LMFDB - Embedded newform 4334.2.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 7 x^{16} - 7 x^{15} + 137 x^{14} - 98 x^{13} - 1048 x^{12} + 1313 x^{11} + 4085 x^{10} + \cdots - 400 $ x^17 - 7x^16 - 7x^15 + 137x^14 - 98x^13 - 1048x^12 + 1313x^11 + 4085x^10 - 6021x^9 - 8879x^8 + 13530x^7 + 11150x^6 - 15676x^5 - 8037x^4 + 8646x^3 + 3040x^2 - 1640x - 400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.32994$ of defining polynomial
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.32994 q^{3} +1.00000 q^{4} +2.68374 q^{5} -1.32994 q^{6} -0.271741 q^{7} +1.00000 q^{8} -1.23125 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.32994 q^{3} +1.00000 q^{4} +2.68374 q^{5} -1.32994 q^{6} -0.271741 q^{7} +1.00000 q^{8} -1.23125 q^{9} +2.68374 q^{10} -1.00000 q^{11} -1.32994 q^{12} -3.60687 q^{13} -0.271741 q^{14} -3.56923 q^{15} +1.00000 q^{16} +3.57613 q^{17} -1.23125 q^{18} -6.16240 q^{19} +2.68374 q^{20} +0.361400 q^{21} -1.00000 q^{22} -1.64935 q^{23} -1.32994 q^{24} +2.20248 q^{25} -3.60687 q^{26} +5.62732 q^{27} -0.271741 q^{28} +9.35997 q^{29} -3.56923 q^{30} -10.4870 q^{31} +1.00000 q^{32} +1.32994 q^{33} +3.57613 q^{34} -0.729283 q^{35} -1.23125 q^{36} -1.20418 q^{37} -6.16240 q^{38} +4.79693 q^{39} +2.68374 q^{40} -8.85415 q^{41} +0.361400 q^{42} +0.180032 q^{43} -1.00000 q^{44} -3.30436 q^{45} -1.64935 q^{46} -11.9099 q^{47} -1.32994 q^{48} -6.92616 q^{49} +2.20248 q^{50} -4.75605 q^{51} -3.60687 q^{52} +4.30849 q^{53} +5.62732 q^{54} -2.68374 q^{55} -0.271741 q^{56} +8.19564 q^{57} +9.35997 q^{58} -9.47874 q^{59} -3.56923 q^{60} +11.7600 q^{61} -10.4870 q^{62} +0.334581 q^{63} +1.00000 q^{64} -9.67990 q^{65} +1.32994 q^{66} +11.6216 q^{67} +3.57613 q^{68} +2.19354 q^{69} -0.729283 q^{70} +2.55648 q^{71} -1.23125 q^{72} -16.4298 q^{73} -1.20418 q^{74} -2.92917 q^{75} -6.16240 q^{76} +0.271741 q^{77} +4.79693 q^{78} +10.8849 q^{79} +2.68374 q^{80} -3.79028 q^{81} -8.85415 q^{82} -12.9708 q^{83} +0.361400 q^{84} +9.59742 q^{85} +0.180032 q^{86} -12.4482 q^{87} -1.00000 q^{88} -10.6565 q^{89} -3.30436 q^{90} +0.980133 q^{91} -1.64935 q^{92} +13.9471 q^{93} -11.9099 q^{94} -16.5383 q^{95} -1.32994 q^{96} +0.238015 q^{97} -6.92616 q^{98} +1.23125 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 17 q^{2} - 7 q^{3} + 17 q^{4} - 4 q^{5} - 7 q^{6} - 5 q^{7} + 17 q^{8} + 12 q^{9}+O(q^{10}) $ 17 * q + 17 * q^2 - 7 * q^3 + 17 * q^4 - 4 * q^5 - 7 * q^6 - 5 * q^7 + 17 * q^8 + 12 * q^9	\( 17 q + 17 q^{2} - 7 q^{3} + 17 q^{4} - 4 q^{5} - 7 q^{6} - 5 q^{7} + 17 q^{8} + 12 q^{9} - 4 q^{10} - 17 q^{11} - 7 q^{12} - 18 q^{13} - 5 q^{14} - 16 q^{15} + 17 q^{16} - 10 q^{17} + 12 q^{18} - 31 q^{19} - 4 q^{20} - 13 q^{21} - 17 q^{22} - 6 q^{23} - 7 q^{24} + 3 q^{25} - 18 q^{26} - 37 q^{27} - 5 q^{28} - 16 q^{29} - 16 q^{30} - 30 q^{31} + 17 q^{32} + 7 q^{33} - 10 q^{34} - 36 q^{35} + 12 q^{36} - 23 q^{37} - 31 q^{38} - 15 q^{39} - 4 q^{40} - 7 q^{41} - 13 q^{42} - 23 q^{43} - 17 q^{44} - 19 q^{45} - 6 q^{46} - 19 q^{47} - 7 q^{48} - 8 q^{49} + 3 q^{50} - 18 q^{51} - 18 q^{52} - 30 q^{53} - 37 q^{54} + 4 q^{55} - 5 q^{56} + 10 q^{57} - 16 q^{58} - 28 q^{59} - 16 q^{60} - 19 q^{61} - 30 q^{62} + 2 q^{63} + 17 q^{64} + 23 q^{65} + 7 q^{66} - 35 q^{67} - 10 q^{68} + q^{69} - 36 q^{70} + q^{71} + 12 q^{72} - 10 q^{73} - 23 q^{74} - 33 q^{75} - 31 q^{76} + 5 q^{77} - 15 q^{78} - 27 q^{79} - 4 q^{80} + 13 q^{81} - 7 q^{82} - 40 q^{83} - 13 q^{84} - 11 q^{85} - 23 q^{86} - 6 q^{87} - 17 q^{88} - 17 q^{89} - 19 q^{90} - 19 q^{91} - 6 q^{92} + 10 q^{93} - 19 q^{94} - 27 q^{95} - 7 q^{96} - 34 q^{97} - 8 q^{98} - 12 q^{99}+O(q^{100}) \) 17 * q + 17 * q^2 - 7 * q^3 + 17 * q^4 - 4 * q^5 - 7 * q^6 - 5 * q^7 + 17 * q^8 + 12 * q^9 - 4 * q^10 - 17 * q^11 - 7 * q^12 - 18 * q^13 - 5 * q^14 - 16 * q^15 + 17 * q^16 - 10 * q^17 + 12 * q^18 - 31 * q^19 - 4 * q^20 - 13 * q^21 - 17 * q^22 - 6 * q^23 - 7 * q^24 + 3 * q^25 - 18 * q^26 - 37 * q^27 - 5 * q^28 - 16 * q^29 - 16 * q^30 - 30 * q^31 + 17 * q^32 + 7 * q^33 - 10 * q^34 - 36 * q^35 + 12 * q^36 - 23 * q^37 - 31 * q^38 - 15 * q^39 - 4 * q^40 - 7 * q^41 - 13 * q^42 - 23 * q^43 - 17 * q^44 - 19 * q^45 - 6 * q^46 - 19 * q^47 - 7 * q^48 - 8 * q^49 + 3 * q^50 - 18 * q^51 - 18 * q^52 - 30 * q^53 - 37 * q^54 + 4 * q^55 - 5 * q^56 + 10 * q^57 - 16 * q^58 - 28 * q^59 - 16 * q^60 - 19 * q^61 - 30 * q^62 + 2 * q^63 + 17 * q^64 + 23 * q^65 + 7 * q^66 - 35 * q^67 - 10 * q^68 + q^69 - 36 * q^70 + q^71 + 12 * q^72 - 10 * q^73 - 23 * q^74 - 33 * q^75 - 31 * q^76 + 5 * q^77 - 15 * q^78 - 27 * q^79 - 4 * q^80 + 13 * q^81 - 7 * q^82 - 40 * q^83 - 13 * q^84 - 11 * q^85 - 23 * q^86 - 6 * q^87 - 17 * q^88 - 17 * q^89 - 19 * q^90 - 19 * q^91 - 6 * q^92 + 10 * q^93 - 19 * q^94 - 27 * q^95 - 7 * q^96 - 34 * q^97 - 8 * q^98 - 12 * 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
$3$	−1.32994	−0.767843	−0.383922	−	0.923366i	$-0.625427\pi$
$3$	−1.32994	−0.767843	−0.383922	+	0.923366i	$0.625427\pi$
$4$	1.00000	0.500000
$5$	2.68374	1.20021	0.600103	−	0.799922i	$-0.295126\pi$
$5$	2.68374	1.20021	0.600103	+	0.799922i	$0.295126\pi$
$6$	−1.32994	−0.542947
$7$	−0.271741	−0.102708	−0.0513542	−	0.998681i	$-0.516354\pi$
$7$	−0.271741	−0.102708	−0.0513542	+	0.998681i	$0.516354\pi$
$8$	1.00000	0.353553
$9$	−1.23125	−0.410416
$10$	2.68374	0.848674
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.32994	−0.383922
$13$	−3.60687	−1.00036	−0.500182	−	0.865920i	$-0.666734\pi$
$13$	−3.60687	−1.00036	−0.500182	+	0.865920i	$0.666734\pi$
$14$	−0.271741	−0.0726258
$15$	−3.56923	−0.921571
$16$	1.00000	0.250000
$17$	3.57613	0.867339	0.433670	−	0.901072i	$-0.357219\pi$
$17$	3.57613	0.867339	0.433670	+	0.901072i	$0.357219\pi$
$18$	−1.23125	−0.290208
$19$	−6.16240	−1.41375	−0.706875	−	0.707338i	$-0.749896\pi$
$19$	−6.16240	−1.41375	−0.706875	+	0.707338i	$0.749896\pi$
$20$	2.68374	0.600103
$21$	0.361400	0.0788640
$22$	−1.00000	−0.213201
$23$	−1.64935	−0.343912	−0.171956	−	0.985105i	$-0.555009\pi$
$23$	−1.64935	−0.343912	−0.171956	+	0.985105i	$0.555009\pi$
$24$	−1.32994	−0.271474
$25$	2.20248	0.440496
$26$	−3.60687	−0.707365
$27$	5.62732	1.08298
$28$	−0.271741	−0.0513542
$29$	9.35997	1.73810	0.869051	−	0.494722i	$-0.164730\pi$
