LMFDB - Embedded newform 4334.2.a.c.1.14

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} - 5 x^{16} - 19 x^{15} + 121 x^{14} + 112 x^{13} - 1172 x^{12} - 25 x^{11} + 5845 x^{10} + \cdots + 16 $ x^17 - 5x^16 - 19x^15 + 121x^14 + 112x^13 - 1172x^12 - 25x^11 + 5845x^10 - 2233x^9 - 16035x^8 + 9174x^7 + 23882x^6 - 15232x^5 - 17609x^4 + 10764x^3 + 4764x^2 - 2368x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$2.18116$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.18116 q^{3} +1.00000 q^{4} +4.06589 q^{5} -2.18116 q^{6} -1.87368 q^{7} -1.00000 q^{8} +1.75745 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.18116 q^{3} +1.00000 q^{4} +4.06589 q^{5} -2.18116 q^{6} -1.87368 q^{7} -1.00000 q^{8} +1.75745 q^{9} -4.06589 q^{10} -1.00000 q^{11} +2.18116 q^{12} -6.00627 q^{13} +1.87368 q^{14} +8.86835 q^{15} +1.00000 q^{16} -5.58917 q^{17} -1.75745 q^{18} -5.01739 q^{19} +4.06589 q^{20} -4.08679 q^{21} +1.00000 q^{22} -3.23213 q^{23} -2.18116 q^{24} +11.5315 q^{25} +6.00627 q^{26} -2.71020 q^{27} -1.87368 q^{28} -4.94777 q^{29} -8.86835 q^{30} -8.03723 q^{31} -1.00000 q^{32} -2.18116 q^{33} +5.58917 q^{34} -7.61818 q^{35} +1.75745 q^{36} -2.57350 q^{37} +5.01739 q^{38} -13.1006 q^{39} -4.06589 q^{40} +9.86578 q^{41} +4.08679 q^{42} +7.73185 q^{43} -1.00000 q^{44} +7.14560 q^{45} +3.23213 q^{46} +3.79248 q^{47} +2.18116 q^{48} -3.48932 q^{49} -11.5315 q^{50} -12.1909 q^{51} -6.00627 q^{52} -2.10424 q^{53} +2.71020 q^{54} -4.06589 q^{55} +1.87368 q^{56} -10.9437 q^{57} +4.94777 q^{58} -13.4652 q^{59} +8.86835 q^{60} -6.80937 q^{61} +8.03723 q^{62} -3.29290 q^{63} +1.00000 q^{64} -24.4208 q^{65} +2.18116 q^{66} +8.66634 q^{67} -5.58917 q^{68} -7.04978 q^{69} +7.61818 q^{70} +15.8383 q^{71} -1.75745 q^{72} +5.11266 q^{73} +2.57350 q^{74} +25.1520 q^{75} -5.01739 q^{76} +1.87368 q^{77} +13.1006 q^{78} +16.5262 q^{79} +4.06589 q^{80} -11.1837 q^{81} -9.86578 q^{82} -1.73384 q^{83} -4.08679 q^{84} -22.7250 q^{85} -7.73185 q^{86} -10.7919 q^{87} +1.00000 q^{88} -10.1689 q^{89} -7.14560 q^{90} +11.2538 q^{91} -3.23213 q^{92} -17.5305 q^{93} -3.79248 q^{94} -20.4002 q^{95} -2.18116 q^{96} -2.42584 q^{97} +3.48932 q^{98} -1.75745 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9}+O(q^{10}) $ 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9	\( 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9} - 6 q^{10} - 17 q^{11} + 5 q^{12} - 16 q^{13} + 