LMFDB - Embedded newform 3201.2.a.t.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3201,2,Mod(1,3201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3201, 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("3201.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3201 = 3 \cdot 11 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3201.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:	$25.5601136870$
Analytic rank:	$0$
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} - 3 x^{16} - 22 x^{15} + 71 x^{14} + 181 x^{13} - 662 x^{12} - 663 x^{11} + 3095 x^{10} + \cdots - 54 $ x^17 - 3x^16 - 22x^15 + 71x^14 + 181x^13 - 662x^12 - 663x^11 + 3095x^10 + 850x^9 - 7636x^8 + 820x^7 + 9596x^6 - 2793x^5 - 5469x^4 + 1733x^3 + 1110x^2 - 171x - 54
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-0.187677$ of defining polynomial
Character	$\chi$	$=$	3201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.187677 q^{2} -1.00000 q^{3} -1.96478 q^{4} -3.94913 q^{5} -0.187677 q^{6} +2.55781 q^{7} -0.744097 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.187677 q^{2} -1.00000 q^{3} -1.96478 q^{4} -3.94913 q^{5} -0.187677 q^{6} +2.55781 q^{7} -0.744097 q^{8} +1.00000 q^{9} -0.741160 q^{10} -1.00000 q^{11} +1.96478 q^{12} -4.51358 q^{13} +0.480042 q^{14} +3.94913 q^{15} +3.78990 q^{16} -5.33936 q^{17} +0.187677 q^{18} -0.767739 q^{19} +7.75916 q^{20} -2.55781 q^{21} -0.187677 q^{22} -6.36652 q^{23} +0.744097 q^{24} +10.5956 q^{25} -0.847095 q^{26} -1.00000 q^{27} -5.02552 q^{28} -6.56328 q^{29} +0.741160 q^{30} -2.00937 q^{31} +2.19947 q^{32} +1.00000 q^{33} -1.00207 q^{34} -10.1011 q^{35} -1.96478 q^{36} -1.00364 q^{37} -0.144087 q^{38} +4.51358 q^{39} +2.93854 q^{40} -1.25262 q^{41} -0.480042 q^{42} -8.54611 q^{43} +1.96478 q^{44} -3.94913 q^{45} -1.19485 q^{46} -10.6092 q^{47} -3.78990 q^{48} -0.457618 q^{49} +1.98855 q^{50} +5.33936 q^{51} +8.86818 q^{52} -13.4585 q^{53} -0.187677 q^{54} +3.94913 q^{55} -1.90326 q^{56} +0.767739 q^{57} -1.23178 q^{58} +13.4357 q^{59} -7.75916 q^{60} +3.78251 q^{61} -0.377112 q^{62} +2.55781 q^{63} -7.16702 q^{64} +17.8247 q^{65} +0.187677 q^{66} -7.87458 q^{67} +10.4906 q^{68} +6.36652 q^{69} -1.89575 q^{70} +7.13783 q^{71} -0.744097 q^{72} -1.69975 q^{73} -0.188360 q^{74} -10.5956 q^{75} +1.50844 q^{76} -2.55781 q^{77} +0.847095 q^{78} +8.22862 q^{79} -14.9668 q^{80} +1.00000 q^{81} -0.235089 q^{82} +10.4416 q^{83} +5.02552 q^{84} +21.0858 q^{85} -1.60391 q^{86} +6.56328 q^{87} +0.744097 q^{88} +2.45137 q^{89} -0.741160 q^{90} -11.5449 q^{91} +12.5088 q^{92} +2.00937 q^{93} -1.99111 q^{94} +3.03190 q^{95} -2.19947 q^{96} +1.00000 q^{97} -0.0858844 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 3 q^{2} - 17 q^{3} + 19 q^{4} - 10 q^{5} + 3 q^{6} + 9 q^{7} + 17 q^{9}+O(q^{10}) $ 17 * q - 3 * q^2 - 17 * q^3 + 19 * q^4 - 10 * q^5 + 3 * q^6 + 9 * q^7 + 17 * q^9	\( 17 q - 3 q^{2} - 17 q^{3} + 19 q^{4} - 10 q^{5} + 3 q^{6} + 9 q^{7} + 17 q^{9} + 17 q^{10} - 17 q^{11} - 19 q^{12} - 2 q^{13} + 10 q^{14} + 10 q^{15} + 15 q^{16} - 2 q^{17} - 3 q^{18} + 25 q^{19} - 32 q^{20} - 9 q^{21} + 3 q^{22} - 3 q^{23} + 35 q^{25} - 7 q^{26} - 17 q^{27} + q^{28} + 4 q^{29} - 17 q^{30} + 44 q^{31} - 3 q^{32} + 17 q^{33} + 22 q^{34} + 4 q^{35} + 19 q^{36} + 13 q^{37} - 2 q^{38} + 2 q^{39} + 41 q^{40} + 5 q^{41} - 10 q^{42} + 27 q^{43} - 19 q^{44} - 10 q^{45} - 29 q^{46} - 10 q^{47} - 15 q^{48} + 12 q^{49} - 2 q^{50} + 2 q^{51} + 32 q^{52} - 45 q^{53} + 3 q^{54} + 10 q^{55} + 35 q^{56} - 25 q^{57} + 17 q^{58} + q^{59} + 32 q^{60} + 22 q^{61} + 23 q^{62} + 9 q^{63} + 24 q^{64} + 23 q^{65} - 3 q^{66} + 7 q^{67} - 10 q^{68} + 3 q^{69} + 40 q^{70} - 12 q^{71} - 21 q^{73} + 45 q^{74} - 35 q^{75} + 34 q^{76} - 9 q^{77} + 7 q^{78} + 24 q^{79} - 50 q^{80} + 17 q^{81} - 6 q^{82} - 26 q^{83} - q^{84} - 43 q^{85} + 9 q^{86} - 4 q^{87} - 40 q^{89} + 17 q^{90} + 38 q^{91} + 47 q^{92} - 44 q^{93} + 52 q^{94} - 12 q^{95} + 3 q^{96} + 17 q^{97} + 15 q^{98} - 17 q^{99}+O(q^{100}) \) 17 * q - 3 * q^2 - 17 * q^3 + 19 * q^4 - 10 * q^5 + 3 * q^6 + 9 * q^7 + 17 * q^9 + 17 * q^10 - 17 * q^11 - 19 * q^12 - 2 * q^13 + 10 * q^14 + 10 * q^15 + 15 * q^16 - 2 * q^17 - 3 * q^18 + 25 * q^19 - 32 * q^20 - 9 * q^21 + 3 * q^22 - 3 * q^23 + 35 * q^25 - 7 * q^26 - 17 * q^27 + q^28 + 4 * q^29 - 17 * q^30 + 44 * q^31 - 3 * q^32 + 17 * q^33 + 22 * q^34 + 4 * q^35 + 19 * q^36 + 13 * q^37 - 2 * q^38 + 2 * q^39 + 41 * q^40 + 5 * q^41 - 10 * q^42 + 27 * q^43 - 19 * q^44 - 10 * q^45 - 29 * q^46 - 10 * q^47 - 15 * q^48 + 12 * q^49 - 2 * q^50 + 2 * q^51 + 32 * q^52 - 45 * q^53 + 3 * q^54 + 10 * q^55 + 35 * q^56 - 25 * q^57 + 17 * q^58 + q^59 + 32 * q^60 + 22 * q^61 + 23 * q^62 + 9 * q^63 + 24 * q^64 + 23 * q^65 - 3 * q^66 + 7 * q^67 - 10 * q^68 + 3 * q^69 + 40 * q^70 - 12 * q^71 - 21 * q^73 + 45 * q^74 - 35 * q^75 + 34 * q^76 - 9 * q^77 + 7 * q^78 + 24 * q^79 - 50 * q^80 + 17 * q^81 - 6 * q^82 - 26 * q^83 - q^84 - 43 * q^85 + 9 * q^86 - 4 * q^87 - 40 * q^89 + 17 * q^90 + 38 * q^91 + 47 * q^92 - 44 * q^93 + 52 * q^94 - 12 * q^95 + 3 * q^96 + 17 * q^97 + 15 * q^98 - 17 * 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 $

$2$	0.187677	0.132708	0.0663538	−	0.997796i	$-0.478863\pi$
$2$	0.187677	0.132708	0.0663538	+	0.997796i	$0.478863\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.96478	−0.982389
$5$	−3.94913	−1.76610	−0.883052	−	0.469276i	$-0.844515\pi$
$5$	−3.94913	−1.76610	−0.883052	+	0.469276i	$0.844515\pi$
$6$	−0.187677	−0.0766188
$7$	2.55781	0.966761	0.483380	−	0.875410i	$-0.339409\pi$
$7$	2.55781	0.966761	0.483380	+	0.875410i	$0.339409\pi$
$8$	−0.744097	−0.263078
$9$	1.00000	0.333333
$10$	−0.741160	−0.234375
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.96478	0.567182
$13$	−4.51358	−1.25184	−0.625921	−	0.779886i	$-0.715277\pi$
$13$	−4.51358	−1.25184	−0.625921	+	0.779886i	$0.715277\pi$
$14$	0.480042	0.128297
$15$	3.94913	1.01966
$16$	3.78990	0.947476
$17$	−5.33936	−1.29498	−0.647492	−	0.762072i	$-0.724182\pi$
$17$	−5.33936	−1.29498	−0.647492	+	0.762072i	$0.724182\pi$
$18$	0.187677	0.0442359
$19$	−0.767739	−0.176131	−0.0880657	−	0.996115i	$-0.528069\pi$
$19$	−0.767739	−0.176131	−0.0880657	+	0.996115i	$0.528069\pi$
$20$	7.75916	1.73500
$21$	−2.55781	−0.558159
$22$	−0.187677	−0.0400129