$29$	9.35997	1.73810	0.869051	+	0.494722i	$0.164730\pi$
$30$	−3.56923	−0.651649
$31$	−10.4870	−1.88352	−0.941761	−	0.336283i	$-0.890830\pi$
$31$	−10.4870	−1.88352	−0.941761	+	0.336283i	$0.890830\pi$
$32$	1.00000	0.176777
$33$	1.32994	0.231514
$34$	3.57613	0.613301
$35$	−0.729283	−0.123271
$36$	−1.23125	−0.205208
$37$	−1.20418	−0.197965	−0.0989827	−	0.995089i	$-0.531559\pi$
$37$	−1.20418	−0.197965	−0.0989827	+	0.995089i	$0.531559\pi$
$38$	−6.16240	−0.999673
$39$	4.79693	0.768123
$40$	2.68374	0.424337
$41$	−8.85415	−1.38279	−0.691393	−	0.722479i	$-0.743003\pi$
$41$	−8.85415	−1.38279	−0.691393	+	0.722479i	$0.743003\pi$
$42$	0.361400	0.0557653
$43$	0.180032	0.0274546	0.0137273	−	0.999906i	$-0.495630\pi$
$43$	0.180032	0.0274546	0.0137273	+	0.999906i	$0.495630\pi$
$44$	−1.00000	−0.150756
$45$	−3.30436	−0.492585
$46$	−1.64935	−0.243183
$47$	−11.9099	−1.73723	−0.868616	−	0.495487i	$-0.834990\pi$
$47$	−11.9099	−1.73723	−0.868616	+	0.495487i	$0.834990\pi$
$48$	−1.32994	−0.191961
$49$	−6.92616	−0.989451
$50$	2.20248	0.311478
$51$	−4.75605	−0.665981
$52$	−3.60687	−0.500182
$53$	4.30849	0.591817	0.295909	−	0.955216i	$-0.404378\pi$
$53$	4.30849	0.591817	0.295909	+	0.955216i	$0.404378\pi$
$54$	5.62732	0.765782
$55$	−2.68374	−0.361876
$56$	−0.271741	−0.0363129
$57$	8.19564	1.08554
$58$	9.35997	1.22902
$59$	−9.47874	−1.23403	−0.617014	−	0.786952i	$-0.711658\pi$
$59$	−9.47874	−1.23403	−0.617014	+	0.786952i	$0.711658\pi$
$60$	−3.56923	−0.460785
$61$	11.7600	1.50572	0.752858	−	0.658183i	$-0.228675\pi$
$61$	11.7600	1.50572	0.752858	+	0.658183i	$0.228675\pi$
$62$	−10.4870	−1.33185
$63$	0.334581	0.0421532
$64$	1.00000	0.125000
$65$	−9.67990	−1.20064
$66$	1.32994	0.163705
$67$	11.6216	1.41981	0.709905	−	0.704297i	$-0.248738\pi$
$67$	11.6216	1.41981	0.709905	+	0.704297i	$0.248738\pi$
$68$	3.57613	0.433670
$69$	2.19354	0.264071
$70$	−0.729283	−0.0871660
$71$	2.55648	0.303398	0.151699	−	0.988427i	$-0.451526\pi$
$71$	2.55648	0.303398	0.151699	+	0.988427i	$0.451526\pi$
$72$	−1.23125	−0.145104
$73$	−16.4298	−1.92296	−0.961482	−	0.274868i	$-0.911366\pi$
$73$	−16.4298	−1.92296	−0.961482	+	0.274868i	$0.911366\pi$
$74$	−1.20418	−0.139983
$75$	−2.92917	−0.338232
$76$	−6.16240	−0.706875
$77$	0.271741	0.0309678
$78$	4.79693	0.543145
$79$	10.8849	1.22465	0.612325	−	0.790606i	$-0.290234\pi$
$79$	10.8849	1.22465	0.612325	+	0.790606i	$0.290234\pi$
$80$	2.68374	0.300052
$81$	−3.79028	−0.421142
$82$	−8.85415	−0.977778
$83$	−12.9708	−1.42373	−0.711863	−	0.702318i	$-0.752148\pi$
$83$	−12.9708	−1.42373	−0.711863	+	0.702318i	$0.752148\pi$
$84$	0.361400	0.0394320
$85$	9.59742	1.04099
$86$	0.180032	0.0194133
$87$	−12.4482	−1.33459
$88$	−1.00000	−0.106600
$89$	−10.6565	−1.12959	−0.564796	−	0.825231i	$-0.691045\pi$
$89$	−10.6565	−1.12959	−0.564796	+	0.825231i	$0.691045\pi$
$90$	−3.30436	−0.348310
$91$	0.980133	0.102746
$92$	−1.64935	−0.171956
$93$	13.9471	1.44625
$94$	−11.9099	−1.22841
$95$	−16.5383	−1.69679
$96$	−1.32994	−0.135737
$97$	0.238015	0.0241668	0.0120834	−	0.999927i	$-0.496154\pi$
$97$	0.238015	0.0241668	0.0120834	+	0.999927i	$0.496154\pi$
$98$	−6.92616	−0.699647
$99$	1.23125	0.123745
$100$	2.20248	0.220248
$101$	9.99957	0.994994	0.497497	−	0.867466i	$-0.334252\pi$
$101$	9.99957	0.994994	0.497497	+	0.867466i	$0.334252\pi$
$102$	−4.75605	−0.470919
$103$	−19.5459	−1.92591	−0.962956	−	0.269659i	$-0.913089\pi$
$103$	−19.5459	−1.92591	−0.962956	+	0.269659i	$0.913089\pi$
$104$	−3.60687	−0.353682
$105$	0.969905	0.0946531
$106$	4.30849	0.418478
$107$	6.44571	0.623130	0.311565	−	0.950225i	$-0.399147\pi$
$107$	6.44571	0.623130	0.311565	+	0.950225i	$0.399147\pi$
$108$	5.62732	0.541490
$109$	8.20912	0.786291	0.393146	−	0.919476i	$-0.371387\pi$
$109$	8.20912	0.786291	0.393146	+	0.919476i	$0.371387\pi$
$110$	−2.68374	−0.255885
$111$	1.60149	0.152007
$112$	−0.271741	−0.0256771
$113$	−20.8137	−1.95799	−0.978994	−	0.203887i	$-0.934642\pi$
$113$	−20.8137	−1.95799	−0.978994	+	0.203887i	$0.934642\pi$
$114$	8.19564	0.767592
$115$	−4.42642	−0.412766
$116$	9.35997	0.869051
$117$	4.44095	0.410566
$118$	−9.47874	−0.872589
$119$	−0.971781	−0.0890830
$120$	−3.56923	−0.325824
$121$	1.00000	0.0909091
$122$	11.7600	1.06470
$123$	11.7755	1.06176
$124$	−10.4870	−0.941761
$125$	−7.50783	−0.671520
$126$	0.334581	0.0298068
$127$	2.37831	0.211041	0.105520	−	0.994417i	$-0.466349\pi$
$127$	2.37831	0.211041	0.105520	+	0.994417i	$0.466349\pi$
$128$	1.00000	0.0883883
$129$	−0.239432	−0.0210808
$130$	−9.67990	−0.848984
$131$	−8.86124	−0.774210	−0.387105	−	0.922036i	$-0.626525\pi$
$131$	−8.86124	−0.774210	−0.387105	+	0.922036i	$0.626525\pi$
$132$	1.32994	0.115757
$133$	1.67458	0.145204
$134$	11.6216	1.00396
$135$	15.1023	1.29980
$136$	3.57613	0.306651
$137$	13.4152	1.14614	0.573069	−	0.819507i	$-0.305753\pi$
$137$	13.4152	1.14614	0.573069	+	0.819507i	$0.305753\pi$
$138$	2.19354	0.186726
$139$	0.621085	0.0526798	0.0263399	−	0.999653i	$-0.491615\pi$
$139$	0.621085	0.0526798	0.0263399	+	0.999653i	$0.491615\pi$
$140$	−0.729283	−0.0616357
$141$	15.8394	1.33392
$142$	2.55648	0.214535
$143$	3.60687	0.301621
$144$	−1.23125	−0.102604
$145$	25.1198	2.08608
$146$	−16.4298	−1.35974
$147$	9.21140	0.759743
$148$	−1.20418	−0.0989827
$149$	−19.5922	−1.60505	−0.802527	−	0.596615i	$-0.796512\pi$
$149$	−19.5922	−1.60505	−0.802527	+	0.596615i	$0.796512\pi$
$150$	−2.92917	−0.239166
$151$	13.4404	1.09377	0.546883	−	0.837209i	$-0.315814\pi$
$151$	13.4404	1.09377	0.546883	+	0.837209i	$0.315814\pi$
$152$	−6.16240	−0.499836
$153$	−4.40311	−0.355970
$154$	0.271741	0.0218975
$155$	−28.1444	−2.26062
$156$	4.79693	0.384062
$157$	20.9249	1.66999	0.834996	−	0.550256i	$-0.185470\pi$
$157$	20.9249	1.66999	0.834996	+	0.550256i	$0.185470\pi$
$158$	10.8849	0.865959
$159$	−5.73005	−0.454423
$160$	2.68374	0.212169
$161$	0.448195	0.0353227
$162$	−3.79028	−0.297792
$163$	3.61003	0.282760	0.141380	−	0.989955i	$-0.454846\pi$
$163$	3.61003	0.282760	0.141380	+	0.989955i	$0.454846\pi$
$164$	−8.85415	−0.691393
$165$	3.56923	0.277864
$166$	−12.9708	−1.00673
$167$	−10.4550	−0.809032	−0.404516	−	0.914531i	$-0.632560\pi$
$167$	−10.4550	−0.809032	−0.404516	+	0.914531i	$0.632560\pi$
$168$	0.361400	0.0278826
$169$	0.00948491	0.000729609 0
$170$	9.59742	0.736088
$171$	7.58745	0.580227
