LMFDB - Embedded newform 3009.2.a.f.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3009,2,Mod(1,3009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3009, 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("3009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3009 = 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3009.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:	$24.0269859682$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 13 x^{14} + 65 x^{13} + 49 x^{12} - 403 x^{11} + 11 x^{10} + 1205 x^{9} - 452 x^{8} + \cdots - 4 $ x^16 - 4x^15 - 13x^14 + 65x^13 + 49x^12 - 403x^11 + 11x^10 + 1205x^9 - 452x^8 - 1783x^7 + 946x^6 + 1190x^5 - 645x^4 - 299x^3 + 119x^2 + 16*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$0.156223$ of defining polynomial
Character	$\chi$	$=$	3009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.156223 q^{2} -1.00000 q^{3} -1.97559 q^{4} -3.39057 q^{5} +0.156223 q^{6} -3.12691 q^{7} +0.621081 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.156223 q^{2} -1.00000 q^{3} -1.97559 q^{4} -3.39057 q^{5} +0.156223 q^{6} -3.12691 q^{7} +0.621081 q^{8} +1.00000 q^{9} +0.529687 q^{10} -2.52294 q^{11} +1.97559 q^{12} +4.22206 q^{13} +0.488496 q^{14} +3.39057 q^{15} +3.85416 q^{16} +1.00000 q^{17} -0.156223 q^{18} -7.16487 q^{19} +6.69840 q^{20} +3.12691 q^{21} +0.394141 q^{22} +2.70660 q^{23} -0.621081 q^{24} +6.49600 q^{25} -0.659584 q^{26} -1.00000 q^{27} +6.17750 q^{28} +8.94262 q^{29} -0.529687 q^{30} +6.87833 q^{31} -1.84427 q^{32} +2.52294 q^{33} -0.156223 q^{34} +10.6020 q^{35} -1.97559 q^{36} +10.1998 q^{37} +1.11932 q^{38} -4.22206 q^{39} -2.10582 q^{40} -3.13030 q^{41} -0.488496 q^{42} -10.9421 q^{43} +4.98430 q^{44} -3.39057 q^{45} -0.422835 q^{46} -9.56930 q^{47} -3.85416 q^{48} +2.77756 q^{49} -1.01483 q^{50} -1.00000 q^{51} -8.34107 q^{52} +4.20732 q^{53} +0.156223 q^{54} +8.55420 q^{55} -1.94206 q^{56} +7.16487 q^{57} -1.39705 q^{58} +1.00000 q^{59} -6.69840 q^{60} +9.20001 q^{61} -1.07456 q^{62} -3.12691 q^{63} -7.42020 q^{64} -14.3152 q^{65} -0.394141 q^{66} -3.39855 q^{67} -1.97559 q^{68} -2.70660 q^{69} -1.65628 q^{70} -10.5701 q^{71} +0.621081 q^{72} +6.33628 q^{73} -1.59345 q^{74} -6.49600 q^{75} +14.1549 q^{76} +7.88899 q^{77} +0.659584 q^{78} +12.6029 q^{79} -13.0678 q^{80} +1.00000 q^{81} +0.489026 q^{82} +1.74375 q^{83} -6.17750 q^{84} -3.39057 q^{85} +1.70941 q^{86} -8.94262 q^{87} -1.56695 q^{88} -5.36888 q^{89} +0.529687 q^{90} -13.2020 q^{91} -5.34715 q^{92} -6.87833 q^{93} +1.49495 q^{94} +24.2930 q^{95} +1.84427 q^{96} -1.28981 q^{97} -0.433920 q^{98} -2.52294 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 16 q^{3} + 10 q^{4} - 3 q^{5} + 4 q^{6} - 3 q^{7} - 9 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 16 * q^3 + 10 * q^4 - 3 * q^5 + 4 * q^6 - 3 * q^7 - 9 * q^8 + 16 * q^9	\( 16 q - 4 q^{2} - 16 q^{3} + 10 q^{4} - 3 q^{5} + 4 q^{6} - 3 q^{7} - 9 q^{8} + 16 q^{9} - 7 q^{11} - 10 q^{12} + 7 q^{13} - 13 q^{14} + 3 q^{15} + 2 q^{16} + 16 q^{17} - 4 q^{18} - 19 q^{19} - 17 q^{20} + 3 q^{21} + 23 q^{22} - 16 q^{23} + 9 q^{24} + 5 q^{25} - 11 q^{26} - 16 q^{27} + 8 q^{28} + 4 q^{29} - 15 q^{31} - 22 q^{32} + 7 q^{33} - 4 q^{34} - 23 q^{35} + 10 q^{36} + 20 q^{37} - 17 q^{38} - 7 q^{39} + 21 q^{40} - 4 q^{41} + 13 q^{42} - 12 q^{43} - 19 q^{44} - 3 q^{45} + 24 q^{46} - 36 q^{47} - 2 q^{48} - 11 q^{49} + 9 q^{50} - 16 q^{51} + 6 q^{52} - 32 q^{53} + 4 q^{54} - 29 q^{55} - 11 q^{56} + 19 q^{57} - 33 q^{58} + 16 q^{59} + 17 q^{60} + 11 q^{62} - 3 q^{63} + 9 q^{64} - 5 q^{65} - 23 q^{66} - 30 q^{67} + 10 q^{68} + 16 q^{69} + 16 q^{70} - 70 q^{71} - 9 q^{72} + 21 q^{73} - 29 q^{74} - 5 q^{75} - 8 q^{76} - 13 q^{77} + 11 q^{78} - 25 q^{79} - 9 q^{80} + 16 q^{81} + 22 q^{82} - 23 q^{83} - 8 q^{84} - 3 q^{85} - 58 q^{86} - 4 q^{87} + 41 q^{88} - 31 q^{89} - 36 q^{91} - 26 q^{92} + 15 q^{93} + 9 q^{94} - 10 q^{95} + 22 q^{96} + 52 q^{97} - 36 q^{98} - 7 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 16 * q^3 + 10 * q^4 - 3 * q^5 + 4 * q^6 - 3 * q^7 - 9 * q^8 + 16 * q^9 - 7 * q^11 - 10 * q^12 + 7 * q^13 - 13 * q^14 + 3 * q^15 + 2 * q^16 + 16 * q^17 - 4 * q^18 - 19 * q^19 - 17 * q^20 + 3 * q^21 + 23 * q^22 - 16 * q^23 + 9 * q^24 + 5 * q^25 - 11 * q^26 - 16 * q^27 + 8 * q^28 + 4 * q^29 - 15 * q^31 - 22 * q^32 + 7 * q^33 - 4 * q^34 - 23 * q^35 + 10 * q^36 + 20 * q^37 - 17 * q^38 - 7 * q^39 + 21 * q^40 - 4 * q^41 + 13 * q^42 - 12 * q^43 - 19 * q^44 - 3 * q^45 + 24 * q^46 - 36 * q^47 - 2 * q^48 - 11 * q^49 + 9 * q^50 - 16 * q^51 + 6 * q^52 - 32 * q^53 + 4 * q^54 - 29 * q^55 - 11 * q^56 + 19 * q^57 - 33 * q^58 + 16 * q^59 + 17 * q^60 + 11 * q^62 - 3 * q^63 + 9 * q^64 - 5 * q^65 - 23 * q^66 - 30 * q^67 + 10 * q^68 + 16 * q^69 + 16 * q^70 - 70 * q^71 - 9 * q^72 + 21 * q^73 - 29 * q^74 - 5 * q^75 - 8 * q^76 - 13 * q^77 + 11 * q^78 - 25 * q^79 - 9 * q^80 + 16 * q^81 + 22 * q^82 - 23 * q^83 - 8 * q^84 - 3 * q^85 - 58 * q^86 - 4 * q^87 + 41 * q^88 - 31 * q^89 - 36 * q^91 - 26 * q^92 + 15 * q^93 + 9 * q^94 - 10 * q^95 + 22 * q^96 + 52 * q^97 - 36 * 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 $

$2$	−0.156223	−0.110467	−0.0552333	−	0.998473i	$-0.517590\pi$
$2$	−0.156223	−0.110467	−0.0552333	+	0.998473i	$0.517590\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.97559	−0.987797
$5$	−3.39057	−1.51631	−0.758156	−	0.652074i	$-0.773899\pi$
$5$	−3.39057	−1.51631	−0.758156	+	0.652074i	$0.773899\pi$
$6$	0.156223	0.0637779
$7$	−3.12691	−1.18186	−0.590930	−	0.806723i	$-0.701239\pi$
$7$	−3.12691	−1.18186	−0.590930	+	0.806723i	$0.701239\pi$
$8$	0.621081	0.219585
$9$	1.00000	0.333333
$10$	0.529687	0.167502
$11$	−2.52294	−0.760694	−0.380347	−	0.924844i	$-0.624195\pi$
$11$	−2.52294	−0.760694	−0.380347	+	0.924844i	$0.624195\pi$
$12$	1.97559	0.570305
$13$	4.22206	1.17099	0.585494	−	0.810677i	$-0.300901\pi$
$13$	4.22206	1.17099	0.585494	+	0.810677i	$0.300901\pi$
$14$	0.488496	0.130556
$15$	3.39057	0.875443
$16$	3.85416	0.963540
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.156223	−0.0368222
$19$	−7.16487	−1.64373	−0.821867	−	0.569680i	$-0.807067\pi$
$19$	−7.16487	−1.64373	−0.821867	+	0.569680i	$0.807067\pi$
$20$	6.69840	1.49781
$21$	3.12691	0.682348
$22$	0.394141	0.0840312