9 q^{14} + 17 q^{16} - 8 q^{17} - 12 q^{18} - 23 q^{19} + 6 q^{20} - 15 q^{21} + 17 q^{22} + 12 q^{23} - 5 q^{24} + 11 q^{25} + 16 q^{26} + 17 q^{27} - 9 q^{28} - 8 q^{31} - 17 q^{32} - 5 q^{33} + 8 q^{34} + 6 q^{35} + 12 q^{36} - 7 q^{37} + 23 q^{38} - 9 q^{39} - 6 q^{40} - 27 q^{41} + 15 q^{42} - 13 q^{43} - 17 q^{44} - 11 q^{45} - 12 q^{46} + 23 q^{47} + 5 q^{48} - 8 q^{49} - 11 q^{50} - 40 q^{51} - 16 q^{52} + 14 q^{53} - 17 q^{54} - 6 q^{55} + 9 q^{56} - 18 q^{57} + 2 q^{59} - 49 q^{61} + 8 q^{62} - 42 q^{63} + 17 q^{64} - 57 q^{65} + 5 q^{66} - 5 q^{67} - 8 q^{68} - 9 q^{69} - 6 q^{70} - 5 q^{71} - 12 q^{72} - 54 q^{73} + 7 q^{74} + 7 q^{75} - 23 q^{76} + 9 q^{77} + 9 q^{78} - 11 q^{79} + 6 q^{80} - 35 q^{81} + 27 q^{82} - 8 q^{83} - 15 q^{84} - 65 q^{85} + 13 q^{86} - 20 q^{87} + 17 q^{88} - 9 q^{89} + 11 q^{90} - 9 q^{91} + 12 q^{92} - 50 q^{93} - 23 q^{94} - 27 q^{95} - 5 q^{96} - 42 q^{97} + 8 q^{98} - 12 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9 - 6 * q^10 - 17 * q^11 + 5 * q^12 - 16 * q^13 + 9 * q^14 + 17 * q^16 - 8 * q^17 - 12 * q^18 - 23 * q^19 + 6 * q^20 - 15 * q^21 + 17 * q^22 + 12 * q^23 - 5 * q^24 + 11 * q^25 + 16 * q^26 + 17 * q^27 - 9 * q^28 - 8 * q^31 - 17 * q^32 - 5 * q^33 + 8 * q^34 + 6 * q^35 + 12 * q^36 - 7 * q^37 + 23 * q^38 - 9 * q^39 - 6 * q^40 - 27 * q^41 + 15 * q^42 - 13 * q^43 - 17 * q^44 - 11 * q^45 - 12 * q^46 + 23 * q^47 + 5 * q^48 - 8 * q^49 - 11 * q^50 - 40 * q^51 - 16 * q^52 + 14 * q^53 - 17 * q^54 - 6 * q^55 + 9 * q^56 - 18 * q^57 + 2 * q^59 - 49 * q^61 + 8 * q^62 - 42 * q^63 + 17 * q^64 - 57 * q^65 + 5 * q^66 - 5 * q^67 - 8 * q^68 - 9 * q^69 - 6 * q^70 - 5 * q^71 - 12 * q^72 - 54 * q^73 + 7 * q^74 + 7 * q^75 - 23 * q^76 + 9 * q^77 + 9 * q^78 - 11 * q^79 + 6 * q^80 - 35 * q^81 + 27 * q^82 - 8 * q^83 - 15 * q^84 - 65 * q^85 + 13 * q^86 - 20 * q^87 + 17 * q^88 - 9 * q^89 + 11 * q^90 - 9 * q^91 + 12 * q^92 - 50 * q^93 - 23 * q^94 - 27 * q^95 - 5 * q^96 - 42 * 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
$3$	2.18116	1.25929	0.629646	−	0.776882i	$-0.283200\pi$
$3$	2.18116	1.25929	0.629646	+	0.776882i	$0.283200\pi$
$4$	1.00000	0.500000
$5$	4.06589	1.81832	0.909161	−	0.416444i	$-0.136724\pi$
$5$	4.06589	1.81832	0.909161	+	0.416444i	$0.136724\pi$
$6$	−2.18116	−0.890454
$7$	−1.87368	−0.708184	−0.354092	−	0.935211i	$-0.615210\pi$
$7$	−1.87368	−0.708184	−0.354092	+	0.935211i	$0.615210\pi$
$8$	−1.00000	−0.353553