$172$	0.180032	0.0137273
$173$	2.20541	0.167674	0.0838371	−	0.996479i	$-0.473282\pi$
$173$	2.20541	0.167674	0.0838371	+	0.996479i	$0.473282\pi$
$174$	−12.4482	−0.943698
$175$	−0.598504	−0.0452427
$176$	−1.00000	−0.0753778
$177$	12.6062	0.947540
$178$	−10.6565	−0.798742
$179$	6.09720	0.455726	0.227863	−	0.973693i	$-0.426826\pi$
$179$	6.09720	0.455726	0.227863	+	0.973693i	$0.426826\pi$
$180$	−3.30436	−0.246292
$181$	20.0184	1.48796	0.743978	−	0.668204i	$-0.232937\pi$
$181$	20.0184	1.48796	0.743978	+	0.668204i	$0.232937\pi$
$182$	0.980133	0.0726523
$183$	−15.6402	−1.15615
$184$	−1.64935	−0.121591
$185$	−3.23170	−0.237600
$186$	13.9471	1.02265
$187$	−3.57613	−0.261513
$188$	−11.9099	−0.868616
$189$	−1.52917	−0.111231
$190$	−16.5383	−1.19981
$191$	8.64204	0.625316	0.312658	−	0.949866i	$-0.398781\pi$
$191$	8.64204	0.625316	0.312658	+	0.949866i	$0.398781\pi$
$192$	−1.32994	−0.0959804
$193$	−1.61666	−0.116370	−0.0581850	−	0.998306i	$-0.518531\pi$
$193$	−1.61666	−0.116370	−0.0581850	+	0.998306i	$0.518531\pi$
$194$	0.238015	0.0170885
$195$	12.8737	0.921907
$196$	−6.92616	−0.494725
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	1.23125	0.0875011
$199$	−4.43218	−0.314189	−0.157094	−	0.987584i	$-0.550213\pi$
$199$	−4.43218	−0.314189	−0.157094	+	0.987584i	$0.550213\pi$
$200$	2.20248	0.155739
$201$	−15.4561	−1.09019
$202$	9.99957	0.703567
$203$	−2.54349	−0.178518
$204$	−4.75605	−0.332990
$205$	−23.7623	−1.65963
$206$	−19.5459	−1.36183
$207$	2.03076	0.141147
$208$	−3.60687	−0.250091
$209$	6.16240	0.426262
$210$	0.969905	0.0669298
$211$	−8.57336	−0.590215	−0.295107	−	0.955464i	$-0.595355\pi$
$211$	−8.57336	−0.590215	−0.295107	+	0.955464i	$0.595355\pi$
$212$	4.30849	0.295909
$213$	−3.39997	−0.232962
$214$	6.44571	0.440620
$215$	0.483159	0.0329512
$216$	5.62732	0.382891
$217$	2.84975	0.193454
$218$	8.20912	0.555992
$219$	21.8507	1.47654
$220$	−2.68374	−0.180938
$221$	−12.8986	−0.867656
$222$	1.60149	0.107485
$223$	2.82962	0.189485	0.0947427	−	0.995502i	$-0.469797\pi$
$223$	2.82962	0.189485	0.0947427	+	0.995502i	$0.469797\pi$
$224$	−0.271741	−0.0181565
$225$	−2.71180	−0.180787
$226$	−20.8137	−1.38451
$227$	−7.05116	−0.468002	−0.234001	−	0.972236i	$-0.575182\pi$
$227$	−7.05116	−0.468002	−0.234001	+	0.972236i	$0.575182\pi$
$228$	8.19564	0.542770
$229$	−4.51045	−0.298059	−0.149029	−	0.988833i	$-0.547615\pi$
$229$	−4.51045	−0.298059	−0.149029	+	0.988833i	$0.547615\pi$
$230$	−4.42642	−0.291870
$231$	−0.361400	−0.0237784
$232$	9.35997	0.614512
$233$	−0.687982	−0.0450712	−0.0225356	−	0.999746i	$-0.507174\pi$
$233$	−0.687982	−0.0450712	−0.0225356	+	0.999746i	$0.507174\pi$
$234$	4.44095	0.290314
$235$	−31.9630	−2.08504
$236$	−9.47874	−0.617014
$237$	−14.4763	−0.940340
$238$	−0.971781	−0.0629912
$239$	−17.8225	−1.15284	−0.576422	−	0.817152i	$-0.695551\pi$
$239$	−17.8225	−1.15284	−0.576422	+	0.817152i	$0.695551\pi$
$240$	−3.56923	−0.230393
$241$	22.0809	1.42236	0.711178	−	0.703012i	$-0.248162\pi$
$241$	22.0809	1.42236	0.711178	+	0.703012i	$0.248162\pi$
$242$	1.00000	0.0642824
$243$	−11.8411	−0.759608
$244$	11.7600	0.752858
$245$	−18.5880	−1.18755
$246$	11.7755	0.750780
$247$	22.2269	1.41427
$248$	−10.4870	−0.665926
$249$	17.2504	1.09320
$250$	−7.50783	−0.474837
$251$	23.3356	1.47293	0.736465	−	0.676475i	$-0.236493\pi$
$251$	23.3356	1.47293	0.736465	+	0.676475i	$0.236493\pi$
$252$	0.334581	0.0210766
$253$	1.64935	0.103693
$254$	2.37831	0.149228
$255$	−12.7640	−0.799314
$256$	1.00000	0.0625000
$257$	6.46621	0.403351	0.201675	−	0.979452i	$-0.435361\pi$
$257$	6.46621	0.403351	0.201675	+	0.979452i	$0.435361\pi$
$258$	−0.239432	−0.0149064
$259$	0.327224	0.0203327
$260$	−9.67990	−0.600322
$261$	−11.5245	−0.713346
$262$	−8.86124	−0.547449
$263$	−6.44521	−0.397429	−0.198714	−	0.980057i	$-0.563677\pi$
$263$	−6.44521	−0.397429	−0.198714	+	0.980057i	$0.563677\pi$
$264$	1.32994	0.0818524
$265$	11.5629	0.710303
$266$	1.67458	0.102675
$267$	14.1726	0.867349
$268$	11.6216	0.709905
$269$	−6.76645	−0.412557	−0.206279	−	0.978493i	$-0.566135\pi$
$269$	−6.76645	−0.412557	−0.206279	+	0.978493i	$0.566135\pi$
$270$	15.1023	0.919096
$271$	−7.24576	−0.440148	−0.220074	−	0.975483i	$-0.570630\pi$
$271$	−7.24576	−0.440148	−0.220074	+	0.975483i	$0.570630\pi$
$272$	3.57613	0.216835
$273$	−1.30352	−0.0788928
$274$	13.4152	0.810443
$275$	−2.20248	−0.132815
$276$	2.19354	0.132035
$277$	−29.2380	−1.75674	−0.878371	−	0.477980i	$-0.841369\pi$
$277$	−29.2380	−1.75674	−0.878371	+	0.477980i	$0.841369\pi$
$278$	0.621085	0.0372502
$279$	12.9121	0.773029
$280$	−0.729283	−0.0435830
$281$	−17.1417	−1.02259	−0.511293	−	0.859406i	$-0.670833\pi$
$281$	−17.1417	−1.02259	−0.511293	+	0.859406i	$0.670833\pi$
$282$	15.8394	0.943225
$283$	−20.8851	−1.24149	−0.620744	−	0.784013i	$-0.713169\pi$
$283$	−20.8851	−1.24149	−0.620744	+	0.784013i	$0.713169\pi$
$284$	2.55648	0.151699
$285$	21.9950	1.30287
$286$	3.60687	0.213278
$287$	2.40604	0.142024
$288$	−1.23125	−0.0725521
$289$	−4.21129	−0.247723
$290$	25.1198	1.47508
$291$	−0.316547	−0.0185563
$292$	−16.4298	−0.961482
$293$	−11.7900	−0.688778	−0.344389	−	0.938827i	$-0.611914\pi$
$293$	−11.7900	−0.688778	−0.344389	+	0.938827i	$0.611914\pi$
$294$	9.21140	0.537220
$295$	−25.4385	−1.48109
$296$	−1.20418	−0.0699914
$297$	−5.62732	−0.326530
$298$	−19.5922	−1.13495
$299$	5.94897	0.344038
$300$	−2.92917	−0.169116
$301$	−0.0489220	−0.00281982
$302$	13.4404	0.773409
$303$	−13.2989	−0.764000
$304$	−6.16240	−0.353438
$305$	31.5609	1.80717
$306$	−4.40311	−0.251709
$307$	0.777064	0.0443494	0.0221747	−	0.999754i	$-0.492941\pi$
$307$	0.777064	0.0443494	0.0221747	+	0.999754i	$0.492941\pi$
$308$	0.271741	0.0154839
$309$	25.9949	1.47880
$310$	−28.1444	−1.59850
$311$	8.64853	0.490413	0.245207	−	0.969471i	$-0.421144\pi$
$311$	8.64853	0.490413	0.245207	+	0.969471i	$0.421144\pi$
$312$	4.79693	0.271573
$313$	2.46956	0.139588	0.0697939	−	0.997561i	$-0.477766\pi$
$313$	2.46956	0.139588	0.0697939	+	0.997561i	$0.477766\pi$
$314$	20.9249	1.18086
$315$	0.897929	0.0505926
$316$	10.8849	0.612325
$317$	−21.7666	−1.22253	−0.611267	−	0.791425i	$-0.709340\pi$
$317$	−21.7666	−1.22253	−0.611267	+	0.791425i	$0.709340\pi$
$318$	−5.73005	−0.321326
$319$	−9.35997	−0.524058
$320$	2.68374	0.150026