$23$	2.70660	0.564366	0.282183	−	0.959361i	$-0.408942\pi$
$23$	2.70660	0.564366	0.282183	+	0.959361i	$0.408942\pi$
$24$	−0.621081	−0.126778
$25$	6.49600	1.29920
$26$	−0.659584	−0.129355
$27$	−1.00000	−0.192450
$28$	6.17750	1.16744
$29$	8.94262	1.66060	0.830302	−	0.557314i	$-0.188168\pi$
$29$	8.94262	1.66060	0.830302	+	0.557314i	$0.188168\pi$
$30$	−0.529687	−0.0967072
$31$	6.87833	1.23538	0.617692	−	0.786420i	$-0.288068\pi$
$31$	6.87833	1.23538	0.617692	+	0.786420i	$0.288068\pi$
$32$	−1.84427	−0.326024
$33$	2.52294	0.439187
$34$	−0.156223	−0.0267921
$35$	10.6020	1.79207
$36$	−1.97559	−0.329266
$37$	10.1998	1.67684	0.838418	−	0.545027i	$-0.183481\pi$
$37$	10.1998	1.67684	0.838418	+	0.545027i	$0.183481\pi$
$38$	1.11932	0.181578
$39$	−4.22206	−0.676070
$40$	−2.10582	−0.332960
$41$	−3.13030	−0.488871	−0.244435	−	0.969666i	$-0.578603\pi$
$41$	−3.13030	−0.488871	−0.244435	+	0.969666i	$0.578603\pi$
$42$	−0.488496	−0.0753766
$43$	−10.9421	−1.66865	−0.834326	−	0.551271i	$-0.814143\pi$
$43$	−10.9421	−1.66865	−0.834326	+	0.551271i	$0.814143\pi$
$44$	4.98430	0.751411
$45$	−3.39057	−0.505437
$46$	−0.422835	−0.0623436
$47$	−9.56930	−1.39583	−0.697913	−	0.716183i	$-0.745888\pi$
$47$	−9.56930	−1.39583	−0.697913	+	0.716183i	$0.745888\pi$
$48$	−3.85416	−0.556300
$49$	2.77756	0.396795
$50$	−1.01483	−0.143518
$51$	−1.00000	−0.140028
$52$	−8.34107	−1.15670
$53$	4.20732	0.577920	0.288960	−	0.957341i	$-0.406691\pi$
$53$	4.20732	0.577920	0.288960	+	0.957341i	$0.406691\pi$
$54$	0.156223	0.0212593
$55$	8.55420	1.15345
$56$	−1.94206	−0.259519
$57$	7.16487	0.949010
$58$	−1.39705	−0.183441
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	−6.69840	−0.864760
$61$	9.20001	1.17794	0.588970	−	0.808155i	$-0.299534\pi$
$61$	9.20001	1.17794	0.588970	+	0.808155i	$0.299534\pi$
$62$	−1.07456	−0.136469
$63$	−3.12691	−0.393954
$64$	−7.42020	−0.927525
$65$	−14.3152	−1.77558
$66$	−0.394141	−0.0485155
$67$	−3.39855	−0.415198	−0.207599	−	0.978214i	$-0.566565\pi$
$67$	−3.39855	−0.415198	−0.207599	+	0.978214i	$0.566565\pi$
$68$	−1.97559	−0.239576
$69$	−2.70660	−0.325837
$70$	−1.65628	−0.197964
$71$	−10.5701	−1.25444	−0.627219	−	0.778843i	$-0.715807\pi$
$71$	−10.5701	−1.25444	−0.627219	+	0.778843i	$0.715807\pi$
$72$	0.621081	0.0731951
$73$	6.33628	0.741606	0.370803	−	0.928712i	$-0.379083\pi$
$73$	6.33628	0.741606	0.370803	+	0.928712i	$0.379083\pi$
$74$	−1.59345	−0.185234
$75$	−6.49600	−0.750093
$76$	14.1549	1.62367
$77$	7.88899	0.899034
$78$	0.659584	0.0746832
$79$	12.6029	1.41794	0.708971	−	0.705238i	$-0.249160\pi$
$79$	12.6029	1.41794	0.708971	+	0.705238i	$0.249160\pi$
$80$	−13.0678	−1.46103
$81$	1.00000	0.111111
$82$	0.489026	0.0540039
$83$	1.74375	0.191402	0.0957008	−	0.995410i	$-0.469491\pi$
$83$	1.74375	0.191402	0.0957008	+	0.995410i	$0.469491\pi$
$84$	−6.17750	−0.674021
$85$	−3.39057	−0.367759
$86$	1.70941	0.184330
$87$	−8.94262	−0.958750
$88$	−1.56695	−0.167037
$89$	−5.36888	−0.569101	−0.284550	−	0.958661i	$-0.591844\pi$
$89$	−5.36888	−0.569101	−0.284550	+	0.958661i	$0.591844\pi$
$90$	0.529687	0.0558339
$91$	−13.2020	−1.38394
$92$	−5.34715	−0.557479
$93$	−6.87833	−0.713249
$94$	1.49495	0.154192
$95$	24.2930	2.49241
$96$	1.84427	0.188230
$97$	−1.28981	−0.130960	−0.0654800	−	0.997854i	$-0.520858\pi$
$97$	−1.28981	−0.130960	−0.0654800	+	0.997854i	$0.520858\pi$
$98$	−0.433920	−0.0438326
$99$	−2.52294	−0.253565
$100$	−12.8335	−1.28335
$101$	12.3507	1.22894	0.614472	−	0.788938i	$-0.289369\pi$
$101$	12.3507	1.22894	0.614472	+	0.788938i	$0.289369\pi$
$102$	0.156223	0.0154684
$103$	19.4664	1.91808	0.959041	−	0.283266i	$-0.0914181\pi$
$103$	19.4664	1.91808	0.959041	+	0.283266i	$0.0914181\pi$
$104$	2.62224	0.257132
$105$	−10.6020	−1.03465
$106$	−0.657282	−0.0638409
$107$	−7.24863	−0.700752	−0.350376	−	0.936609i	$-0.613946\pi$
$107$	−7.24863	−0.700752	−0.350376	+	0.936609i	$0.613946\pi$
$108$	1.97559	0.190102
$109$	−3.95504	−0.378824	−0.189412	−	0.981898i	$-0.560658\pi$
$109$	−3.95504	−0.378824	−0.189412	+	0.981898i	$0.560658\pi$
$110$	−1.33637	−0.127418
$111$	−10.1998	−0.968122
$112$	−12.0516	−1.13877
$113$	−10.8942	−1.02484	−0.512421	−	0.858735i	$-0.671251\pi$
$113$	−10.8942	−1.02484	−0.512421	+	0.858735i	$0.671251\pi$
$114$	−1.11932	−0.104834
$115$	−9.17694	−0.855754
$116$	−17.6670	−1.64034
$117$	4.22206	0.390329
$118$	−0.156223	−0.0143815
$119$	−3.12691	−0.286643
$120$	2.10582	0.192234
$121$	−4.63480	−0.421345
$122$	−1.43726	−0.130123
$123$	3.13030	0.282250
$124$	−13.5888	−1.22031
$125$	−5.07229	−0.453679
$126$	0.488496	0.0435187
$127$	−18.5868	−1.64931	−0.824657	−	0.565634i	$-0.808632\pi$
$127$	−18.5868	−1.64931	−0.824657	+	0.565634i	$0.808632\pi$
$128$	4.84775	0.428485
$129$	10.9421	0.963397
$130$	2.23637	0.196142
$131$	−8.42529	−0.736121	−0.368060	−	0.929802i	$-0.619978\pi$
$131$	−8.42529	−0.736121	−0.368060	+	0.929802i	$0.619978\pi$
$132$	−4.98430	−0.433827
$133$	22.4039	1.94266
$134$	0.530932	0.0458656
$135$	3.39057	0.291814
$136$	0.621081	0.0532572
$137$	17.0138	1.45358	0.726792	−	0.686858i	$-0.241010\pi$
$137$	17.0138	1.45358	0.726792	+	0.686858i	$0.241010\pi$
$138$	0.422835	0.0359941
$139$	−11.0627	−0.938330	−0.469165	−	0.883110i	$-0.655445\pi$
$139$	−11.0627	−0.938330	−0.469165	+	0.883110i	$0.655445\pi$
$140$	−20.9453	−1.77020
$141$	9.56930	0.805880
$142$	1.65130	0.138574
$143$	−10.6520	−0.890763
$144$	3.85416	0.321180
$145$	−30.3206	−2.51799
$146$	−0.989875	−0.0819227
$147$	−2.77756	−0.229090
$148$	−20.1507	−1.65637
$149$	−13.6014	−1.11427	−0.557133	−	0.830423i	$-0.688099\pi$
$149$	−13.6014	−1.11427	−0.557133	+	0.830423i	$0.688099\pi$
$150$	1.01483	0.0828602
$151$	−12.5999	−1.02537	−0.512683	−	0.858578i	$-0.671348\pi$
$151$	−12.5999	−1.02537	−0.512683	+	0.858578i	$0.671348\pi$
$152$	−4.44996	−0.360939
$153$	1.00000	0.0808452
$154$	−1.23244	−0.0993132
$155$	−23.3215	−1.87323
$156$	8.34107	0.667820
$157$	5.06699	0.404390	0.202195	−	0.979345i	$-0.435193\pi$
$157$	5.06699	0.404390	0.202195	+	0.979345i	$0.435193\pi$
$158$	−1.96887	−0.156635
$159$	−4.20732	−0.333662
$160$	6.25314	0.494354
$161$	−8.46330	−0.667002
$162$	−0.156223	−0.0122741
$163$	−2.64537	−0.207201	−0.103601	−	0.994619i	$-0.533036\pi$
$163$	−2.64537	−0.207201	−0.103601	+	0.994619i	$0.533036\pi$
$164$	6.18420	0.482905
$165$	−8.55420	−0.665944
$166$	−0.272415	−0.0211435