$9$	1.75745	0.585817
$10$	−4.06589	−1.28575
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.18116	0.629646
$13$	−6.00627	−1.66584	−0.832919	−	0.553395i	$-0.813332\pi$
$13$	−6.00627	−1.66584	−0.832919	+	0.553395i	$0.813332\pi$
$14$	1.87368	0.500762
$15$	8.86835	2.28980
$16$	1.00000	0.250000
$17$	−5.58917	−1.35557	−0.677787	−	0.735258i	$-0.737061\pi$
$17$	−5.58917	−1.35557	−0.677787	+	0.735258i	$0.737061\pi$
$18$	−1.75745	−0.414235
$19$	−5.01739	−1.15107	−0.575534	−	0.817778i	$-0.695206\pi$
$19$	−5.01739	−1.15107	−0.575534	+	0.817778i	$0.695206\pi$
$20$	4.06589	0.909161
$21$	−4.08679	−0.891811
$22$	1.00000	0.213201
$23$	−3.23213	−0.673945	−0.336973	−	0.941514i	$-0.609403\pi$
$23$	−3.23213	−0.673945	−0.336973	+	0.941514i	$0.609403\pi$
$24$	−2.18116	−0.445227
$25$	11.5315	2.30630
$26$	6.00627	1.17793
$27$	−2.71020	−0.521578
$28$	−1.87368	−0.354092
$29$	−4.94777	−0.918777	−0.459389	−	0.888235i	$-0.651931\pi$
$29$	−4.94777	−0.918777	−0.459389	+	0.888235i	$0.651931\pi$
$30$	−8.86835	−1.61913
$31$	−8.03723	−1.44353	−0.721765	−	0.692139i	$-0.756669\pi$
$31$	−8.03723	−1.44353	−0.721765	+	0.692139i	$0.756669\pi$
$32$	−1.00000	−0.176777
$33$	−2.18116	−0.379691
$34$	5.58917	0.958535
$35$	−7.61818	−1.28771
$36$	1.75745	0.292908
$37$	−2.57350	−0.423081	−0.211540	−	0.977369i	$-0.567848\pi$
$37$	−2.57350	−0.423081	−0.211540	+	0.977369i	$0.567848\pi$
$38$	5.01739	0.813928
$39$	−13.1006	−2.09778
$40$	−4.06589	−0.642874
$41$	9.86578	1.54078	0.770388	−	0.637576i	$-0.220063\pi$
$41$	9.86578	1.54078	0.770388	+	0.637576i	$0.220063\pi$
$42$	4.08679	0.630606
$43$	7.73185	1.17910	0.589548	−	0.807733i	$-0.299306\pi$
$43$	7.73185	1.17910	0.589548	+	0.807733i	$0.299306\pi$
$44$	−1.00000	−0.150756
$45$	7.14560	1.06520
$46$	3.23213	0.476551
$47$	3.79248	0.553190	0.276595	−	0.960987i	$-0.410794\pi$
$47$	3.79248	0.553190	0.276595	+	0.960987i	$0.410794\pi$
$48$	2.18116	0.314823
$49$	−3.48932	−0.498475
$50$	−11.5315	−1.63080
$51$	−12.1909	−1.70706
$52$	−6.00627	−0.832919
$53$	−2.10424	−0.289039	−0.144520	−	0.989502i	$-0.546164\pi$
$53$	−2.10424	−0.289039	−0.144520	+	0.989502i	$0.546164\pi$
$54$	2.71020	0.368811
$55$	−4.06589	−0.548245
$56$	1.87368	0.250381
$57$	−10.9437	−1.44953
$58$	4.94777	0.649674
$59$	−13.4652	−1.75302	−0.876510	−	0.481384i	$-0.840134\pi$
$59$	−13.4652	−1.75302	−0.876510	+	0.481384i	$0.840134\pi$
$60$	8.86835	1.14490
$61$	−6.80937	−0.871850	−0.435925	−	0.899983i	$-0.643579\pi$