$23$	−6.36652	−1.32751	−0.663756	−	0.747950i	$-0.731038\pi$
$23$	−6.36652	−1.32751	−0.663756	+	0.747950i	$0.731038\pi$
$24$	0.744097	0.151888
$25$	10.5956	2.11912
$26$	−0.847095	−0.166129
$27$	−1.00000	−0.192450
$28$	−5.02552	−0.949735
$29$	−6.56328	−1.21877	−0.609385	−	0.792874i	$-0.708584\pi$
$29$	−6.56328	−1.21877	−0.609385	+	0.792874i	$0.708584\pi$
$30$	0.741160	0.135317
$31$	−2.00937	−0.360893	−0.180447	−	0.983585i	$-0.557754\pi$
$31$	−2.00937	−0.360893	−0.180447	+	0.983585i	$0.557754\pi$
$32$	2.19947	0.388815
$33$	1.00000	0.174078
$34$	−1.00207	−0.171854
$35$	−10.1011	−1.70740
$36$	−1.96478	−0.327463
$37$	−1.00364	−0.164998	−0.0824988	−	0.996591i	$-0.526290\pi$
$37$	−1.00364	−0.164998	−0.0824988	+	0.996591i	$0.526290\pi$
$38$	−0.144087	−0.0233740
$39$	4.51358	0.722751
$40$	2.93854	0.464623
$41$	−1.25262	−0.195627	−0.0978135	−	0.995205i	$-0.531185\pi$
$41$	−1.25262	−0.195627	−0.0978135	+	0.995205i	$0.531185\pi$
$42$	−0.480042	−0.0740720
$43$	−8.54611	−1.30327	−0.651634	−	0.758533i	$-0.725916\pi$
$43$	−8.54611	−1.30327	−0.651634	+	0.758533i	$0.725916\pi$
$44$	1.96478	0.296201
$45$	−3.94913	−0.588701
$46$	−1.19485	−0.176171
$47$	−10.6092	−1.54752	−0.773759	−	0.633480i	$-0.781626\pi$
$47$	−10.6092	−1.54752	−0.773759	+	0.633480i	$0.781626\pi$
$48$	−3.78990	−0.547026
$49$	−0.457618	−0.0653740
$50$	1.98855	0.281224
$51$	5.33936	0.747660
$52$	8.86818	1.22980
$53$	−13.4585	−1.84867	−0.924333	−	0.381586i	$-0.875378\pi$
$53$	−13.4585	−1.84867	−0.924333	+	0.381586i	$0.875378\pi$
$54$	−0.187677	−0.0255396
$55$	3.94913	0.532500
$56$	−1.90326	−0.254334
$57$	0.767739	0.101690
$58$	−1.23178	−0.161740
$59$	13.4357	1.74918	0.874589	−	0.484865i	$-0.161131\pi$
$59$	13.4357	1.74918	0.874589	+	0.484865i	$0.161131\pi$
$60$	−7.75916	−1.00170
$61$	3.78251	0.484301	0.242150	−	0.970239i	$-0.422147\pi$
$61$	3.78251	0.484301	0.242150	+	0.970239i	$0.422147\pi$
$62$	−0.377112	−0.0478933
$63$	2.55781	0.322254
$64$	−7.16702	−0.895877
$65$	17.8247	2.21088
$66$	0.187677	0.0231014
$67$	−7.87458	−0.962033	−0.481017	−	0.876712i	$-0.659732\pi$
$67$	−7.87458	−0.962033	−0.481017	+	0.876712i	$0.659732\pi$
$68$	10.4906	1.27218
$69$	6.36652	0.766439
$70$	−1.89575	−0.226585
$71$	7.13783	0.847105	0.423553	−	0.905872i	$-0.360783\pi$
$71$	7.13783	0.847105	0.423553	+	0.905872i	$0.360783\pi$
$72$	−0.744097	−0.0876927
$73$	−1.69975	−0.198940	−0.0994701	−	0.995041i	$-0.531715\pi$
$73$	−1.69975	−0.198940	−0.0994701	+	0.995041i	$0.531715\pi$
$74$	−0.188360	−0.0218964
$75$	−10.5956	−1.22348
$76$	1.50844	0.173030
$77$	−2.55781	−0.291489
$78$	0.847095	0.0959146
$79$	8.22862	0.925792	0.462896	−	0.886413i	$-0.346810\pi$
$79$	8.22862	0.925792	0.462896	+	0.886413i	$0.346810\pi$
$80$	−14.9668	−1.67334
$81$	1.00000	0.111111
$82$	−0.235089	−0.0259612
$83$	10.4416	1.14612	0.573058	−	0.819515i	$-0.305757\pi$
$83$	10.4416	1.14612	0.573058	+	0.819515i	$0.305757\pi$
$84$	5.02552	0.548330
$85$	21.0858	2.28708
$86$	−1.60391	−0.172954
$87$	6.56328	0.703658
$88$	0.744097	0.0793210
$89$	2.45137	0.259845	0.129923	−	0.991524i	$-0.458527\pi$
$89$	2.45137	0.259845	0.129923	+	0.991524i	$0.458527\pi$
$90$	−0.741160	−0.0781251
$91$	−11.5449	−1.21023
$92$	12.5088	1.30413
$93$	2.00937	0.208362
$94$	−1.99111	−0.205367
$95$	3.03190	0.311066
$96$	−2.19947	−0.224483
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	−0.0858844	−0.00867563
$99$	−1.00000	−0.100504
$100$	−20.8180	−2.08180
$101$	−6.83968	−0.680574	−0.340287	−	0.940322i	$-0.610524\pi$
$101$	−6.83968	−0.680574	−0.340287	+	0.940322i	$0.610524\pi$
$102$	1.00207	0.0992201
$103$	13.3266	1.31311	0.656555	−	0.754278i	$-0.272013\pi$
$103$	13.3266	1.31311	0.656555	+	0.754278i	$0.272013\pi$
$104$	3.35854	0.329332
$105$	10.1011	0.985767
$106$	−2.52585	−0.245332
$107$	−15.9534	−1.54228	−0.771139	−	0.636667i	$-0.780313\pi$
$107$	−15.9534	−1.54228	−0.771139	+	0.636667i	$0.780313\pi$
$108$	1.96478	0.189061
$109$	18.4439	1.76660	0.883301	−	0.468806i	$-0.155316\pi$
$109$	18.4439	1.76660	0.883301	+	0.468806i	$0.155316\pi$
$110$	0.741160	0.0706669
$111$	1.00364	0.0952614
$112$	9.69385	0.915983
$113$	0.768399	0.0722849	0.0361424	−	0.999347i	$-0.488493\pi$
$113$	0.768399	0.0722849	0.0361424	+	0.999347i	$0.488493\pi$
$114$	0.144087	0.0134950
$115$	25.1422	2.34452
$116$	12.8954	1.19731
$117$	−4.51358	−0.417281
$118$	2.52157	0.232129
$119$	−13.6571	−1.25194
$120$	−2.93854	−0.268250
$121$	1.00000	0.0909091
$122$	0.709890	0.0642704
$123$	1.25262	0.112945
$124$	3.94796	0.354537
$125$	−22.0978	−1.97648
$126$	0.480042	0.0427655
$127$	−10.9285	−0.969750	−0.484875	−	0.874584i	$-0.661135\pi$
$127$	−10.9285	−0.969750	−0.484875	+	0.874584i	$0.661135\pi$
$128$	−5.74403	−0.507705
$129$	8.54611	0.752443
$130$	3.34529	0.293401
$131$	−4.16461	−0.363864	−0.181932	−	0.983311i	$-0.558235\pi$
$131$	−4.16461	−0.363864	−0.181932	+	0.983311i	$0.558235\pi$
$132$	−1.96478	−0.171012
$133$	−1.96373	−0.170277
$134$	−1.47788	−0.127669
$135$	3.94913	0.339887
$136$	3.97300	0.340682
$137$	−4.50848	−0.385185	−0.192593	−	0.981279i	$-0.561690\pi$
$137$	−4.50848	−0.385185	−0.192593	+	0.981279i	$0.561690\pi$
$138$	1.19485	0.101712
$139$	6.50399	0.551661	0.275831	−	0.961206i	$-0.411047\pi$
$139$	6.50399	0.551661	0.275831	+	0.961206i	$0.411047\pi$
$140$	19.8464	1.67733
$141$	10.6092	0.893460
$142$	1.33961	0.112417
$143$	4.51358	0.377445
$144$	3.78990	0.315825
$145$	25.9192	2.15247
$146$	−0.319003	−0.0264009
$147$	0.457618	0.0377437
$148$	1.97193	0.162092
$149$	22.0333	1.80504	0.902520	−	0.430649i	$-0.141715\pi$
$149$	22.0333	1.80504	0.902520	+	0.430649i	$0.141715\pi$
$150$	−1.98855	−0.162365
$151$	−7.75911	−0.631427	−0.315714	−	0.948855i	$-0.602244\pi$
$151$	−7.75911	−0.631427	−0.315714	+	0.948855i	$0.602244\pi$
$152$	0.571273	0.0463363
$153$	−5.33936	−0.431661
$154$	−0.480042	−0.0386829
$155$	7.93525	0.637375
$156$	−8.86818	−0.710023
$157$	0.942622	0.0752294	0.0376147	−	0.999292i	$-0.488024\pi$
$157$	0.942622	0.0752294	0.0376147	+	0.999292i	$0.488024\pi$
$158$	1.54432	0.122860
$159$	13.4585	1.06733
$160$	−8.68600	−0.686688
$161$	−16.2843	−1.28339
$162$	0.187677	0.0147453
$163$	−20.8563	−1.63359	−0.816797	−	0.576926i	$-0.804252\pi$
$163$	−20.8563	−1.63359	−0.816797	+	0.576926i	$0.804252\pi$
$164$	2.46113	0.192182
$165$	−3.94913	−0.307439
$166$	1.95965	0.152098