$167$	−5.44066	−0.421011	−0.210505	−	0.977593i	$-0.567511\pi$
$167$	−5.44066	−0.421011	−0.210505	+	0.977593i	$0.567511\pi$
$168$	1.94206	0.149833
$169$	4.82575	0.371212
$170$	0.529687	0.0406251
$171$	−7.16487	−0.547911
$172$	21.6171	1.64829
$173$	13.6885	1.04072	0.520359	−	0.853948i	$-0.325798\pi$
$173$	13.6885	1.04072	0.520359	+	0.853948i	$0.325798\pi$
$174$	1.39705	0.105910
$175$	−20.3124	−1.53547
$176$	−9.72380	−0.732959
$177$	−1.00000	−0.0751646
$178$	0.838745	0.0628666
$179$	3.99171	0.298355	0.149177	−	0.988810i	$-0.452337\pi$
$179$	3.99171	0.298355	0.149177	+	0.988810i	$0.452337\pi$
$180$	6.69840	0.499269
$181$	−0.291449	−0.0216632	−0.0108316	−	0.999941i	$-0.503448\pi$
$181$	−0.291449	−0.0216632	−0.0108316	+	0.999941i	$0.503448\pi$
$182$	2.06246	0.152880
$183$	−9.20001	−0.680084
$184$	1.68102	0.123926
$185$	−34.5832	−2.54261
$186$	1.07456	0.0787902
$187$	−2.52294	−0.184495
$188$	18.9050	1.37879
$189$	3.12691	0.227449
$190$	−3.79514	−0.275328
$191$	16.7969	1.21538	0.607691	−	0.794174i	$-0.292096\pi$
$191$	16.7969	1.21538	0.607691	+	0.794174i	$0.292096\pi$
$192$	7.42020	0.535507
$193$	18.0830	1.30164	0.650822	−	0.759231i	$-0.274425\pi$
$193$	18.0830	1.30164	0.650822	+	0.759231i	$0.274425\pi$
$194$	0.201498	0.0144667
$195$	14.3152	1.02513
$196$	−5.48734	−0.391953
$197$	−17.9406	−1.27822	−0.639109	−	0.769116i	$-0.720697\pi$
$197$	−17.9406	−1.27822	−0.639109	+	0.769116i	$0.720697\pi$
$198$	0.394141	0.0280104
$199$	15.9553	1.13104	0.565521	−	0.824734i	$-0.308675\pi$
$199$	15.9553	1.13104	0.565521	+	0.824734i	$0.308675\pi$
$200$	4.03454	0.285285
$201$	3.39855	0.239715
$202$	−1.92947	−0.135757
$203$	−27.9628	−1.96260
$204$	1.97559	0.138319
$205$	10.6135	0.741280
$206$	−3.04111	−0.211884
$207$	2.70660	0.188122
$208$	16.2725	1.12829
$209$	18.0765	1.25038
$210$	1.65628	0.114294
$211$	24.2686	1.67072	0.835360	−	0.549703i	$-0.185259\pi$
$211$	24.2686	1.67072	0.835360	+	0.549703i	$0.185259\pi$
$212$	−8.31196	−0.570868
$213$	10.5701	0.724251
$214$	1.13241	0.0774097
$215$	37.1000	2.53020
$216$	−0.621081	−0.0422592
$217$	−21.5079	−1.46005
$218$	0.617870	0.0418474
$219$	−6.33628	−0.428166
$220$	−16.8996	−1.13937
$221$	4.22206	0.284006
$222$	1.59345	0.106945
$223$	−13.6706	−0.915452	−0.457726	−	0.889093i	$-0.651336\pi$
$223$	−13.6706	−0.915452	−0.457726	+	0.889093i	$0.651336\pi$
$224$	5.76687	0.385315
$225$	6.49600	0.433066
$226$	1.70193	0.113211
$227$	12.4397	0.825652	0.412826	−	0.910810i	$-0.364542\pi$
$227$	12.4397	0.825652	0.412826	+	0.910810i	$0.364542\pi$
$228$	−14.1549	−0.937429
$229$	10.9329	0.722466	0.361233	−	0.932476i	$-0.382356\pi$
$229$	10.9329	0.722466	0.361233	+	0.932476i	$0.382356\pi$
$230$	1.43365	0.0945323
$231$	−7.88899	−0.519057
$232$	5.55409	0.364644
$233$	−23.0814	−1.51212	−0.756058	−	0.654505i	$-0.772877\pi$
$233$	−23.0814	−1.51212	−0.756058	+	0.654505i	$0.772877\pi$
$234$	−0.659584	−0.0431183
$235$	32.4454	2.11651
$236$	−1.97559	−0.128600
$237$	−12.6029	−0.818649
$238$	0.488496	0.0316645
$239$	−24.1919	−1.56484	−0.782422	−	0.622749i	$-0.786016\pi$
$239$	−24.1919	−1.56484	−0.782422	+	0.622749i	$0.786016\pi$
$240$	13.0678	0.843524
$241$	19.1287	1.23219	0.616094	−	0.787673i	$-0.288714\pi$
$241$	19.1287	1.23219	0.616094	+	0.787673i	$0.288714\pi$
$242$	0.724064	0.0465446
$243$	−1.00000	−0.0641500
$244$	−18.1755	−1.16357
$245$	−9.41754	−0.601664
$246$	−0.489026	−0.0311792
$247$	−30.2505	−1.92479
$248$	4.27200	0.271272
$249$	−1.74375	−0.110506
$250$	0.792410	0.0501164
$251$	5.63807	0.355872	0.177936	−	0.984042i	$-0.443058\pi$
$251$	5.63807	0.355872	0.177936	+	0.984042i	$0.443058\pi$
$252$	6.17750	0.389146
$253$	−6.82858	−0.429309
$254$	2.90369	0.182194
$255$	3.39057	0.212326
$256$	14.0831	0.880192
$257$	−16.5378	−1.03160	−0.515799	−	0.856710i	$-0.672505\pi$
$257$	−16.5378	−1.03160	−0.515799	+	0.856710i	$0.672505\pi$
$258$	−1.70941	−0.106423
$259$	−31.8938	−1.98179
$260$	28.2810	1.75391
$261$	8.94262	0.553535
$262$	1.31623	0.0813168
$263$	15.7729	0.972600	0.486300	−	0.873792i	$-0.338346\pi$
$263$	15.7729	0.972600	0.486300	+	0.873792i	$0.338346\pi$
$264$	1.56695	0.0964389
$265$	−14.2652	−0.876306
$266$	−3.50001	−0.214599
$267$	5.36888	0.328570
$268$	6.71415	0.410132
$269$	9.39578	0.572871	0.286435	−	0.958100i	$-0.407530\pi$
$269$	9.39578	0.572871	0.286435	+	0.958100i	$0.407530\pi$
$270$	−0.529687	−0.0322357
$271$	−18.6250	−1.13139	−0.565693	−	0.824616i	$-0.691391\pi$
$271$	−18.6250	−1.13139	−0.565693	+	0.824616i	$0.691391\pi$
$272$	3.85416	0.233693
$273$	13.2020	0.799020
$274$	−2.65795	−0.160573
$275$	−16.3890	−0.988293
$276$	5.34715	0.321861
$277$	−1.04274	−0.0626521	−0.0313260	−	0.999509i	$-0.509973\pi$
$277$	−1.04274	−0.0626521	−0.0313260	+	0.999509i	$0.509973\pi$
$278$	1.72826	0.103654
$279$	6.87833	0.411795
$280$	6.58471	0.393512
$281$	−24.0538	−1.43493	−0.717465	−	0.696595i	$-0.754698\pi$
$281$	−24.0538	−1.43493	−0.717465	+	0.696595i	$0.754698\pi$
$282$	−1.49495	−0.0890228
$283$	6.89511	0.409872	0.204936	−	0.978775i	$-0.434301\pi$
$283$	6.89511	0.409872	0.204936	+	0.978775i	$0.434301\pi$
$284$	20.8822	1.23913
$285$	−24.2930	−1.43899
$286$	1.66409	0.0983995
$287$	9.78817	0.577777
$288$	−1.84427	−0.108675
$289$	1.00000	0.0588235
$290$	4.73679	0.278154
$291$	1.28981	0.0756098
$292$	−12.5179	−0.732556
$293$	−18.8882	−1.10346	−0.551730	−	0.834023i	$-0.686032\pi$
$293$	−18.8882	−1.10346	−0.551730	+	0.834023i	$0.686032\pi$
$294$	0.433920	0.0253068
$295$	−3.39057	−0.197407
$296$	6.33490	0.368209
$297$	2.52294	0.146396
$298$	2.12485	0.123089
$299$	11.4274	0.660865
$300$	12.8335	0.740940
$301$	34.2149	1.97212
$302$	1.96840	0.113269
$303$	−12.3507	−0.709532
$304$	−27.6145	−1.58380
$305$	−31.1933	−1.78612
$306$	−0.156223	−0.00893070
$307$	10.8392	0.618623	0.309312	−	0.950961i	$-0.399901\pi$
$307$	10.8392	0.618623	0.309312	+	0.950961i	$0.399901\pi$
$308$	−15.5854	−0.888063
$309$	−19.4664	−1.10741
$310$	3.64336	0.206929
$311$	−6.37014	−0.361217	−0.180609	−	0.983555i	$-0.557807\pi$
$311$	−6.37014	−0.361217	−0.180609	+	0.983555i	$0.557807\pi$
$312$	−2.62224	−0.148455
$313$	11.0483	0.624489	0.312245	−	0.950002i	$-0.398919\pi$
$313$	11.0483	0.624489	0.312245	+	0.950002i	$0.398919\pi$
$314$	−0.791582	−0.0446716
$315$	10.6020	0.597356
$316$	−24.8983	−1.40064