$61$	−6.80937	−0.871850	−0.435925	+	0.899983i	$0.643579\pi$
$62$	8.03723	1.02073
$63$	−3.29290	−0.414866
$64$	1.00000	0.125000
$65$	−24.4208	−3.02903
$66$	2.18116	0.268482
$67$	8.66634	1.05876	0.529381	−	0.848384i	$-0.322424\pi$
$67$	8.66634	1.05876	0.529381	+	0.848384i	$0.322424\pi$
$68$	−5.58917	−0.677787
$69$	−7.04978	−0.848694
$70$	7.61818	0.910547
$71$	15.8383	1.87967	0.939833	−	0.341634i	$-0.110980\pi$
$71$	15.8383	1.87967	0.939833	+	0.341634i	$0.110980\pi$
$72$	−1.75745	−0.207117
$73$	5.11266	0.598392	0.299196	−	0.954192i	$-0.403282\pi$
$73$	5.11266	0.598392	0.299196	+	0.954192i	$0.403282\pi$
$74$	2.57350	0.299163
$75$	25.1520	2.90430
$76$	−5.01739	−0.575534
$77$	1.87368	0.213526
$78$	13.1006	1.48335
$79$	16.5262	1.85934	0.929671	−	0.368390i	$-0.120091\pi$
$79$	16.5262	1.85934	0.929671	+	0.368390i	$0.120091\pi$
$80$	4.06589	0.454581
$81$	−11.1837	−1.24264
$82$	−9.86578	−1.08949
$83$	−1.73384	−0.190314	−0.0951571	−	0.995462i	$-0.530335\pi$
$83$	−1.73384	−0.190314	−0.0951571	+	0.995462i	$0.530335\pi$
$84$	−4.08679	−0.445906
$85$	−22.7250	−2.46487
$86$	−7.73185	−0.833747
$87$	−10.7919	−1.15701
$88$	1.00000	0.106600
$89$	−10.1689	−1.07790	−0.538948	−	0.842339i	$-0.681178\pi$
$89$	−10.1689	−1.07790	−0.538948	+	0.842339i	$0.681178\pi$
$90$	−7.14560	−0.753213
$91$	11.2538	1.17972
$92$	−3.23213	−0.336973
$93$	−17.5305	−1.81783
$94$	−3.79248	−0.391164
$95$	−20.4002	−2.09301
$96$	−2.18116	−0.222614
$97$	−2.42584	−0.246307	−0.123154	−	0.992388i	$-0.539301\pi$
$97$	−2.42584	−0.246307	−0.123154	+	0.992388i	$0.539301\pi$
$98$	3.48932	0.352475
$99$	−1.75745	−0.176630
$100$	11.5315	1.15315
$101$	7.22896	0.719308	0.359654	−	0.933086i	$-0.382895\pi$
$101$	7.22896	0.719308	0.359654	+	0.933086i	$0.382895\pi$
$102$	12.1909	1.20708
$103$	−1.53845	−0.151588	−0.0757942	−	0.997123i	$-0.524149\pi$
$103$	−1.53845	−0.151588	−0.0757942	+	0.997123i	$0.524149\pi$
$104$	6.00627	0.588963
$105$	−16.6165	−1.62160
$106$	2.10424	0.204382
$107$	−7.74471	−0.748709	−0.374355	−	0.927286i	$-0.622136\pi$
$107$	−7.74471	−0.748709	−0.374355	+	0.927286i	$0.622136\pi$
$108$	−2.71020	−0.260789
$109$	−1.90203	−0.182181	−0.0910906	−	0.995843i	$-0.529035\pi$
$109$	−1.90203	−0.182181	−0.0910906	+	0.995843i	$0.529035\pi$
$110$	4.06589	0.387668
$111$	−5.61321	−0.532783
$112$	−1.87368	−0.177046
$113$	−17.3199	−1.62931	−0.814657	−	0.579943i	$-0.803075\pi$