$167$	9.83202	0.760825	0.380412	−	0.924817i	$-0.375782\pi$
$167$	9.83202	0.760825	0.380412	+	0.924817i	$0.375782\pi$
$168$	1.90326	0.146840
$169$	7.37242	0.567109
$170$	3.95732	0.303513
$171$	−0.767739	−0.0587105
$172$	16.7912	1.28032
$173$	2.63105	0.200035	0.100018	−	0.994986i	$-0.468110\pi$
$173$	2.63105	0.200035	0.100018	+	0.994986i	$0.468110\pi$
$174$	1.23178	0.0933807
$175$	27.1015	2.04868
$176$	−3.78990	−0.285675
$177$	−13.4357	−1.00989
$178$	0.460067	0.0344834
$179$	−1.84292	−0.137747	−0.0688733	−	0.997625i	$-0.521940\pi$
$179$	−1.84292	−0.137747	−0.0688733	+	0.997625i	$0.521940\pi$
$180$	7.75916	0.578333
$181$	9.27816	0.689640	0.344820	−	0.938669i	$-0.387940\pi$
$181$	9.27816	0.689640	0.344820	+	0.938669i	$0.387940\pi$
$182$	−2.16671	−0.160607
$183$	−3.78251	−0.279611
$184$	4.73731	0.349239
$185$	3.96351	0.291403
$186$	0.377112	0.0276512
$187$	5.33936	0.390452
$188$	20.8448	1.52026
$189$	−2.55781	−0.186053
$190$	0.569018	0.0412809
$191$	−15.9183	−1.15181	−0.575903	−	0.817518i	$-0.695349\pi$
$191$	−15.9183	−1.15181	−0.575903	+	0.817518i	$0.695349\pi$
$192$	7.16702	0.517235
$193$	−0.293409	−0.0211201	−0.0105600	−	0.999944i	$-0.503361\pi$
$193$	−0.293409	−0.0211201	−0.0105600	+	0.999944i	$0.503361\pi$
$194$	0.187677	0.0134744
$195$	−17.8247	−1.27645
$196$	0.899117	0.0642227
$197$	17.6783	1.25953	0.629763	−	0.776787i	$-0.283152\pi$
$197$	17.6783	1.25953	0.629763	+	0.776787i	$0.283152\pi$
$198$	−0.187677	−0.0133376
$199$	12.3696	0.876860	0.438430	−	0.898765i	$-0.355535\pi$
$199$	12.3696	0.876860	0.438430	+	0.898765i	$0.355535\pi$
$200$	−7.88416	−0.557495
$201$	7.87458	0.555430
$202$	−1.28365	−0.0903173
$203$	−16.7876	−1.17826
$204$	−10.4906	−0.734492
$205$	4.94677	0.345498
$206$	2.50110	0.174260
$207$	−6.36652	−0.442504
$208$	−17.1060	−1.18609
$209$	0.767739	0.0531056
$210$	1.89575	0.130819
$211$	−21.6529	−1.49065	−0.745323	−	0.666704i	$-0.767705\pi$
$211$	−21.6529	−1.49065	−0.745323	+	0.666704i	$0.767705\pi$
$212$	26.4429	1.81611
$213$	−7.13783	−0.489076
$214$	−2.99409	−0.204672
$215$	33.7497	2.30171
$216$	0.744097	0.0506294
$217$	−5.13958	−0.348897
$218$	3.46149	0.234442
$219$	1.69975	0.114858
$220$	−7.75916	−0.523122
$221$	24.0996	1.62112
$222$	0.188360	0.0126419
$223$	−2.05159	−0.137385	−0.0686923	−	0.997638i	$-0.521883\pi$
$223$	−2.05159	−0.137385	−0.0686923	+	0.997638i	$0.521883\pi$
$224$	5.62583	0.375891
$225$	10.5956	0.706374
$226$	0.144211	0.00959276
$227$	−16.8777	−1.12021	−0.560106	−	0.828421i	$-0.689240\pi$
$227$	−16.8777	−1.12021	−0.560106	+	0.828421i	$0.689240\pi$
$228$	−1.50844	−0.0998987
$229$	16.9164	1.11787	0.558935	−	0.829212i	$-0.311210\pi$
$229$	16.9164	1.11787	0.558935	+	0.829212i	$0.311210\pi$
$230$	4.71861	0.311136
$231$	2.55781	0.168291
$232$	4.88372	0.320632
$233$	−2.19940	−0.144088	−0.0720438	−	0.997401i	$-0.522952\pi$
$233$	−2.19940	−0.144088	−0.0720438	+	0.997401i	$0.522952\pi$
$234$	−0.847095	−0.0553763
$235$	41.8973	2.73308
$236$	−26.3981	−1.71837
$237$	−8.22862	−0.534506
$238$	−2.56311	−0.166142
$239$	26.7605	1.73099	0.865497	−	0.500913i	$-0.167002\pi$
$239$	26.7605	1.73099	0.865497	+	0.500913i	$0.167002\pi$
$240$	14.9668	0.966104
$241$	−4.22968	−0.272457	−0.136229	−	0.990677i	$-0.543498\pi$
$241$	−4.22968	−0.272457	−0.136229	+	0.990677i	$0.543498\pi$
$242$	0.187677	0.0120643
$243$	−1.00000	−0.0641500
$244$	−7.43179	−0.475771
$245$	1.80719	0.115457
$246$	0.235089	0.0149887
$247$	3.46525	0.220489
$248$	1.49517	0.0949431
$249$	−10.4416	−0.661711
$250$	−4.14724	−0.262295
$251$	−27.3226	−1.72459	−0.862295	−	0.506407i	$-0.830973\pi$
$251$	−27.3226	−1.72459	−0.862295	+	0.506407i	$0.830973\pi$
$252$	−5.02552	−0.316578
$253$	6.36652	0.400260
$254$	−2.05103	−0.128693
$255$	−21.0858	−1.32044
$256$	13.2560	0.828501
$257$	24.8695	1.55132	0.775658	−	0.631153i	$-0.217418\pi$
$257$	24.8695	1.55132	0.775658	+	0.631153i	$0.217418\pi$
$258$	1.60391	0.0998549
$259$	−2.56712	−0.159513
$260$	−35.0216	−2.17195
$261$	−6.56328	−0.406257
$262$	−0.781602	−0.0482875
$263$	15.7343	0.970217	0.485109	−	0.874454i	$-0.338780\pi$
$263$	15.7343	0.970217	0.485109	+	0.874454i	$0.338780\pi$
$264$	−0.744097	−0.0457960
$265$	53.1493	3.26494
$266$	−0.368547	−0.0225971
$267$	−2.45137	−0.150022
$268$	15.4718	0.945090
$269$	7.23088	0.440874	0.220437	−	0.975401i	$-0.429252\pi$
$269$	7.23088	0.440874	0.220437	+	0.975401i	$0.429252\pi$
$270$	0.741160	0.0451056
$271$	5.86234	0.356112	0.178056	−	0.984020i	$-0.443019\pi$
$271$	5.86234	0.356112	0.178056	+	0.984020i	$0.443019\pi$
$272$	−20.2357	−1.22697
$273$	11.5449	0.698728
$274$	−0.846137	−0.0511170
$275$	−10.5956	−0.638939
$276$	−12.5088	−0.752941
$277$	−15.5838	−0.936342	−0.468171	−	0.883638i	$-0.655087\pi$
$277$	−15.5838	−0.936342	−0.468171	+	0.883638i	$0.655087\pi$
$278$	1.22065	0.0732097
$279$	−2.00937	−0.120298
$280$	7.51621	0.449179
$281$	10.4271	0.622030	0.311015	−	0.950405i	$-0.399331\pi$
$281$	10.4271	0.622030	0.311015	+	0.950405i	$0.399331\pi$
$282$	1.99111	0.118569
$283$	−28.4509	−1.69123	−0.845616	−	0.533791i	$-0.820767\pi$
$283$	−28.4509	−1.69123	−0.845616	+	0.533791i	$0.820767\pi$
$284$	−14.0243	−0.832186
$285$	−3.03190	−0.179594
$286$	0.847095	0.0500898
$287$	−3.20397	−0.189125
$288$	2.19947	0.129605
$289$	11.5087	0.676984
$290$	4.86444	0.285650
$291$	−1.00000	−0.0586210
$292$	3.33962	0.195437
$293$	−8.16718	−0.477132	−0.238566	−	0.971126i	$-0.576677\pi$
$293$	−8.16718	−0.477132	−0.238566	+	0.971126i	$0.576677\pi$
$294$	0.0858844	0.00500888
$295$	−53.0593	−3.08923
$296$	0.746806	0.0434072
$297$	1.00000	0.0580259
$298$	4.13514	0.239543
$299$	28.7358	1.66183
$300$	20.8180	1.20193
$301$	−21.8593	−1.25995
$302$	−1.45621	−0.0837952
$303$	6.83968	0.392929
$304$	−2.90966	−0.166880
$305$	−14.9376	−0.855325
$306$	−1.00207	−0.0572848
$307$	25.8739	1.47670	0.738349	−	0.674418i	$-0.235606\pi$
$307$	25.8739	1.47670	0.738349	+	0.674418i	$0.235606\pi$
$308$	5.02552	0.286356
$309$	−13.3266	−0.758125
$310$	1.48926	0.0845845
$311$	14.8930	0.844506	0.422253	−	0.906478i	$-0.361239\pi$
$311$	14.8930	0.844506	0.422253	+	0.906478i	$0.361239\pi$
$312$	−3.35854	−0.190140
$313$	14.5684	0.823455	0.411728	−	0.911307i	$-0.364925\pi$
$313$	14.5684	0.823455	0.411728	+	0.911307i	$0.364925\pi$
$314$	0.176908	0.00998352
$315$	−10.1011	−0.569133
$316$	−16.1674	−0.909488