$321$	−8.57243	−0.478467
$322$	0.448195	0.0249769
$323$	−22.0375	−1.22620
$324$	−3.79028	−0.210571
$325$	−7.94405	−0.440657
$326$	3.61003	0.199941
$327$	−10.9177	−0.603749
$328$	−8.85415	−0.488889
$329$	3.23640	0.178428
$330$	3.56923	0.196480
$331$	−19.9807	−1.09824	−0.549119	−	0.835744i	$-0.685037\pi$
$331$	−19.9807	−1.09824	−0.549119	+	0.835744i	$0.685037\pi$
$332$	−12.9708	−0.711863
$333$	1.48264	0.0812483
$334$	−10.4550	−0.572072
$335$	31.1895	1.70407
$336$	0.361400	0.0197160
$337$	−22.9422	−1.24974	−0.624870	−	0.780729i	$-0.714848\pi$
$337$	−22.9422	−1.24974	−0.624870	+	0.780729i	$0.714848\pi$
$338$	0.00948491	0.000515911 0
$339$	27.6811	1.50343
$340$	9.59742	0.520493
$341$	10.4870	0.567903
$342$	7.58745	0.410282
$343$	3.78431	0.204333
$344$	0.180032	0.00970667
$345$	5.88689	0.316940
$346$	2.20541	0.118564
$347$	−13.7000	−0.735454	−0.367727	−	0.929934i	$-0.619864\pi$
$347$	−13.7000	−0.735454	−0.367727	+	0.929934i	$0.619864\pi$
$348$	−12.4482	−0.667295
$349$	−9.90034	−0.529953	−0.264977	−	0.964255i	$-0.585364\pi$
$349$	−9.90034	−0.529953	−0.264977	+	0.964255i	$0.585364\pi$
$350$	−0.598504	−0.0319914
$351$	−20.2970	−1.08337
$352$	−1.00000	−0.0533002
$353$	4.36758	0.232463	0.116231	−	0.993222i	$-0.462919\pi$
$353$	4.36758	0.232463	0.116231	+	0.993222i	$0.462919\pi$
$354$	12.6062	0.670012
$355$	6.86093	0.364140
$356$	−10.6565	−0.564796
$357$	1.29241	0.0684018
$358$	6.09720	0.322247
$359$	−1.83834	−0.0970240	−0.0485120	−	0.998823i	$-0.515448\pi$
$359$	−1.83834	−0.0970240	−0.0485120	+	0.998823i	$0.515448\pi$
$360$	−3.30436	−0.174155
$361$	18.9751	0.998691
$362$	20.0184	1.05214
$363$	−1.32994	−0.0698039
$364$	0.980133	0.0513729
$365$	−44.0934	−2.30795
$366$	−15.6402	−0.817524
$367$	−0.968828	−0.0505724	−0.0252862	−	0.999680i	$-0.508050\pi$
$367$	−0.968828	−0.0505724	−0.0252862	+	0.999680i	$0.508050\pi$
$368$	−1.64935	−0.0859781
$369$	10.9017	0.567518
$370$	−3.23170	−0.168008
$371$	−1.17079	−0.0607846
$372$	13.9471	0.723125
$373$	20.6354	1.06846	0.534230	−	0.845339i	$-0.320602\pi$
$373$	20.6354	1.06846	0.534230	+	0.845339i	$0.320602\pi$
$374$	−3.57613	−0.184917
$375$	9.98499	0.515623
$376$	−11.9099	−0.614204
$377$	−33.7601	−1.73874
$378$	−1.52917	−0.0786522
$379$	−30.1912	−1.55082	−0.775408	−	0.631461i	$-0.782456\pi$
$379$	−30.1912	−1.55082	−0.775408	+	0.631461i	$0.782456\pi$
$380$	−16.5383	−0.848397
$381$	−3.16302	−0.162046
$382$	8.64204	0.442165
$383$	12.2954	0.628265	0.314132	−	0.949379i	$-0.398286\pi$
$383$	12.2954	0.628265	0.314132	+	0.949379i	$0.398286\pi$
$384$	−1.32994	−0.0678684
$385$	0.729283	0.0371677
$386$	−1.61666	−0.0822860
$387$	−0.221664	−0.0112678
$388$	0.238015	0.0120834
$389$	32.2302	1.63414	0.817069	−	0.576540i	$-0.195598\pi$
$389$	32.2302	1.63414	0.817069	+	0.576540i	$0.195598\pi$
$390$	12.8737	0.651887
$391$	−5.89828	−0.298289
$392$	−6.92616	−0.349824
$393$	11.7849	0.594472
$394$	1.00000	0.0503793
$395$	29.2124	1.46983
$396$	1.23125	0.0618726
$397$	−3.24381	−0.162802	−0.0814010	−	0.996681i	$-0.525939\pi$
$397$	−3.24381	−0.162802	−0.0814010	+	0.996681i	$0.525939\pi$
$398$	−4.43218	−0.222165
$399$	−2.22709	−0.111494
$400$	2.20248	0.110124
$401$	30.2432	1.51027	0.755136	−	0.655568i	$-0.227571\pi$
$401$	30.2432	1.51027	0.755136	+	0.655568i	$0.227571\pi$
$402$	−15.4561	−0.770882
$403$	37.8252	1.88421
$404$	9.99957	0.497497
$405$	−10.1721	−0.505457
$406$	−2.54349	−0.126231
$407$	1.20418	0.0596888
$408$	−4.75605	−0.235460
$409$	6.99000	0.345633	0.172817	−	0.984954i	$-0.444713\pi$
$409$	6.99000	0.345633	0.172817	+	0.984954i	$0.444713\pi$
$410$	−23.7623	−1.17354
$411$	−17.8415	−0.880055
$412$	−19.5459	−0.962956
$413$	2.57576	0.126745
$414$	2.03076	0.0998062
$415$	−34.8102	−1.70877
$416$	−3.60687	−0.176841
$417$	−0.826009	−0.0404498
$418$	6.16240	0.301413
$419$	−11.2348	−0.548856	−0.274428	−	0.961608i	$-0.588488\pi$
$419$	−11.2348	−0.548856	−0.274428	+	0.961608i	$0.588488\pi$
$420$	0.969905	0.0473265
$421$	−26.2564	−1.27966	−0.639828	−	0.768518i	$-0.720995\pi$
$421$	−26.2564	−1.27966	−0.639828	+	0.768518i	$0.720995\pi$
$422$	−8.57336	−0.417345
$423$	14.6640	0.712988
$424$	4.30849	0.209239
$425$	7.87636	0.382059
$426$	−3.39997	−0.164729
$427$	−3.19568	−0.154650
$428$	6.44571	0.311565
$429$	−4.79693	−0.231598
$430$	0.483159	0.0233000
$431$	−0.347528	−0.0167398	−0.00836992	−	0.999965i	$-0.502664\pi$
$431$	−0.347528	−0.0167398	−0.00836992	+	0.999965i	$0.502664\pi$
$432$	5.62732	0.270745
$433$	7.61179	0.365799	0.182900	−	0.983132i	$-0.441452\pi$
$433$	7.61179	0.365799	0.182900	+	0.983132i	$0.441452\pi$
$434$	2.84975	0.136792
$435$	−33.4079	−1.60178
$436$	8.20912	0.393146
$437$	10.1639	0.486206
$438$	21.8507	1.04407
$439$	−2.35708	−0.112497	−0.0562485	−	0.998417i	$-0.517914\pi$
$439$	−2.35708	−0.112497	−0.0562485	+	0.998417i	$0.517914\pi$
$440$	−2.68374	−0.127942
$441$	8.52783	0.406087
$442$	−12.8986	−0.613525
$443$	−1.67201	−0.0794398	−0.0397199	−	0.999211i	$-0.512647\pi$
$443$	−1.67201	−0.0794398	−0.0397199	+	0.999211i	$0.512647\pi$
$444$	1.60149	0.0760033
$445$	−28.5994	−1.35574
$446$	2.82962	0.133986
$447$	26.0565	1.23243
$448$	−0.271741	−0.0128386
$449$	29.2307	1.37948	0.689740	−	0.724057i	$-0.257725\pi$
$449$	29.2307	1.37948	0.689740	+	0.724057i	$0.257725\pi$
$450$	−2.71180	−0.127836
$451$	8.85415	0.416926
$452$	−20.8137	−0.978994
$453$	−17.8750	−0.839841
$454$	−7.05116	−0.330927
$455$	2.63043	0.123316
$456$	8.19564	0.383796
$457$	18.3621	0.858944	0.429472	−	0.903080i	$-0.358700\pi$
$457$	18.3621	0.858944	0.429472	+	0.903080i	$0.358700\pi$
$458$	−4.51045	−0.210759
$459$	20.1240	0.939310
$460$	−4.42642	−0.206383
$461$	−10.7615	−0.501213	−0.250607	−	0.968089i	$-0.580630\pi$
$461$	−10.7615	−0.501213	−0.250607	+	0.968089i	$0.580630\pi$
$462$	−0.361400	−0.0168139
$463$	16.6266	0.772705	0.386352	−	0.922351i	$-0.373735\pi$
$463$	16.6266	0.772705	0.386352	+	0.922351i	$0.373735\pi$
$464$	9.35997	0.434526
$465$	37.4305	1.73580
$466$	−0.687982	−0.0318701
$467$	43.0229	1.99086	0.995430	−	0.0954929i	$-0.0304427\pi$
$467$	43.0229	1.99086	0.995430	+	0.0954929i	$0.0304427\pi$
$468$	4.44095	0.205283
$469$	−3.15808	−0.145826
$470$	−31.9630	−1.47434
$471$	−27.8290	−1.28229
$472$	−9.47874	−0.436295
$473$	−0.180032	−0.00827787