$113$	−17.3199	−1.62931	−0.814657	+	0.579943i	$0.803075\pi$
$114$	10.9437	1.02497
$115$	−13.1415	−1.22545
$116$	−4.94777	−0.459389
$117$	−10.5557	−0.975876
$118$	13.4652	1.23957
$119$	10.4723	0.959996
$120$	−8.86835	−0.809566
$121$	1.00000	0.0909091
$122$	6.80937	0.616491
$123$	21.5188	1.94029
$124$	−8.03723	−0.721765
$125$	26.5563	2.37527
$126$	3.29290	0.293355
$127$	−8.85269	−0.785549	−0.392774	−	0.919635i	$-0.628485\pi$
$127$	−8.85269	−0.785549	−0.392774	+	0.919635i	$0.628485\pi$
$128$	−1.00000	−0.0883883
$129$	16.8644	1.48483
$130$	24.4208	2.14185
$131$	−20.9243	−1.82817	−0.914084	−	0.405524i	$-0.867089\pi$
$131$	−20.9243	−1.82817	−0.914084	+	0.405524i	$0.867089\pi$
$132$	−2.18116	−0.189845
$133$	9.40098	0.815168
$134$	−8.66634	−0.748658
$135$	−11.0194	−0.948397
$136$	5.58917	0.479268
$137$	16.8779	1.44197	0.720987	−	0.692948i	$-0.243689\pi$
$137$	16.8779	1.44197	0.720987	+	0.692948i	$0.243689\pi$
$138$	7.04978	0.600117
$139$	20.2348	1.71629	0.858145	−	0.513407i	$-0.171617\pi$
$139$	20.2348	1.71629	0.858145	+	0.513407i	$0.171617\pi$
$140$	−7.61818	−0.643854
$141$	8.27199	0.696627
$142$	−15.8383	−1.32912
$143$	6.00627	0.502269
$144$	1.75745	0.146454
$145$	−20.1171	−1.67063
$146$	−5.11266	−0.423127
$147$	−7.61077	−0.627725
$148$	−2.57350	−0.211540
$149$	−15.9531	−1.30693	−0.653465	−	0.756957i	$-0.726685\pi$
$149$	−15.9531	−1.30693	−0.653465	+	0.756957i	$0.726685\pi$
$150$	−25.1520	−2.05365
$151$	13.7076	1.11551	0.557754	−	0.830007i	$-0.311663\pi$
$151$	13.7076	1.11551	0.557754	+	0.830007i	$0.311663\pi$
$152$	5.01739	0.406964
$153$	−9.82269	−0.794118
$154$	−1.87368	−0.150985
$155$	−32.6785	−2.62480
$156$	−13.1006	−1.04889
$157$	3.99929	0.319178	0.159589	−	0.987184i	$-0.448983\pi$
$157$	3.99929	0.319178	0.159589	+	0.987184i	$0.448983\pi$
$158$	−16.5262	−1.31475
$159$	−4.58968	−0.363985
$160$	−4.06589	−0.321437
$161$	6.05598	0.477278
$162$	11.1837	0.878676
$163$	0.303565	0.0237770	0.0118885	−	0.999929i	$-0.496216\pi$
$163$	0.303565	0.0237770	0.0118885	+	0.999929i	$0.496216\pi$
$164$	9.86578	0.770388
$165$	−8.86835	−0.690400
$166$	1.73384	0.134572
$167$	6.52698	0.505073	0.252536	−	0.967587i	$-0.418735\pi$
$167$	6.52698	0.505073	0.252536	+	0.967587i	$0.418735\pi$
$168$	4.08679	0.315303
$169$	23.0752	1.77502
$170$	22.7250	1.74293
$171$	−8.81781	−0.674315
$172$	7.73185	0.589548
$173$	19.5086	1.48321	0.741605	−	0.670837i	$-0.234065\pi$
$173$	19.5086	1.48321	0.741605	+	0.670837i	$0.234065\pi$