$317$	−31.7445	−1.78295	−0.891473	−	0.453073i	$-0.850328\pi$
$317$	−31.7445	−1.78295	−0.891473	+	0.453073i	$0.850328\pi$
$318$	0.657282	0.0368585
$319$	−22.5617	−1.26321
$320$	25.1588	1.40642
$321$	7.24863	0.404579
$322$	1.32217	0.0736814
$323$	−7.16487	−0.398664
$324$	−1.97559	−0.109755
$325$	27.4265	1.52135
$326$	0.413268	0.0228888
$327$	3.95504	0.218714
$328$	−1.94417	−0.107349
$329$	29.9223	1.64967
$330$	1.33637	0.0735645
$331$	29.9484	1.64611	0.823056	−	0.567961i	$-0.192268\pi$
$331$	29.9484	1.64611	0.823056	+	0.567961i	$0.192268\pi$
$332$	−3.44495	−0.189066
$333$	10.1998	0.558946
$334$	0.849958	0.0465076
$335$	11.5230	0.629570
$336$	12.0516	0.657469
$337$	−15.5330	−0.846137	−0.423069	−	0.906098i	$-0.639047\pi$
$337$	−15.5330	−0.846137	−0.423069	+	0.906098i	$0.639047\pi$
$338$	−0.753895	−0.0410065
$339$	10.8942	0.591692
$340$	6.69840	0.363272
$341$	−17.3536	−0.939749
$342$	1.11932	0.0605259
$343$	13.2032	0.712904
$344$	−6.79592	−0.366411
$345$	9.17694	0.494070
$346$	−2.13846	−0.114965
$347$	−8.44628	−0.453420	−0.226710	−	0.973962i	$-0.572797\pi$
$347$	−8.44628	−0.453420	−0.226710	+	0.973962i	$0.572797\pi$
$348$	17.6670	0.947050
$349$	15.1848	0.812823	0.406412	−	0.913690i	$-0.366780\pi$
$349$	15.1848	0.812823	0.406412	+	0.913690i	$0.366780\pi$
$350$	3.17327	0.169618
$351$	−4.22206	−0.225357
$352$	4.65298	0.248005
$353$	0.186802	0.00994247	0.00497123	−	0.999988i	$-0.498418\pi$
$353$	0.186802	0.00994247	0.00497123	+	0.999988i	$0.498418\pi$
$354$	0.156223	0.00830318
$355$	35.8387	1.90212
$356$	10.6067	0.562156
$357$	3.12691	0.165494
$358$	−0.623599	−0.0329582
$359$	29.2055	1.54141	0.770703	−	0.637195i	$-0.219905\pi$
$359$	29.2055	1.54141	0.770703	+	0.637195i	$0.219905\pi$
$360$	−2.10582	−0.110987
$361$	32.3353	1.70186
$362$	0.0455311	0.00239306
$363$	4.63480	0.243264
$364$	26.0818	1.36706
$365$	−21.4836	−1.12450
$366$	1.43726	0.0751266
$367$	−10.1179	−0.528152	−0.264076	−	0.964502i	$-0.585067\pi$
$367$	−10.1179	−0.528152	−0.264076	+	0.964502i	$0.585067\pi$
$368$	10.4317	0.543789
$369$	−3.13030	−0.162957
$370$	5.40270	0.280873
$371$	−13.1559	−0.683021
$372$	13.5888	0.704546
$373$	−14.2587	−0.738288	−0.369144	−	0.929372i	$-0.620349\pi$
$373$	−14.2587	−0.738288	−0.369144	+	0.929372i	$0.620349\pi$
$374$	0.394141	0.0203806
$375$	5.07229	0.261932
$376$	−5.94331	−0.306503
$377$	37.7563	1.94455
$378$	−0.488496	−0.0251255
$379$	20.6516	1.06080	0.530401	−	0.847747i	$-0.322041\pi$
$379$	20.6516	1.06080	0.530401	+	0.847747i	$0.322041\pi$
$380$	−47.9931	−2.46200
$381$	18.5868	0.952231
$382$	−2.62407	−0.134259
$383$	−7.83957	−0.400583	−0.200292	−	0.979736i	$-0.564189\pi$
$383$	−7.83957	−0.400583	−0.200292	+	0.979736i	$0.564189\pi$
$384$	−4.84775	−0.247386
$385$	−26.7482	−1.36322
$386$	−2.82499	−0.143788
$387$	−10.9421	−0.556218
$388$	2.54813	0.129362
$389$	−21.2940	−1.07965	−0.539824	−	0.841778i	$-0.681509\pi$
$389$	−21.2940	−1.07965	−0.539824	+	0.841778i	$0.681509\pi$
$390$	−2.23637	−0.113243
$391$	2.70660	0.136879
$392$	1.72509	0.0871303
$393$	8.42529	0.424999
$394$	2.80275	0.141200
$395$	−42.7312	−2.15004
$396$	4.98430	0.250470
$397$	10.8465	0.544371	0.272186	−	0.962245i	$-0.412254\pi$
$397$	10.8465	0.544371	0.272186	+	0.962245i	$0.412254\pi$
$398$	−2.49259	−0.124942
$399$	−22.4039	−1.12160
$400$	25.0366	1.25183
$401$	−29.7971	−1.48800	−0.743999	−	0.668181i	$-0.767073\pi$
$401$	−29.7971	−1.48800	−0.743999	+	0.668181i	$0.767073\pi$
$402$	−0.530932	−0.0264805
$403$	29.0407	1.44662
$404$	−24.4001	−1.21395
$405$	−3.39057	−0.168479
$406$	4.36844	0.216802
$407$	−25.7334	−1.27556
$408$	−0.621081	−0.0307481
$409$	−21.0388	−1.04030	−0.520151	−	0.854074i	$-0.674124\pi$
$409$	−21.0388	−1.04030	−0.520151	+	0.854074i	$0.674124\pi$
$410$	−1.65808	−0.0818867
$411$	−17.0138	−0.839227
$412$	−38.4577	−1.89468
$413$	−3.12691	−0.153865
$414$	−0.422835	−0.0207812
$415$	−5.91232	−0.290224
$416$	−7.78662	−0.381770
$417$	11.0627	0.541745
$418$	−2.82397	−0.138125
$419$	2.76272	0.134968	0.0674838	−	0.997720i	$-0.478503\pi$
$419$	2.76272	0.134968	0.0674838	+	0.997720i	$0.478503\pi$
$420$	20.9453	1.02203
$421$	−12.4596	−0.607244	−0.303622	−	0.952792i	$-0.598196\pi$
$421$	−12.4596	−0.607244	−0.303622	+	0.952792i	$0.598196\pi$
$422$	−3.79132	−0.184559
$423$	−9.56930	−0.465275
$424$	2.61309	0.126903
$425$	6.49600	0.315102
$426$	−1.65130	−0.0800055
$427$	−28.7676	−1.39216
$428$	14.3204	0.692200
$429$	10.6520	0.514282
$430$	−5.79588	−0.279502
$431$	19.8094	0.954186	0.477093	−	0.878853i	$-0.341690\pi$
$431$	19.8094	0.954186	0.477093	+	0.878853i	$0.341690\pi$
$432$	−3.85416	−0.185433
$433$	20.4944	0.984897	0.492448	−	0.870342i	$-0.336102\pi$
$433$	20.4944	0.984897	0.492448	+	0.870342i	$0.336102\pi$
$434$	3.36004	0.161287
$435$	30.3206	1.45376
$436$	7.81356	0.374202
$437$	−19.3925	−0.927667
$438$	0.989875	0.0472981
$439$	12.5847	0.600633	0.300316	−	0.953840i	$-0.402908\pi$
$439$	12.5847	0.600633	0.300316	+	0.953840i	$0.402908\pi$
$440$	5.31285	0.253280
$441$	2.77756	0.132265
$442$	−0.659584	−0.0313732
$443$	−17.2365	−0.818930	−0.409465	−	0.912326i	$-0.634285\pi$
$443$	−17.2365	−0.818930	−0.409465	+	0.912326i	$0.634285\pi$
$444$	20.1507	0.956308
$445$	18.2036	0.862934
$446$	2.13567	0.101127
$447$	13.6014	0.643322
$448$	23.2023	1.09621
$449$	−32.8557	−1.55056	−0.775278	−	0.631620i	$-0.782390\pi$
$449$	−32.8557	−1.55056	−0.775278	+	0.631620i	$0.782390\pi$
$450$	−1.01483	−0.0478394
$451$	7.89754	0.371881
$452$	21.5225	1.01234
$453$	12.5999	0.591995
$454$	−1.94337	−0.0912070
$455$	44.7623	2.09849
$456$	4.44996	0.208389
$457$	23.3274	1.09121	0.545606	−	0.838042i	$-0.316300\pi$
$457$	23.3274	1.09121	0.545606	+	0.838042i	$0.316300\pi$
$458$	−1.70797	−0.0798084
$459$	−1.00000	−0.0466760
$460$	18.1299	0.845311
$461$	−15.4201	−0.718184	−0.359092	−	0.933302i	$-0.616914\pi$
$461$	−15.4201	−0.718184	−0.359092	+	0.933302i	$0.616914\pi$
$462$	1.23244	0.0573385
$463$	−1.15073	−0.0534790	−0.0267395	−	0.999642i	$-0.508512\pi$
$463$	−1.15073	−0.0534790	−0.0267395	+	0.999642i	$0.508512\pi$
$464$	34.4663	1.60006
$465$	23.3215	1.08151
$466$	3.60586	0.167038
$467$	1.98012	0.0916290	0.0458145	−	0.998950i	$-0.485412\pi$
$467$	1.98012	0.0916290	0.0458145	+	0.998950i	$0.485412\pi$
$468$	−8.34107	−0.385566
$469$	10.6269	0.490707
$470$	−5.06873	−0.233803
