LMFDB - Embedded newform 4334.2.a.d.1.5

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			1.5
Root			$1.67442$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.67442 q^{3} +1.00000 q^{4} -0.572222 q^{5} -1.67442 q^{6} -0.229301 q^{7} +1.00000 q^{8} -0.196306 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.67442 q^{3} +1.00000 q^{4} -0.572222 q^{5} -1.67442 q^{6} -0.229301 q^{7} +1.00000 q^{8} -0.196306 q^{9} -0.572222 q^{10} -1.00000 q^{11} -1.67442 q^{12} +1.39275 q^{13} -0.229301 q^{14} +0.958143 q^{15} +1.00000 q^{16} -2.96018 q^{17} -0.196306 q^{18} +6.23629 q^{19} -0.572222 q^{20} +0.383948 q^{21} -1.00000 q^{22} +0.283546 q^{23} -1.67442 q^{24} -4.67256 q^{25} +1.39275 q^{26} +5.35197 q^{27} -0.229301 q^{28} -2.13992 q^{29} +0.958143 q^{30} -1.81886 q^{31} +1.00000 q^{32} +1.67442 q^{33} -2.96018 q^{34} +0.131211 q^{35} -0.196306 q^{36} +11.2482 q^{37} +6.23629 q^{38} -2.33205 q^{39} -0.572222 q^{40} -3.81278 q^{41} +0.383948 q^{42} -4.03160 q^{43} -1.00000 q^{44} +0.112331 q^{45} +0.283546 q^{46} +1.60211 q^{47} -1.67442 q^{48} -6.94742 q^{49} -4.67256 q^{50} +4.95659 q^{51} +1.39275 q^{52} -0.559798 q^{53} +5.35197 q^{54} +0.572222 q^{55} -0.229301 q^{56} -10.4422 q^{57} -2.13992 q^{58} +3.35869 q^{59} +0.958143 q^{60} -5.56259 q^{61} -1.81886 q^{62} +0.0450132 q^{63} +1.00000 q^{64} -0.796963 q^{65} +1.67442 q^{66} -7.29496 q^{67} -2.96018 q^{68} -0.474776 q^{69} +0.131211 q^{70} +5.81690 q^{71} -0.196306 q^{72} -15.9763 q^{73} +11.2482 q^{74} +7.82385 q^{75} +6.23629 q^{76} +0.229301 q^{77} -2.33205 q^{78} -4.30809 q^{79} -0.572222 q^{80} -8.37255 q^{81} -3.81278 q^{82} -9.51503 q^{83} +0.383948 q^{84} +1.69388 q^{85} -4.03160 q^{86} +3.58312 q^{87} -1.00000 q^{88} -5.63164 q^{89} +0.112331 q^{90} -0.319360 q^{91} +0.283546 q^{92} +3.04554 q^{93} +1.60211 q^{94} -3.56854 q^{95} -1.67442 q^{96} +5.17365 q^{97} -6.94742 q^{98} +0.196306 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.67442	−0.966729	−0.483364	−	0.875419i	$-0.660585\pi$
$3$	−1.67442	−0.966729	−0.483364	+	0.875419i	$0.660585\pi$
$4$	1.00000	0.500000
$5$	−0.572222	−0.255906	−0.127953	−	0.991780i	$-0.540841\pi$
$5$	−0.572222	−0.255906	−0.127953	+	0.991780i	$0.540841\pi$
$6$	−1.67442	−0.683581
$7$	−0.229301	−0.0866678	−0.0433339	−	0.999061i	$-0.513798\pi$
$7$	−0.229301	−0.0866678	−0.0433339	+	0.999061i	$0.513798\pi$
$8$	1.00000	0.353553
$9$	−0.196306	−0.0654353
$10$	−0.572222	−0.180953
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.67442	−0.483364
$13$	1.39275	0.386279	0.193140	−	0.981171i	$-0.438133\pi$
$13$	1.39275	0.386279	0.193140	+	0.981171i	$0.438133\pi$
$14$	−0.229301	−0.0612834
$15$	0.958143	0.247391
$16$	1.00000	0.250000
$17$	−2.96018	−0.717949	−0.358975	−	0.933347i	$-0.616874\pi$
$17$	−2.96018	−0.717949	−0.358975	+	0.933347i	$0.616874\pi$
$18$	−0.196306	−0.0462697
$19$	6.23629	1.43070	0.715351	−	0.698765i	$-0.246267\pi$
$19$	6.23629	1.43070	0.715351	+	0.698765i	$0.246267\pi$
$20$	−0.572222	−0.127953
$21$	0.383948	0.0837842
$22$	−1.00000	−0.213201
$23$	0.283546	0.0591234	0.0295617	−	0.999563i	$-0.490589\pi$
$23$	0.283546	0.0591234	0.0295617	+	0.999563i	$0.490589\pi$
$24$	−1.67442	−0.341790
$25$	−4.67256	−0.934512
$26$	1.39275	0.273141
$27$	5.35197	1.02999
$28$	−0.229301	−0.0433339
$29$	−2.13992	−0.397372	−0.198686	−	0.980063i	$-0.563667\pi$
$29$	−2.13992	−0.397372	−0.198686	+	0.980063i	$0.563667\pi$
$30$	0.958143	0.174932
$31$	−1.81886	−0.326676	−0.163338	−	0.986570i	$-0.552226\pi$
$31$	−1.81886	−0.326676	−0.163338	+	0.986570i	$0.552226\pi$
$32$	1.00000	0.176777
$33$	1.67442	0.291480
$34$	−2.96018	−0.507667
$35$	0.131211	0.0221788
$36$	−0.196306	−0.0327177
$37$	11.2482	1.84919	0.924596	−	0.380950i	$-0.124403\pi$
$37$	11.2482	1.84919	0.924596	+	0.380950i	$0.124403\pi$
$38$	6.23629	1.01166
$39$	−2.33205	−0.373428
$40$	−0.572222	−0.0904763
$41$	−3.81278	−0.595456	−0.297728	−	0.954651i	$-0.596229\pi$
$41$	−3.81278	−0.595456	−0.297728	+	0.954651i	$0.596229\pi$
$42$	0.383948	0.0592444
$43$	−4.03160	−0.614812	−0.307406	−	0.951578i	$-0.599461\pi$
$43$	−4.03160	−0.614812	−0.307406	+	0.951578i	$0.599461\pi$
$44$	−1.00000	−0.150756
$45$	0.112331	0.0167453
$46$	0.283546	0.0418066
$47$	1.60211	0.233692	0.116846	−	0.993150i	$-0.462722\pi$
$47$	1.60211	0.233692	0.116846	+	0.993150i	$0.462722\pi$
$48$	−1.67442	−0.241682
$49$	−6.94742	−0.992489
$50$	−4.67256	−0.660800
$51$	4.95659	0.694062
$52$	1.39275	0.193140
$53$	−0.559798	−0.0768942	−0.0384471	−	0.999261i	$-0.512241\pi$
$53$	−0.559798	−0.0768942	−0.0384471	+	0.999261i	$0.512241\pi$
$54$	5.35197	0.728311
$55$	0.572222	0.0771585
$56$	−0.229301	−0.0306417
$57$	−10.4422	−1.38310
$58$	−2.13992	−0.280985
$59$	3.35869	0.437264	0.218632	−	0.975807i	$-0.429841\pi$
$59$	3.35869	0.437264	0.218632	+	0.975807i	$0.429841\pi$
$60$	0.958143	0.123696
$61$	−5.56259	−0.712217	−0.356108	−	0.934445i	$-0.615897\pi$
$61$	−5.56259	−0.712217	−0.356108	+	0.934445i	$0.615897\pi$
$62$	−1.81886	−0.230995
$63$	0.0450132	0.00567113
$64$	1.00000	0.125000
$65$	−0.796963	−0.0988511
$66$	1.67442	0.206107
$67$	−7.29496	−0.891221	−0.445611	−	0.895227i	$-0.647013\pi$
$67$	−7.29496	−0.891221	−0.445611	+	0.895227i	$0.647013\pi$
$68$	−2.96018	−0.358975
$69$	−0.474776	−0.0571563
$70$	0.131211	0.0156828
$71$	5.81690	0.690339	0.345170	−	0.938540i	$-0.387821\pi$
$71$	5.81690	0.690339	0.345170	+	0.938540i	$0.387821\pi$
$72$	−0.196306	−0.0231349
$73$	−15.9763	−1.86989	−0.934944	−	0.354794i	$-0.884551\pi$
$73$	−15.9763	−1.86989	−0.934944	+	0.354794i	$0.884551\pi$
$74$	11.2482	1.30758
$75$	7.82385	0.903420
$76$	6.23629	0.715351
