$
$632$	7.94777	0.316145
$633$	14.7754	0.587271
$634$	−21.6517	−0.859901
$635$	2.03762	0.0808604
$636$	−1.65120	−0.0654742
$637$	6.22014	0.246451
$638$	0.0707196	0.00279982
$639$	−3.96899	−0.157011
$640$	−1.44966	−0.0573027
$641$	12.6500	0.499645	0.249823	−	0.968292i	$-0.419628\pi$
$641$	12.6500	0.499645	0.249823	+	0.968292i	$0.419628\pi$
$642$	−0.579917	−0.0228875
$643$	31.2782	1.23349	0.616747	−	0.787162i	$-0.288450\pi$
$643$	31.2782	1.23349	0.616747	+	0.787162i	$0.288450\pi$
$644$	−8.11388	−0.319732
$645$	−5.37710	−0.211723
$646$	10.9310	0.430074
$647$	29.2020	1.14805	0.574024	−	0.818839i	$-0.305382\pi$
$647$	29.2020	1.14805	0.574024	+	0.818839i	$0.305382\pi$
$648$	−4.98703	−0.195909
$649$	−0.139928	−0.00549266
$650$	18.0291	0.707158
$651$	−2.51190	−0.0984489
$652$	11.7413	0.459824
$653$	−8.40767	−0.329018	−0.164509	−	0.986376i	$-0.552604\pi$
$653$	−8.40767	−0.329018	−0.164509	+	0.986376i	$0.552604\pi$
$654$	12.0615	0.471641
$655$	20.2541	0.791391
$656$	5.26102	0.205408
$657$	22.6188	0.882444
$658$	−3.31714	−0.129316
$659$	6.67436	0.259996	0.129998	−	0.991514i	$-0.458503\pi$
$659$	6.67436	0.259996	0.129998	+	0.991514i	$0.458503\pi$
$660$	−0.0306427	−0.00119276
$661$	−10.8115	−0.420520	−0.210260	−	0.977646i	$-0.567431\pi$
$661$	−10.8115	−0.420520	−0.210260	+	0.977646i	$0.567431\pi$
$662$	−8.21795	−0.319400
$663$	−23.4043	−0.908947
$664$	3.11054	0.120712
$665$	−2.88868	−0.112018
$666$	17.0773	0.661732
$667$	18.6199	0.720966
$668$	−9.95291	−0.385090
$669$	−11.3856	−0.440192
$670$	0.922317	0.0356322
$671$	0.191202	0.00738128
$672$	0.685916	0.0264598
$673$	−21.6068	−0.832880	−0.416440	−	0.909163i	$-0.636722\pi$
$673$	−21.6068	−0.832880	−0.416440	+	0.909163i	$0.636722\pi$
$674$	−0.122451	−0.00471664
$675$	10.9934	0.423135
$676$	25.6902	0.988084
$677$	29.8146	1.14587	0.572934	−	0.819602i	$-0.305805\pi$
$677$	29.8146	1.14587	0.572934	+	0.819602i	$0.305805\pi$
$678$	−9.01558	−0.346241
$679$	−18.0193	−0.691518
$680$	7.95223	0.304954
$681$	1.72667	0.0661663
$682$	0.112855	0.00432145
$683$	−3.13287	−0.119876	−0.0599380	−	0.998202i	$-0.519090\pi$
$683$	−3.13287	−0.119876	−0.0599380	+	0.998202i	$0.519090\pi$
$684$	−5.04049	−0.192728
$685$	3.08015	0.117686
$686$	1.00000	0.0381802
$687$	6.50452	0.248163
$688$	−5.40770	−0.206167
$689$	−14.9737	−0.570451
$690$	−8.06798	−0.307143
$691$	17.5682	0.668324	0.334162	−	0.942516i	$-0.391547\pi$
$691$	17.5682	0.668324	0.334162	+	0.942516i	$0.391547\pi$
$692$	15.1987	0.577767
$693$	−0.0779523	−0.00296116
$694$	−15.9204	−0.604329
$695$	−18.6212	−0.706342
$696$	−1.57405	−0.0596644
$697$	−28.8598	−1.09314
$698$	15.4343	0.584198