$317$	−10.6191	−0.596427	−0.298213	−	0.954499i	$-0.596391\pi$
$317$	−10.6191	−0.596427	−0.298213	+	0.954499i	$0.596391\pi$
$318$	2.52585	0.141643
$319$	6.56328	0.367473
$320$	28.3035	1.58221
$321$	15.9534	0.890434
$322$	−3.05619	−0.170315
$323$	4.09923	0.228087
$324$	−1.96478	−0.109154
$325$	−47.8241	−2.65281
$326$	−3.91425	−0.216790
$327$	−18.4439	−1.01995
$328$	0.932074	0.0514652
$329$	−27.1364	−1.49608
$330$	−0.741160	−0.0407995
$331$	14.1900	0.779952	0.389976	−	0.920825i	$-0.372483\pi$
$331$	14.1900	0.779952	0.389976	+	0.920825i	$0.372483\pi$
$332$	−20.5155	−1.12593
$333$	−1.00364	−0.0549992
$334$	1.84524	0.100967
$335$	31.0977	1.69905
$336$	−9.69385	−0.528843
$337$	1.33129	0.0725202	0.0362601	−	0.999342i	$-0.488456\pi$
$337$	1.33129	0.0725202	0.0362601	+	0.999342i	$0.488456\pi$
$338$	1.38363	0.0752597
$339$	−0.768399	−0.0417337
$340$	−41.4289	−2.24680
$341$	2.00937	0.108813
$342$	−0.144087	−0.00779133
$343$	−19.0752	−1.02996
$344$	6.35913	0.342862
$345$	−25.1422	−1.35361
$346$	0.493788	0.0265462
$347$	−36.7105	−1.97072	−0.985361	−	0.170478i	$-0.945469\pi$
$347$	−36.7105	−1.97072	−0.985361	+	0.170478i	$0.945469\pi$
$348$	−12.8954	−0.691265
$349$	−18.8479	−1.00890	−0.504452	−	0.863440i	$-0.668306\pi$
$349$	−18.8479	−1.00890	−0.504452	+	0.863440i	$0.668306\pi$
$350$	5.08633	0.271876
$351$	4.51358	0.240917
$352$	−2.19947	−0.117232
$353$	−12.9271	−0.688039	−0.344019	−	0.938963i	$-0.611789\pi$
$353$	−12.9271	−0.688039	−0.344019	+	0.938963i	$0.611789\pi$
$354$	−2.52157	−0.134020
$355$	−28.1882	−1.49608
$356$	−4.81641	−0.255269
$357$	13.6571	0.722808
$358$	−0.345874	−0.0182800
$359$	−28.7653	−1.51817	−0.759086	−	0.650990i	$-0.774354\pi$
$359$	−28.7653	−1.51817	−0.759086	+	0.650990i	$0.774354\pi$
$360$	2.93854	0.154874
$361$	−18.4106	−0.968978
$362$	1.74130	0.0915205
$363$	−1.00000	−0.0524864
$364$	22.6831	1.18892
$365$	6.71252	0.351349
$366$	−0.709890	−0.0371065
$367$	34.7566	1.81428	0.907141	−	0.420827i	$-0.138260\pi$
$367$	34.7566	1.81428	0.907141	+	0.420827i	$0.138260\pi$
$368$	−24.1285	−1.25779
$369$	−1.25262	−0.0652090
$370$	0.743859	0.0386714
$371$	−34.4243	−1.78722
$372$	−3.94796	−0.204692
$373$	−0.746130	−0.0386332	−0.0193166	−	0.999813i	$-0.506149\pi$
$373$	−0.746130	−0.0386332	−0.0193166	+	0.999813i	$0.506149\pi$
$374$	1.00207	0.0518160
$375$	22.0978	1.14112
$376$	7.89431	0.407118
$377$	29.6239	1.52571
$378$	−0.480042	−0.0246907
$379$	−30.5061	−1.56699	−0.783496	−	0.621397i	$-0.786565\pi$
$379$	−30.5061	−1.56699	−0.783496	+	0.621397i	$0.786565\pi$
$380$	−5.95701	−0.305588
$381$	10.9285	0.559885
$382$	−2.98749	−0.152853
$383$	38.3423	1.95920	0.979600	−	0.200960i	$-0.0644060\pi$
$383$	38.3423	1.95920	0.979600	+	0.200960i	$0.0644060\pi$
$384$	5.74403	0.293124
$385$	10.1011	0.514800
$386$	−0.0550662	−0.00280280
$387$	−8.54611	−0.434423
$388$	−1.96478	−0.0997465
$389$	15.8934	0.805826	0.402913	−	0.915238i	$-0.367998\pi$
$389$	15.8934	0.805826	0.402913	+	0.915238i	$0.367998\pi$
$390$	−3.34529	−0.169395
$391$	33.9931	1.71911
$392$	0.340512	0.0171985
$393$	4.16461	0.210077
$394$	3.31781	0.167149
$395$	−32.4959	−1.63504
$396$	1.96478	0.0987338
$397$	10.9314	0.548632	0.274316	−	0.961640i	$-0.411549\pi$
$397$	10.9314	0.548632	0.274316	+	0.961640i	$0.411549\pi$
$398$	2.32149	0.116366
$399$	1.96373	0.0983095
$400$	40.1563	2.00782
$401$	2.30982	0.115347	0.0576733	−	0.998336i	$-0.481632\pi$
$401$	2.30982	0.115347	0.0576733	+	0.998336i	$0.481632\pi$
$402$	1.47788	0.0737098
$403$	9.06944	0.451781
$404$	13.4385	0.668588
$405$	−3.94913	−0.196234
$406$	−3.15065	−0.156364
$407$	1.00364	0.0497486
$408$	−3.97300	−0.196693
$409$	31.7052	1.56772	0.783862	−	0.620935i	$-0.213247\pi$
$409$	31.7052	1.56772	0.783862	+	0.620935i	$0.213247\pi$
$410$	0.928395	0.0458502
$411$	4.50848	0.222387
$412$	−26.1838	−1.28999
$413$	34.3659	1.69104
$414$	−1.19485	−0.0587236
$415$	−41.2353	−2.02416
$416$	−9.92750	−0.486736
$417$	−6.50399	−0.318502
$418$	0.144087	0.00704752
$419$	−27.4350	−1.34029	−0.670144	−	0.742231i	$-0.733768\pi$
$419$	−27.4350	−1.34029	−0.670144	+	0.742231i	$0.733768\pi$
$420$	−19.8464	−0.968407
$421$	−21.5117	−1.04842	−0.524209	−	0.851590i	$-0.675639\pi$
$421$	−21.5117	−1.04842	−0.524209	+	0.851590i	$0.675639\pi$
$422$	−4.06374	−0.197820
$423$	−10.6092	−0.515839
$424$	10.0144	0.486344
$425$	−56.5737	−2.74423
$426$	−1.33961	−0.0649042
$427$	9.67493	0.468203
$428$	31.3450	1.51512
$429$	−4.51358	−0.217918
$430$	6.33403	0.305454
$431$	2.58448	0.124490	0.0622450	−	0.998061i	$-0.480174\pi$
$431$	2.58448	0.124490	0.0622450	+	0.998061i	$0.480174\pi$
$432$	−3.78990	−0.182342
$433$	−25.7741	−1.23862	−0.619312	−	0.785145i	$-0.712588\pi$
$433$	−25.7741	−1.23862	−0.619312	+	0.785145i	$0.712588\pi$
$434$	−0.964580	−0.0463013
$435$	−25.9192	−1.24273
$436$	−36.2381	−1.73549
$437$	4.88783	0.233816
$438$	0.319003	0.0152426
$439$	−29.8386	−1.42412	−0.712060	−	0.702119i	$-0.752238\pi$
$439$	−29.8386	−1.42412	−0.712060	+	0.702119i	$0.752238\pi$
$440$	−2.93854	−0.140089
$441$	−0.457618	−0.0217913
$442$	4.52294	0.215134
$443$	−13.7447	−0.653032	−0.326516	−	0.945192i	$-0.605875\pi$
$443$	−13.7447	−0.653032	−0.326516	+	0.945192i	$0.605875\pi$
$444$	−1.97193	−0.0935837
$445$	−9.68079	−0.458914
$446$	−0.385036	−0.0182320
$447$	−22.0333	−1.04214
$448$	−18.3319	−0.866099
$449$	−24.1560	−1.13999	−0.569997	−	0.821647i	$-0.693056\pi$
$449$	−24.1560	−1.13999	−0.569997	+	0.821647i	$0.693056\pi$
$450$	1.98855	0.0937412
$451$	1.25262	0.0589838
$452$	−1.50973	−0.0710119
$453$	7.75911	0.364555
$454$	−3.16756	−0.148661
$455$	45.5922	2.13739
$456$	−0.571273	−0.0267523
$457$	12.0160	0.562083	0.281041	−	0.959696i	$-0.409320\pi$
$457$	12.0160	0.562083	0.281041	+	0.959696i	$0.409320\pi$
$458$	3.17483	0.148350
$459$	5.33936	0.249220
$460$	−49.3988	−2.30323
$461$	36.3195	1.69157	0.845784	−	0.533525i	$-0.179133\pi$
$461$	36.3195	1.69157	0.845784	+	0.533525i	$0.179133\pi$
$462$	0.480042	0.0223336
$463$	−26.3572	−1.22492	−0.612462	−	0.790500i	$-0.709821\pi$
$463$	−26.3572	−1.22492	−0.612462	+	0.790500i	$0.709821\pi$
$464$	−24.8742	−1.15476
$465$	−7.93525	−0.367988
$466$	−0.412777	−0.0191215
$467$	−23.0638	−1.06726	−0.533632	−	0.845717i	$-0.679173\pi$
$467$	−23.0638	−1.06726	−0.533632	+	0.845717i	$0.679173\pi$
$468$	8.86818	0.409932
$469$	−20.1417	−0.930056