$471$	−5.06699	−0.233474
$472$	0.621081	0.0285876
$473$	27.6062	1.26933
$474$	1.96887	0.0904334
$475$	−46.5429	−2.13554
$476$	6.17750	0.283145
$477$	4.20732	0.192640
$478$	3.77934	0.172863
$479$	24.8953	1.13749	0.568747	−	0.822513i	$-0.307428\pi$
$479$	24.8953	1.13749	0.568747	+	0.822513i	$0.307428\pi$
$480$	−6.25314	−0.285416
$481$	43.0641	1.96355
$482$	−2.98835	−0.136116
$483$	8.46330	0.385094
$484$	9.15648	0.416204
$485$	4.37318	0.198576
$486$	0.156223	0.00708644
$487$	−35.1952	−1.59485	−0.797424	−	0.603420i	$-0.793804\pi$
$487$	−35.1952	−1.59485	−0.797424	+	0.603420i	$0.793804\pi$
$488$	5.71395	0.258658
$489$	2.64537	0.119628
$490$	1.47124	0.0664638
$491$	−14.6718	−0.662129	−0.331064	−	0.943608i	$-0.607408\pi$
$491$	−14.6718	−0.662129	−0.331064	+	0.943608i	$0.607408\pi$
$492$	−6.18420	−0.278805
$493$	8.94262	0.402756
$494$	4.72583	0.212625
$495$	8.55420	0.384483
$496$	26.5102	1.19034
$497$	33.0517	1.48257
$498$	0.272415	0.0122072
$499$	−11.4846	−0.514122	−0.257061	−	0.966395i	$-0.582754\pi$
$499$	−11.4846	−0.514122	−0.257061	+	0.966395i	$0.582754\pi$
$500$	10.0208	0.448143
$501$	5.44066	0.243071
$502$	−0.880798	−0.0393119
$503$	12.4878	0.556805	0.278402	−	0.960465i	$-0.410195\pi$
$503$	12.4878	0.556805	0.278402	+	0.960465i	$0.410195\pi$
$504$	−1.94206	−0.0865064
$505$	−41.8761	−1.86346
$506$	1.06678	0.0474244
$507$	−4.82575	−0.214319
$508$	36.7200	1.62919
$509$	−35.4421	−1.57094	−0.785471	−	0.618899i	$-0.787579\pi$
$509$	−35.4421	−1.57094	−0.785471	+	0.618899i	$0.787579\pi$
$510$	−0.529687	−0.0234549
$511$	−19.8130	−0.876474
$512$	−11.8956	−0.525717
$513$	7.16487	0.316337
$514$	2.58359	0.113957
$515$	−66.0023	−2.90841
$516$	−21.6171	−0.951641
$517$	24.1427	1.06180
$518$	4.98257	0.218921
$519$	−13.6885	−0.600859
$520$	−8.89089	−0.389891
$521$	−13.1277	−0.575137	−0.287568	−	0.957760i	$-0.592847\pi$
$521$	−13.1277	−0.575137	−0.287568	+	0.957760i	$0.592847\pi$
$522$	−1.39705	−0.0611471
$523$	23.8891	1.04460	0.522298	−	0.852763i	$-0.325075\pi$
$523$	23.8891	1.04460	0.522298	+	0.852763i	$0.325075\pi$
$524$	16.6449	0.727138
$525$	20.3124	0.886506
$526$	−2.46410	−0.107440
$527$	6.87833	0.299625
$528$	9.72380	0.423174
$529$	−15.6743	−0.681491
$530$	2.22856	0.0968026
$531$	1.00000	0.0433963
$532$	−44.2610	−1.91896
$533$	−13.2163	−0.572462
$534$	−0.838745	−0.0362961
$535$	24.5770	1.06256
$536$	−2.11077	−0.0911714
$537$	−3.99171	−0.172255
$538$	−1.46784	−0.0632831
$539$	−7.00761	−0.301839
$540$	−6.69840	−0.288253
$541$	−9.51984	−0.409290	−0.204645	−	0.978836i	$-0.565604\pi$
$541$	−9.51984	−0.409290	−0.204645	+	0.978836i	$0.565604\pi$
$542$	2.90965	0.124980
$543$	0.291449	0.0125073
$544$	−1.84427	−0.0790725
$545$	13.4099	0.574415
$546$	−2.06246	−0.0882651
$547$	32.7982	1.40235	0.701174	−	0.712990i	$-0.252660\pi$
$547$	32.7982	1.40235	0.701174	+	0.712990i	$0.252660\pi$
$548$	−33.6123	−1.43585
$549$	9.20001	0.392647
$550$	2.56034	0.109173
$551$	−64.0727	−2.72959
$552$	−1.68102	−0.0715489
$553$	−39.4083	−1.67581
$554$	0.162900	0.00692096
$555$	34.5832	1.46797
$556$	21.8555	0.926880
$557$	24.7310	1.04789	0.523944	−	0.851753i	$-0.324460\pi$
$557$	24.7310	1.04789	0.523944	+	0.851753i	$0.324460\pi$
$558$	−1.07456	−0.0454896
$559$	−46.1981	−1.95397
$560$	40.8619	1.72673
$561$	2.52294	0.106518
$562$	3.75777	0.158512
$563$	−9.71835	−0.409580	−0.204790	−	0.978806i	$-0.565651\pi$
$563$	−9.71835	−0.409580	−0.204790	+	0.978806i	$0.565651\pi$
$564$	−18.9050	−0.796046
$565$	36.9376	1.55398
$566$	−1.07718	−0.0452771
$567$	−3.12691	−0.131318
$568$	−6.56488	−0.275456
$569$	−5.77333	−0.242030	−0.121015	−	0.992651i	$-0.538615\pi$
$569$	−5.77333	−0.242030	−0.121015	+	0.992651i	$0.538615\pi$
$570$	3.79514	0.158961
$571$	−26.0991	−1.09221	−0.546106	−	0.837716i	$-0.683890\pi$
$571$	−26.0991	−1.09221	−0.546106	+	0.837716i	$0.683890\pi$
$572$	21.0440	0.879893
$573$	−16.7969	−0.701701
$574$	−1.52914	−0.0638251
$575$	17.5821	0.733224
$576$	−7.42020	−0.309175
$577$	−15.7973	−0.657652	−0.328826	−	0.944391i	$-0.606653\pi$
$577$	−15.7973	−0.657652	−0.328826	+	0.944391i	$0.606653\pi$
$578$	−0.156223	−0.00649804
$579$	−18.0830	−0.751504
$580$	59.9013	2.48726
$581$	−5.45255	−0.226210
$582$	−0.201498	−0.00835235
$583$	−10.6148	−0.439620
$584$	3.93534	0.162846
$585$	−14.3152	−0.591860
$586$	2.95078	0.121896
$587$	30.5373	1.26041	0.630204	−	0.776429i	$-0.282971\pi$
$587$	30.5373	1.26041	0.630204	+	0.776429i	$0.282971\pi$
$588$	5.48734	0.226294
$589$	−49.2823	−2.03064
$590$	0.529687	0.0218069
$591$	17.9406	0.737979
$592$	39.3117	1.61570
$593$	−27.5279	−1.13044	−0.565218	−	0.824941i	$-0.691208\pi$
$593$	−27.5279	−1.13044	−0.565218	+	0.824941i	$0.691208\pi$
$594$	−0.394141	−0.0161718
$595$	10.6020	0.434640
$596$	26.8708	1.10067
$597$	−15.9553	−0.653008
$598$	−1.78523	−0.0730035
$599$	−34.1042	−1.39346	−0.696729	−	0.717334i	$-0.745362\pi$
$599$	−34.1042	−1.39346	−0.696729	+	0.717334i	$0.745362\pi$
$600$	−4.03454	−0.164709
$601$	−31.0625	−1.26707	−0.633533	−	0.773716i	$-0.718396\pi$
$601$	−31.0625	−1.26707	−0.633533	+	0.773716i	$0.718396\pi$
$602$	−5.34517	−0.217853
$603$	−3.39855	−0.138399
$604$	24.8923	1.01285
$605$	15.7146	0.638890
$606$	1.92947	0.0783795
$607$	−29.1021	−1.18122	−0.590608	−	0.806958i	$-0.701112\pi$
$607$	−29.1021	−1.18122	−0.590608	+	0.806958i	$0.701112\pi$
$608$	13.2140	0.535897
$609$	27.9628	1.13311
$610$	4.87312	0.197307
$611$	−40.4021	−1.63449
$612$	−1.97559	−0.0798587
$613$	32.4862	1.31211	0.656053	−	0.754715i	$-0.272225\pi$
$613$	32.4862	1.31211	0.656053	+	0.754715i	$0.272225\pi$
$614$	−1.69333	−0.0683372
$615$	−10.6135	−0.427978
$616$	4.89970	0.197415
$617$	−38.2308	−1.53912	−0.769558	−	0.638577i	$-0.779523\pi$
$617$	−38.2308	−1.53912	−0.769558	+	0.638577i	$0.779523\pi$
$618$	3.04111	0.122331
$619$	27.4393	1.10288	0.551439	−	0.834215i	$-0.314079\pi$
$619$	27.4393	1.10288	0.551439	+	0.834215i	$0.314079\pi$
$620$	46.0738	1.85037
$621$	−2.70660	−0.108612
$622$	0.995164	0.0399025
$623$	16.7880	0.672598
$624$	−16.2725	−0.651421
$625$	−15.2820	−0.611281
$626$	−1.72601	−0.0689852
$627$	−18.0765	−0.721906
$628$	−10.0103	−0.399455
$629$	10.1998	0.406693
$630$	−1.65628	−0.0659879
$631$	−26.0746	−1.03801	−0.519007	−	0.854770i	$-0.673698\pi$
$631$	−26.0746	−1.03801	−0.519007	+	0.854770i	$0.673698\pi$