$474$	−14.4763	−0.664921
$475$	−13.5726	−0.622752
$476$	−0.971781	−0.0445415
$477$	−5.30483	−0.242892
$478$	−17.8225	−0.815183
$479$	24.2790	1.10934	0.554668	−	0.832072i	$-0.312845\pi$
$479$	24.2790	1.10934	0.554668	+	0.832072i	$0.312845\pi$
$480$	−3.56923	−0.162912
$481$	4.34331	0.198038
$482$	22.0809	1.00576
$483$	−0.596074	−0.0271223
$484$	1.00000	0.0454545
$485$	0.638771	0.0290051
$486$	−11.8411	−0.537124
$487$	39.4202	1.78630	0.893151	−	0.449757i	$-0.148489\pi$
$487$	39.4202	1.78630	0.893151	+	0.449757i	$0.148489\pi$
$488$	11.7600	0.532351
$489$	−4.80114	−0.217115
$490$	−18.5880	−0.839722
$491$	−0.458752	−0.0207032	−0.0103516	−	0.999946i	$-0.503295\pi$
$491$	−0.458752	−0.0207032	−0.0103516	+	0.999946i	$0.503295\pi$
$492$	11.7755	0.530882
$493$	33.4725	1.50752
$494$	22.2269	1.00004
$495$	3.30436	0.148520
$496$	−10.4870	−0.470881
$497$	−0.694699	−0.0311615
$498$	17.2504	0.773008
$499$	−19.2814	−0.863152	−0.431576	−	0.902077i	$-0.642042\pi$
$499$	−19.2814	−0.863152	−0.431576	+	0.902077i	$0.642042\pi$
$500$	−7.50783	−0.335760
$501$	13.9046	0.621210
$502$	23.3356	1.04152
$503$	30.7646	1.37173	0.685863	−	0.727730i	$-0.259425\pi$
$503$	30.7646	1.37173	0.685863	+	0.727730i	$0.259425\pi$
$504$	0.334581	0.0149034
$505$	26.8363	1.19420
$506$	1.64935	0.0733224
$507$	−0.0126144	−0.000560225 0
$508$	2.37831	0.105520
$509$	19.7735	0.876445	0.438223	−	0.898866i	$-0.355608\pi$
$509$	19.7735	0.876445	0.438223	+	0.898866i	$0.355608\pi$
$510$	−12.7640	−0.565201
$511$	4.46465	0.197505
$512$	1.00000	0.0441942
$513$	−34.6778	−1.53106
$514$	6.46621	0.285212
$515$	−52.4561	−2.31149
$516$	−0.239432	−0.0105404
$517$	11.9099	0.523795
$518$	0.327224	0.0143774
$519$	−2.93307	−0.128748
$520$	−9.67990	−0.424492
$521$	−14.2723	−0.625281	−0.312640	−	0.949872i	$-0.601214\pi$
$521$	−14.2723	−0.625281	−0.312640	+	0.949872i	$0.601214\pi$
$522$	−11.5245	−0.504412
$523$	−20.2731	−0.886481	−0.443240	−	0.896403i	$-0.646171\pi$
$523$	−20.2731	−0.886481	−0.443240	+	0.896403i	$0.646171\pi$
$524$	−8.86124	−0.387105
$525$	0.795977	0.0347393
$526$	−6.44521	−0.281024
$527$	−37.5029	−1.63365
$528$	1.32994	0.0578784
$529$	−20.2797	−0.881724
$530$	11.5629	0.502260
$531$	11.6707	0.506465
$532$	1.67458	0.0726021
$533$	31.9357	1.38329
$534$	14.1726	0.613308
$535$	17.2986	0.747885
$536$	11.6216	0.501979
$537$	−8.10893	−0.349926
$538$	−6.76645	−0.291722
$539$	6.92616	0.298331
$540$	15.1023	0.649899
$541$	39.0439	1.67863	0.839314	−	0.543646i	$-0.182957\pi$
$541$	39.0439	1.67863	0.839314	+	0.543646i	$0.182957\pi$
$542$	−7.24576	−0.311232
$543$	−26.6233	−1.14252
$544$	3.57613	0.153325
$545$	22.0312	0.943712
$546$	−1.30352	−0.0557856
$547$	−4.68882	−0.200480	−0.100240	−	0.994963i	$-0.531961\pi$
$547$	−4.68882	−0.200480	−0.100240	+	0.994963i	$0.531961\pi$
$548$	13.4152	0.573069
$549$	−14.4795	−0.617970
$550$	−2.20248	−0.0939141
$551$	−57.6798	−2.45724
$552$	2.19354	0.0933632
$553$	−2.95788	−0.125782
$554$	−29.2380	−1.24220
$555$	4.29798	0.182439
$556$	0.621085	0.0263399
$557$	−7.24995	−0.307190	−0.153595	−	0.988134i	$-0.549085\pi$
$557$	−7.24995	−0.307190	−0.153595	+	0.988134i	$0.549085\pi$
$558$	12.9121	0.546614
$559$	−0.649351	−0.0274646
$560$	−0.729283	−0.0308178
$561$	4.75605	0.200801
$562$	−17.1417	−0.723078
$563$	−34.0895	−1.43670	−0.718351	−	0.695681i	$-0.755103\pi$
$563$	−34.0895	−1.43670	−0.718351	+	0.695681i	$0.755103\pi$
$564$	15.8394	0.666961
$565$	−55.8587	−2.34999
$566$	−20.8851	−0.877865
$567$	1.02997	0.0432548
$568$	2.55648	0.107267
$569$	−19.4256	−0.814363	−0.407181	−	0.913347i	$-0.633488\pi$
$569$	−19.4256	−0.814363	−0.407181	+	0.913347i	$0.633488\pi$
$570$	21.9950	0.921269
$571$	−10.1776	−0.425917	−0.212959	−	0.977061i	$-0.568310\pi$
$571$	−10.1776	−0.425917	−0.212959	+	0.977061i	$0.568310\pi$
$572$	3.60687	0.150811
$573$	−11.4934	−0.480145
$574$	2.40604	0.100426
$575$	−3.63265	−0.151492
$576$	−1.23125	−0.0513021
$577$	41.1795	1.71432	0.857162	−	0.515047i	$-0.172226\pi$
$577$	41.1795	1.71432	0.857162	+	0.515047i	$0.172226\pi$
$578$	−4.21129	−0.175166
$579$	2.15007	0.0893539
$580$	25.1198	1.04304
$581$	3.52469	0.146229
$582$	−0.316547	−0.0131213
$583$	−4.30849	−0.178440
$584$	−16.4298	−0.679870
$585$	11.9184	0.492764
$586$	−11.7900	−0.487040
$587$	32.2171	1.32974	0.664872	−	0.746957i	$-0.268486\pi$
$587$	32.2171	1.32974	0.664872	+	0.746957i	$0.268486\pi$
$588$	9.21140	0.379872
$589$	64.6251	2.66283
$590$	−25.4385	−1.04729
$591$	−1.32994	−0.0547066
$592$	−1.20418	−0.0494914
$593$	25.5535	1.04935	0.524677	−	0.851301i	$-0.324186\pi$
$593$	25.5535	1.04935	0.524677	+	0.851301i	$0.324186\pi$
$594$	−5.62732	−0.230892
$595$	−2.60801	−0.106918
$596$	−19.5922	−0.802527
$597$	5.89455	0.241248
$598$	5.94897	0.243272
$599$	11.0570	0.451775	0.225888	−	0.974153i	$-0.427472\pi$
$599$	11.0570	0.451775	0.225888	+	0.974153i	$0.427472\pi$
$600$	−2.92917	−0.119583
$601$	−38.3474	−1.56422	−0.782111	−	0.623140i	$-0.785857\pi$
$601$	−38.3474	−1.56422	−0.782111	+	0.623140i	$0.785857\pi$
$602$	−0.0489220	−0.00199391
$603$	−14.3091	−0.582713
$604$	13.4404	0.546883
$605$	2.68374	0.109110
$606$	−13.2989	−0.540230
$607$	−3.49790	−0.141975	−0.0709877	−	0.997477i	$-0.522615\pi$
$607$	−3.49790	−0.141975	−0.0709877	+	0.997477i	$0.522615\pi$
$608$	−6.16240	−0.249918
$609$	3.38269	0.137074
$610$	31.5609	1.27786
$611$	42.9573	1.73786
$612$	−4.40311	−0.177985
$613$	41.1305	1.66125	0.830623	−	0.556835i	$-0.187985\pi$
$613$	41.1305	1.66125	0.830623	+	0.556835i	$0.187985\pi$
$614$	0.777064	0.0313597
$615$	31.6025	1.27434
$616$	0.271741	0.0109488
$617$	10.2204	0.411459	0.205729	−	0.978609i	$-0.434043\pi$
$617$	10.2204	0.411459	0.205729	+	0.978609i	$0.434043\pi$
$618$	25.9949	1.04567
$619$	21.6292	0.869349	0.434675	−	0.900588i	$-0.356863\pi$
$619$	21.6292	0.869349	0.434675	+	0.900588i	$0.356863\pi$
$620$	−28.1444	−1.13031
$621$	−9.28140	−0.372450
$622$	8.64853	0.346775
$623$	2.89582	0.116019
$624$	4.79693	0.192031
$625$	−31.1615	−1.24646
$626$	2.46956	0.0987034
$627$	−8.19564	−0.327302
$628$	20.9249	0.834996
$629$	−4.30630	−0.171703
$630$	0.897929	0.0357744
$631$	14.4724	0.576137	0.288068	−	0.957610i	$-0.406987\pi$
$631$	14.4724	0.576137	0.288068	+	0.957610i	$0.406987\pi$
$632$	10.8849	0.432979