$470$	7.86315	0.362700
$471$	−0.942622	−0.0434337
$472$	−9.99746	−0.460171
$473$	8.54611	0.392950
$474$	−1.54432	−0.0709331
$475$	−8.13466	−0.373244
$476$	26.8331	1.22989
$477$	−13.4585	−0.616222
$478$	5.02234	0.229716
$479$	−6.67899	−0.305171	−0.152585	−	0.988290i	$-0.548760\pi$
$479$	−6.67899	−0.305171	−0.152585	+	0.988290i	$0.548760\pi$
$480$	8.68600	0.396460
$481$	4.53001	0.206551
$482$	−0.793813	−0.0361572
$483$	16.2843	0.740963
$484$	−1.96478	−0.0893081
$485$	−3.94913	−0.179321
$486$	−0.187677	−0.00851320
$487$	3.30911	0.149950	0.0749751	−	0.997185i	$-0.476112\pi$
$487$	3.30911	0.149950	0.0749751	+	0.997185i	$0.476112\pi$
$488$	−2.81455	−0.127409
$489$	20.8563	0.943156
$490$	0.339168	0.0153221
$491$	−32.2493	−1.45539	−0.727695	−	0.685901i	$-0.759408\pi$
$491$	−32.2493	−1.45539	−0.727695	+	0.685901i	$0.759408\pi$
$492$	−2.46113	−0.110956
$493$	35.0437	1.57829
$494$	0.650348	0.0292606
$495$	3.94913	0.177500
$496$	−7.61531	−0.341938
$497$	18.2572	0.818948
$498$	−1.95965	−0.0878141
$499$	23.7104	1.06142	0.530711	−	0.847553i	$-0.321925\pi$
$499$	23.7104	1.06142	0.530711	+	0.847553i	$0.321925\pi$
$500$	43.4172	1.94168
$501$	−9.83202	−0.439262
$502$	−5.12783	−0.228866
$503$	5.98247	0.266745	0.133372	−	0.991066i	$-0.457419\pi$
$503$	5.98247	0.266745	0.133372	+	0.991066i	$0.457419\pi$
$504$	−1.90326	−0.0847779
$505$	27.0108	1.20196
$506$	1.19485	0.0531175
$507$	−7.37242	−0.327420
$508$	21.4721	0.952671
$509$	−29.8873	−1.32473	−0.662365	−	0.749181i	$-0.730447\pi$
$509$	−29.8873	−1.32473	−0.662365	+	0.749181i	$0.730447\pi$
$510$	−3.95732	−0.175233
$511$	−4.34763	−0.192328
$512$	13.9759	0.617654
$513$	0.767739	0.0338965
$514$	4.66743	0.205872
$515$	−52.6285	−2.31909
$516$	−16.7912	−0.739191
$517$	10.6092	0.466594
$518$	−0.481789	−0.0211686
$519$	−2.63105	−0.115490
$520$	−13.2633	−0.581635
$521$	−22.3843	−0.980676	−0.490338	−	0.871532i	$-0.663127\pi$
$521$	−22.3843	−0.980676	−0.490338	+	0.871532i	$0.663127\pi$
$522$	−1.23178	−0.0539134
$523$	−7.27382	−0.318062	−0.159031	−	0.987274i	$-0.550837\pi$
$523$	−7.27382	−0.318062	−0.159031	+	0.987274i	$0.550837\pi$
$524$	8.18254	0.357456
$525$	−27.1015	−1.18281
$526$	2.95296	0.128755
$527$	10.7287	0.467351
$528$	3.78990	0.164934
$529$	17.5326	0.762286
$530$	9.97490	0.433282
$531$	13.4357	0.583059
$532$	3.85829	0.167278
$533$	5.65382	0.244894
$534$	−0.460067	−0.0199090
$535$	63.0022	2.72382
$536$	5.85945	0.253090
$537$	1.84292	0.0795281
$538$	1.35707	0.0585074
$539$	0.457618	0.0197110
$540$	−7.75916	−0.333901
$541$	16.8970	0.726457	0.363229	−	0.931700i	$-0.381674\pi$
$541$	16.8970	0.726457	0.363229	+	0.931700i	$0.381674\pi$
$542$	1.10023	0.0472588
$543$	−9.27816	−0.398164
$544$	−11.7438	−0.503510
$545$	−72.8372	−3.12000
$546$	2.16671	0.0927265
$547$	4.76248	0.203629	0.101815	−	0.994803i	$-0.467535\pi$
$547$	4.76248	0.203629	0.101815	+	0.994803i	$0.467535\pi$
$548$	8.85816	0.378402
$549$	3.78251	0.161434
$550$	−1.98855	−0.0847921
$551$	5.03889	0.214664
$552$	−4.73731	−0.201633
$553$	21.0472	0.895019
$554$	−2.92473	−0.124260
$555$	−3.96351	−0.168241
$556$	−12.7789	−0.541946
$557$	−31.2860	−1.32563	−0.662816	−	0.748783i	$-0.730639\pi$
$557$	−31.2860	−1.32563	−0.662816	+	0.748783i	$0.730639\pi$
$558$	−0.377112	−0.0159644
$559$	38.5735	1.63149
$560$	−38.2822	−1.61772
$561$	−5.33936	−0.225428
$562$	1.95693	0.0825482
$563$	−20.6840	−0.871725	−0.435863	−	0.900013i	$-0.643557\pi$
$563$	−20.6840	−0.871725	−0.435863	+	0.900013i	$0.643557\pi$
$564$	−20.8448	−0.877725
$565$	−3.03451	−0.127663
$566$	−5.33958	−0.224439
$567$	2.55781	0.107418
$568$	−5.31124	−0.222855
$569$	−4.10094	−0.171920	−0.0859602	−	0.996299i	$-0.527396\pi$
$569$	−4.10094	−0.171920	−0.0859602	+	0.996299i	$0.527396\pi$
$570$	−0.569018	−0.0238335
$571$	12.6348	0.528752	0.264376	−	0.964420i	$-0.414834\pi$
$571$	12.6348	0.528752	0.264376	+	0.964420i	$0.414834\pi$
$572$	−8.86818	−0.370797
$573$	15.9183	0.664995
$574$	−0.601312	−0.0250983
$575$	−67.4571	−2.81316
$576$	−7.16702	−0.298626
$577$	21.2046	0.882758	0.441379	−	0.897321i	$-0.354489\pi$
$577$	21.2046	0.882758	0.441379	+	0.897321i	$0.354489\pi$
$578$	2.15992	0.0898410
$579$	0.293409	0.0121937
$580$	−50.9255	−2.11457
$581$	26.7077	1.10802
$582$	−0.187677	−0.00777946
$583$	13.4585	0.557394
$584$	1.26478	0.0523368
$585$	17.8247	0.736961
$586$	−1.53279	−0.0633190
$587$	25.8362	1.06637	0.533187	−	0.845998i	$-0.320994\pi$
$587$	25.8362	1.06637	0.533187	+	0.845998i	$0.320994\pi$
$588$	−0.899117	−0.0370790
$589$	1.54267	0.0635646
$590$	−9.95800	−0.409964
$591$	−17.6783	−0.727188
$592$	−3.80370	−0.156331
$593$	−12.8024	−0.525731	−0.262866	−	0.964832i	$-0.584668\pi$
$593$	−12.8024	−0.525731	−0.262866	+	0.964832i	$0.584668\pi$
$594$	0.187677	0.00770048
$595$	53.9334	2.21106
$596$	−43.2906	−1.77325
$597$	−12.3696	−0.506255
$598$	5.39305	0.220538
$599$	37.1446	1.51769	0.758844	−	0.651273i	$-0.225765\pi$
$599$	37.1446	1.51769	0.758844	+	0.651273i	$0.225765\pi$
$600$	7.88416	0.321870
$601$	−0.807639	−0.0329443	−0.0164721	−	0.999864i	$-0.505243\pi$
$601$	−0.807639	−0.0329443	−0.0164721	+	0.999864i	$0.505243\pi$
$602$	−4.10249	−0.167205
$603$	−7.87458	−0.320678
$604$	15.2449	0.620307
$605$	−3.94913	−0.160555
$606$	1.28365	0.0521447
$607$	15.3878	0.624571	0.312286	−	0.949988i	$-0.398905\pi$
$607$	15.3878	0.624571	0.312286	+	0.949988i	$0.398905\pi$
$608$	−1.68862	−0.0684826
$609$	16.7876	0.680268
$610$	−2.80345	−0.113508
$611$	47.8857	1.93725
$612$	10.4906	0.424059
$613$	7.78827	0.314565	0.157283	−	0.987554i	$-0.449727\pi$
$613$	7.78827	0.314565	0.157283	+	0.987554i	$0.449727\pi$
$614$	4.85593	0.195969
$615$	−4.94677	−0.199473
$616$	1.90326	0.0766845
$617$	24.0184	0.966945	0.483473	−	0.875359i	$-0.339375\pi$
$617$	24.0184	0.966945	0.483473	+	0.875359i	$0.339375\pi$
$618$	−2.50110	−0.100609
$619$	48.2653	1.93995	0.969973	−	0.243215i	$-0.0782019\pi$
$619$	48.2653	1.93995	0.969973	+	0.243215i	$0.0782019\pi$
$620$	−15.5910	−0.626150
$621$	6.36652	0.255480
$622$	2.79508	0.112072
$623$	6.27015	0.251208
$624$	17.1060	0.684790
$625$	34.2889	1.37156
$626$	2.73416	0.109279
$627$	−0.767739	−0.0306606
$628$	−1.85204	−0.0739046
$629$	5.35880	0.213669
$630$	−1.89575	−0.0755283
$631$	−9.75365	−0.388287	−0.194143	−	0.980973i	$-0.562193\pi$
$631$	−9.75365	−0.388287	−0.194143	+	0.980973i	$0.562193\pi$