$632$	7.82745	0.311359
$633$	−24.2686	−0.964591
$634$	4.95923	0.196956
$635$	63.0200	2.50087
$636$	8.31196	0.329591
$637$	11.7270	0.464642
$638$	3.52466	0.139543
$639$	−10.5701	−0.418146
$640$	−16.4367	−0.649716
$641$	3.44975	0.136257	0.0681285	−	0.997677i	$-0.478297\pi$
$641$	3.44975	0.136257	0.0681285	+	0.997677i	$0.478297\pi$
$642$	−1.13241	−0.0446925
$643$	−31.1958	−1.23024	−0.615121	−	0.788433i	$-0.710893\pi$
$643$	−31.1958	−1.23024	−0.615121	+	0.788433i	$0.710893\pi$
$644$	16.7201	0.658862
$645$	−37.1000	−1.46081
$646$	1.11932	0.0440390
$647$	24.4493	0.961201	0.480601	−	0.876940i	$-0.340419\pi$
$647$	24.4493	0.961201	0.480601	+	0.876940i	$0.340419\pi$
$648$	0.621081	0.0243984
$649$	−2.52294	−0.0990339
$650$	−4.28465	−0.168058
$651$	21.5079	0.842961
$652$	5.22617	0.204673
$653$	18.6953	0.731604	0.365802	−	0.930693i	$-0.380795\pi$
$653$	18.6953	0.731604	0.365802	+	0.930693i	$0.380795\pi$
$654$	−0.617870	−0.0241606
$655$	28.5666	1.11619
$656$	−12.0647	−0.471047
$657$	6.33628	0.247202
$658$	−4.67457	−0.182234
$659$	20.9194	0.814905	0.407452	−	0.913226i	$-0.366417\pi$
$659$	20.9194	0.814905	0.407452	+	0.913226i	$0.366417\pi$
$660$	16.8996	0.657817
$661$	−9.20385	−0.357988	−0.178994	−	0.983850i	$-0.557284\pi$
$661$	−9.20385	−0.357988	−0.178994	+	0.983850i	$0.557284\pi$
$662$	−4.67864	−0.181840
$663$	−4.22206	−0.163971
$664$	1.08301	0.0420290
$665$	−75.9621	−2.94568
$666$	−1.59345	−0.0617448
$667$	24.2041	0.937188
$668$	10.7485	0.415873
$669$	13.6706	0.528536
$670$	−1.80017	−0.0695465
$671$	−23.2110	−0.896052
$672$	−5.76687	−0.222462
$673$	49.4943	1.90786	0.953932	−	0.300022i	$-0.0969939\pi$
$673$	49.4943	1.90786	0.953932	+	0.300022i	$0.0969939\pi$
$674$	2.42662	0.0934699
$675$	−6.49600	−0.250031
$676$	−9.53372	−0.366682
$677$	15.8270	0.608281	0.304141	−	0.952627i	$-0.401631\pi$
$677$	15.8270	0.608281	0.304141	+	0.952627i	$0.401631\pi$
$678$	−1.70193	−0.0653622
$679$	4.03311	0.154776
$680$	−2.10582	−0.0807545
$681$	−12.4397	−0.476690
$682$	2.71103	0.103811
$683$	15.1488	0.579653	0.289826	−	0.957079i	$-0.406402\pi$
$683$	15.1488	0.579653	0.289826	+	0.957079i	$0.406402\pi$
$684$	14.1549	0.541225
$685$	−57.6864	−2.20409
$686$	−2.06264	−0.0787521
$687$	−10.9329	−0.417116
$688$	−42.1726	−1.60781
$689$	17.7635	0.676737
$690$	−1.43365	−0.0545782
$691$	−22.1471	−0.842515	−0.421257	−	0.906941i	$-0.638411\pi$
$691$	−22.1471	−0.842515	−0.421257	+	0.906941i	$0.638411\pi$
$692$	−27.0429	−1.02802
$693$	7.88899	0.299678
$694$	1.31951	0.0500878
$695$	37.5091	1.42280
$696$	−5.55409	−0.210527
$697$	−3.13030	−0.118569
$698$	−2.37222	−0.0897899
$699$	23.0814	0.873021
$700$	40.1290	1.51674
$701$	24.1100	0.910623	0.455311	−	0.890332i	$-0.349528\pi$
$701$	24.1100	0.910623	0.455311	+	0.890332i	$0.349528\pi$
$702$	0.659584	0.0248944
$703$	−73.0802	−2.75627
$704$	18.7207	0.705563
$705$	−32.4454	−1.22196
$706$	−0.0291828	−0.00109831
$707$	−38.6197	−1.45244
$708$	1.97559	0.0742474
$709$	−18.1348	−0.681066	−0.340533	−	0.940233i	$-0.610608\pi$
$709$	−18.1348	−0.681066	−0.340533	+	0.940233i	$0.610608\pi$
$710$	−5.59884	−0.210121
$711$	12.6029	0.472647
$712$	−3.33451	−0.124966
$713$	18.6169	0.697208
$714$	−0.488496	−0.0182815
$715$	36.1163	1.35067
$716$	−7.88601	−0.294714
$717$	24.1919	0.903463
$718$	−4.56258	−0.170274
$719$	−8.46388	−0.315650	−0.157825	−	0.987467i	$-0.550448\pi$
$719$	−8.46388	−0.315650	−0.157825	+	0.987467i	$0.550448\pi$
$720$	−13.0678	−0.487009
$721$	−60.8697	−2.26691
$722$	−5.05153	−0.187999
$723$	−19.1287	−0.711404
$724$	0.575784	0.0213988
$725$	58.0913	2.15745
$726$	−0.724064	−0.0268725
$727$	12.2968	0.456062	0.228031	−	0.973654i	$-0.426771\pi$
$727$	12.2968	0.456062	0.228031	+	0.973654i	$0.426771\pi$
$728$	−8.19950	−0.303894
$729$	1.00000	0.0370370
$730$	3.35625	0.124220
$731$	−10.9421	−0.404708
$732$	18.1755	0.671785
$733$	−40.6504	−1.50146	−0.750729	−	0.660611i	$-0.770297\pi$
$733$	−40.6504	−1.50146	−0.750729	+	0.660611i	$0.770297\pi$
$734$	1.58066	0.0583432
$735$	9.41754	0.347371
$736$	−4.99171	−0.183997
$737$	8.57431	0.315839
$738$	0.489026	0.0180013
$739$	−20.6526	−0.759718	−0.379859	−	0.925044i	$-0.624027\pi$
$739$	−20.6526	−0.759718	−0.379859	+	0.925044i	$0.624027\pi$
$740$	68.3223	2.51158
$741$	30.2505	1.11128
$742$	2.05526	0.0754510
$743$	51.0453	1.87267	0.936335	−	0.351109i	$-0.114195\pi$
$743$	51.0453	1.87267	0.936335	+	0.351109i	$0.114195\pi$
$744$	−4.27200	−0.156619
$745$	46.1164	1.68957
$746$	2.22754	0.0815562
$747$	1.74375	0.0638005
$748$	4.98430	0.182244
$749$	22.6658	0.828191
$750$	−0.792410	−0.0289347
$751$	7.21279	0.263198	0.131599	−	0.991303i	$-0.457989\pi$
$751$	7.21279	0.263198	0.131599	+	0.991303i	$0.457989\pi$
$752$	−36.8816	−1.34493
$753$	−5.63807	−0.205463
$754$	−5.89841	−0.214807
$755$	42.7209	1.55477
$756$	−6.17750	−0.224674
$757$	−24.5042	−0.890622	−0.445311	−	0.895376i	$-0.646907\pi$
$757$	−24.5042	−0.890622	−0.445311	+	0.895376i	$0.646907\pi$
$758$	−3.22627	−0.117183
$759$	6.82858	0.247862
$760$	15.0879	0.547297
$761$	−19.8151	−0.718298	−0.359149	−	0.933280i	$-0.616933\pi$
$761$	−19.8151	−0.718298	−0.359149	+	0.933280i	$0.616933\pi$
$762$	−2.90369	−0.105190
$763$	12.3671	0.447718
$764$	−33.1839	−1.20055
$765$	−3.39057	−0.122586
$766$	1.22472	0.0442511
$767$	4.22206	0.152450
$768$	−14.0831	−0.508179
$769$	3.72808	0.134438	0.0672189	−	0.997738i	$-0.478587\pi$
$769$	3.72808	0.134438	0.0672189	+	0.997738i	$0.478587\pi$
$770$	4.17870	0.150590
$771$	16.5378	0.595593
$772$	−35.7247	−1.28576
$773$	−20.2913	−0.729829	−0.364914	−	0.931041i	$-0.618902\pi$
$773$	−20.2913	−0.729829	−0.364914	+	0.931041i	$0.618902\pi$
$774$	1.70941	0.0614435
$775$	44.6816	1.60501
$776$	−0.801074	−0.0287569
$777$	31.8938	1.14419
$778$	3.32662	0.119265
$779$	22.4282	0.803573
$780$	−28.2810	−1.01262
$781$	26.6676	0.954244
$782$	−0.422835	−0.0151205
$783$	−8.94262	−0.319583
$784$	10.7052	0.382328
$785$	−17.1800	−0.613181
$786$	−1.31623	−0.0469482
$787$	35.4974	1.26535	0.632673	−	0.774419i	$-0.281958\pi$
$787$	35.4974	1.26535	0.632673	+	0.774419i	$0.281958\pi$
$788$	35.4434	1.26262
$789$	−15.7729	−0.561531
$790$	6.67562	0.237508
$791$	34.0652	1.21122
$792$	−1.56695	−0.0556790
$793$	38.8429	1.37935
$794$	−1.69448	−0.0601348
$795$	14.2652	0.505936
$796$	−31.5212	−1.11724