$174$	10.7919	0.818129
$175$	−21.6063	−1.63328
$176$	−1.00000	−0.0753778
$177$	−29.3697	−2.20756
$178$	10.1689	0.762188
$179$	−10.2202	−0.763896	−0.381948	−	0.924184i	$-0.624747\pi$
$179$	−10.2202	−0.763896	−0.381948	+	0.924184i	$0.624747\pi$
$180$	7.14560	0.532602
$181$	−11.2021	−0.832645	−0.416322	−	0.909217i	$-0.636681\pi$
$181$	−11.2021	−0.832645	−0.416322	+	0.909217i	$0.636681\pi$
$182$	−11.2538	−0.834189
$183$	−14.8523	−1.09791
$184$	3.23213	0.238276
$185$	−10.4636	−0.769298
$186$	17.5305	1.28540
$187$	5.58917	0.408721
$188$	3.79248	0.276595
$189$	5.07804	0.369373
$190$	20.4002	1.47998
$191$	4.70127	0.340172	0.170086	−	0.985429i	$-0.445595\pi$
$191$	4.70127	0.340172	0.170086	+	0.985429i	$0.445595\pi$
$192$	2.18116	0.157412
$193$	−23.3245	−1.67894	−0.839469	−	0.543408i	$-0.817134\pi$
$193$	−23.3245	−1.67894	−0.839469	+	0.543408i	$0.817134\pi$
$194$	2.42584	0.174165
$195$	−53.2657	−3.81444
$196$	−3.48932	−0.249237
$197$	−1.00000	−0.0712470
$197$	−1.00000	−0.0712470
$198$	1.75745	0.124897
$199$	−4.61639	−0.327247	−0.163624	−	0.986523i	$-0.552318\pi$
$199$	−4.61639	−0.327247	−0.163624	+	0.986523i	$0.552318\pi$
$200$	−11.5315	−0.815399
$201$	18.9027	1.33329
$202$	−7.22896	−0.508628
$203$	9.27053	0.650664
$204$	−12.1909	−0.853532
$205$	40.1132	2.80163
$206$	1.53845	0.107189
$207$	−5.68031	−0.394809
$208$	−6.00627	−0.416460
$209$	5.01739	0.347060
$210$	16.6165	1.14664
$211$	−7.40084	−0.509494	−0.254747	−	0.967008i	$-0.581992\pi$
$211$	−7.40084	−0.509494	−0.254747	+	0.967008i	$0.581992\pi$
$212$	−2.10424	−0.144520
$213$	34.5459	2.36705
$214$	7.74471	0.529417
$215$	31.4369	2.14398
$216$	2.71020	0.184406
$217$	15.0592	1.02229
$218$	1.90203	0.128821
$219$	11.1515	0.753550
$220$	−4.06589	−0.274122
$221$	33.5701	2.25817
$222$	5.61321	0.376734
$223$	22.2940	1.49292	0.746459	−	0.665432i	$-0.231753\pi$
$223$	22.2940	1.49292	0.746459	+	0.665432i	$0.231753\pi$
$224$	1.87368	0.125191
$225$	20.2660	1.35107
$226$	17.3199	1.15210
$227$	16.5920	1.10125	0.550626	−	0.834752i	$-0.314389\pi$
$227$	16.5920	1.10125	0.550626	+	0.834752i	$0.314389\pi$
$228$	−10.9437	−0.724765
$229$	−4.84592	−0.320228	−0.160114	−	0.987099i	$-0.551186\pi$
$229$	−4.84592	−0.320228	−0.160114	+	0.987099i	$0.551186\pi$
$230$	13.1415	0.866524
$231$	4.08679	0.268891
$232$	4.94777	0.324837
$233$	−13.6461	−0.893985	−0.446993	−	0.894538i	$-0.647505\pi$
$233$	−13.6461	−0.893985	−0.446993	+	0.894538i	$0.647505\pi$