$77$	0.229301	0.0261313
$78$	−2.33205	−0.264053
$79$	−4.30809	−0.484698	−0.242349	−	0.970189i	$-0.577918\pi$
$79$	−4.30809	−0.484698	−0.242349	+	0.970189i	$0.577918\pi$
$80$	−0.572222	−0.0639764
$81$	−8.37255	−0.930283
$82$	−3.81278	−0.421051
$83$	−9.51503	−1.04441	−0.522205	−	0.852820i	$-0.674890\pi$
$83$	−9.51503	−1.04441	−0.522205	+	0.852820i	$0.674890\pi$
$84$	0.383948	0.0418921
$85$	1.69388	0.183727
$86$	−4.03160	−0.434738
$87$	3.58312	0.384151
$88$	−1.00000	−0.106600
$89$	−5.63164	−0.596953	−0.298476	−	0.954417i	$-0.596478\pi$
$89$	−5.63164	−0.596953	−0.298476	+	0.954417i	$0.596478\pi$
$90$	0.112331	0.0118407
$91$	−0.319360	−0.0334780
$92$	0.283546	0.0295617
$93$	3.04554	0.315807
$94$	1.60211	0.165246
$95$	−3.56854	−0.366125
$96$	−1.67442	−0.170895
$97$	5.17365	0.525305	0.262652	−	0.964891i	$-0.415403\pi$
$97$	5.17365	0.525305	0.262652	+	0.964891i	$0.415403\pi$
$98$	−6.94742	−0.701795
$99$	0.196306	0.0197295
$100$	−4.67256	−0.467256
$101$	13.7697	1.37013	0.685066	−	0.728481i	$-0.259773\pi$
$101$	13.7697	1.37013	0.685066	+	0.728481i	$0.259773\pi$
$102$	4.95659	0.490776
$103$	−9.75521	−0.961209	−0.480605	−	0.876937i	$-0.659583\pi$
$103$	−9.75521	−0.961209	−0.480605	+	0.876937i	$0.659583\pi$
$104$	1.39275	0.136570
$105$	−0.219703	−0.0214409
$106$	−0.559798	−0.0543724
$107$	−3.93702	−0.380607	−0.190303	−	0.981725i	$-0.560947\pi$
$107$	−3.93702	−0.380607	−0.190303	+	0.981725i	$0.560947\pi$
$108$	5.35197	0.514994
$109$	−3.96921	−0.380181	−0.190091	−	0.981767i	$-0.560878\pi$
$109$	−3.96921	−0.380181	−0.190091	+	0.981767i	$0.560878\pi$
$110$	0.572222	0.0545593
$111$	−18.8342	−1.78767
$112$	−0.229301	−0.0216669
$113$	11.3093	1.06389	0.531945	−	0.846779i	$-0.321461\pi$
$113$	11.3093	1.06389	0.531945	+	0.846779i	$0.321461\pi$
$114$	−10.4422	−0.978000
$115$	−0.162251	−0.0151300
$116$	−2.13992	−0.198686
$117$	−0.273405	−0.0252763
$118$	3.35869	0.309192
$119$	0.678773	0.0622230
$120$	0.958143	0.0874661
$121$	1.00000	0.0909091
$122$	−5.56259	−0.503613
$123$	6.38420	0.575644
$124$	−1.81886	−0.163338
$125$	5.53486	0.495053
$126$	0.0450132	0.00401010
$127$	−11.4306	−1.01430	−0.507149	−	0.861859i	$-0.669301\pi$
$127$	−11.4306	−1.01430	−0.507149	+	0.861859i	$0.669301\pi$
$128$	1.00000	0.0883883
$129$	6.75060	0.594357
$130$	−0.796963	−0.0698983
$131$	−1.08843	−0.0950965	−0.0475482	−	0.998869i	$-0.515141\pi$
$131$	−1.08843	−0.0950965	−0.0475482	+	0.998869i	$0.515141\pi$
$132$	1.67442	0.145740
$133$	−1.42999	−0.123996
$134$	−7.29496	−0.630188
$135$	−3.06252	−0.263580
$136$	−2.96018	−0.253833
$137$	−13.3068	−1.13688	−0.568438	−	0.822726i	$-0.692452\pi$
$137$	−13.3068	−1.13688	−0.568438	+	0.822726i	$0.692452\pi$
$138$	−0.474776	−0.0404156
$139$	−11.7713	−0.998426	−0.499213	−	0.866479i	$-0.666377\pi$
$139$	−11.7713	−0.998426	−0.499213	+	0.866479i	$0.666377\pi$
$140$	0.131211	0.0110894
$141$	−2.68262	−0.225917
$142$	5.81690	0.488143
$143$	−1.39275	−0.116468
$144$	−0.196306	−0.0163588
$145$	1.22451	0.101690
$146$	−15.9763	−1.32221
$147$	11.6329	0.959467
$148$	11.2482	0.924596
$149$	16.9306	1.38701	0.693505	−	0.720451i	$-0.256065\pi$
$149$	16.9306	1.38701	0.693505	+	0.720451i	$0.256065\pi$
$150$	7.82385	0.638814
$151$	−19.7165	−1.60451	−0.802255	−	0.596982i	$-0.796366\pi$
$151$	−19.7165	−1.60451	−0.802255	+	0.596982i	$0.796366\pi$
$152$	6.23629	0.505830
$153$	0.581101	0.0469792
$154$	0.229301	0.0184776
$155$	1.04079	0.0835983
$156$	−2.33205	−0.186714
$157$	1.24198	0.0991206	0.0495603	−	0.998771i	$-0.484218\pi$
$157$	1.24198	0.0991206	0.0495603	+	0.998771i	$0.484218\pi$
$158$	−4.30809	−0.342733
$159$	0.937340	0.0743359
$160$	−0.572222	−0.0452382
$161$	−0.0650175	−0.00512409
$162$	−8.37255	−0.657809
$163$	−16.7105	−1.30887	−0.654435	−	0.756118i	$-0.727094\pi$
$163$	−16.7105	−1.30887	−0.654435	+	0.756118i	$0.727094\pi$
$164$	−3.81278	−0.297728
$165$	−0.958143	−0.0745913
$166$	−9.51503	−0.738509
$167$	−10.7661	−0.833106	−0.416553	−	0.909112i	$-0.636762\pi$
$167$	−10.7661	−0.833106	−0.416553	+	0.909112i	$0.636762\pi$
$168$	0.383948	0.0296222
$169$	−11.0602	−0.850788
$170$	1.69388	0.129915
$171$	−1.22422	−0.0936185
$172$	−4.03160	−0.307406
$173$	14.9061	1.13329	0.566645	−	0.823962i	$-0.308241\pi$
$173$	14.9061	1.13329	0.566645	+	0.823962i	$0.308241\pi$
$174$	3.58312	0.271636
$175$	1.07142	0.0809921
$176$	−1.00000	−0.0753778
$177$	−5.62387	−0.422716
$178$	−5.63164	−0.422109
$179$	−12.1773	−0.910174	−0.455087	−	0.890447i	$-0.650392\pi$
$179$	−12.1773	−0.910174	−0.455087	+	0.890447i	$0.650392\pi$
$180$	0.112331	0.00837263
$181$	7.11818	0.529090	0.264545	−	0.964373i	$-0.414778\pi$
$181$	7.11818	0.529090	0.264545	+	0.964373i	$0.414778\pi$
$182$	−0.319360	−0.0236725
$183$	9.31414	0.688521
$184$	0.283546	0.0209033
$185$	−6.43647	−0.473219
$186$	3.04554	0.223310
$187$	2.96018	0.216470
$188$	1.60211	0.116846
$189$	−1.22721	−0.0892667
$190$	−3.56854	−0.258889
$191$	−5.52828	−0.400012	−0.200006	−	0.979795i	$-0.564096\pi$
$191$	−5.52828	−0.400012	−0.200006	+	0.979795i	$0.564096\pi$
$192$	−1.67442	−0.120841
$193$	−15.3421	−1.10435	−0.552173	−	0.833729i	$-0.686201\pi$
$193$	−15.3421	−1.10435	−0.552173	+	0.833729i	$0.686201\pi$
$194$	5.17365	0.371447
$195$	1.33445	0.0955622
$196$	−6.94742	−0.496244
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	0.196306	0.0139509
$199$	−3.81226	−0.270244	−0.135122	−	0.990829i	$-0.543143\pi$
$199$	−3.81226	−0.270244	−0.135122	+	0.990829i	$0.543143\pi$
$200$	−4.67256	−0.330400
$201$	12.2148	0.861569
$202$	13.7697	0.968829
$203$	0.490686	0.0344394
$204$	4.95659	0.347031
$205$	2.18176	0.152381
$206$	−9.75521	−0.679677
$207$	−0.0556617	−0.00386876