$633$	11.4021	0.453192
$634$	−21.7666	−0.864461
$635$	6.38278	0.253293
$636$	−5.73005	−0.227211
$637$	24.9817	0.989812
$638$	−9.35997	−0.370565
$639$	−3.14766	−0.124519
$640$	2.68374	0.106084
$641$	23.6523	0.934209	0.467104	−	0.884202i	$-0.345297\pi$
$641$	23.6523	0.934209	0.467104	+	0.884202i	$0.345297\pi$
$642$	−8.57243	−0.338327
$643$	10.4406	0.411738	0.205869	−	0.978580i	$-0.433998\pi$
$643$	10.4406	0.411738	0.205869	+	0.978580i	$0.433998\pi$
$644$	0.448195	0.0176614
$645$	−0.642575	−0.0253014
$646$	−22.0375	−0.867055
$647$	−25.6243	−1.00740	−0.503698	−	0.863880i	$-0.668028\pi$
$647$	−25.6243	−1.00740	−0.503698	+	0.863880i	$0.668028\pi$
$648$	−3.79028	−0.148896
$649$	9.47874	0.372073
$650$	−7.94405	−0.311591
$651$	−3.79001	−0.148542
$652$	3.61003	0.141380
$653$	39.0811	1.52936	0.764680	−	0.644410i	$-0.222897\pi$
$653$	39.0811	1.52936	0.764680	+	0.644410i	$0.222897\pi$
$654$	−10.9177	−0.426915
$655$	−23.7813	−0.929212
$656$	−8.85415	−0.345697
$657$	20.2292	0.789216
$658$	3.23640	0.126168
$659$	−18.4135	−0.717290	−0.358645	−	0.933474i	$-0.616761\pi$
$659$	−18.4135	−0.717290	−0.358645	+	0.933474i	$0.616761\pi$
$660$	3.56923	0.138932
$661$	−38.4565	−1.49579	−0.747893	−	0.663820i	$-0.768934\pi$
$661$	−38.4565	−1.49579	−0.747893	+	0.663820i	$0.768934\pi$
$662$	−19.9807	−0.776572
$663$	17.1544	0.666224
$664$	−12.9708	−0.503363
$665$	4.49413	0.174275
$666$	1.48264	0.0574512
$667$	−15.4378	−0.597755
$668$	−10.4550	−0.404516
$669$	−3.76324	−0.145495
$670$	31.1895	1.20496
$671$	−11.7600	−0.453990
$672$	0.361400	0.0139413
$673$	45.2089	1.74268	0.871338	−	0.490684i	$-0.163253\pi$
$673$	45.2089	1.74268	0.871338	+	0.490684i	$0.163253\pi$
$674$	−22.9422	−0.883700
$675$	12.3941	0.477048
$676$	0.00948491	0.000364804 0
$677$	15.2279	0.585255	0.292628	−	0.956226i	$-0.405470\pi$
$677$	15.2279	0.585255	0.292628	+	0.956226i	$0.405470\pi$
$678$	27.6811	1.06308
$679$	−0.0646784	−0.00248213
$680$	9.59742	0.368044
$681$	9.37764	0.359352
$682$	10.4870	0.401568
$683$	−24.5435	−0.939132	−0.469566	−	0.882897i	$-0.655590\pi$
$683$	−24.5435	−0.939132	−0.469566	+	0.882897i	$0.655590\pi$
$684$	7.58745	0.290113
$685$	36.0030	1.37560
$686$	3.78431	0.144486
$687$	5.99864	0.228863
$688$	0.180032	0.00686365
$689$	−15.5402	−0.592033
$690$	5.88689	0.224110
$691$	−7.04551	−0.268024	−0.134012	−	0.990980i	$-0.542786\pi$
$691$	−7.04551	−0.268024	−0.134012	+	0.990980i	$0.542786\pi$
$692$	2.20541	0.0838371
$693$	−0.334581	−0.0127097
$694$	−13.7000	−0.520045
$695$	1.66683	0.0632266
$696$	−12.4482	−0.471849
$697$	−31.6636	−1.19934
$698$	−9.90034	−0.374733
$699$	0.914977	0.0346076
$700$	−0.598504	−0.0226213
$701$	−0.445643	−0.0168317	−0.00841584	−	0.999965i	$-0.502679\pi$
$701$	−0.445643	−0.0168317	−0.00841584	+	0.999965i	$0.502679\pi$
$702$	−20.2970	−0.766061
$703$	7.42062	0.279874
$704$	−1.00000	−0.0376889
$705$	42.5090	1.60098
$706$	4.36758	0.164376
$707$	−2.71729	−0.102194
$708$	12.6062	0.473770
$709$	30.9623	1.16281	0.581407	−	0.813613i	$-0.302502\pi$
$709$	30.9623	1.16281	0.581407	+	0.813613i	$0.302502\pi$
$710$	6.86093	0.257486
$711$	−13.4021	−0.502617
$712$	−10.6565	−0.399371
$713$	17.2967	0.647767
$714$	1.29241	0.0483674
$715$	9.67990	0.362008
$716$	6.09720	0.227863
$717$	23.7030	0.885203
$718$	−1.83834	−0.0686063
$719$	30.2763	1.12912	0.564558	−	0.825393i	$-0.309046\pi$
$719$	30.2763	1.12912	0.564558	+	0.825393i	$0.309046\pi$
$720$	−3.30436	−0.123146
$721$	5.31141	0.197807
$722$	18.9751	0.706181
$723$	−29.3664	−1.09215
$724$	20.0184	0.743978
$725$	20.6151	0.765627
$726$	−1.32994	−0.0493588
$727$	−7.48315	−0.277535	−0.138767	−	0.990325i	$-0.544314\pi$
$727$	−7.48315	−0.277535	−0.138767	+	0.990325i	$0.544314\pi$
$728$	0.980133	0.0363262
$729$	27.1189	1.00440
$730$	−44.0934	−1.63197
$731$	0.643818	0.0238125
$732$	−15.6402	−0.578077
$733$	−28.3823	−1.04832	−0.524162	−	0.851619i	$-0.675621\pi$
$733$	−28.3823	−1.04832	−0.524162	+	0.851619i	$0.675621\pi$
$734$	−0.968828	−0.0357601
$735$	24.7210	0.911849
$736$	−1.64935	−0.0607957
$737$	−11.6216	−0.428089
$738$	10.9017	0.401296
$739$	−15.0288	−0.552845	−0.276422	−	0.961036i	$-0.589149\pi$
$739$	−15.0288	−0.552845	−0.276422	+	0.961036i	$0.589149\pi$
$740$	−3.23170	−0.118800
$741$	−29.5606	−1.08594
$742$	−1.17079	−0.0429812
$743$	−26.1346	−0.958784	−0.479392	−	0.877601i	$-0.659143\pi$
$743$	−26.1346	−0.958784	−0.479392	+	0.877601i	$0.659143\pi$
$744$	13.9471	0.511327
$745$	−52.5804	−1.92640
$746$	20.6354	0.755515
$747$	15.9702	0.584321
$748$	−3.57613	−0.130756
$749$	−1.75156	−0.0640007
$750$	9.98499	0.364600
$751$	27.3873	0.999379	0.499689	−	0.866205i	$-0.333448\pi$
$751$	27.3873	0.999379	0.499689	+	0.866205i	$0.333448\pi$
$752$	−11.9099	−0.434308
$753$	−31.0351	−1.13098
$754$	−33.7601	−1.22947
$755$	36.0706	1.31275
$756$	−1.52917	−0.0556155
$757$	0.878830	0.0319416	0.0159708	−	0.999872i	$-0.494916\pi$
$757$	0.878830	0.0319416	0.0159708	+	0.999872i	$0.494916\pi$
$758$	−30.1912	−1.09659
$759$	−2.19354	−0.0796204
$760$	−16.5383	−0.599907
$761$	−6.89700	−0.250016	−0.125008	−	0.992156i	$-0.539896\pi$
$761$	−6.89700	−0.250016	−0.125008	+	0.992156i	$0.539896\pi$
$762$	−3.16302	−0.114584
$763$	−2.23076	−0.0807588
$764$	8.64204	0.312658
$765$	−11.8168	−0.427238
$766$	12.2954	0.444250
$767$	34.1886	1.23448
$768$	−1.32994	−0.0479902
$769$	−17.2658	−0.622620	−0.311310	−	0.950308i	$-0.600768\pi$
$769$	−17.2658	−0.622620	−0.311310	+	0.950308i	$0.600768\pi$
$770$	0.729283	0.0262815
$771$	−8.59969	−0.309710
$772$	−1.61666	−0.0581850
$773$	4.87017	0.175168	0.0875840	−	0.996157i	$-0.472085\pi$
$773$	4.87017	0.175168	0.0875840	+	0.996157i	$0.472085\pi$
$774$	−0.221664	−0.00796755
$775$	−23.0974	−0.829684
$776$	0.238015	0.00854424
$777$	−0.435190	−0.0156123
$778$	32.2302	1.15551
$779$	54.5628	1.95492
$780$	12.8737	0.460953
$781$	−2.55648	−0.0914779
$782$	−5.89828	−0.210922
$783$	52.6716	1.88233
$784$	−6.92616	−0.247363
$785$	56.1572	2.00434
$786$	11.7849	0.420355
$787$	−44.0096	−1.56877	−0.784387	−	0.620272i	$-0.787022\pi$
$787$	−44.0096	−1.56877	−0.784387	+	0.620272i	$0.787022\pi$
$788$	1.00000	0.0356235
$789$	8.57176	0.305163
$790$	29.2124	1.03933
$791$	5.65594	0.201102
$792$	1.23125	0.0437505
$793$	−42.4168	−1.50626
$794$	−3.24381	−0.115118