$632$	−6.12290	−0.243556
$633$	21.6529	0.860624
$634$	−1.99296	−0.0791504
$635$	43.1581	1.71268
$636$	−26.4429	−1.04853
$637$	2.06550	0.0818379
$638$	1.23178	0.0487665
$639$	7.13783	0.282368
$640$	22.6839	0.896660
$641$	−5.38115	−0.212543	−0.106271	−	0.994337i	$-0.533891\pi$
$641$	−5.38115	−0.212543	−0.106271	+	0.994337i	$0.533891\pi$
$642$	2.99409	0.118167
$643$	0.454789	0.0179351	0.00896757	−	0.999960i	$-0.497145\pi$
$643$	0.454789	0.0179351	0.00896757	+	0.999960i	$0.497145\pi$
$644$	31.9951	1.26078
$645$	−33.7497	−1.32889
$646$	0.769332	0.0302690
$647$	8.82516	0.346953	0.173476	−	0.984838i	$-0.444500\pi$
$647$	8.82516	0.346953	0.173476	+	0.984838i	$0.444500\pi$
$648$	−0.744097	−0.0292309
$649$	−13.4357	−0.527397
$650$	−8.97549	−0.352048
$651$	5.13958	0.201436
$652$	40.9780	1.60482
$653$	−29.2566	−1.14490	−0.572450	−	0.819940i	$-0.694007\pi$
$653$	−29.2566	−1.14490	−0.572450	+	0.819940i	$0.694007\pi$
$654$	−3.46149	−0.135355
$655$	16.4466	0.642621
$656$	−4.74733	−0.185352
$657$	−1.69975	−0.0663134
$658$	−5.09288	−0.198541
$659$	−5.22537	−0.203552	−0.101776	−	0.994807i	$-0.532452\pi$
$659$	−5.22537	−0.203552	−0.101776	+	0.994807i	$0.532452\pi$
$660$	7.75916	0.302025
$661$	−16.1052	−0.626418	−0.313209	−	0.949684i	$-0.601404\pi$
$661$	−16.1052	−0.626418	−0.313209	+	0.949684i	$0.601404\pi$
$662$	2.66313	0.103506
$663$	−24.0996	−0.935952
$664$	−7.76958	−0.301518
$665$	7.75502	0.300727
$666$	−0.188360	−0.00729881
$667$	41.7853	1.61793
$668$	−19.3177	−0.747425
$669$	2.05159	0.0793191
$670$	5.83633	0.225477
$671$	−3.78251	−0.146022
$672$	−5.62583	−0.217021
$673$	−21.1011	−0.813387	−0.406693	−	0.913565i	$-0.633318\pi$
$673$	−21.1011	−0.813387	−0.406693	+	0.913565i	$0.633318\pi$
$674$	0.249853	0.00962399
$675$	−10.5956	−0.407825
$676$	−14.4852	−0.557121
$677$	32.0448	1.23158	0.615791	−	0.787910i	$-0.288837\pi$
$677$	32.0448	1.23158	0.615791	+	0.787910i	$0.288837\pi$
$678$	−0.144211	−0.00553838
$679$	2.55781	0.0981597
$680$	−15.6899	−0.601680
$681$	16.8777	0.646755
$682$	0.377112	0.0144404
$683$	37.6212	1.43953	0.719767	−	0.694216i	$-0.244249\pi$
$683$	37.6212	1.43953	0.719767	+	0.694216i	$0.244249\pi$
$684$	1.50844	0.0576765
$685$	17.8046	0.680277
$686$	−3.57997	−0.136684
$687$	−16.9164	−0.645402
$688$	−32.3889	−1.23482
$689$	60.7460	2.31424
$690$	−4.71861	−0.179634
$691$	−6.09997	−0.232054	−0.116027	−	0.993246i	$-0.537016\pi$
$691$	−6.09997	−0.232054	−0.116027	+	0.993246i	$0.537016\pi$
$692$	−5.16943	−0.196512
$693$	−2.55781	−0.0971631
$694$	−6.88971	−0.261530
$695$	−25.6851	−0.974291
$696$	−4.88372	−0.185117
$697$	6.68821	0.253334
$698$	−3.53732	−0.133889
$699$	2.19940	0.0831891
$700$	−53.2485	−2.01260
$701$	−13.7018	−0.517509	−0.258755	−	0.965943i	$-0.583312\pi$
$701$	−13.7018	−0.517509	−0.258755	+	0.965943i	$0.583312\pi$
$702$	0.847095	0.0319715
$703$	0.770534	0.0290613
$704$	7.16702	0.270117
$705$	−41.8973	−1.57794
$706$	−2.42611	−0.0913080
$707$	−17.4946	−0.657952
$708$	26.3981	0.992103
$709$	35.7401	1.34225	0.671123	−	0.741346i	$-0.265812\pi$
$709$	35.7401	1.34225	0.671123	+	0.741346i	$0.265812\pi$
$710$	−5.29028	−0.198541
$711$	8.22862	0.308597
$712$	−1.82406	−0.0683596
$713$	12.7927	0.479090
$714$	2.56311	0.0959221
$715$	−17.8247	−0.666606
$716$	3.62094	0.135321
$717$	−26.7605	−0.999390
$718$	−5.39858	−0.201473
$719$	18.1622	0.677337	0.338668	−	0.940906i	$-0.390023\pi$
$719$	18.1622	0.677337	0.338668	+	0.940906i	$0.390023\pi$
$720$	−14.9668	−0.557780
$721$	34.0869	1.26946
$722$	−3.45524	−0.128591
$723$	4.22968	0.157303
$724$	−18.2295	−0.677494
$725$	−69.5419	−2.58272
$726$	−0.187677	−0.00696535
$727$	−3.36572	−0.124828	−0.0624138	−	0.998050i	$-0.519880\pi$
$727$	−3.36572	−0.124828	−0.0624138	+	0.998050i	$0.519880\pi$
$728$	8.59051	0.318386
$729$	1.00000	0.0370370
$730$	1.25978	0.0466267
$731$	45.6307	1.68771
$732$	7.43179	0.274687
$733$	43.1412	1.59346	0.796729	−	0.604337i	$-0.206562\pi$
$733$	43.1412	1.59346	0.796729	+	0.604337i	$0.206562\pi$
$734$	6.52302	0.240769
$735$	−1.80719	−0.0666593
$736$	−14.0030	−0.516157
$737$	7.87458	0.290064
$738$	−0.235089	−0.00865374
$739$	−15.1758	−0.558252	−0.279126	−	0.960254i	$-0.590045\pi$
$739$	−15.1758	−0.558252	−0.279126	+	0.960254i	$0.590045\pi$
$740$	−7.78741	−0.286271
$741$	−3.46525	−0.127299
$742$	−6.46064	−0.237178
$743$	36.9554	1.35576	0.677882	−	0.735171i	$-0.262898\pi$
$743$	36.9554	1.35576	0.677882	+	0.735171i	$0.262898\pi$
$744$	−1.49517	−0.0548154
$745$	−87.0124	−3.18789
$746$	−0.140031	−0.00512692
$747$	10.4416	0.382039
$748$	−10.4906	−0.383576
$749$	−40.8058	−1.49101
$750$	4.14724	0.151436
$751$	−7.51454	−0.274210	−0.137105	−	0.990557i	$-0.543780\pi$
$751$	−7.51454	−0.274210	−0.137105	+	0.990557i	$0.543780\pi$
$752$	−40.2080	−1.46624
$753$	27.3226	0.995692
$754$	5.55972	0.202473
$755$	30.6417	1.11517
$756$	5.02552	0.182777
$757$	−15.6818	−0.569965	−0.284982	−	0.958533i	$-0.591988\pi$
$757$	−15.6818	−0.569965	−0.284982	+	0.958533i	$0.591988\pi$
$758$	−5.72529	−0.207952
$759$	−6.36652	−0.231090
$760$	−2.25603	−0.0818348
$761$	34.5789	1.25348	0.626742	−	0.779227i	$-0.284388\pi$
$761$	34.5789	1.25348	0.626742	+	0.779227i	$0.284388\pi$
$762$	2.05103	0.0743011
$763$	47.1759	1.70788
$764$	31.2759	1.13152
$765$	21.0858	0.762359
$766$	7.19596	0.260001
$767$	−60.6431	−2.18970
$768$	−13.2560	−0.478335
$769$	−18.9373	−0.682897	−0.341449	−	0.939900i	$-0.610918\pi$
$769$	−18.9373	−0.682897	−0.341449	+	0.939900i	$0.610918\pi$
$770$	1.89575	0.0683179
$771$	−24.8695	−0.895653
$772$	0.576484	0.0207481
$773$	−55.0943	−1.98160	−0.990801	−	0.135325i	$-0.956792\pi$
$773$	−55.0943	−1.98160	−0.990801	+	0.135325i	$0.956792\pi$
$774$	−1.60391	−0.0576513
$775$	−21.2905	−0.764776
$776$	−0.744097	−0.0267115
$777$	2.56712	0.0920949
$778$	2.98282	0.106939
$779$	0.961689	0.0344561
$780$	35.0216	1.25397
$781$	−7.13783	−0.255412
$782$	6.37973	0.228139
$783$	6.56328	0.234553
$784$	−1.73433	−0.0619403
$785$	−3.72254	−0.132863
$786$	0.781602	0.0278788
$787$	−18.4114	−0.656294	−0.328147	−	0.944627i	$-0.606424\pi$
$787$	−18.4114	−0.656294	−0.328147	+	0.944627i	$0.606424\pi$
$788$	−34.7339	−1.23734
$789$	−15.7343	−0.560155
$790$	−6.09873	−0.216983
$791$	1.96542	0.0698822
$792$	0.744097	0.0264403
$793$	−17.0727	−0.606268
$794$	2.05157	0.0728076