$699$	4.58136	0.173283
$700$	2.89850	0.109553
$701$	16.6710	0.629654	0.314827	−	0.949149i	$-0.398053\pi$
$701$	16.6710	0.629654	0.314827	+	0.949149i	$0.398053\pi$
$702$	23.5917	0.890410
$703$	13.4529	0.507386
$704$	−0.0308170	−0.00116146
$705$	−3.29837	−0.124224
$706$	12.2792	0.462133
$707$	−6.47759	−0.243615
$708$	3.11447	0.117049
$709$	−3.03723	−0.114065	−0.0570327	−	0.998372i	$-0.518164\pi$
$709$	−3.03723	−0.114065	−0.0570327	+	0.998372i	$0.518164\pi$
$710$	−2.27461	−0.0853647
$711$	20.1040	0.753960
$712$	−9.22104	−0.345573
$713$	29.7139	1.11279
$714$	−3.76266	−0.140814
$715$	−0.277879	−0.0103921
$716$	23.3175	0.871418
$717$	−5.93911	−0.221800
$718$	−8.69460	−0.324480
$719$	38.2013	1.42467	0.712333	−	0.701841i	$-0.247638\pi$
$719$	38.2013	1.42467	0.712333	+	0.701841i	$0.247638\pi$
$720$	−3.66693	−0.136659
$721$	−13.5189	−0.503470
$722$	15.0293	0.559332
$723$	20.7758	0.772662
$724$	10.4772	0.389384
$725$	−6.65153	−0.247032
$726$	7.54442	0.280000
$727$	−11.0846	−0.411104	−0.205552	−	0.978646i	$-0.565899\pi$
$727$	−11.0846	−0.411104	−0.205552	+	0.978646i	$0.565899\pi$
$728$	6.22014	0.230534
$729$	−4.81019	−0.178155
$730$	12.9627	0.479773
$731$	29.6645	1.09718
$732$	−4.25572	−0.157296
$733$	−4.23493	−0.156421	−0.0782103	−	0.996937i	$-0.524921\pi$
$733$	−4.23493	−0.156421	−0.0782103	+	0.996937i	$0.524921\pi$
$734$	−19.3936	−0.715831
$735$	0.994342	0.0366769
$736$	−8.11388	−0.299082
$737$	0.0196068	0.000722225 0
$738$	13.3079	0.489869
$739$	−31.7481	−1.16787	−0.583937	−	0.811799i	$-0.698489\pi$
$739$	−31.7481	−1.16787	−0.583937	+	0.811799i	$0.698489\pi$
$740$	9.78693	0.359775
$741$	8.50171	0.312318
$742$	−2.40729	−0.0883743
$743$	−28.5024	−1.04565	−0.522826	−	0.852439i	$-0.675122\pi$
$743$	−28.5024	−1.04565	−0.522826	+	0.852439i	$0.675122\pi$
$744$	−2.51190	−0.0920905
$745$	27.6195	1.01190
$746$	10.3958	0.380618
$747$	7.86817	0.287881
$748$	0.169050	0.00618108
$749$	−0.845463	−0.0308926
$750$	7.85381	0.286780
$751$	−48.3090	−1.76282	−0.881411	−	0.472351i	$-0.843406\pi$
$751$	−48.3090	−1.76282	−0.881411	+	0.472351i	$0.843406\pi$
$752$	−3.31714	−0.120964
$753$	−18.8295	−0.686183
$754$	−14.2741	−0.519833
$755$	−21.3289	−0.776239
$756$	3.79278	0.137942
$757$	−12.3826	−0.450053	−0.225027	−	0.974353i	$-0.572247\pi$
$757$	−12.3826	−0.450053	−0.225027	+	0.974353i	$0.572247\pi$
$758$	−12.1040	−0.439637
$759$	−0.171510	−0.00622543
$760$	−2.88868	−0.104784
$761$	−5.64665	−0.204691	−0.102345	−	0.994749i	$-0.532635\pi$
$761$	−5.64665	−0.204691	−0.102345	+	0.994749i	$0.532635\pi$
$762$	−0.964115	−0.0349262
$763$	17.5845	0.636602
$764$	10.2549	0.371010
$765$	20.1153	0.727271
$766$	24.9672	0.902102