$795$	−15.3780	−0.545401
$796$	−4.43218	−0.157094
$797$	31.0899	1.10126	0.550630	−	0.834749i	$-0.314387\pi$
$797$	31.0899	1.10126	0.550630	+	0.834749i	$0.314387\pi$
$798$	−2.22709	−0.0788382
$799$	−42.5912	−1.50677
$800$	2.20248	0.0778694
$801$	13.1209	0.463603
$802$	30.2432	1.06792
$803$	16.4298	0.579795
$804$	−15.4561	−0.545096
$805$	1.20284	0.0423945
$806$	37.8252	1.33234
$807$	8.99899	0.316780
$808$	9.99957	0.351784
$809$	−50.9272	−1.79050	−0.895252	−	0.445560i	$-0.853005\pi$
$809$	−50.9272	−1.79050	−0.895252	+	0.445560i	$0.853005\pi$
$810$	−10.1721	−0.357412
$811$	7.62740	0.267834	0.133917	−	0.990993i	$-0.457244\pi$
$811$	7.62740	0.267834	0.133917	+	0.990993i	$0.457244\pi$
$812$	−2.54349	−0.0892589
$813$	9.63645	0.337965
$814$	1.20418	0.0422064
$815$	9.68840	0.339370
$816$	−4.75605	−0.166495
$817$	−1.10943	−0.0388140
$818$	6.99000	0.244400
$819$	−1.20679	−0.0421686
$820$	−23.7623	−0.829815
$821$	17.3713	0.606263	0.303132	−	0.952949i	$-0.401968\pi$
$821$	17.3713	0.606263	0.303132	+	0.952949i	$0.401968\pi$
$822$	−17.8415	−0.622293
$823$	−41.5824	−1.44947	−0.724736	−	0.689027i	$-0.758038\pi$
$823$	−41.5824	−1.44947	−0.724736	+	0.689027i	$0.758038\pi$
$824$	−19.5459	−0.680913
$825$	2.92917	0.101981
$826$	2.57576	0.0896223
$827$	−6.01167	−0.209046	−0.104523	−	0.994522i	$-0.533332\pi$
$827$	−6.01167	−0.209046	−0.104523	+	0.994522i	$0.533332\pi$
$828$	2.03076	0.0705737
$829$	31.2841	1.08654	0.543271	−	0.839557i	$-0.317186\pi$
$829$	31.2841	1.08654	0.543271	+	0.839557i	$0.317186\pi$
$830$	−34.8102	−1.20828
$831$	38.8849	1.34890
$832$	−3.60687	−0.125046
$833$	−24.7688	−0.858190
$834$	−0.826009	−0.0286023
$835$	−28.0585	−0.971006
$836$	6.16240	0.213131
$837$	−59.0138	−2.03982
$838$	−11.2348	−0.388100
$839$	−9.97992	−0.344545	−0.172273	−	0.985049i	$-0.555111\pi$
$839$	−9.97992	−0.344545	−0.172273	+	0.985049i	$0.555111\pi$
$840$	0.969905	0.0334649
$841$	58.6090	2.02100
$842$	−26.2564	−0.904854
$843$	22.7975	0.785186
$844$	−8.57336	−0.295107
$845$	0.0254551	0.000875681 0
$846$	14.6640	0.504159
$847$	−0.271741	−0.00933713
$848$	4.30849	0.147954
$849$	27.7760	0.953269
$850$	7.87636	0.270157
$851$	1.98610	0.0680828
$852$	−3.39997	−0.116481
$853$	28.7327	0.983790	0.491895	−	0.870655i	$-0.336304\pi$
$853$	28.7327	0.983790	0.491895	+	0.870655i	$0.336304\pi$
$854$	−3.19568	−0.109354
$855$	20.3628	0.696392
$856$	6.44571	0.220310
$857$	−21.8785	−0.747355	−0.373678	−	0.927559i	$-0.621903\pi$
$857$	−21.8785	−0.747355	−0.373678	+	0.927559i	$0.621903\pi$
$858$	−4.79693	−0.163764
$859$	10.7430	0.366547	0.183274	−	0.983062i	$-0.441331\pi$
$859$	10.7430	0.366547	0.183274	+	0.983062i	$0.441331\pi$
$860$	0.483159	0.0164756
$861$	−3.19989	−0.109052
$862$	−0.347528	−0.0118369
$863$	18.2964	0.622816	0.311408	−	0.950276i	$-0.399199\pi$
$863$	18.2964	0.622816	0.311408	+	0.950276i	$0.399199\pi$
$864$	5.62732	0.191445
$865$	5.91876	0.201244
$866$	7.61179	0.258659
$867$	5.60077	0.190212
$868$	2.84975	0.0967268
$869$	−10.8849	−0.369246
$870$	−33.4079	−1.13263
$871$	−41.9177	−1.42033
$872$	8.20912	0.277996
$873$	−0.293056	−0.00991844
$874$	10.1639	0.343800
$875$	2.04018	0.0689708
$876$	21.8507	0.738268
$877$	38.4394	1.29801	0.649004	−	0.760785i	$-0.275186\pi$
$877$	38.4394	1.29801	0.649004	+	0.760785i	$0.275186\pi$
$878$	−2.35708	−0.0795474
$879$	15.6800	0.528874
$880$	−2.68374	−0.0904690
$881$	14.8593	0.500622	0.250311	−	0.968165i	$-0.419467\pi$
$881$	14.8593	0.500622	0.250311	+	0.968165i	$0.419467\pi$
$882$	8.52783	0.287147
$883$	45.6494	1.53622	0.768112	−	0.640316i	$-0.221197\pi$
$883$	45.6494	1.53622	0.768112	+	0.640316i	$0.221197\pi$
$884$	−12.8986	−0.433828
$885$	33.8318	1.13724
$886$	−1.67201	−0.0561724
$887$	−23.9765	−0.805050	−0.402525	−	0.915409i	$-0.631867\pi$
$887$	−23.9765	−0.805050	−0.402525	+	0.915409i	$0.631867\pi$
$888$	1.60149	0.0537424
$889$	−0.646284	−0.0216757
$890$	−28.5994	−0.958655
$891$	3.79028	0.126979
$892$	2.82962	0.0947427
$893$	73.3933	2.45601
$894$	26.0565	0.871460
$895$	16.3633	0.546966
$896$	−0.271741	−0.00907823
$897$	−7.91180	−0.264167
$898$	29.2307	0.975440
$899$	−98.1580	−3.27375
$900$	−2.71180	−0.0903934
$901$	15.4077	0.513306
$902$	8.85415	0.294811
$903$	0.0650636	0.00216518
$904$	−20.8137	−0.692254
$905$	53.7243	1.78585
$906$	−17.8750	−0.593857
$907$	−5.51123	−0.182997	−0.0914987	−	0.995805i	$-0.529166\pi$
$907$	−5.51123	−0.182997	−0.0914987	+	0.995805i	$0.529166\pi$
$908$	−7.05116	−0.234001
$909$	−12.3120	−0.408362
$910$	2.63043	0.0871978
$911$	−30.1539	−0.999044	−0.499522	−	0.866301i	$-0.666491\pi$
$911$	−30.1539	−0.999044	−0.499522	+	0.866301i	$0.666491\pi$
$912$	8.19564	0.271385
$913$	12.9708	0.429270
$914$	18.3621	0.607365
$915$	−41.9742	−1.38762
$916$	−4.51045	−0.149029
$917$	2.40796	0.0795179
$918$	20.1240	0.664193
$919$	19.0499	0.628397	0.314198	−	0.949357i	$-0.398264\pi$
$919$	19.0499	0.628397	0.314198	+	0.949357i	$0.398264\pi$
$920$	−4.42642	−0.145935
$921$	−1.03345	−0.0340534
$922$	−10.7615	−0.354411
$923$	−9.22087	−0.303509
$924$	−0.361400	−0.0118892
$925$	−2.65218	−0.0872030
$926$	16.6266	0.546385
$927$	24.0658	0.790426
$928$	9.35997	0.307256
$929$	10.5452	0.345978	0.172989	−	0.984924i	$-0.444657\pi$
$929$	10.5452	0.345978	0.172989	+	0.984924i	$0.444657\pi$
$930$	37.4305	1.22740
$931$	42.6817	1.39884
$932$	−0.687982	−0.0225356
$933$	−11.5021	−0.376561
$934$	43.0229	1.40775
$935$	−9.59742	−0.313869
$936$	4.44095	0.145157
$937$	−6.40672	−0.209299	−0.104649	−	0.994509i	$-0.533372\pi$
$937$	−6.40672	−0.209299	−0.104649	+	0.994509i	$0.533372\pi$
$938$	−3.15808	−0.103115
$939$	−3.28438	−0.107182
$940$	−31.9630	−1.04252
$941$	−56.6070	−1.84534	−0.922668	−	0.385594i	$-0.873996\pi$
$941$	−56.6070	−1.84534	−0.922668	+	0.385594i	$0.873996\pi$
$942$	−27.8290	−0.906718
$943$	14.6036	0.475557
$944$	−9.47874	−0.308507
$945$	−4.10391	−0.133500
$946$	−0.180032	−0.00585334
$947$	26.9351	0.875272	0.437636	−	0.899152i	$-0.355816\pi$
$947$	26.9351	0.875272	0.437636	+	0.899152i	$0.355816\pi$
$948$	−14.4763	−0.470170
$949$	59.2601	1.92367
$950$	−13.5726	−0.440352
$951$	28.9483	0.938714
$952$	−0.971781	−0.0314956
$953$	40.0547	1.29750	0.648750	−	0.761001i	$-0.275292\pi$
$953$	40.0547	1.29750	0.648750	+	0.761001i	$0.275292\pi$