$797$	−18.9752	−0.672138	−0.336069	−	0.941837i	$-0.609097\pi$
$797$	−18.9752	−0.672138	−0.336069	+	0.941837i	$0.609097\pi$
$798$	3.50001	0.123899
$799$	−9.56930	−0.338537
$800$	−11.9804	−0.423570
$801$	−5.36888	−0.189700
$802$	4.65501	0.164374
$803$	−15.9860	−0.564135
$804$	−6.71415	−0.236790
$805$	28.6955	1.01138
$806$	−4.53683	−0.159803
$807$	−9.39578	−0.330747
$808$	7.67081	0.269858
$809$	−35.6264	−1.25256	−0.626279	−	0.779599i	$-0.715423\pi$
$809$	−35.6264	−1.25256	−0.626279	+	0.779599i	$0.715423\pi$
$810$	0.529687	0.0186113
$811$	45.9964	1.61515	0.807576	−	0.589764i	$-0.200779\pi$
$811$	45.9964	1.61515	0.807576	+	0.589764i	$0.200779\pi$
$812$	55.2431	1.93865
$813$	18.6250	0.653206
$814$	4.02016	0.140907
$815$	8.96932	0.314181
$816$	−3.85416	−0.134923
$817$	78.3986	2.74282
$818$	3.28675	0.114919
$819$	−13.2020	−0.461315
$820$	−20.9680	−0.732234
$821$	−27.7472	−0.968382	−0.484191	−	0.874962i	$-0.660886\pi$
$821$	−27.7472	−0.968382	−0.484191	+	0.874962i	$0.660886\pi$
$822$	2.65795	0.0927066
$823$	−19.9468	−0.695303	−0.347651	−	0.937624i	$-0.613021\pi$
$823$	−19.9468	−0.695303	−0.347651	+	0.937624i	$0.613021\pi$
$824$	12.0902	0.421183
$825$	16.3890	0.570591
$826$	0.488496	0.0169970
$827$	15.4228	0.536304	0.268152	−	0.963377i	$-0.413587\pi$
$827$	15.4228	0.536304	0.268152	+	0.963377i	$0.413587\pi$
$828$	−5.34715	−0.185826
$829$	−21.2620	−0.738458	−0.369229	−	0.929338i	$-0.620378\pi$
$829$	−21.2620	−0.738458	−0.369229	+	0.929338i	$0.620378\pi$
$830$	0.923643	0.0320601
$831$	1.04274	0.0361722
$832$	−31.3285	−1.08612
$833$	2.77756	0.0962369
$834$	−1.72826	−0.0598448
$835$	18.4470	0.638383
$836$	−35.7118	−1.23512
$837$	−6.87833	−0.237750
$838$	−0.431601	−0.0149094
$839$	6.35131	0.219271	0.109636	−	0.993972i	$-0.465032\pi$
$839$	6.35131	0.219271	0.109636	+	0.993972i	$0.465032\pi$
$840$	−6.58471	−0.227194
$841$	50.9705	1.75760
$842$	1.94648	0.0670802
$843$	24.0538	0.828457
$844$	−47.9449	−1.65033
$845$	−16.3621	−0.562872
$846$	1.49495	0.0513974
$847$	14.4926	0.497971
$848$	16.2157	0.556849
$849$	−6.89511	−0.236639
$850$	−1.01483	−0.0348083
$851$	27.6068	0.946349
$852$	−20.8822	−0.715413
$853$	28.7375	0.983953	0.491977	−	0.870608i	$-0.336275\pi$
$853$	28.7375	0.983953	0.491977	+	0.870608i	$0.336275\pi$
$854$	4.49417	0.153787
$855$	24.2930	0.830804
$856$	−4.50199	−0.153875
$857$	−27.2661	−0.931392	−0.465696	−	0.884945i	$-0.654196\pi$
$857$	−27.2661	−0.931392	−0.465696	+	0.884945i	$0.654196\pi$
$858$	−1.66409	−0.0568110
$859$	−14.4100	−0.491664	−0.245832	−	0.969312i	$-0.579061\pi$
$859$	−14.4100	−0.491664	−0.245832	+	0.969312i	$0.579061\pi$
$860$	−73.2945	−2.49932
$861$	−9.78817	−0.333580
$862$	−3.09469	−0.105406
$863$	−34.2404	−1.16556	−0.582779	−	0.812631i	$-0.698035\pi$
$863$	−34.2404	−1.16556	−0.582779	+	0.812631i	$0.698035\pi$
$864$	1.84427	0.0627434
$865$	−46.4119	−1.57805
$866$	−3.20170	−0.108798
$867$	−1.00000	−0.0339618
$868$	42.4909	1.44223
$869$	−31.7964	−1.07862
$870$	−4.73679	−0.160592
$871$	−14.3488	−0.486192
$872$	−2.45640	−0.0831842
$873$	−1.28981	−0.0436533
$874$	3.02955	0.102476
$875$	15.8606	0.536186
$876$	12.5179	0.422941
$877$	17.8687	0.603382	0.301691	−	0.953406i	$-0.402449\pi$
$877$	17.8687	0.603382	0.301691	+	0.953406i	$0.402449\pi$
$878$	−1.96602	−0.0663499
$879$	18.8882	0.637083
$880$	32.9693	1.11139
$881$	−21.9037	−0.737954	−0.368977	−	0.929439i	$-0.620292\pi$
$881$	−21.9037	−0.737954	−0.368977	+	0.929439i	$0.620292\pi$
$882$	−0.433920	−0.0146109
$883$	−25.8490	−0.869889	−0.434944	−	0.900457i	$-0.643232\pi$
$883$	−25.8490	−0.869889	−0.434944	+	0.900457i	$0.643232\pi$
$884$	−8.34107	−0.280540
$885$	3.39057	0.113973
$886$	2.69274	0.0904644
$887$	−40.8417	−1.37133	−0.685665	−	0.727917i	$-0.740489\pi$
$887$	−40.8417	−1.37133	−0.685665	+	0.727917i	$0.740489\pi$
$888$	−6.33490	−0.212585
$889$	58.1193	1.94926
$890$	−2.84383	−0.0953253
$891$	−2.52294	−0.0845215
$892$	27.0076	0.904281
$893$	68.5627	2.29436
$894$	−2.12485	−0.0710656
$895$	−13.5342	−0.452399
$896$	−15.1585	−0.506409
$897$	−11.4274	−0.381551
$898$	5.13283	0.171285
$899$	61.5103	2.05148
$900$	−12.8335	−0.427782
$901$	4.20732	0.140166
$902$	−1.23378	−0.0410804
$903$	−34.2149	−1.13860
$904$	−6.76618	−0.225040
$905$	0.988178	0.0328482
$906$	−1.96840	−0.0653957
$907$	15.2275	0.505622	0.252811	−	0.967516i	$-0.418645\pi$
$907$	15.2275	0.505622	0.252811	+	0.967516i	$0.418645\pi$
$908$	−24.5758	−0.815577
$909$	12.3507	0.409648
$910$	−6.99292	−0.231813
$911$	−36.3007	−1.20270	−0.601348	−	0.798988i	$-0.705369\pi$
$911$	−36.3007	−1.20270	−0.601348	+	0.798988i	$0.705369\pi$
$912$	27.6145	0.914409
$913$	−4.39937	−0.145598
$914$	−3.64429	−0.120542
$915$	31.1933	1.03122
$916$	−21.5990	−0.713650
$917$	26.3451	0.869992
$918$	0.156223	0.00515614
$919$	52.2106	1.72227	0.861134	−	0.508378i	$-0.169755\pi$
$919$	52.2106	1.72227	0.861134	+	0.508378i	$0.169755\pi$
$920$	−5.69962	−0.187911
$921$	−10.8392	−0.357162
$922$	2.40897	0.0793353
$923$	−44.6275	−1.46893
$924$	15.5854	0.512723
$925$	66.2579	2.17854
$926$	0.179771	0.00590765
$927$	19.4664	0.639361
$928$	−16.4926	−0.541397
$929$	41.3662	1.35718	0.678591	−	0.734517i	$-0.262591\pi$
$929$	41.3662	1.35718	0.678591	+	0.734517i	$0.262591\pi$
$930$	−3.64336	−0.119470
$931$	−19.9009	−0.652225
$932$	45.5996	1.49366
$933$	6.37014	0.208549
$934$	−0.309341	−0.0101219
$935$	8.55420	0.279752
$936$	2.62224	0.0857105
$937$	−54.3294	−1.77487	−0.887433	−	0.460937i	$-0.847513\pi$
$937$	−54.3294	−1.77487	−0.887433	+	0.460937i	$0.847513\pi$
$938$	−1.66018	−0.0542067
$939$	−11.0483	−0.360549
$940$	−64.0990	−2.09068
$941$	−2.28248	−0.0744067	−0.0372033	−	0.999308i	$-0.511845\pi$
$941$	−2.28248	−0.0744067	−0.0372033	+	0.999308i	$0.511845\pi$
$942$	0.791582	0.0257911
$943$	−8.47248	−0.275902
$944$	3.85416	0.125442
$945$	−10.6020	−0.344884
$946$	−4.31273	−0.140219
$947$	−4.28207	−0.139148	−0.0695742	−	0.997577i	$-0.522164\pi$
$947$	−4.28207	−0.139148	−0.0695742	+	0.997577i	$0.522164\pi$
$948$	24.8983	0.808659
$949$	26.7521	0.868411
$950$	7.27110	0.235906
$951$	31.7445	1.02938
$952$	−1.94206	−0.0629426
$953$	−3.81901	−0.123710	−0.0618549	−	0.998085i	$-0.519702\pi$
$953$	−3.81901	−0.123710	−0.0618549	+	0.998085i	$0.519702\pi$
$954$	−0.657282	−0.0212803
$955$	−56.9512	−1.84290
$956$	47.7934	1.54575