$234$	10.5557	0.690048
$235$	15.4198	1.00588
$236$	−13.4652	−0.876510
$237$	36.0462	2.34146
$238$	−10.4723	−0.678820
$239$	5.72010	0.370003	0.185001	−	0.982738i	$-0.440771\pi$
$239$	5.72010	0.370003	0.185001	+	0.982738i	$0.440771\pi$
$240$	8.86835	0.572450
$241$	7.80759	0.502931	0.251465	−	0.967866i	$-0.419088\pi$
$241$	7.80759	0.502931	0.251465	+	0.967866i	$0.419088\pi$
$242$	−1.00000	−0.0642824
$243$	−16.2629	−1.04326
$244$	−6.80937	−0.435925
$245$	−14.1872	−0.906388
$246$	−21.5188	−1.37199
$247$	30.1358	1.91749
$248$	8.03723	0.510365
$249$	−3.78179	−0.239661
$250$	−26.5563	−1.67957
$251$	27.4196	1.73071	0.865354	−	0.501161i	$-0.167093\pi$
$251$	27.4196	1.73071	0.865354	+	0.501161i	$0.167093\pi$
$252$	−3.29290	−0.207433
$253$	3.23213	0.203202
$254$	8.85269	0.555467
$255$	−49.5668	−3.10399
$256$	1.00000	0.0625000
$257$	−6.12661	−0.382167	−0.191084	−	0.981574i	$-0.561200\pi$
$257$	−6.12661	−0.382167	−0.191084	+	0.981574i	$0.561200\pi$
$258$	−16.8644	−1.04993
$259$	4.82192	0.299619
$260$	−24.4208	−1.51452
$261$	−8.69545	−0.538235
$262$	20.9243	1.29271
$263$	3.14555	0.193963	0.0969813	−	0.995286i	$-0.469081\pi$
$263$	3.14555	0.193963	0.0969813	+	0.995286i	$0.469081\pi$
$264$	2.18116	0.134241
$265$	−8.55561	−0.525567
$266$	−9.40098	−0.576411
$267$	−22.1799	−1.35739
$268$	8.66634	0.529381
$269$	−7.80341	−0.475783	−0.237891	−	0.971292i	$-0.576456\pi$
$269$	−7.80341	−0.475783	−0.237891	+	0.971292i	$0.576456\pi$
$270$	11.0194	0.670618
$271$	−25.2844	−1.53592	−0.767958	−	0.640500i	$-0.778727\pi$
$271$	−25.2844	−1.53592	−0.767958	+	0.640500i	$0.778727\pi$
$272$	−5.58917	−0.338893
$273$	24.5464	1.48561
$274$	−16.8779	−1.01963
$275$	−11.5315	−0.695375
$276$	−7.04978	−0.424347
$277$	23.3902	1.40538	0.702689	−	0.711497i	$-0.251982\pi$
$277$	23.3902	1.40538	0.702689	+	0.711497i	$0.251982\pi$
$278$	−20.2348	−1.21360
$279$	−14.1250	−0.845644
$280$	7.61818	0.455273
$281$	−7.05567	−0.420906	−0.210453	−	0.977604i	$-0.567494\pi$
$281$	−7.05567	−0.420906	−0.210453	+	0.977604i	$0.567494\pi$
$282$	−8.27199	−0.492590
$283$	0.310870	0.0184793	0.00923965	−	0.999957i	$-0.497059\pi$
$283$	0.310870	0.0184793	0.00923965	+	0.999957i	$0.497059\pi$
$284$	15.8383	0.939833
$285$	−44.4960	−2.63571
$286$	−6.00627	−0.355158
$287$	−18.4853	−1.09115
$288$	−1.75745	−0.103559
$289$	14.2389	0.837581
$290$	20.1171	1.18132
$291$	−5.29115	−0.310172
$292$	5.11266	0.299196