$208$	1.39275	0.0965699
$209$	−6.23629	−0.431373
$210$	−0.219703	−0.0151610
$211$	−5.45510	−0.375545	−0.187772	−	0.982213i	$-0.560127\pi$
$211$	−5.45510	−0.375545	−0.187772	+	0.982213i	$0.560127\pi$
$212$	−0.559798	−0.0384471
$213$	−9.73995	−0.667371
$214$	−3.93702	−0.269129
$215$	2.30697	0.157334
$216$	5.35197	0.364155
$217$	0.417066	0.0283123
$218$	−3.96921	−0.268829
$219$	26.7512	1.80768
$220$	0.572222	0.0385792
$221$	−4.12279	−0.277329
$222$	−18.8342	−1.26407
$223$	4.89586	0.327851	0.163925	−	0.986473i	$-0.447584\pi$
$223$	4.89586	0.327851	0.163925	+	0.986473i	$0.447584\pi$
$224$	−0.229301	−0.0153208
$225$	0.917251	0.0611501
$226$	11.3093	0.752283
$227$	−14.6339	−0.971285	−0.485643	−	0.874158i	$-0.661414\pi$
$227$	−14.6339	−0.971285	−0.485643	+	0.874158i	$0.661414\pi$
$228$	−10.4422	−0.691551
$229$	−26.4046	−1.74487	−0.872433	−	0.488734i	$-0.837459\pi$
$229$	−26.4046	−1.74487	−0.872433	+	0.488734i	$0.837459\pi$
$230$	−0.162251	−0.0106985
$231$	−0.383948	−0.0252619
$232$	−2.13992	−0.140492
$233$	0.213394	0.0139799	0.00698996	−	0.999976i	$-0.497775\pi$
$233$	0.213394	0.0139799	0.00698996	+	0.999976i	$0.497775\pi$
$234$	−0.273405	−0.0178731
$235$	−0.916766	−0.0598032
$236$	3.35869	0.218632
$237$	7.21357	0.468572
$238$	0.678773	0.0439983
$239$	12.6492	0.818207	0.409103	−	0.912488i	$-0.365842\pi$
$239$	12.6492	0.818207	0.409103	+	0.912488i	$0.365842\pi$
$240$	0.958143	0.0618479
$241$	−0.743580	−0.0478982	−0.0239491	−	0.999713i	$-0.507624\pi$
$241$	−0.743580	−0.0478982	−0.0239491	+	0.999713i	$0.507624\pi$
$242$	1.00000	0.0642824
$243$	−2.03672	−0.130656
$244$	−5.56259	−0.356108
$245$	3.97547	0.253983
$246$	6.38420	0.407042
$247$	8.68559	0.552651
$248$	−1.81886	−0.115498
$249$	15.9322	1.00966
$250$	5.53486	0.350055
$251$	−17.9805	−1.13492	−0.567460	−	0.823401i	$-0.692074\pi$
$251$	−17.9805	−1.13492	−0.567460	+	0.823401i	$0.692074\pi$
$252$	0.0450132	0.00283557
$253$	−0.283546	−0.0178264
$254$	−11.4306	−0.717217
$255$	−2.83628	−0.177614
$256$	1.00000	0.0625000
$257$	22.7345	1.41814	0.709068	−	0.705140i	$-0.249116\pi$
$257$	22.7345	1.41814	0.709068	+	0.705140i	$0.249116\pi$
$258$	6.75060	0.420274
$259$	−2.57923	−0.160265
$260$	−0.796963	−0.0494256
$261$	0.420078	0.0260022
$262$	−1.08843	−0.0672434
$263$	21.0300	1.29676	0.648382	−	0.761315i	$-0.275446\pi$
$263$	21.0300	1.29676	0.648382	+	0.761315i	$0.275446\pi$
$264$	1.67442	0.103054
$265$	0.320329	0.0196777
$266$	−1.42999	−0.0876783
$267$	9.42975	0.577091
$268$	−7.29496	−0.445611
$269$	−19.2123	−1.17139	−0.585697	−	0.810530i	$-0.699179\pi$
$269$	−19.2123	−1.17139	−0.585697	+	0.810530i	$0.699179\pi$
$270$	−3.06252	−0.186379
$271$	25.7076	1.56162	0.780812	−	0.624766i	$-0.214806\pi$
$271$	25.7076	1.56162	0.780812	+	0.624766i	$0.214806\pi$
$272$	−2.96018	−0.179487
$273$	0.534743	0.0323641
$274$	−13.3068	−0.803892
$275$	4.67256	0.281766
$276$	−0.474776	−0.0285782
$277$	−6.47691	−0.389160	−0.194580	−	0.980887i	$-0.562334\pi$
$277$	−6.47691	−0.389160	−0.194580	+	0.980887i	$0.562334\pi$
$278$	−11.7713	−0.705994
$279$	0.357052	0.0213762
$280$	0.131211	0.00784138
$281$	16.5808	0.989127	0.494563	−	0.869142i	$-0.335328\pi$
$281$	16.5808	0.989127	0.494563	+	0.869142i	$0.335328\pi$
$282$	−2.68262	−0.159748
$283$	−8.33125	−0.495241	−0.247621	−	0.968857i	$-0.579649\pi$
$283$	−8.33125	−0.495241	−0.247621	+	0.968857i	$0.579649\pi$
$284$	5.81690	0.345170
$285$	5.97525	0.353944
$286$	−1.39275	−0.0823551
$287$	0.874275	0.0516068
$288$	−0.196306	−0.0115674
$289$	−8.23734	−0.484549
$290$	1.22451	0.0719056
$291$	−8.66288	−0.507827
$292$	−15.9763	−0.934944
$293$	−24.0716	−1.40628	−0.703140	−	0.711051i	$-0.748219\pi$
$293$	−24.0716	−1.40628	−0.703140	+	0.711051i	$0.748219\pi$
$294$	11.6329	0.678446
$295$	−1.92192	−0.111898
$296$	11.2482	0.653788
$297$	−5.35197	−0.310553
$298$	16.9306	0.980765
$299$	0.394909	0.0228382
$300$	7.82385	0.451710
$301$	0.924450	0.0532844
$302$	−19.7165	−1.13456
$303$	−23.0562	−1.32455
$304$	6.23629	0.357676
$305$	3.18304	0.182260
$306$	0.581101	0.0332193
$307$	−21.0399	−1.20081	−0.600405	−	0.799696i	$-0.704994\pi$
$307$	−21.0399	−1.20081	−0.600405	+	0.799696i	$0.704994\pi$
$308$	0.229301	0.0130657
$309$	16.3343	0.929229
$310$	1.04079	0.0591129
$311$	−4.46866	−0.253395	−0.126697	−	0.991941i	$-0.540438\pi$
$311$	−4.46866	−0.253395	−0.126697	+	0.991941i	$0.540438\pi$
$312$	−2.33205	−0.132027
$313$	7.26228	0.410489	0.205244	−	0.978711i	$-0.434201\pi$
$313$	7.26228	0.410489	0.205244	+	0.978711i	$0.434201\pi$
$314$	1.24198	0.0700888
$315$	−0.0257576	−0.00145127
$316$	−4.30809	−0.242349
$317$	12.3355	0.692831	0.346415	−	0.938081i	$-0.387399\pi$
$317$	12.3355	0.692831	0.346415	+	0.938081i	$0.387399\pi$
$318$	0.937340	0.0525634
$319$	2.13992	0.119812
$320$	−0.572222	−0.0319882
$321$	6.59225	0.367943
$322$	−0.0650175	−0.00362328
$323$	−18.4605	−1.02717
$324$	−8.37255	−0.465141
$325$	−6.50771	−0.360983
$326$	−16.7105	−0.925511
$327$	6.64613	0.367532
$328$	−3.81278	−0.210525
$329$	−0.367367	−0.0202536
$330$	−0.958143	−0.0527440
$331$	11.1035	0.610306	0.305153	−	0.952303i	$-0.401292\pi$
$331$	11.1035	0.610306	0.305153	+	0.952303i	$0.401292\pi$
$332$	−9.51503	−0.522205
$333$	−2.20809	−0.121002
$334$	−10.7661	−0.589095
$335$	4.17434	0.228069
$336$	0.383948	0.0209461
$337$	−1.89035	−0.102974	−0.0514869	−	0.998674i	$-0.516396\pi$
$337$	−1.89035	−0.102974	−0.0514869	+	0.998674i	$0.516396\pi$
$338$	−11.0602	−0.601598
$339$	−18.9366	−1.02849
$340$	1.69388	0.0918636
$341$	1.81886	0.0984966
$342$	−1.22422	−0.0661982
$343$	3.19816	0.172685
$344$	−4.03160	−0.217369
$345$	0.271677	0.0146266
$346$	14.9061	0.801357