$795$	−53.1493	−1.88501
$796$	−24.3036	−0.861417
$797$	−21.2778	−0.753699	−0.376849	−	0.926275i	$-0.622993\pi$
$797$	−21.2778	−0.753699	−0.376849	+	0.926275i	$0.622993\pi$
$798$	0.368547	0.0130464
$799$	56.6466	2.00401
$800$	23.3047	0.823947
$801$	2.45137	0.0866151
$802$	0.433499	0.0153074
$803$	1.69975	0.0599828
$804$	−15.4718	−0.545648
$805$	64.3089	2.26659
$806$	1.70213	0.0599548
$807$	−7.23088	−0.254539
$808$	5.08939	0.179044
$809$	19.7026	0.692708	0.346354	−	0.938104i	$-0.387420\pi$
$809$	19.7026	0.692708	0.346354	+	0.938104i	$0.387420\pi$
$810$	−0.741160	−0.0260417
$811$	−8.62921	−0.303013	−0.151506	−	0.988456i	$-0.548412\pi$
$811$	−8.62921	−0.303013	−0.151506	+	0.988456i	$0.548412\pi$
$812$	32.9839	1.15751
$813$	−5.86234	−0.205601
$814$	0.188360	0.00660202
$815$	82.3643	2.88509
$816$	20.2357	0.708390
$817$	6.56118	0.229547
$818$	5.95034	0.208049
$819$	−11.5449	−0.403411
$820$	−9.71931	−0.339413
$821$	−22.8184	−0.796367	−0.398183	−	0.917306i	$-0.630359\pi$
$821$	−22.8184	−0.796367	−0.398183	+	0.917306i	$0.630359\pi$
$822$	0.846137	0.0295124
$823$	22.1194	0.771032	0.385516	−	0.922701i	$-0.374023\pi$
$823$	22.1194	0.771032	0.385516	+	0.922701i	$0.374023\pi$
$824$	−9.91630	−0.345451
$825$	10.5956	0.368892
$826$	6.44969	0.224414
$827$	−27.9353	−0.971406	−0.485703	−	0.874124i	$-0.661436\pi$
$827$	−27.9353	−0.971406	−0.485703	+	0.874124i	$0.661436\pi$
$828$	12.5088	0.434711
$829$	−34.3133	−1.19175	−0.595874	−	0.803078i	$-0.703194\pi$
$829$	−34.3133	−1.19175	−0.595874	+	0.803078i	$0.703194\pi$
$830$	−7.73891	−0.268622
$831$	15.5838	0.540597
$832$	32.3489	1.12150
$833$	2.44339	0.0846583
$834$	−1.22065	−0.0422676
$835$	−38.8279	−1.34369
$836$	−1.50844	−0.0521704
$837$	2.00937	0.0694539
$838$	−5.14892	−0.177866
$839$	0.910193	0.0314234	0.0157117	−	0.999877i	$-0.494999\pi$
$839$	0.910193	0.0314234	0.0157117	+	0.999877i	$0.494999\pi$
$840$	−7.51621	−0.259334
$841$	14.0766	0.485402
$842$	−4.03726	−0.139133
$843$	−10.4271	−0.359129
$844$	42.5431	1.46439
$845$	−29.1146	−1.00157
$846$	−1.99111	−0.0684558
$847$	2.55781	0.0878873
$848$	−51.0064	−1.75157
$849$	28.4509	0.976433
$850$	−10.6176	−0.364180
$851$	6.38970	0.219036
$852$	14.0243	0.480463
$853$	−3.37018	−0.115393	−0.0576964	−	0.998334i	$-0.518376\pi$
$853$	−3.37018	−0.115393	−0.0576964	+	0.998334i	$0.518376\pi$
$854$	1.81576	0.0621341
$855$	3.03190	0.103689
$856$	11.8709	0.405740
$857$	−38.2467	−1.30648	−0.653241	−	0.757150i	$-0.726591\pi$
$857$	−38.2467	−1.30648	−0.653241	+	0.757150i	$0.726591\pi$
$858$	−0.847095	−0.0289194
$859$	51.8427	1.76885	0.884426	−	0.466681i	$-0.154550\pi$
$859$	51.8427	1.76885	0.884426	+	0.466681i	$0.154550\pi$
$860$	−66.3106	−2.26117
$861$	3.20397	0.109191
$862$	0.485047	0.0165208
$863$	28.8825	0.983171	0.491585	−	0.870829i	$-0.336418\pi$
$863$	28.8825	0.983171	0.491585	+	0.870829i	$0.336418\pi$
$864$	−2.19947	−0.0748276
$865$	−10.3904	−0.353283
$866$	−4.83720	−0.164375
$867$	−11.5087	−0.390857
$868$	10.0981	0.342753
$869$	−8.22862	−0.279137
$870$	−4.86444	−0.164920
$871$	35.5426	1.20431
$872$	−13.7240	−0.464755
$873$	1.00000	0.0338449
$874$	0.917333	0.0310292
$875$	−56.5219	−1.91079
$876$	−3.33962	−0.112835
$877$	−14.9448	−0.504650	−0.252325	−	0.967642i	$-0.581195\pi$
$877$	−14.9448	−0.504650	−0.252325	+	0.967642i	$0.581195\pi$
$878$	−5.60002	−0.188992
$879$	8.16718	0.275472
$880$	14.9668	0.504531
$881$	−7.43940	−0.250640	−0.125320	−	0.992116i	$-0.539996\pi$
$881$	−7.43940	−0.250640	−0.125320	+	0.992116i	$0.539996\pi$
$882$	−0.0858844	−0.00289188
$883$	7.09532	0.238776	0.119388	−	0.992848i	$-0.461907\pi$
$883$	7.09532	0.238776	0.119388	+	0.992848i	$0.461907\pi$
$884$	−47.3504	−1.59257
$885$	53.0593	1.78357
$886$	−2.57957	−0.0866624
$887$	39.9112	1.34009	0.670044	−	0.742321i	$-0.266275\pi$
$887$	39.9112	1.34009	0.670044	+	0.742321i	$0.266275\pi$
$888$	−0.746806	−0.0250612
$889$	−27.9531	−0.937516
$890$	−1.81686	−0.0609013
$891$	−1.00000	−0.0335013
$892$	4.03092	0.134965
$893$	8.14514	0.272567
$894$	−4.13514	−0.138300
$895$	7.27794	0.243275
$896$	−14.6921	−0.490829
$897$	−28.7358	−0.959461
$898$	−4.53353	−0.151286
$899$	13.1880	0.439846
$900$	−20.8180	−0.693934
$901$	71.8597	2.39399
$902$	0.235089	0.00782760
$903$	21.8593	0.727432
$904$	−0.571764	−0.0190166
$905$	−36.6406	−1.21798
$906$	1.45621	0.0483792
$907$	41.0189	1.36201	0.681005	−	0.732278i	$-0.261543\pi$
$907$	41.0189	1.36201	0.681005	+	0.732278i	$0.261543\pi$
$908$	33.1609	1.10048
$909$	−6.83968	−0.226858
$910$	8.55660	0.283649
$911$	−39.3471	−1.30363	−0.651814	−	0.758379i	$-0.725992\pi$
$911$	−39.3471	−1.30363	−0.651814	+	0.758379i	$0.725992\pi$
$912$	2.90966	0.0963484
$913$	−10.4416	−0.345567
$914$	2.25512	0.0745927
$915$	14.9376	0.493822
$916$	−33.2370	−1.09818
$917$	−10.6523	−0.351769
$918$	1.00207	0.0330734
$919$	20.1097	0.663357	0.331679	−	0.943392i	$-0.392385\pi$
$919$	20.1097	0.663357	0.331679	+	0.943392i	$0.392385\pi$
$920$	−18.7082	−0.616792
$921$	−25.8739	−0.852573
$922$	6.81634	0.224484
$923$	−32.2172	−1.06044
$924$	−5.02552	−0.165328
$925$	−10.6342	−0.349650
$926$	−4.94664	−0.162557
$927$	13.3266	0.437704
$928$	−14.4358	−0.473877
$929$	−44.6540	−1.46505	−0.732526	−	0.680739i	$-0.761659\pi$
$929$	−44.6540	−1.46505	−0.732526	+	0.680739i	$0.761659\pi$
$930$	−1.48926	−0.0488349
$931$	0.351331	0.0115144
$932$	4.32134	0.141550
$933$	−14.8930	−0.487576
$934$	−4.32854	−0.141634
$935$	−21.0858	−0.689579
$936$	3.35854	0.109777
$937$	−14.3184	−0.467762	−0.233881	−	0.972265i	$-0.575143\pi$
$937$	−14.3184	−0.467762	−0.233881	+	0.972265i	$0.575143\pi$
$938$	−3.78013	−0.123426
$939$	−14.5684	−0.475422
$940$	−82.3188	−2.68494
$941$	−40.5879	−1.32313	−0.661564	−	0.749889i	$-0.730107\pi$
$941$	−40.5879	−1.32313	−0.661564	+	0.749889i	$0.730107\pi$
$942$	−0.176908	−0.00576399
$943$	7.97486	0.259697
$944$	50.9200	1.65730
$945$	10.1011	0.328589
$946$	1.60391	0.0521475
$947$	22.6547	0.736177	0.368089	−	0.929791i	$-0.380012\pi$
$947$	22.6547	0.736177	0.368089	+	0.929791i	$0.380012\pi$
$948$	16.1674	0.525093
$949$	7.67194	0.249042
$950$	−1.52669	−0.0495323
$951$	10.6191	0.344347
$952$	10.1622	0.329358
$953$	−27.8901	−0.903448	−0.451724	−	0.892158i	$-0.649191\pi$
$953$	−27.8901	−0.903448	−0.451724	+	0.892158i	$0.649191\pi$
$954$	−2.52585	−0.0817774
$955$	62.8633	2.03421