$957$	22.5617	0.729315
$958$	−3.88922	−0.125655
$959$	−53.2005	−1.71793
$960$	−25.1588	−0.811995
$961$	16.3114	0.526173
$962$	−6.72762	−0.216907
$963$	−7.24863	−0.233584
$964$	−37.7905	−1.21715
$965$	−61.3118	−1.97370
$966$	−1.32217	−0.0425400
$967$	−52.6522	−1.69318	−0.846590	−	0.532246i	$-0.821348\pi$
$967$	−52.6522	−1.69318	−0.846590	+	0.532246i	$0.821348\pi$
$968$	−2.87858	−0.0925212
$969$	7.16487	0.230169
$970$	−0.683193	−0.0219360
$971$	−55.9281	−1.79482	−0.897409	−	0.441199i	$-0.854553\pi$
$971$	−55.9281	−1.79482	−0.897409	+	0.441199i	$0.854553\pi$
$972$	1.97559	0.0633672
$973$	34.5922	1.10898
$974$	5.49832	0.176177
$975$	−27.4265	−0.878350
$976$	35.4583	1.13499
$977$	19.0024	0.607941	0.303970	−	0.952681i	$-0.401688\pi$
$977$	19.0024	0.607941	0.303970	+	0.952681i	$0.401688\pi$
$978$	−0.413268	−0.0132149
$979$	13.5453	0.432911
$980$	18.6052	0.594322
$981$	−3.95504	−0.126275
$982$	2.29208	0.0731431
$983$	54.4337	1.73617	0.868083	−	0.496419i	$-0.165352\pi$
$983$	54.4337	1.73617	0.868083	+	0.496419i	$0.165352\pi$
$984$	1.94417	0.0619779
$985$	60.8291	1.93818
$986$	−1.39705	−0.0444910
$987$	−29.9223	−0.952438
$988$	59.7626	1.90130
$989$	−29.6159	−0.941730
$990$	−1.33637	−0.0424725
$991$	−42.8062	−1.35978	−0.679891	−	0.733313i	$-0.737973\pi$
$991$	−42.8062	−1.35978	−0.679891	+	0.733313i	$0.737973\pi$
$992$	−12.6855	−0.402765
$993$	−29.9484	−0.950383
$994$	−5.16345	−0.163775
$995$	−54.0977	−1.71501
$996$	3.44495	0.109157
$997$	15.1146	0.478684	0.239342	−	0.970935i	$-0.423068\pi$
$997$	15.1146	0.478684	0.239342	+	0.970935i	$0.423068\pi$
$998$	1.79417	0.0567933
$999$	−10.1998	−0.322707

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3009.2.a.f.1.9	✓	16
3.2	odd	2		9027.2.a.m.1.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3009.2.a.f.1.9	✓	16	1.1	even	1	trivial
9027.2.a.m.1.8		16	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3009 = 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3009.a (trivial)

\(f(q)\)	\(=\)	\(q-0.156223 q^{2} -1.00000 q^{3} -1.97559 q^{4} -3.39057 q^{5} +0.156223 q^{6} -3.12691 q^{7} +0.621081 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.156223 q^{2} -1.00000 q^{3} -1.97559 q^{4} -3.39057 q^{5} +0.156223 q^{6} -3.12691 q^{7} +0.621081 q^{8} +1.00000 q^{9} +0.529687 q^{10} -2.52294 q^{11} +1.97559 q^{12} +4.22206 q^{13} +0.488496 q^{14} +3.39057 q^{15} +3.85416 q^{16} +1.00000 q^{17} -0.156223 q^{18} -7.16487 q^{19} +6.69840 q^{20} +3.12691 q^{21} +0.394141 q^{22} +2.70660 q^{23} -0.621081 q^{24} +6.49600 q^{25} -0.659584 q^{26} -1.00000 q^{27} +6.17750 q^{28} +8.94262 q^{29} -0.529687 q^{30} +6.87833 q^{31} -1.84427 q^{32} +2.52294 q^{33} -0.156223 q^{34} +10.6020 q^{35} -1.97559 q^{36} +10.1998 q^{37} +1.11932 q^{38} -4.22206 q^{39} -2.10582 q^{40} -3.13030 q^{41} -0.488496 q^{42} -10.9421 q^{43} +4.98430 q^{44} -3.39057 q^{45} -0.422835 q^{46} -9.56930 q^{47} -3.85416 q^{48} +2.77756 q^{49} -1.01483 q^{50} -1.00000 q^{51} -8.34107 q^{52} +4.20732 q^{53} +0.156223 q^{54} +8.55420 q^{55} -1.94206 q^{56} +7.16487 q^{57} -1.39705 q^{58} +1.00000 q^{59} -6.69840 q^{60} +9.20001 q^{61} -1.07456 q^{62} -3.12691 q^{63} -7.42020 q^{64} -14.3152 q^{65} -0.394141 q^{66} -3.39855 q^{67} -1.97559 q^{68} -2.70660 q^{69} -1.65628 q^{70} -10.5701 q^{71} +0.621081 q^{72} +6.33628 q^{73} -1.59345 q^{74} -6.49600 q^{75} +14.1549 q^{76} +7.88899 q^{77} +0.659584 q^{78} +12.6029 q^{79} -13.0678 q^{80} +1.00000 q^{81} +0.489026 q^{82} +1.74375 q^{83} -6.17750 q^{84} -3.39057 q^{85} +1.70941 q^{86} -8.94262 q^{87} -1.56695 q^{88} -5.36888 q^{89} +0.529687 q^{90} -13.2020 q^{91} -5.34715 q^{92} -6.87833 q^{93} +1.49495 q^{94} +24.2930 q^{95} +1.84427 q^{96} -1.28981 q^{97} -0.433920 q^{98} -2.52294 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 16 q^{3} + 10 q^{4} - 3 q^{5} + 4 q^{6} - 3 q^{7} - 9 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 16 * q^3 + 10 * q^4 - 3 * q^5 + 4 * q^6 - 3 * q^7 - 9 * q^8 + 16 * q^9	\( 16 q - 4 q^{2} - 16 q^{3} + 10 q^{4} - 3 q^{5} + 4 q^{6} - 3 q^{7} - 9 q^{8} + 16 q^{9} - 7 q^{11} - 10 q^{12} + 7 q^{13} - 13 q^{14} + 3 q^{15} + 2 q^{16} + 16 q^{17} - 4 q^{18} - 19 q^{19} - 17 q^{20} + 3 q^{21} + 23 q^{22} - 16 q^{23} + 9 q^{24} + 5 q^{25} - 11 q^{26} - 16 q^{27} + 8 q^{28} + 4 q^{29} - 15 q^{31} - 22 q^{32} + 7 q^{33} - 4 q^{34} - 23 q^{35} + 10 q^{36} + 20 q^{37} - 17 q^{38} - 7 q^{39} + 21 q^{40} - 4 q^{41} + 13 q^{42} - 12 q^{43} - 19 q^{44} - 3 q^{45} + 24 q^{46} - 36 q^{47} - 2 q^{48} - 11 q^{49} + 9 q^{50} - 16 q^{51} + 6 q^{52} - 32 q^{53} + 4 q^{54} - 29 q^{55} - 11 q^{56} + 19 q^{57} - 33 q^{58} + 16 q^{59} + 17 q^{60} + 11 q^{62} - 3 q^{63} + 9 q^{64} - 5 q^{65} - 23 q^{66} - 30 q^{67} + 10 q^{68} + 16 q^{69} + 16 q^{70} - 70 q^{71} - 9 q^{72} + 21 q^{73} - 29 q^{74} - 5 q^{75} - 8 q^{76} - 13 q^{77} + 11 q^{78} - 25 q^{79} - 9 q^{80} + 16 q^{81} + 22 q^{82} - 23 q^{83} - 8 q^{84} - 3 q^{85} - 58 q^{86} - 4 q^{87} + 41 q^{88} - 31 q^{89} - 36 q^{91} - 26 q^{92} + 15 q^{93} + 9 q^{94} - 10 q^{95} + 22 q^{96} + 52 q^{97} - 36 q^{98} - 7 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 16 * q^3 + 10 * q^4 - 3 * q^5 + 4 * q^6 - 3 * q^7 - 9 * q^8 + 16 * q^9 - 7 * q^11 - 10 * q^12 + 7 * q^13 - 13 * q^14 + 3 * q^15 + 2 * q^16 + 16 * q^17 - 4 * q^18 - 19 * q^19 - 17 * q^20 + 3 * q^21 + 23 * q^22 - 16 * q^23 + 9 * q^24 + 5 * q^25 - 11 * q^26 - 16 * q^27 + 8 * q^28 + 4 * q^29 - 15 * q^31 - 22 * q^32 + 7 * q^33 - 4 * q^34 - 23 * q^35 + 10 * q^36 + 20 * q^37 - 17 * q^38 - 7 * q^39 + 21 * q^40 - 4 * q^41 + 13 * q^42 - 12 * q^43 - 19 * q^44 - 3 * q^45 + 24 * q^46 - 36 * q^47 - 2 * q^48 - 11 * q^49 + 9 * q^50 - 16 * q^51 + 6 * q^52 - 32 * q^53 + 4 * q^54 - 29 * q^55 - 11 * q^56 + 19 * q^57 - 33 * q^58 + 16 * q^59 + 17 * q^60 + 11 * q^62 - 3 * q^63 + 9 * q^64 - 5 * q^65 - 23 * q^66 - 30 * q^67 + 10 * q^68 + 16 * q^69 + 16 * q^70 - 70 * q^71 - 9 * q^72 + 21 * q^73 - 29 * q^74 - 5 * q^75 - 8 * q^76 - 13 * q^77 + 11 * q^78 - 25 * q^79 - 9 * q^80 + 16 * q^81 + 22 * q^82 - 23 * q^83 - 8 * q^84 - 3 * q^85 - 58 * q^86 - 4 * q^87 + 41 * q^88 - 31 * q^89 - 36 * q^91 - 26 * q^92 + 15 * q^93 + 9 * q^94 - 10 * q^95 + 22 * q^96 + 52 * q^97 - 36 * q^98 - 7 * q^99

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