$347$	28.2368	1.51583	0.757914	−	0.652354i	$-0.226218\pi$
$347$	28.2368	1.51583	0.757914	+	0.652354i	$0.226218\pi$
$348$	3.58312	0.192076
$349$	26.4102	1.41371	0.706854	−	0.707360i	$-0.250114\pi$
$349$	26.4102	1.41371	0.706854	+	0.707360i	$0.250114\pi$
$350$	1.07142	0.0572701
$351$	7.45396	0.397863
$352$	−1.00000	−0.0533002
$353$	−0.0926545	−0.00493150	−0.00246575	−	0.999997i	$-0.500785\pi$
$353$	−0.0926545	−0.00493150	−0.00246575	+	0.999997i	$0.500785\pi$
$354$	−5.62387	−0.298905
$355$	−3.32856	−0.176662
$356$	−5.63164	−0.298476
$357$	−1.13655	−0.0601528
$358$	−12.1773	−0.643591
$359$	−25.7063	−1.35673	−0.678363	−	0.734727i	$-0.737310\pi$
$359$	−25.7063	−1.35673	−0.678363	+	0.734727i	$0.737310\pi$
$360$	0.112331	0.00592035
$361$	19.8913	1.04691
$362$	7.11818	0.374123
$363$	−1.67442	−0.0878844
$364$	−0.319360	−0.0167390
$365$	9.14202	0.478515
$366$	9.31414	0.486858
$367$	−14.2824	−0.745535	−0.372768	−	0.927925i	$-0.621591\pi$
$367$	−14.2824	−0.745535	−0.372768	+	0.927925i	$0.621591\pi$
$368$	0.283546	0.0147809
$369$	0.748471	0.0389638
$370$	−6.43647	−0.334616
$371$	0.128363	0.00666425
$372$	3.04554	0.157904
$373$	−10.7647	−0.557378	−0.278689	−	0.960381i	$-0.589900\pi$
$373$	−10.7647	−0.557378	−0.278689	+	0.960381i	$0.589900\pi$
$374$	2.96018	0.153067
$375$	−9.26769	−0.478582
$376$	1.60211	0.0826228
$377$	−2.98037	−0.153497
$378$	−1.22721	−0.0631211
$379$	1.62465	0.0834526	0.0417263	−	0.999129i	$-0.486714\pi$
$379$	1.62465	0.0834526	0.0417263	+	0.999129i	$0.486714\pi$
$380$	−3.56854	−0.183062
$381$	19.1396	0.980551
$382$	−5.52828	−0.282851
$383$	−29.5760	−1.51126	−0.755631	−	0.654997i	$-0.772670\pi$
$383$	−29.5760	−1.51126	−0.755631	+	0.654997i	$0.772670\pi$
$384$	−1.67442	−0.0854476
$385$	−0.131211	−0.00668715
$386$	−15.3421	−0.780891
$387$	0.791426	0.0402304
$388$	5.17365	0.262652
$389$	18.1243	0.918940	0.459470	−	0.888193i	$-0.348039\pi$
$389$	18.1243	0.918940	0.459470	+	0.888193i	$0.348039\pi$
$390$	1.33445	0.0675727
$391$	−0.839347	−0.0424476
$392$	−6.94742	−0.350898
$393$	1.82249	0.0919325
$394$	1.00000	0.0503793
$395$	2.46519	0.124037
$396$	0.196306	0.00986474
$397$	−18.4265	−0.924801	−0.462401	−	0.886671i	$-0.653012\pi$
$397$	−18.4265	−0.924801	−0.462401	+	0.886671i	$0.653012\pi$
$398$	−3.81226	−0.191091
$399$	2.39441	0.119870
$400$	−4.67256	−0.233628
$401$	−1.55343	−0.0775747	−0.0387873	−	0.999247i	$-0.512349\pi$
$401$	−1.55343	−0.0775747	−0.0387873	+	0.999247i	$0.512349\pi$
$402$	12.2148	0.609221
$403$	−2.53321	−0.126188
$404$	13.7697	0.685066
$405$	4.79096	0.238065
$406$	0.490686	0.0243523
$407$	−11.2482	−0.557552
$408$	4.95659	0.245388
$409$	−22.4410	−1.10963	−0.554817	−	0.831972i	$-0.687212\pi$
$409$	−22.4410	−1.10963	−0.554817	+	0.831972i	$0.687212\pi$
$410$	2.18176	0.107749
$411$	22.2812	1.09905
$412$	−9.75521	−0.480605
$413$	−0.770152	−0.0378967
$414$	−0.0556617	−0.00273563
$415$	5.44471	0.267270
$416$	1.39275	0.0682852
$417$	19.7101	0.965207
$418$	−6.23629	−0.305027
$419$	−19.9049	−0.972419	−0.486210	−	0.873842i	$-0.661621\pi$
$419$	−19.9049	−0.972419	−0.486210	+	0.873842i	$0.661621\pi$
$420$	−0.219703	−0.0107204
$421$	22.0309	1.07372	0.536861	−	0.843671i	$-0.319610\pi$
$421$	22.0309	1.07372	0.536861	+	0.843671i	$0.319610\pi$
$422$	−5.45510	−0.265550
$423$	−0.314505	−0.0152917
$424$	−0.559798	−0.0271862
$425$	13.8316	0.670932
$426$	−9.73995	−0.471902
$427$	1.27551	0.0617263
$428$	−3.93702	−0.190303
$429$	2.33205	0.112593
$430$	2.30697	0.111252
$431$	−12.7023	−0.611849	−0.305924	−	0.952056i	$-0.598965\pi$
$431$	−12.7023	−0.611849	−0.305924	+	0.952056i	$0.598965\pi$
$432$	5.35197	0.257497
$433$	3.60471	0.173232	0.0866158	−	0.996242i	$-0.472395\pi$
$433$	3.60471	0.173232	0.0866158	+	0.996242i	$0.472395\pi$
$434$	0.417066	0.0200198
$435$	−2.05034	−0.0983065
$436$	−3.96921	−0.190091
$437$	1.76827	0.0845880
$438$	26.7512	1.27822
$439$	11.7024	0.558527	0.279263	−	0.960215i	$-0.409910\pi$
$439$	11.7024	0.558527	0.279263	+	0.960215i	$0.409910\pi$
$440$	0.572222	0.0272796
$441$	1.36382	0.0649438
$442$	−4.12279	−0.196101
$443$	38.6230	1.83504	0.917518	−	0.397695i	$-0.130190\pi$
$443$	38.6230	1.83504	0.917518	+	0.397695i	$0.130190\pi$
$444$	−18.8342	−0.893833
$445$	3.22255	0.152764
$446$	4.89586	0.231826
$447$	−28.3490	−1.34086
$448$	−0.229301	−0.0108335
$449$	4.02983	0.190179	0.0950897	−	0.995469i	$-0.469686\pi$
$449$	4.02983	0.190179	0.0950897	+	0.995469i	$0.469686\pi$
$450$	0.917251	0.0432396
$451$	3.81278	0.179537
$452$	11.3093	0.531945
$453$	33.0138	1.55113
$454$	−14.6339	−0.686802
$455$	0.182745	0.00856720
$456$	−10.4422	−0.489000
$457$	34.2265	1.60105	0.800524	−	0.599301i	$-0.204555\pi$
$457$	34.2265	1.60105	0.800524	+	0.599301i	$0.204555\pi$
$458$	−26.4046	−1.23381
$459$	−15.8428	−0.739478
$460$	−0.162251	−0.00756501
$461$	−7.87853	−0.366940	−0.183470	−	0.983025i	$-0.558733\pi$
$461$	−7.87853	−0.366940	−0.183470	+	0.983025i	$0.558733\pi$
$462$	−0.383948	−0.0178629
$463$	5.99730	0.278718	0.139359	−	0.990242i	$-0.455496\pi$
$463$	5.99730	0.278718	0.139359	+	0.990242i	$0.455496\pi$
$464$	−2.13992	−0.0993431
$465$	−1.74272	−0.0808169
$466$	0.213394	0.00988529
$467$	12.9907	0.601137	0.300568	−	0.953760i	$-0.402824\pi$
$467$	12.9907	0.601137	0.300568	+	0.953760i	$0.402824\pi$
$468$	−0.273405	−0.0126382
$469$	1.67274	0.0772401
$470$	−0.916766	−0.0422873
$471$	−2.07960	−0.0958227
$472$	3.35869	0.154596
$473$	4.03160	0.185373
$474$	7.21357	0.331330
$475$	−29.1394	−1.33701
$476$	0.678773	0.0311115
$477$	0.109892	0.00503160
$478$	12.6492	0.578559
$479$	1.50954	0.0689725	0.0344863	−	0.999405i	$-0.489021\pi$
$479$	1.50954	0.0689725	0.0344863	+	0.999405i	$0.489021\pi$