$767$	28.2432	1.01980
$768$	0.685916	0.0247509
$769$	14.5728	0.525510	0.262755	−	0.964863i	$-0.415369\pi$
$769$	14.5728	0.525510	0.262755	+	0.964863i	$0.415369\pi$
$770$	−0.0446741	−0.00160994
$771$	−12.1040	−0.435914
$772$	9.26826	0.333572
$773$	4.71945	0.169747	0.0848734	−	0.996392i	$-0.472951\pi$
$773$	4.71945	0.169747	0.0848734	+	0.996392i	$0.472951\pi$
$774$	−13.6789	−0.491677
$775$	−10.6146	−0.381288
$776$	−18.0193	−0.646855
$777$	−4.63076	−0.166128
$778$	7.59387	0.272253
$779$	10.4835	0.375609
$780$	6.18495	0.221457
$781$	−0.0483541	−0.00173025
$782$	44.5095	1.59166
$783$	−8.70376	−0.311047
$784$	1.00000	0.0357143
$785$	−7.62825	−0.272264
$786$	−9.58336	−0.341827
$787$	−27.2083	−0.969871	−0.484935	−	0.874550i	$-0.661157\pi$
$787$	−27.2083	−0.969871	−0.484935	+	0.874550i	$0.661157\pi$
$788$	10.5984	0.377554
$789$	21.6793	0.771803
$790$	11.5215	0.409918
$791$	−13.1439	−0.467342
$792$	−0.0779523	−0.00276991
$793$	−38.5924	−1.37046
$794$	27.8996	0.990119
$795$	−2.39367	−0.0848946
$796$	19.5234	0.691987
$797$	32.0017	1.13356	0.566779	−	0.823870i	$-0.308189\pi$
$797$	32.0017	1.13356	0.566779	+	0.823870i	$0.308189\pi$
$798$	1.36680	0.0483843
$799$	18.1965	0.643746
$800$	2.89850	0.102477
$801$	−23.3248	−0.824141
$802$	29.8254	1.05317
$803$	0.275564	0.00972445
$804$	−0.436401	−0.0153907
$805$	−11.7623	−0.414568
$806$	−22.7788	−0.802350
$807$	6.01512	0.211742
$808$	−6.47759	−0.227881
$809$	−19.2720	−0.677568	−0.338784	−	0.940864i	$-0.610016\pi$
$809$	−19.2720	−0.677568	−0.338784	+	0.940864i	$0.610016\pi$
$810$	−7.22948	−0.254018
$811$	32.7314	1.14935	0.574677	−	0.818380i	$-0.305128\pi$
$811$	32.7314	1.14935	0.574677	+	0.818380i	$0.305128\pi$
$812$	−2.29482	−0.0805325
$813$	2.37879	0.0834278
$814$	0.208052	0.00729223
$815$	17.0208	0.596214
$816$	−3.76266	−0.131719
$817$	−10.7758	−0.376996
$818$	20.0637	0.701510
$819$	15.7340	0.549790
$820$	7.62667	0.266335
$821$	18.9537	0.661488	0.330744	−	0.943721i	$-0.392700\pi$
$821$	18.9537	0.661488	0.330744	+	0.943721i	$0.392700\pi$
$822$	−1.45740	−0.0508325
$823$	14.1095	0.491827	0.245914	−	0.969292i	$-0.420912\pi$
$823$	14.1095	0.491827	0.245914	+	0.969292i	$0.420912\pi$
$824$	−13.5189	−0.470953
$825$	0.0612681	0.00213308
$826$	4.54061	0.157988
$827$	−50.3314	−1.75020	−0.875098	−	0.483946i	$-0.839203\pi$
$827$	−50.3314	−1.75020	−0.875098	+	0.483946i	$0.839203\pi$
$828$	−20.5242	−0.713266
$829$	31.8882	1.10752	0.553762	−	0.832675i	$-0.313192\pi$
$829$	31.8882	1.10752	0.553762	+	0.832675i	$0.313192\pi$
$830$	4.50921	0.156517
$831$	−4.90502	−0.170153
$832$	6.22014	0.215645
$833$	−5.48560	−0.190065
$834$	8.81076	0.305092