$954$	−5.30483	−0.171750
$955$	23.1930	0.750509
$956$	−17.8225	−0.576422
$957$	12.4482	0.402394
$958$	24.2790	0.784419
$959$	−3.64546	−0.117718
$960$	−3.56923	−0.115196
$961$	78.9773	2.54766
$962$	4.34331	0.140034
$963$	−7.93628	−0.255743
$964$	22.0809	0.711178
$965$	−4.33871	−0.139668
$966$	−0.596074	−0.0191784
$967$	45.0785	1.44963	0.724813	−	0.688946i	$-0.241926\pi$
$967$	45.0785	1.44963	0.724813	+	0.688946i	$0.241926\pi$
$968$	1.00000	0.0321412
$969$	29.3087	0.941531
$970$	0.638771	0.0205097
$971$	−29.2455	−0.938532	−0.469266	−	0.883057i	$-0.655482\pi$
$971$	−29.2455	−0.938532	−0.469266	+	0.883057i	$0.655482\pi$
$972$	−11.8411	−0.379804
$973$	−0.168774	−0.00541066
$974$	39.4202	1.26311
$975$	10.5651	0.338355
$976$	11.7600	0.376429
$977$	13.3235	0.426257	0.213129	−	0.977024i	$-0.431635\pi$
$977$	13.3235	0.426257	0.213129	+	0.977024i	$0.431635\pi$
$978$	−4.80114	−0.153524
$979$	10.6565	0.340585
$980$	−18.5880	−0.593773
$981$	−10.1075	−0.322707
$982$	−0.458752	−0.0146394
$983$	39.4702	1.25890	0.629452	−	0.777039i	$-0.283279\pi$
$983$	39.4702	1.25890	0.629452	+	0.777039i	$0.283279\pi$
$984$	11.7755	0.375390
$985$	2.68374	0.0855112
$986$	33.4725	1.06598
$987$	−4.30422	−0.137005
$988$	22.2269	0.707133
$989$	−0.296935	−0.00944198
$990$	3.30436	0.105019
$991$	−48.0900	−1.52763	−0.763814	−	0.645436i	$-0.776676\pi$
$991$	−48.0900	−1.52763	−0.763814	+	0.645436i	$0.776676\pi$
$992$	−10.4870	−0.332963
$993$	26.5732	0.843275
$994$	−0.694699	−0.0220345
$995$	−11.8948	−0.377091
$996$	17.2504	0.546599
$997$	31.0979	0.984881	0.492440	−	0.870346i	$-0.336105\pi$
$997$	31.0979	0.984881	0.492440	+	0.870346i	$0.336105\pi$
$998$	−19.2814	−0.610341
$999$	−6.77629	−0.214392

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.d.1.6	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.d.1.6	✓	17	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.32994 q^{3} +1.00000 q^{4} +2.68374 q^{5} -1.32994 q^{6} -0.271741 q^{7} +1.00000 q^{8} -1.23125 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.32994 q^{3} +1.00000 q^{4} +2.68374 q^{5} -1.32994 q^{6} -0.271741 q^{7} +1.00000 q^{8} -1.23125 q^{9} +2.68374 q^{10} -1.00000 q^{11} -1.32994 q^{12} -3.60687 q^{13} -0.271741 q^{14} -3.56923 q^{15} +1.00000 q^{16} +3.57613 q^{17} -1.23125 q^{18} -6.16240 q^{19} +2.68374 q^{20} +0.361400 q^{21} -1.00000 q^{22} -1.64935 q^{23} -1.32994 q^{24} +2.20248 q^{25} -3.60687 q^{26} +5.62732 q^{27} -0.271741 q^{28} +9.35997 q^{29} -3.56923 q^{30} -10.4870 q^{31} +1.00000 q^{32} +1.32994 q^{33} +3.57613 q^{34} -0.729283 q^{35} -1.23125 q^{36} -1.20418 q^{37} -6.16240 q^{38} +4.79693 q^{39} +2.68374 q^{40} -8.85415 q^{41} +0.361400 q^{42} +0.180032 q^{43} -1.00000 q^{44} -3.30436 q^{45} -1.64935 q^{46} -11.9099 q^{47} -1.32994 q^{48} -6.92616 q^{49} +2.20248 q^{50} -4.75605 q^{51} -3.60687 q^{52} +4.30849 q^{53} +5.62732 q^{54} -2.68374 q^{55} -0.271741 q^{56} +8.19564 q^{57} +9.35997 q^{58} -9.47874 q^{59} -3.56923 q^{60} +11.7600 q^{61} -10.4870 q^{62} +0.334581 q^{63} +1.00000 q^{64} -9.67990 q^{65} +1.32994 q^{66} +11.6216 q^{67} +3.57613 q^{68} +2.19354 q^{69} -0.729283 q^{70} +2.55648 q^{71} -1.23125 q^{72} -16.4298 q^{73} -1.20418 q^{74} -2.92917 q^{75} -6.16240 q^{76} +0.271741 q^{77} +4.79693 q^{78} +10.8849 q^{79} +2.68374 q^{80} -3.79028 q^{81} -8.85415 q^{82} -12.9708 q^{83} +0.361400 q^{84} +9.59742 q^{85} +0.180032 q^{86} -12.4482 q^{87} -1.00000 q^{88} -10.6565 q^{89} -3.30436 q^{90} +0.980133 q^{91} -1.64935 q^{92} +13.9471 q^{93} -11.9099 q^{94} -16.5383 q^{95} -1.32994 q^{96} +0.238015 q^{97} -6.92616 q^{98} +1.23125 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 17 q^{2} - 7 q^{3} + 17 q^{4} - 4 q^{5} - 7 q^{6} - 5 q^{7} + 17 q^{8} + 12 q^{9}+O(q^{10}) \) 17 * q + 17 * q^2 - 7 * q^3 + 17 * q^4 - 4 * q^5 - 7 * q^6 - 5 * q^7 + 17 * q^8 + 12 * q^9	\( 17 q + 17 q^{2} - 7 q^{3} + 17 q^{4} - 4 q^{5} - 7 q^{6} - 5 q^{7} + 17 q^{8} + 12 q^{9} - 4 q^{10} - 17 q^{11} - 7 q^{12} - 18 q^{13} - 5 q^{14} - 16 q^{15} + 17 q^{16} - 10 q^{17} + 12 q^{18} - 31 q^{19} - 4 q^{20} - 13 q^{21} - 17 q^{22} - 6 q^{23} - 7 q^{24} + 3 q^{25} - 18 q^{26} - 37 q^{27} - 5 q^{28} - 16 q^{29} - 16 q^{30} - 30 q^{31} + 17 q^{32} + 7 q^{33} - 10 q^{34} - 36 q^{35} + 12 q^{36} - 23 q^{37} - 31 q^{38} - 15 q^{39} - 4 q^{40} - 7 q^{41} - 13 q^{42} - 23 q^{43} - 17 q^{44} - 19 q^{45} - 6 q^{46} - 19 q^{47} - 7 q^{48} - 8 q^{49} + 3 q^{50} - 18 q^{51} - 18 q^{52} - 30 q^{53} - 37 q^{54} + 4 q^{55} - 5 q^{56} + 10 q^{57} - 16 q^{58} - 28 q^{59} - 16 q^{60} - 19 q^{61} - 30 q^{62} + 2 q^{63} + 17 q^{64} + 23 q^{65} + 7 q^{66} - 35 q^{67} - 10 q^{68} + q^{69} - 36 q^{70} + q^{71} + 12 q^{72} - 10 q^{73} - 23 q^{74} - 33 q^{75} - 31 q^{76} + 5 q^{77} - 15 q^{78} - 27 q^{79} - 4 q^{80} + 13 q^{81} - 7 q^{82} - 40 q^{83} - 13 q^{84} - 11 q^{85} - 23 q^{86} - 6 q^{87} - 17 q^{88} - 17 q^{89} - 19 q^{90} - 19 q^{91} - 6 q^{92} + 10 q^{93} - 19 q^{94} - 27 q^{95} - 7 q^{96} - 34 q^{97} - 8 q^{98} - 12 q^{99}+O(q^{100}) \) 17 * q + 17 * q^2 - 7 * q^3 + 17 * q^4 - 4 * q^5 - 7 * q^6 - 5 * q^7 + 17 * q^8 + 12 * q^9 - 4 * q^10 - 17 * q^11 - 7 * q^12 - 18 * q^13 - 5 * q^14 - 16 * q^15 + 17 * q^16 - 10 * q^17 + 12 * q^18 - 31 * q^19 - 4 * q^20 - 13 * q^21 - 17 * q^22 - 6 * q^23 - 7 * q^24 + 3 * q^25 - 18 * q^26 - 37 * q^27 - 5 * q^28 - 16 * q^29 - 16 * q^30 - 30 * q^31 + 17 * q^32 + 7 * q^33 - 10 * q^34 - 36 * q^35 + 12 * q^36 - 23 * q^37 - 31 * q^38 - 15 * q^39 - 4 * q^40 - 7 * q^41 - 13 * q^42 - 23 * q^43 - 17 * q^44 - 19 * q^45 - 6 * q^46 - 19 * q^47 - 7 * q^48 - 8 * q^49 + 3 * q^50 - 18 * q^51 - 18 * q^52 - 30 * q^53 - 37 * q^54 + 4 * q^55 - 5 * q^56 + 10 * q^57 - 16 * q^58 - 28 * q^59 - 16 * q^60 - 19 * q^61 - 30 * q^62 + 2 * q^63 + 17 * q^64 + 23 * q^65 + 7 * q^66 - 35 * q^67 - 10 * q^68 + q^69 - 36 * q^70 + q^71 + 12 * q^72 - 10 * q^73 - 23 * q^74 - 33 * q^75 - 31 * q^76 + 5 * q^77 - 15 * q^78 - 27 * q^79 - 4 * q^80 + 13 * q^81 - 7 * q^82 - 40 * q^83 - 13 * q^84 - 11 * q^85 - 23 * q^86 - 6 * q^87 - 17 * q^88 - 17 * q^89 - 19 * q^90 - 19 * q^91 - 6 * q^92 + 10 * q^93 - 19 * q^94 - 27 * q^95 - 7 * q^96 - 34 * q^97 - 8 * q^98 - 12 * q^99

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