$480$	0.958143	0.0437330
$481$	15.6659	0.714305
$482$	−0.743580	−0.0338692
$483$	0.108867	0.00495361
$484$	1.00000	0.0454545
$485$	−2.96048	−0.134428
$486$	−2.03672	−0.0923875
$487$	19.0024	0.861082	0.430541	−	0.902571i	$-0.358323\pi$
$487$	19.0024	0.861082	0.430541	+	0.902571i	$0.358323\pi$
$488$	−5.56259	−0.251807
$489$	27.9805	1.26532
$490$	3.97547	0.179593
$491$	−25.9240	−1.16993	−0.584966	−	0.811057i	$-0.698892\pi$
$491$	−25.9240	−1.16993	−0.584966	+	0.811057i	$0.698892\pi$
$492$	6.38420	0.287822
$493$	6.33453	0.285293
$494$	8.68559	0.390783
$495$	−0.112331	−0.00504889
$496$	−1.81886	−0.0816691
$497$	−1.33382	−0.0598301
$498$	15.9322	0.713938
$499$	−31.3245	−1.40228	−0.701139	−	0.713025i	$-0.747325\pi$
$499$	−31.3245	−1.40228	−0.701139	+	0.713025i	$0.747325\pi$
$500$	5.53486	0.247526
$501$	18.0270	0.805387
$502$	−17.9805	−0.802510
$503$	3.34630	0.149204	0.0746020	−	0.997213i	$-0.476231\pi$
$503$	3.34630	0.149204	0.0746020	+	0.997213i	$0.476231\pi$
$504$	0.0450132	0.00200505
$505$	−7.87931	−0.350625
$506$	−0.283546	−0.0126052
$507$	18.5195	0.822481
$508$	−11.4306	−0.507149
$509$	20.6669	0.916044	0.458022	−	0.888941i	$-0.348558\pi$
$509$	20.6669	0.916044	0.458022	+	0.888941i	$0.348558\pi$
$510$	−2.83628	−0.125592
$511$	3.66340	0.162059
$512$	1.00000	0.0441942
$513$	33.3764	1.47361
$514$	22.7345	1.00277
$515$	5.58215	0.245979
$516$	6.75060	0.297178
$517$	−1.60211	−0.0704609
$518$	−2.57923	−0.113325
$519$	−24.9591	−1.09558
$520$	−0.796963	−0.0349491
$521$	−7.63186	−0.334358	−0.167179	−	0.985927i	$-0.553466\pi$
$521$	−7.63186	−0.334358	−0.167179	+	0.985927i	$0.553466\pi$
$522$	0.420078	0.0183863
$523$	10.5022	0.459227	0.229614	−	0.973282i	$-0.426254\pi$
$523$	10.5022	0.459227	0.229614	+	0.973282i	$0.426254\pi$
$524$	−1.08843	−0.0475482
$525$	−1.79402	−0.0782974
$526$	21.0300	0.916951
$527$	5.38414	0.234537
$528$	1.67442	0.0728699
$529$	−22.9196	−0.996504
$530$	0.320329	0.0139142
$531$	−0.659331	−0.0286125
$532$	−1.42999	−0.0619979
$533$	−5.31025	−0.230012
$534$	9.42975	0.408065
$535$	2.25285	0.0973994
$536$	−7.29496	−0.315094
$537$	20.3900	0.879892
$538$	−19.2123	−0.828301
$539$	6.94742	0.299247
$540$	−3.06252	−0.131790
$541$	23.3301	1.00304	0.501520	−	0.865146i	$-0.332774\pi$
$541$	23.3301	1.00304	0.501520	+	0.865146i	$0.332774\pi$
$542$	25.7076	1.10423
$543$	−11.9188	−0.511486
$544$	−2.96018	−0.126917
$545$	2.27127	0.0972905
$546$	0.534743	0.0228849
$547$	−5.39369	−0.230618	−0.115309	−	0.993330i	$-0.536786\pi$
$547$	−5.39369	−0.230618	−0.115309	+	0.993330i	$0.536786\pi$
$548$	−13.3068	−0.568438
$549$	1.09197	0.0466041
$550$	4.67256	0.199239
$551$	−13.3451	−0.568522
$552$	−0.474776	−0.0202078
$553$	0.987851	0.0420077
$554$	−6.47691	−0.275177
$555$	10.7774	0.457474
$556$	−11.7713	−0.499213
$557$	36.0352	1.52686	0.763431	−	0.645890i	$-0.223513\pi$
$557$	36.0352	1.52686	0.763431	+	0.645890i	$0.223513\pi$
$558$	0.357052	0.0151152
$559$	−5.61501	−0.237489
$560$	0.131211	0.00554469
$561$	−4.95659	−0.209268
$562$	16.5808	0.699418
$563$	−3.49773	−0.147412	−0.0737059	−	0.997280i	$-0.523483\pi$
$563$	−3.49773	−0.147412	−0.0737059	+	0.997280i	$0.523483\pi$
$564$	−2.68262	−0.112959
$565$	−6.47143	−0.272255
$566$	−8.33125	−0.350188
$567$	1.91984	0.0806255
$568$	5.81690	0.244072
$569$	37.2681	1.56236	0.781180	−	0.624306i	$-0.214618\pi$
$569$	37.2681	1.56236	0.781180	+	0.624306i	$0.214618\pi$
$570$	5.97525	0.250276
$571$	−31.5095	−1.31863	−0.659315	−	0.751867i	$-0.729154\pi$
$571$	−31.5095	−1.31863	−0.659315	+	0.751867i	$0.729154\pi$
$572$	−1.39275	−0.0582338
$573$	9.25668	0.386703
$574$	0.874275	0.0364915
$575$	−1.32489	−0.0552516
$576$	−0.196306	−0.00817941
$577$	9.47924	0.394626	0.197313	−	0.980341i	$-0.436778\pi$
$577$	9.47924	0.394626	0.197313	+	0.980341i	$0.436778\pi$
$578$	−8.23734	−0.342628
$579$	25.6891	1.06760
$580$	1.22451	0.0508449
$581$	2.18181	0.0905167
$582$	−8.66288	−0.359088
$583$	0.559798	0.0231845
$584$	−15.9763	−0.661106
$585$	0.156449	0.00646835
$586$	−24.0716	−0.994391
$587$	16.4989	0.680982	0.340491	−	0.940248i	$-0.389407\pi$
$587$	16.4989	0.680982	0.340491	+	0.940248i	$0.389407\pi$
$588$	11.6329	0.479734
$589$	−11.3429	−0.467377
$590$	−1.92192	−0.0791241
$591$	−1.67442	−0.0688766
$592$	11.2482	0.462298
$593$	−6.61924	−0.271820	−0.135910	−	0.990721i	$-0.543396\pi$
$593$	−6.61924	−0.271820	−0.135910	+	0.990721i	$0.543396\pi$
$594$	−5.35197	−0.219594
$595$	−0.388409	−0.0159232
$596$	16.9306	0.693505
$597$	6.38334	0.261253
$598$	0.394909	0.0161490
$599$	11.3551	0.463955	0.231978	−	0.972721i	$-0.425480\pi$
$599$	11.3551	0.463955	0.231978	+	0.972721i	$0.425480\pi$
$600$	7.82385	0.319407
$601$	4.48047	0.182762	0.0913811	−	0.995816i	$-0.470872\pi$
$601$	4.48047	0.182762	0.0913811	+	0.995816i	$0.470872\pi$
$602$	0.924450	0.0376778
$603$	1.43204	0.0583173
$604$	−19.7165	−0.802255
$605$	−0.572222	−0.0232642
$606$	−23.0562	−0.936595
$607$	−7.82103	−0.317446	−0.158723	−	0.987323i	$-0.550738\pi$
$607$	−7.82103	−0.317446	−0.158723	+	0.987323i	$0.550738\pi$
$608$	6.23629	0.252915
$609$	−0.821615	−0.0332935
$610$	3.18304	0.128878
$611$	2.23135	0.0902706
$612$	0.581101	0.0234896
$613$	−20.4180	−0.824676	−0.412338	−	0.911031i	$-0.635288\pi$
$613$	−20.4180	−0.824676	−0.412338	+	0.911031i	$0.635288\pi$
$614$	−21.0399	−0.849101
$615$	−3.65319	−0.147311
$616$	0.229301	0.00923881
$617$	−34.5968	−1.39281	−0.696407	−	0.717647i	$-0.745219\pi$
$617$	−34.5968	−1.39281	−0.696407	+	0.717647i	$0.745219\pi$
$618$	16.3343	0.657064
$619$	38.3199	1.54021	0.770104	−	0.637919i	$-0.220204\pi$
$619$	38.3199	1.54021	0.770104	+	0.637919i	$0.220204\pi$