$835$	−14.4283	−0.499312
$836$	−0.0614081	−0.00212385
$837$	−13.8896	−0.480094
$838$	−35.1960	−1.21582
$839$	27.8915	0.962921	0.481460	−	0.876468i	$-0.340107\pi$
$839$	27.8915	0.962921	0.481460	+	0.876468i	$0.340107\pi$
$840$	0.994342	0.0343081
$841$	−23.7338	−0.818407
$842$	22.9700	0.791600
$843$	−1.18612	−0.0408521
$844$	21.5412	0.741478
$845$	37.2419	1.28116
$846$	−8.39077	−0.288481
$847$	10.9991	0.377932
$848$	−2.40729	−0.0826666
$849$	−4.24077	−0.145543
$850$	−15.9000	−0.545365
$851$	54.7785	1.87778
$852$	1.07625	0.0368717
$853$	−1.47676	−0.0505634	−0.0252817	−	0.999680i	$-0.508048\pi$
$853$	−1.47676	−0.0505634	−0.0252817	+	0.999680i	$0.508048\pi$
$854$	−6.20443	−0.212311
$855$	−7.30698	−0.249894
$856$	−0.845463	−0.0288973
$857$	51.1010	1.74558	0.872788	−	0.488100i	$-0.162310\pi$
$857$	51.1010	1.74558	0.872788	+	0.488100i	$0.162310\pi$
$858$	0.131481	0.00448868
$859$	36.8114	1.25599	0.627994	−	0.778218i	$-0.283876\pi$
$859$	36.8114	1.25599	0.627994	+	0.778218i	$0.283876\pi$
$860$	−7.83931	−0.267318
$861$	−3.60862	−0.122981
$862$	−1.00000	−0.0340601
$863$	−10.8980	−0.370971	−0.185486	−	0.982647i	$-0.559386\pi$
$863$	−10.8980	−0.370971	−0.185486	+	0.982647i	$0.559386\pi$
$864$	3.79278	0.129033
$865$	22.0328	0.749139
$866$	30.5862	1.03936
$867$	8.97986	0.304972
$868$	−3.66210	−0.124300
$869$	0.244927	0.00830857
$870$	−2.28184	−0.0773615
$871$	−3.95745	−0.134093
$872$	17.5845	0.595486
$873$	−45.5802	−1.54266
$874$	−16.1683	−0.546900
$875$	11.4501	0.387084
$876$	−6.13342	−0.207229
$877$	−21.8750	−0.738666	−0.369333	−	0.929297i	$-0.620414\pi$
$877$	−21.8750	−0.738666	−0.369333	+	0.929297i	$0.620414\pi$
$878$	−21.7019	−0.732405
$879$	−8.71255	−0.293867
$880$	−0.0446741	−0.00150596
$881$	−39.1598	−1.31933	−0.659663	−	0.751561i	$-0.729301\pi$
$881$	−39.1598	−1.31933	−0.659663	+	0.751561i	$0.729301\pi$
$882$	2.52952	0.0851734
$883$	24.2995	0.817742	0.408871	−	0.912592i	$-0.365923\pi$
$883$	24.2995	0.817742	0.408871	+	0.912592i	$0.365923\pi$
$884$	−34.1212	−1.14762
$885$	4.51491	0.151767
$886$	−18.8299	−0.632602
$887$	36.8751	1.23814	0.619072	−	0.785334i	$-0.287509\pi$
$887$	36.8751	1.23814	0.619072	+	0.785334i	$0.287509\pi$
$888$	−4.63076	−0.155398
$889$	−1.40559	−0.0471419
$890$	−13.3673	−0.448074
$891$	−0.153685	−0.00514866
$892$	−16.5991	−0.555779
$893$	−6.60996	−0.221194
$894$	−13.0684	−0.437071
$895$	33.8024	1.12989
$896$	1.00000	0.0334077
$897$	34.6178	1.15586
$898$	−14.2002	−0.473867
$899$	8.40388	0.280285
$900$	7.33181	0.244394
$901$	13.2054	0.439936
$902$	0.162129	0.00539831
$903$	3.70923	0.123435
$904$	−13.1439	−0.437158
$905$	15.1884	0.504880