$956$	−52.5785	−1.70051
$957$	−6.56328	−0.212161
$958$	−1.25349	−0.0404985
$959$	−11.5318	−0.372382
$960$	−28.3035	−0.913491
$961$	−26.9624	−0.869756
$962$	0.850179	0.0274109
$963$	−15.9534	−0.514093
$964$	8.31037	0.267659
$965$	1.15871	0.0373002
$966$	3.05619	0.0983314
$967$	−7.36027	−0.236690	−0.118345	−	0.992973i	$-0.537759\pi$
$967$	−7.36027	−0.236690	−0.118345	+	0.992973i	$0.537759\pi$
$968$	−0.744097	−0.0239162
$969$	−4.09923	−0.131686
$970$	−0.741160	−0.0237972
$971$	22.0843	0.708720	0.354360	−	0.935109i	$-0.384699\pi$
$971$	22.0843	0.708720	0.354360	+	0.935109i	$0.384699\pi$
$972$	1.96478	0.0630203
$973$	16.6360	0.533324
$974$	0.621044	0.0198995
$975$	47.8241	1.53160
$976$	14.3353	0.458863
$977$	−54.4242	−1.74119	−0.870593	−	0.492004i	$-0.836264\pi$
$977$	−54.4242	−1.74119	−0.870593	+	0.492004i	$0.836264\pi$
$978$	3.91425	0.125164
$979$	−2.45137	−0.0783463
$980$	−3.55073	−0.113424
$981$	18.4439	0.588868
$982$	−6.05244	−0.193141
$983$	18.9876	0.605611	0.302805	−	0.953052i	$-0.402077\pi$
$983$	18.9876	0.605611	0.302805	+	0.953052i	$0.402077\pi$
$984$	−0.932074	−0.0297134
$985$	−69.8139	−2.22445
$986$	6.57689	0.209451
$987$	27.1364	0.863762
$988$	−6.80845	−0.216606
$989$	54.4089	1.73010
$990$	0.741160	0.0235556
$991$	−40.0511	−1.27227	−0.636133	−	0.771579i	$-0.719467\pi$
$991$	−40.0511	−1.27227	−0.636133	+	0.771579i	$0.719467\pi$
$992$	−4.41955	−0.140321
$993$	−14.1900	−0.450305
$994$	3.42646	0.108681
$995$	−48.8493	−1.54863
$996$	20.5155	0.650057
$997$	21.8132	0.690831	0.345416	−	0.938450i	$-0.387738\pi$
$997$	21.8132	0.690831	0.345416	+	0.938450i	$0.387738\pi$
$998$	4.44989	0.140859
$999$	1.00364	0.0317538

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3201.2.a.t.1.10	✓	17
3.2	odd	2		9603.2.a.z.1.8		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3201.2.a.t.1.10	✓	17	1.1	even	1	trivial
9603.2.a.z.1.8		17	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:	\( N \)	\(=\)	\( 3201 = 3 \cdot 11 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3201.a (trivial)

\(f(q)\)	\(=\)	\(q+0.187677 q^{2} -1.00000 q^{3} -1.96478 q^{4} -3.94913 q^{5} -0.187677 q^{6} +2.55781 q^{7} -0.744097 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.187677 q^{2} -1.00000 q^{3} -1.96478 q^{4} -3.94913 q^{5} -0.187677 q^{6} +2.55781 q^{7} -0.744097 q^{8} +1.00000 q^{9} -0.741160 q^{10} -1.00000 q^{11} +1.96478 q^{12} -4.51358 q^{13} +0.480042 q^{14} +3.94913 q^{15} +3.78990 q^{16} -5.33936 q^{17} +0.187677 q^{18} -0.767739 q^{19} +7.75916 q^{20} -2.55781 q^{21} -0.187677 q^{22} -6.36652 q^{23} +0.744097 q^{24} +10.5956 q^{25} -0.847095 q^{26} -1.00000 q^{27} -5.02552 q^{28} -6.56328 q^{29} +0.741160 q^{30} -2.00937 q^{31} +2.19947 q^{32} +1.00000 q^{33} -1.00207 q^{34} -10.1011 q^{35} -1.96478 q^{36} -1.00364 q^{37} -0.144087 q^{38} +4.51358 q^{39} +2.93854 q^{40} -1.25262 q^{41} -0.480042 q^{42} -8.54611 q^{43} +1.96478 q^{44} -3.94913 q^{45} -1.19485 q^{46} -10.6092 q^{47} -3.78990 q^{48} -0.457618 q^{49} +1.98855 q^{50} +5.33936 q^{51} +8.86818 q^{52} -13.4585 q^{53} -0.187677 q^{54} +3.94913 q^{55} -1.90326 q^{56} +0.767739 q^{57} -1.23178 q^{58} +13.4357 q^{59} -7.75916 q^{60} +3.78251 q^{61} -0.377112 q^{62} +2.55781 q^{63} -7.16702 q^{64} +17.8247 q^{65} +0.187677 q^{66} -7.87458 q^{67} +10.4906 q^{68} +6.36652 q^{69} -1.89575 q^{70} +7.13783 q^{71} -0.744097 q^{72} -1.69975 q^{73} -0.188360 q^{74} -10.5956 q^{75} +1.50844 q^{76} -2.55781 q^{77} +0.847095 q^{78} +8.22862 q^{79} -14.9668 q^{80} +1.00000 q^{81} -0.235089 q^{82} +10.4416 q^{83} +5.02552 q^{84} +21.0858 q^{85} -1.60391 q^{86} +6.56328 q^{87} +0.744097 q^{88} +2.45137 q^{89} -0.741160 q^{90} -11.5449 q^{91} +12.5088 q^{92} +2.00937 q^{93} -1.99111 q^{94} +3.03190 q^{95} -2.19947 q^{96} +1.00000 q^{97} -0.0858844 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 3 q^{2} - 17 q^{3} + 19 q^{4} - 10 q^{5} + 3 q^{6} + 9 q^{7} + 17 q^{9}+O(q^{10}) \) 17 * q - 3 * q^2 - 17 * q^3 + 19 * q^4 - 10 * q^5 + 3 * q^6 + 9 * q^7 + 17 * q^9	\( 17 q - 3 q^{2} - 17 q^{3} + 19 q^{4} - 10 q^{5} + 3 q^{6} + 9 q^{7} + 17 q^{9} + 17 q^{10} - 17 q^{11} - 19 q^{12} - 2 q^{13} + 10 q^{14} + 10 q^{15} + 15 q^{16} - 2 q^{17} - 3 q^{18} + 25 q^{19} - 32 q^{20} - 9 q^{21} + 3 q^{22} - 3 q^{23} + 35 q^{25} - 7 q^{26} - 17 q^{27} + q^{28} + 4 q^{29} - 17 q^{30} + 44 q^{31} - 3 q^{32} + 17 q^{33} + 22 q^{34} + 4 q^{35} + 19 q^{36} + 13 q^{37} - 2 q^{38} + 2 q^{39} + 41 q^{40} + 5 q^{41} - 10 q^{42} + 27 q^{43} - 19 q^{44} - 10 q^{45} - 29 q^{46} - 10 q^{47} - 15 q^{48} + 12 q^{49} - 2 q^{50} + 2 q^{51} + 32 q^{52} - 45 q^{53} + 3 q^{54} + 10 q^{55} + 35 q^{56} - 25 q^{57} + 17 q^{58} + q^{59} + 32 q^{60} + 22 q^{61} + 23 q^{62} + 9 q^{63} + 24 q^{64} + 23 q^{65} - 3 q^{66} + 7 q^{67} - 10 q^{68} + 3 q^{69} + 40 q^{70} - 12 q^{71} - 21 q^{73} + 45 q^{74} - 35 q^{75} + 34 q^{76} - 9 q^{77} + 7 q^{78} + 24 q^{79} - 50 q^{80} + 17 q^{81} - 6 q^{82} - 26 q^{83} - q^{84} - 43 q^{85} + 9 q^{86} - 4 q^{87} - 40 q^{89} + 17 q^{90} + 38 q^{91} + 47 q^{92} - 44 q^{93} + 52 q^{94} - 12 q^{95} + 3 q^{96} + 17 q^{97} + 15 q^{98} - 17 q^{99}+O(q^{100}) \) 17 * q - 3 * q^2 - 17 * q^3 + 19 * q^4 - 10 * q^5 + 3 * q^6 + 9 * q^7 + 17 * q^9 + 17 * q^10 - 17 * q^11 - 19 * q^12 - 2 * q^13 + 10 * q^14 + 10 * q^15 + 15 * q^16 - 2 * q^17 - 3 * q^18 + 25 * q^19 - 32 * q^20 - 9 * q^21 + 3 * q^22 - 3 * q^23 + 35 * q^25 - 7 * q^26 - 17 * q^27 + q^28 + 4 * q^29 - 17 * q^30 + 44 * q^31 - 3 * q^32 + 17 * q^33 + 22 * q^34 + 4 * q^35 + 19 * q^36 + 13 * q^37 - 2 * q^38 + 2 * q^39 + 41 * q^40 + 5 * q^41 - 10 * q^42 + 27 * q^43 - 19 * q^44 - 10 * q^45 - 29 * q^46 - 10 * q^47 - 15 * q^48 + 12 * q^49 - 2 * q^50 + 2 * q^51 + 32 * q^52 - 45 * q^53 + 3 * q^54 + 10 * q^55 + 35 * q^56 - 25 * q^57 + 17 * q^58 + q^59 + 32 * q^60 + 22 * q^61 + 23 * q^62 + 9 * q^63 + 24 * q^64 + 23 * q^65 - 3 * q^66 + 7 * q^67 - 10 * q^68 + 3 * q^69 + 40 * q^70 - 12 * q^71 - 21 * q^73 + 45 * q^74 - 35 * q^75 + 34 * q^76 - 9 * q^77 + 7 * q^78 + 24 * q^79 - 50 * q^80 + 17 * q^81 - 6 * q^82 - 26 * q^83 - q^84 - 43 * q^85 + 9 * q^86 - 4 * q^87 - 40 * q^89 + 17 * q^90 + 38 * q^91 + 47 * q^92 - 44 * q^93 + 52 * q^94 - 12 * q^95 + 3 * q^96 + 17 * q^97 + 15 * q^98 - 17 * q^99

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