$620$	1.04079	0.0417992
$621$	1.51753	0.0608964
$622$	−4.46866	−0.179177
$623$	1.29134	0.0517366
$624$	−2.33205	−0.0933569
$625$	20.1956	0.807825
$626$	7.26228	0.290259
$627$	10.4422	0.417021
$628$	1.24198	0.0495603
$629$	−33.2967	−1.32763
$630$	−0.0257576	−0.00102621
$631$	−26.0275	−1.03614	−0.518069	−	0.855339i	$-0.673349\pi$
$631$	−26.0275	−1.03614	−0.518069	+	0.855339i	$0.673349\pi$
$632$	−4.30809	−0.171367
$633$	9.13415	0.363050
$634$	12.3355	0.489905
$635$	6.54082	0.259564
$636$	0.937340	0.0371679
$637$	−9.67602	−0.383378
$638$	2.13992	0.0847201
$639$	−1.14189	−0.0451725
$640$	−0.572222	−0.0226191
$641$	11.9631	0.472516	0.236258	−	0.971690i	$-0.424079\pi$
$641$	11.9631	0.472516	0.236258	+	0.971690i	$0.424079\pi$
$642$	6.59225	0.260175
$643$	−4.03967	−0.159309	−0.0796546	−	0.996823i	$-0.525382\pi$
$643$	−4.03967	−0.159309	−0.0796546	+	0.996823i	$0.525382\pi$
$644$	−0.0650175	−0.00256205
$645$	−3.86284	−0.152099
$646$	−18.4605	−0.726320
$647$	−37.7777	−1.48519	−0.742597	−	0.669738i	$-0.766406\pi$
$647$	−37.7777	−1.48519	−0.742597	+	0.669738i	$0.766406\pi$
$648$	−8.37255	−0.328905
$649$	−3.35869	−0.131840
$650$	−6.50771	−0.255253
$651$	−0.698346	−0.0273703
$652$	−16.7105	−0.654435
$653$	5.23983	0.205050	0.102525	−	0.994730i	$-0.467308\pi$
$653$	5.23983	0.205050	0.102525	+	0.994730i	$0.467308\pi$
$654$	6.64613	0.259884
$655$	0.622823	0.0243357
$656$	−3.81278	−0.148864
$657$	3.13625	0.122357
$658$	−0.367367	−0.0143215
$659$	−3.58338	−0.139589	−0.0697943	−	0.997561i	$-0.522234\pi$
$659$	−3.58338	−0.139589	−0.0697943	+	0.997561i	$0.522234\pi$
$660$	−0.958143	−0.0372957
$661$	9.91112	0.385498	0.192749	−	0.981248i	$-0.438260\pi$
$661$	9.91112	0.385498	0.192749	+	0.981248i	$0.438260\pi$
$662$	11.1035	0.431552
$663$	6.90330	0.268102
$664$	−9.51503	−0.369255
$665$	0.818272	0.0317312
$666$	−2.20809	−0.0855616
$667$	−0.606764	−0.0234940
$668$	−10.7661	−0.416553
$669$	−8.19774	−0.316943
$670$	4.17434	0.161269
$671$	5.56259	0.214741
$672$	0.383948	0.0148111
$673$	21.5741	0.831619	0.415810	−	0.909452i	$-0.363498\pi$
$673$	21.5741	0.831619	0.415810	+	0.909452i	$0.363498\pi$
$674$	−1.89035	−0.0728134
$675$	−25.0074	−0.962536
$676$	−11.0602	−0.425394
$677$	31.0485	1.19329	0.596645	−	0.802506i	$-0.296500\pi$
$677$	31.0485	1.19329	0.596645	+	0.802506i	$0.296500\pi$
$678$	−18.9366	−0.727254
$679$	−1.18633	−0.0455270
$680$	1.69388	0.0649574
$681$	24.5033	0.938969
$682$	1.81886	0.0696476
$683$	12.0263	0.460174	0.230087	−	0.973170i	$-0.426099\pi$
$683$	12.0263	0.460174	0.230087	+	0.973170i	$0.426099\pi$
$684$	−1.22422	−0.0468092
$685$	7.61444	0.290933
$686$	3.19816	0.122106
$687$	44.2125	1.68681
$688$	−4.03160	−0.153703
$689$	−0.779659	−0.0297027
$690$	0.271677	0.0103426
$691$	31.7497	1.20782	0.603909	−	0.797054i	$-0.293609\pi$
$691$	31.7497	1.20782	0.603909	+	0.797054i	$0.293609\pi$
$692$	14.9061	0.566645
$693$	−0.0450132	−0.00170991
$694$	28.2368	1.07185
$695$	6.73578	0.255503
$696$	3.58312	0.135818
$697$	11.2865	0.427507
$698$	26.4102	0.999642
$699$	−0.357312	−0.0135148
$700$	1.07142	0.0404960
$701$	−12.3335	−0.465831	−0.232916	−	0.972497i	$-0.574827\pi$
$701$	−12.3335	−0.465831	−0.232916	+	0.972497i	$0.574827\pi$
$702$	7.45396	0.281332
$703$	70.1470	2.64564
$704$	−1.00000	−0.0376889
$705$	1.53505	0.0578135
$706$	−0.0926545	−0.00348710
$707$	−3.15740	−0.118746
$708$	−5.62387	−0.211358
$709$	−4.35143	−0.163421	−0.0817107	−	0.996656i	$-0.526038\pi$
$709$	−4.35143	−0.163421	−0.0817107	+	0.996656i	$0.526038\pi$
$710$	−3.32856	−0.124919
$711$	0.845704	0.0317164
$712$	−5.63164	−0.211055
$713$	−0.515729	−0.0193142
$714$	−1.13655	−0.0425345
$715$	0.796963	0.0298047
$716$	−12.1773	−0.455087
$717$	−21.1801	−0.790984
$718$	−25.7063	−0.959350
$719$	−4.35832	−0.162538	−0.0812690	−	0.996692i	$-0.525897\pi$
$719$	−4.35832	−0.162538	−0.0812690	+	0.996692i	$0.525897\pi$
$720$	0.112331	0.00418632
$721$	2.23688	0.0833058
$722$	19.8913	0.740277
$723$	1.24507	0.0463046
$724$	7.11818	0.264545
$725$	9.99889	0.371349
$726$	−1.67442	−0.0621437
$727$	31.1834	1.15653	0.578264	−	0.815850i	$-0.303730\pi$
$727$	31.1834	1.15653	0.578264	+	0.815850i	$0.303730\pi$
$728$	−0.319360	−0.0118363
$729$	28.5280	1.05659
$730$	9.14202	0.338361
$731$	11.9342	0.441404
$732$	9.31414	0.344260
$733$	−9.53254	−0.352092	−0.176046	−	0.984382i	$-0.556331\pi$
$733$	−9.53254	−0.352092	−0.176046	+	0.984382i	$0.556331\pi$
$734$	−14.2824	−0.527173
$735$	−6.65662	−0.245533
$736$	0.283546	0.0104516
$737$	7.29496	0.268713
$738$	0.748471	0.0275516
$739$	6.50572	0.239317	0.119658	−	0.992815i	$-0.461820\pi$
$739$	6.50572	0.239317	0.119658	+	0.992815i	$0.461820\pi$
$740$	−6.43647	−0.236609
$741$	−14.5434	−0.534264
$742$	0.128363	0.00471234
$743$	22.1086	0.811087	0.405543	−	0.914076i	$-0.367082\pi$
$743$	22.1086	0.811087	0.405543	+	0.914076i	$0.367082\pi$
$744$	3.04554	0.111655
$745$	−9.68808	−0.354944
$746$	−10.7647	−0.394125
$747$	1.86786	0.0683413
$748$	2.96018	0.108235
$749$	0.902765	0.0329863
$750$	−9.26769	−0.338408
$751$	21.4213	0.781674	0.390837	−	0.920460i	$-0.372186\pi$
$751$	21.4213	0.781674	0.390837	+	0.920460i	$0.372186\pi$
$752$	1.60211	0.0584231
$753$	30.1070	1.09716
$754$	−2.98037	−0.108539
$755$	11.2822	0.410603
$756$	−1.22721	−0.0446333
$757$	−2.60516	−0.0946860	−0.0473430	−	0.998879i	$-0.515075\pi$
$757$	−2.60516	−0.0946860	−0.0473430	+	0.998879i	$0.515075\pi$
$758$	1.62465	0.0590099
$759$	0.474776	0.0172333
$760$	−3.56854	−0.129445
$761$	−14.0832	−0.510516	−0.255258	−	0.966873i	$-0.582160\pi$
$761$	−14.0832	−0.510516	−0.255258	+	0.966873i	$0.582160\pi$
$762$	19.1396	0.693354
$763$	0.910144	0.0329494