$906$	10.0919	0.335282
$907$	10.8381	0.359874	0.179937	−	0.983678i	$-0.442411\pi$
$907$	10.8381	0.359874	0.179937	+	0.983678i	$0.442411\pi$
$908$	2.51733	0.0835404
$909$	−16.3852	−0.543463
$910$	9.01707	0.298913
$911$	−27.6501	−0.916087	−0.458044	−	0.888930i	$-0.651450\pi$
$911$	−27.6501	−0.916087	−0.458044	+	0.888930i	$0.651450\pi$
$912$	1.36680	0.0452594
$913$	0.0958576	0.00317242
$914$	6.48130	0.214382
$915$	−6.16932	−0.203952
$916$	9.48297	0.313326
$917$	−13.9716	−0.461384
$918$	−20.8057	−0.686690
$919$	20.4983	0.676177	0.338088	−	0.941114i	$-0.390220\pi$
$919$	20.4983	0.676177	0.338088	+	0.941114i	$0.390220\pi$
$920$	−11.7623	−0.387793
$921$	7.76594	0.255896
$922$	36.2829	1.19491
$923$	9.75984	0.321249
$924$	0.0211379	0.000695386 0
$925$	−19.5684	−0.643404
$926$	−21.2718	−0.699035
$927$	−34.1963	−1.12315
$928$	−2.29482	−0.0753312
$929$	12.9612	0.425243	0.212621	−	0.977135i	$-0.431800\pi$
$929$	12.9612	0.425243	0.212621	+	0.977135i	$0.431800\pi$
$930$	−3.64138	−0.119406
$931$	1.99267	0.0653071
$932$	6.67919	0.218784
$933$	−19.1113	−0.625675
$934$	−31.3240	−1.02495
$935$	0.245064	0.00801445
$936$	15.7340	0.514281
$937$	−33.4423	−1.09251	−0.546256	−	0.837618i	$-0.683947\pi$
$937$	−33.4423	−1.09251	−0.546256	+	0.837618i	$0.683947\pi$
$938$	−0.636232	−0.0207737
$939$	−1.81418	−0.0592035
$940$	−4.80871	−0.156843
$941$	−11.1379	−0.363084	−0.181542	−	0.983383i	$-0.558109\pi$
$941$	−11.1379	−0.363084	−0.181542	+	0.983383i	$0.558109\pi$
$942$	3.60937	0.117600
$943$	42.6873	1.39009
$944$	4.54061	0.147784
$945$	5.49823	0.178858
$946$	−0.166649	−0.00541824
$947$	−34.2659	−1.11349	−0.556745	−	0.830683i	$-0.687950\pi$
$947$	−34.2659	−1.11349	−0.556745	+	0.830683i	$0.687950\pi$
$948$	−5.45150	−0.177056
$949$	−55.6202	−1.80551
$950$	5.77574	0.187390
$951$	14.8513	0.481585
$952$	−5.48560	−0.177789
$953$	37.6925	1.22098	0.610490	−	0.792024i	$-0.290973\pi$
$953$	37.6925	1.22098	0.610490	+	0.792024i	$0.290973\pi$
$954$	−6.08928	−0.197148
$955$	14.8661	0.481056
$956$	−8.65865	−0.280041
$957$	−0.0485077	−0.00156803
$958$	−13.2576	−0.428334
$959$	−2.12475	−0.0686116
$960$	0.994342	0.0320922
$961$	−17.5890	−0.567387
$962$	−41.9935	−1.35392
$963$	−2.13862	−0.0689159
$964$	30.2892	0.975549
$965$	13.4358	0.432513
$966$	5.56544	0.179065
$967$	−24.3424	−0.782798	−0.391399	−	0.920221i	$-0.628009\pi$
$967$	−24.3424	−0.782798	−0.391399	+	0.920221i	$0.628009\pi$
$968$	10.9991	0.353523
$969$	−7.49773	−0.240862
$970$	−26.1218	−0.838720
$971$	−44.0029	−1.41212	−0.706061	−	0.708151i	$-0.749529\pi$
$971$	−44.0029	−1.41212	−0.706061	+	0.708151i	$0.749529\pi$
$972$	14.7990	0.474679
$973$	12.8453	0.411800