$764$	−5.52828	−0.200006
$765$	−0.332519	−0.0120222
$766$	−29.5760	−1.06862
$767$	4.67782	0.168906
$768$	−1.67442	−0.0604206
$769$	36.0257	1.29912	0.649559	−	0.760311i	$-0.274953\pi$
$769$	36.0257	1.29912	0.649559	+	0.760311i	$0.274953\pi$
$770$	−0.131211	−0.00472853
$771$	−38.0671	−1.37095
$772$	−15.3421	−0.552173
$773$	−18.1534	−0.652931	−0.326466	−	0.945209i	$-0.605858\pi$
$773$	−18.1534	−0.652931	−0.326466	+	0.945209i	$0.605858\pi$
$774$	0.791426	0.0284472
$775$	8.49872	0.305283
$776$	5.17365	0.185723
$777$	4.31872	0.154933
$778$	18.1243	0.649789
$779$	−23.7776	−0.851920
$780$	1.33445	0.0477811
$781$	−5.81690	−0.208145
$782$	−0.839347	−0.0300150
$783$	−11.4528	−0.409288
$784$	−6.94742	−0.248122
$785$	−0.710687	−0.0253655
$786$	1.82249	0.0650061
$787$	−18.6023	−0.663102	−0.331551	−	0.943437i	$-0.607572\pi$
$787$	−18.6023	−0.663102	−0.331551	+	0.943437i	$0.607572\pi$
$788$	1.00000	0.0356235
$789$	−35.2131	−1.25362
$790$	2.46519	0.0877074
$791$	−2.59324	−0.0922049
$792$	0.196306	0.00697543
$793$	−7.74730	−0.275115
$794$	−18.4265	−0.653933
$795$	−0.536367	−0.0190230
$796$	−3.81226	−0.135122
$797$	9.69805	0.343523	0.171761	−	0.985139i	$-0.445054\pi$
$797$	9.69805	0.343523	0.171761	+	0.985139i	$0.445054\pi$
$798$	2.39441	0.0847611
$799$	−4.74255	−0.167779
$800$	−4.67256	−0.165200
$801$	1.10552	0.0390618
$802$	−1.55343	−0.0548536
$803$	15.9763	0.563793
$804$	12.2148	0.430785
$805$	0.0372045	0.00131128
$806$	−2.53321	−0.0892286
$807$	32.1695	1.13242
$808$	13.7697	0.484415
$809$	−23.0658	−0.810951	−0.405475	−	0.914106i	$-0.632894\pi$
$809$	−23.0658	−0.810951	−0.405475	+	0.914106i	$0.632894\pi$
$810$	4.79096	0.168337
$811$	−37.8890	−1.33046	−0.665231	−	0.746637i	$-0.731667\pi$
$811$	−37.8890	−1.33046	−0.665231	+	0.746637i	$0.731667\pi$
$812$	0.490686	0.0172197
$813$	−43.0453	−1.50967
$814$	−11.2482	−0.394249
$815$	9.56215	0.334947
$816$	4.95659	0.173516
$817$	−25.1422	−0.879614
$818$	−22.4410	−0.784630
$819$	0.0626922	0.00219064
$820$	2.18176	0.0761903
$821$	−26.5776	−0.927563	−0.463782	−	0.885950i	$-0.653508\pi$
$821$	−26.5776	−0.927563	−0.463782	+	0.885950i	$0.653508\pi$
$822$	22.2812	0.777146
$823$	40.9621	1.42785	0.713925	−	0.700222i	$-0.246916\pi$
$823$	40.9621	1.42785	0.713925	+	0.700222i	$0.246916\pi$
$824$	−9.75521	−0.339839
$825$	−7.82385	−0.272391
$826$	−0.770152	−0.0267970
$827$	7.00186	0.243479	0.121739	−	0.992562i	$-0.461153\pi$
$827$	7.00186	0.243479	0.121739	+	0.992562i	$0.461153\pi$
$828$	−0.0556617	−0.00193438
$829$	−18.4924	−0.642268	−0.321134	−	0.947034i	$-0.604064\pi$
$829$	−18.4924	−0.642268	−0.321134	+	0.947034i	$0.604064\pi$
$830$	5.44471	0.188989
$831$	10.8451	0.376212
$832$	1.39275	0.0482849
$833$	20.5656	0.712556
$834$	19.7101	0.682504
$835$	6.16060	0.213196
$836$	−6.23629	−0.215687
$837$	−9.73446	−0.336472
$838$	−19.9049	−0.687604
$839$	41.4289	1.43028	0.715142	−	0.698979i	$-0.246362\pi$
$839$	41.4289	1.43028	0.715142	+	0.698979i	$0.246362\pi$
$840$	−0.219703	−0.00758049
$841$	−24.4208	−0.842095
$842$	22.0309	0.759236
$843$	−27.7633	−0.956218
$844$	−5.45510	−0.187772
$845$	6.32892	0.217722
$846$	−0.314505	−0.0108129
$847$	−0.229301	−0.00787889
$848$	−0.559798	−0.0192236
$849$	13.9500	0.478764
$850$	13.8316	0.474421
$851$	3.18938	0.109331
$852$	−9.73995	−0.333685
$853$	31.6394	1.08331	0.541656	−	0.840601i	$-0.317798\pi$
$853$	31.6394	1.08331	0.541656	+	0.840601i	$0.317798\pi$
$854$	1.27551	0.0436471
$855$	0.700526	0.0239575
$856$	−3.93702	−0.134565
$857$	19.5925	0.669266	0.334633	−	0.942349i	$-0.391388\pi$
$857$	19.5925	0.669266	0.334633	+	0.942349i	$0.391388\pi$
$858$	2.33205	0.0796150
$859$	−50.0877	−1.70897	−0.854485	−	0.519477i	$-0.826127\pi$
$859$	−50.0877	−1.70897	−0.854485	+	0.519477i	$0.826127\pi$
$860$	2.30697	0.0786670
$861$	−1.46391	−0.0498898
$862$	−12.7023	−0.432642
$863$	27.1557	0.924391	0.462195	−	0.886778i	$-0.347062\pi$
$863$	27.1557	0.924391	0.462195	+	0.886778i	$0.347062\pi$
$864$	5.35197	0.182078
$865$	−8.52961	−0.290015
$866$	3.60471	0.122493
$867$	13.7928	0.468428
$868$	0.417066	0.0141562
$869$	4.30809	0.146142
$870$	−2.05034	−0.0695132
$871$	−10.1601	−0.344260
$872$	−3.96921	−0.134414
$873$	−1.01562	−0.0343735
$874$	1.76827	0.0598128
$875$	−1.26915	−0.0429051
$876$	26.7512	0.903838
$877$	54.4137	1.83742	0.918711	−	0.394931i	$-0.129231\pi$
$877$	54.4137	1.83742	0.918711	+	0.394931i	$0.129231\pi$
$878$	11.7024	0.394938
$879$	40.3061	1.35949
$880$	0.572222	0.0192896
$881$	−21.2010	−0.714280	−0.357140	−	0.934051i	$-0.616248\pi$
$881$	−21.2010	−0.714280	−0.357140	+	0.934051i	$0.616248\pi$
$882$	1.36382	0.0459222
$883$	23.6909	0.797261	0.398631	−	0.917112i	$-0.369486\pi$
$883$	23.6909	0.797261	0.398631	+	0.917112i	$0.369486\pi$
$884$	−4.12279	−0.138664
$885$	3.21810	0.108175
$886$	38.6230	1.29757
$887$	−26.4115	−0.886812	−0.443406	−	0.896321i	$-0.646230\pi$
$887$	−26.4115	−0.886812	−0.443406	+	0.896321i	$0.646230\pi$
$888$	−18.8342	−0.632036
$889$	2.62104	0.0879069
$890$	3.22255	0.108020
$891$	8.37255	0.280491
$892$	4.89586	0.163925
$893$	9.99125	0.334344
$894$	−28.3490	−0.948134
$895$	6.96813	0.232919
$896$	−0.229301	−0.00766042
$897$	−0.661244	−0.0220783
$898$	4.02983	0.134477
$899$	3.89220	0.129812
$900$	0.917251	0.0305750
$901$	1.65710	0.0552061
$902$	3.81278	0.126952
$903$	−1.54792	−0.0515116
$904$	11.3093	0.376142
$905$	−4.07318	−0.135397
$906$	33.0138	1.09681
$907$	38.8890	1.29129	0.645645	−	0.763638i	$-0.276589\pi$
$907$	38.8890	1.29129	0.645645	+	0.763638i	$0.276589\pi$
$908$	−14.6339	−0.485643
$909$	−2.70306	−0.0896550
$910$	0.182745	0.00605793
$911$	−11.3270	−0.375279	−0.187639	−	0.982238i	$-0.560084\pi$