$974$	7.13345	0.228570
$975$	−12.3664	−0.396042
$976$	−6.20443	−0.198599
$977$	−7.29605	−0.233421	−0.116711	−	0.993166i	$-0.537235\pi$
$977$	−7.29605	−0.233421	−0.116711	+	0.993166i	$0.537235\pi$
$978$	−8.05354	−0.257524
$979$	−0.284165	−0.00908196
$980$	1.44966	0.0463076
$981$	44.4803	1.42015
$982$	−2.55846	−0.0816438
$983$	−33.3403	−1.06339	−0.531695	−	0.846936i	$-0.678445\pi$
$983$	−33.3403	−1.06339	−0.531695	+	0.846936i	$0.678445\pi$
$984$	−3.60862	−0.115038
$985$	15.3641	0.489541
$986$	12.5885	0.400898
$987$	2.27528	0.0724229
$988$	12.3947	0.394327
$989$	−43.8775	−1.39522
$990$	−0.113004	−0.00359150
$991$	18.3156	0.581815	0.290907	−	0.956751i	$-0.406043\pi$
$991$	18.3156	0.581815	0.290907	+	0.956751i	$0.406043\pi$
$992$	−3.66210	−0.116272
$993$	5.63682	0.178879
$994$	1.56907	0.0497679
$995$	28.3022	0.897239
$996$	−2.13357	−0.0676046
$997$	−42.8296	−1.35643	−0.678214	−	0.734864i	$-0.737246\pi$
$997$	−42.8296	−1.35643	−0.678214	+	0.734864i	$0.737246\pi$
$998$	−25.5539	−0.808894
$999$	−25.6059	−0.810134

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.n.1.14	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.n.1.14	✓	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.685916 q^{3} +1.00000 q^{4} +1.44966 q^{5} -0.685916 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.52952 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.685916 q^{3} +1.00000 q^{4} +1.44966 q^{5} -0.685916 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.52952 q^{9} -1.44966 q^{10} -0.0308170 q^{11} +0.685916 q^{12} +6.22014 q^{13} +1.00000 q^{14} +0.994342 q^{15} +1.00000 q^{16} -5.48560 q^{17} +2.52952 q^{18} +1.99267 q^{19} +1.44966 q^{20} -0.685916 q^{21} +0.0308170 q^{22} +8.11388 q^{23} -0.685916 q^{24} -2.89850 q^{25} -6.22014 q^{26} -3.79278 q^{27} -1.00000 q^{28} +2.29482 q^{29} -0.994342 q^{30} +3.66210 q^{31} -1.00000 q^{32} -0.0211379 q^{33} +5.48560 q^{34} -1.44966 q^{35} -2.52952 q^{36} +6.75121 q^{37} -1.99267 q^{38} +4.26649 q^{39} -1.44966 q^{40} +5.26102 q^{41} +0.685916 q^{42} -5.40770 q^{43} -0.0308170 q^{44} -3.66693 q^{45} -8.11388 q^{46} -3.31714 q^{47} +0.685916 q^{48} +1.00000 q^{49} +2.89850 q^{50} -3.76266 q^{51} +6.22014 q^{52} -2.40729 q^{53} +3.79278 q^{54} -0.0446741 q^{55} +1.00000 q^{56} +1.36680 q^{57} -2.29482 q^{58} +4.54061 q^{59} +0.994342 q^{60} -6.20443 q^{61} -3.66210 q^{62} +2.52952 q^{63} +1.00000 q^{64} +9.01707 q^{65} +0.0211379 q^{66} -0.636232 q^{67} -5.48560 q^{68} +5.56544 q^{69} +1.44966 q^{70} +1.56907 q^{71} +2.52952 q^{72} -8.94194 q^{73} -6.75121 q^{74} -1.98812 q^{75} +1.99267 q^{76} +0.0308170 q^{77} -4.26649 