$911$	−11.3270	−0.375279	−0.187639	+	0.982238i	$0.560084\pi$
$912$	−10.4422	−0.345775
$913$	9.51503	0.314901
$914$	34.2265	1.13211
$915$	−5.32976	−0.176196
$916$	−26.4046	−0.872433
$917$	0.249578	0.00824180
$918$	−15.8428	−0.522890
$919$	−29.2857	−0.966046	−0.483023	−	0.875608i	$-0.660461\pi$
$919$	−29.2857	−0.966046	−0.483023	+	0.875608i	$0.660461\pi$
$920$	−0.162251	−0.00534927
$921$	35.2297	1.16086
$922$	−7.87853	−0.259466
$923$	8.10149	0.266664
$924$	−0.383948	−0.0126309
$925$	−52.5579	−1.72809
$926$	5.99730	0.197083
$927$	1.91500	0.0628970
$928$	−2.13992	−0.0702462
$929$	27.1209	0.889809	0.444904	−	0.895578i	$-0.353238\pi$
$929$	27.1209	0.889809	0.444904	+	0.895578i	$0.353238\pi$
$930$	−1.74272	−0.0571462
$931$	−43.3261	−1.41996
$932$	0.213394	0.00698996
$933$	7.48243	0.244964
$934$	12.9907	0.425068
$935$	−1.69388	−0.0553958
$936$	−0.273405	−0.00893653
$937$	27.2467	0.890112	0.445056	−	0.895503i	$-0.353184\pi$
$937$	27.2467	0.890112	0.445056	+	0.895503i	$0.353184\pi$
$938$	1.67274	0.0546170
$939$	−12.1601	−0.396831
$940$	−0.916766	−0.0299016
$941$	−24.3634	−0.794225	−0.397113	−	0.917770i	$-0.629988\pi$
$941$	−24.3634	−0.794225	−0.397113	+	0.917770i	$0.629988\pi$
$942$	−2.07960	−0.0677569
$943$	−1.08110	−0.0352054
$944$	3.35869	0.109316
$945$	0.702239	0.0228438
$946$	4.03160	0.131078
$947$	−6.49194	−0.210960	−0.105480	−	0.994421i	$-0.533638\pi$
$947$	−6.49194	−0.210960	−0.105480	+	0.994421i	$0.533638\pi$
$948$	7.21357	0.234286
$949$	−22.2510	−0.722300
$950$	−29.1394	−0.945408
$951$	−20.6549	−0.669780
$952$	0.678773	0.0219992
$953$	−27.1881	−0.880709	−0.440354	−	0.897824i	$-0.645147\pi$
$953$	−27.1881	−0.880709	−0.440354	+	0.897824i	$0.645147\pi$
$954$	0.109892	0.00355788
$955$	3.16341	0.102365
$956$	12.6492	0.409103
$957$	−3.58312	−0.115826
$958$	1.50954	0.0487709
$959$	3.05126	0.0985304
$960$	0.958143	0.0309239
$961$	−27.6918	−0.893283
$962$	15.6659	0.505090
$963$	0.772861	0.0249051
$964$	−0.743580	−0.0239491
$965$	8.77908	0.282608
$966$	0.108867	0.00350273
$967$	44.8963	1.44377	0.721883	−	0.692015i	$-0.243277\pi$
$967$	44.8963	1.44377	0.721883	+	0.692015i	$0.243277\pi$
$968$	1.00000	0.0321412
$969$	30.9108	0.992996
$970$	−2.96048	−0.0950553
$971$	−30.0521	−0.964419	−0.482210	−	0.876056i	$-0.660166\pi$
$971$	−30.0521	−0.964419	−0.482210	+	0.876056i	$0.660166\pi$
$972$	−2.03672	−0.0653279
$973$	2.69917	0.0865313
$974$	19.0024	0.608877
$975$	10.8967	0.348973
$976$	−5.56259	−0.178054
$977$	47.5237	1.52042	0.760209	−	0.649679i	$-0.225097\pi$
$977$	47.5237	1.52042	0.760209	+	0.649679i	$0.225097\pi$
$978$	27.9805	0.894718
$979$	5.63164	0.179988
$980$	3.97547	0.126992
$981$	0.779179	0.0248773
$982$	−25.9240	−0.827267
$983$	21.4320	0.683574	0.341787	−	0.939777i	$-0.388968\pi$
$983$	21.4320	0.683574	0.341787	+	0.939777i	$0.388968\pi$
$984$	6.38420	0.203521
$985$	−0.572222	−0.0182325
$986$	6.33453	0.201733
$987$	0.615128	0.0195797
$988$	8.68559	0.276325
$989$	−1.14314	−0.0363498
$990$	−0.112331	−0.00357010
$991$	1.88765	0.0599633	0.0299817	−	0.999550i	$-0.490455\pi$
$991$	1.88765	0.0599633	0.0299817	+	0.999550i	$0.490455\pi$
$992$	−1.81886	−0.0577488
$993$	−18.5920	−0.590000
$994$	−1.33382	−0.0423063
$995$	2.18146	0.0691569
$996$	15.9322	0.504831
$997$	30.5616	0.967895	0.483948	−	0.875097i	$-0.339203\pi$
$997$	30.5616	0.967895	0.483948	+	0.875097i	$0.339203\pi$
$998$	−31.3245	−0.991560
$999$	60.2000	1.90464

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.d.1.5	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.d.1.5	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.67442 q^{3} +1.00000 q^{4} -0.572222 q^{5} -1.67442 q^{6} -0.229301 q^{7} +1.00000 q^{8} -0.196306 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.67442 q^{3} +1.00000 q^{4} -0.572222 q^{5} -1.67442 q^{6} -0.229301 q^{7} +1.00000 q^{8} -0.196306 q^{9} -0.572222 q^{10} -1.00000 q^{11} -1.67442 q^{12} +1.39275 q^{13} -0.229301 q^{14} +0.958143 q^{15} +1.00000 q^{16} -2.96018 q^{17} -0.196306 q^{18} +6.23629 q^{19} -0.572222 q^{20} +0.383948 q^{21} -1.00000 q^{22} +0.283546 q^{23} -1.67442 q^{24} -4.67256 q^{25} +1.39275 q^{26} +5.35197 q^{27} -0.229301 q^{28} -2.13992 q^{29} +0.958143 q^{30} -1.81886 q^{31} +1.00000 q^{32} +1.67442 q^{33} -2.96018 q^{34} +0.131211 q^{35} -0.196306 q^{36} +11.2482 q^{37} +6.23629 q^{38} -2.33205 q^{39} -0.572222 q^{40} -3.81278 q^{41} +0.383948 q^{42} -4.03160 q^{43} -1.00000 q^{44} +0.112331 q^{45} +0.283546 q^{46} +1.60211 q^{47} -1.67442 q^{48} -6.94742 q^{49} -4.67256 q^{50} +4.95659 q^{51} +1.39275 q^{52} -0.559798 q^{53} +5.35197 q^{54} +0.572222 q^{55} -0.229301 q^{56} -10.4422 q^{57} -2.13992 q^{58} +3.35869 q^{59} +0.958143 q^{60} -5.56259 q^{61} -1.81886 q^{62} +0.0450132 q^{63} +1.00000 q^{64} -0.796963 q^{65} +1.67442 q^{66} -7.29496 q^{67} -2.96018 q^{68} -0.474776 q^{69} +0.131211 q^{70} +5.81690 q^{71} -0.196306 q^{72} -15.9763 q^{73} +11.2482 q^{74} +7.82385 q^{75} +6.23629 q^{76} +0.229301 q^{77} -2.33205 q^{78} -4.30809 q^{79} -0.572222 q^{80} -8.37255 q^{81} -3.81278 q^{82} -9.51503 q^{83} +0.383948 q^{84} +1.69388 q^{85} -4.03160 q^{86} +3.58312 q^{87} -1.00000 q^{88} -5.63164 q^{89} +0.112331 q^{90} -0.319360 q^{91} +0.283546 q^{92} +3.04554 q^{93} +1.60211 q^{94} -3.56854 q^{95} -1.67442 q^{96} +5.17365 q^{97} -6.94742 q^{98} +0.196306 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 17 q^{2} - 7 q^{3} + 17 q^{4} - 4 q^{5} - 7 q^{6} - 5 q^{7} + 17 q^{8} + 12 q^{9}+O(q^{10}) \) 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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