q^{78} -7.94777 q^{79} +1.44966 q^{80} +4.98703 q^{81} -5.26102 q^{82} -3.11054 q^{83} -0.685916 q^{84} -7.95223 q^{85} +5.40770 q^{86} +1.57405 q^{87} +0.0308170 q^{88} +9.22104 q^{89} +3.66693 q^{90} -6.22014 q^{91} +8.11388 q^{92} +2.51190 q^{93} +3.31714 q^{94} +2.88868 q^{95} -0.685916 q^{96} +18.0193 q^{97} -1.00000 q^{98} +0.0779523 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9} - 8 q^{10} + 15 q^{11} + 7 q^{12} - 7 q^{13} + 24 q^{14} + 13 q^{15} + 24 q^{16} - 5 q^{17} - 19 q^{18} + 6 q^{19} + 8 q^{20} - 7 q^{21} - 15 q^{22} + 3 q^{23} - 7 q^{24} + 12 q^{25} + 7 q^{26} + 22 q^{27} - 24 q^{28} + 5 q^{29} - 13 q^{30} + 13 q^{31} - 24 q^{32} - 8 q^{33} + 5 q^{34} - 8 q^{35} + 19 q^{36} + 2 q^{37} - 6 q^{38} + 7 q^{39} - 8 q^{40} + 25 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 41 q^{45} - 3 q^{46} + 35 q^{47} + 7 q^{48} + 24 q^{49} - 12 q^{50} + 31 q^{51} - 7 q^{52} + 2 q^{53} - 22 q^{54} + 14 q^{55} + 24 q^{56} - 13 q^{57} - 5 q^{58} + 35 q^{59} + 13 q^{60} - 7 q^{61} - 13 q^{62} - 19 q^{63} + 24 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} - 5 q^{68} + 6 q^{69} + 8 q^{70} + 58 q^{71} - 19 q^{72} + 9 q^{73} - 2 q^{74} + 7 q^{75} + 6 q^{76} - 15 q^{77} - 7 q^{78} + 31 q^{79} + 8 q^{80} + 16 q^{81} - 25 q^{82} - q^{83} - 7 q^{84} - 4 q^{85} + 15 q^{86} + 30 q^{87} - 15 q^{88} + 45 q^{89} - 41 q^{90} + 7 q^{91} + 3 q^{92} + 25 q^{93} - 35 q^{94} - 10 q^{95} - 7 q^{96} - 9 q^{97} - 24 q^{98} + 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9 - 8 * q^10 + 15 * q^11 + 7 * q^12 - 7 * q^13 + 24 * q^14 + 13 * q^15 + 24 * q^16 - 5 * q^17 - 19 * q^18 + 6 * q^19 + 8 * q^20 - 7 * q^21 - 15 * q^22 + 3 * q^23 - 7 * q^24 + 12 * q^25 + 7 * q^26 + 22 * q^27 - 24 * q^28 + 5 * q^29 - 13 * q^30 + 13 * q^31 - 24 * q^32 - 8 * q^33 + 5 * q^34 - 8 * q^35 + 19 * q^36 + 2 * q^37 - 6 * q^38 + 7 * q^39 - 8 * q^40 + 25 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 41 * q^45 - 3 * q^46 + 35 * q^47 + 7 * q^48 + 24 * q^49 - 12 * q^50 + 31 * q^51 - 7 * q^52 + 2 * q^53 - 22 * q^54 + 14 * q^55 + 24 * q^56 - 13 * q^57 - 5 * q^58 + 35 * q^59 + 13 * q^60 - 7 * q^61 - 13 * q^62 - 19 * q^63 + 24 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 - 5 * q^68 + 6 * q^69 + 8 * q^70 + 58 * q^71 - 19 * q^72 + 9 * q^73 - 2 * q^74 + 7 * q^75 + 6 * q^76 - 15 * q^77 - 7 * q^78 + 31 * q^79 + 8 * q^80 + 16 * q^81 - 25 * q^82 - q^83 - 7 * q^84 - 4 * q^85 + 15 * q^86 + 30 * q^87 - 15 * q^88 + 45 * q^89 - 41 * q^90 + 7 * q^91 + 3 * q^92 + 25 * q^93 - 35 * q^94 - 10 * q^95 - 7 * q^96 - 9 * q^97 - 24 * q^98 + 64 * q^99

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