$293$	26.6602	1.55751	0.778753	−	0.627330i	$-0.215852\pi$
$293$	26.6602	1.55751	0.778753	+	0.627330i	$0.215852\pi$
$294$	7.61077	0.443869
$295$	−54.7481	−3.18755
$296$	2.57350	0.149582
$297$	2.71020	0.157262
$298$	15.9531	0.924139
$299$	19.4130	1.12268
$300$	25.1520	1.45215
$301$	−14.4870	−0.835018
$302$	−13.7076	−0.788783
$303$	15.7675	0.905819
$304$	−5.01739	−0.287767
$305$	−27.6862	−1.58530
$306$	9.82269	0.561526
$307$	10.5098	0.599823	0.299912	−	0.953967i	$-0.403043\pi$
$307$	10.5098	0.599823	0.299912	+	0.953967i	$0.403043\pi$
$308$	1.87368	0.106763
$309$	−3.35561	−0.190894
$310$	32.6785	1.85602
$311$	−22.1835	−1.25791	−0.628957	−	0.777440i	$-0.716518\pi$
$311$	−22.1835	−1.25791	−0.628957	+	0.777440i	$0.716518\pi$
$312$	13.1006	0.741676
$313$	6.56662	0.371167	0.185584	−	0.982628i	$-0.440582\pi$
$313$	6.56662	0.371167	0.185584	+	0.982628i	$0.440582\pi$
$314$	−3.99929	−0.225693
$315$	−13.3886	−0.754361
$316$	16.5262	0.929671
$317$	26.5182	1.48941	0.744705	−	0.667394i	$-0.232590\pi$
$317$	26.5182	1.48941	0.744705	+	0.667394i	$0.232590\pi$
$318$	4.58968	0.257376
$319$	4.94777	0.277022
$320$	4.06589	0.227290
$321$	−16.8924	−0.942844
$322$	−6.05598	−0.337486
$323$	28.0430	1.56036
$324$	−11.1837	−0.621318
$325$	−69.2612	−3.84192
$326$	−0.303565	−0.0168129
$327$	−4.14862	−0.229419
$328$	−9.86578	−0.544746
$329$	−7.10589	−0.391760
$330$	8.86835	0.488187
$331$	13.6354	0.749470	0.374735	−	0.927132i	$-0.377734\pi$
$331$	13.6354	0.749470	0.374735	+	0.927132i	$0.377734\pi$
$332$	−1.73384	−0.0951571
$333$	−4.52280	−0.247848
$334$	−6.52698	−0.357141
$335$	35.2364	1.92517
$336$	−4.08679	−0.222953
$337$	8.34144	0.454387	0.227194	−	0.973850i	$-0.427045\pi$
$337$	8.34144	0.454387	0.227194	+	0.973850i	$0.427045\pi$
$338$	−23.0752	−1.25513
$339$	−37.7773	−2.05178
$340$	−22.7250	−1.23244
$341$	8.03723	0.435240
$342$	8.81781	0.476812
$343$	19.6536	1.06120
$344$	−7.73185	−0.416874
$345$	−28.6637	−1.54320
$346$	−19.5086	−1.04879
$347$	9.90408	0.531679	0.265839	−	0.964017i	$-0.414351\pi$
$347$	9.90408	0.531679	0.265839	+	0.964017i	$0.414351\pi$
$348$	−10.7919	−0.578505
$349$	−25.9365	−1.38835	−0.694174	−	0.719808i	$-0.744230\pi$
$349$	−25.9365	−1.38835	−0.694174	+	0.719808i	$0.744230\pi$
$350$	21.6063	1.15491
$351$	16.2782	0.868864
$352$	1.00000	0.0533002
$353$	−22.3697	−1.19062	−0.595308	−	0.803497i	$-0.702970\pi$
$353$	−22.3697	−1.19062	−0.595308	+	0.803497i	$0.702970\pi$
$354$	29.3697	1.56098
$355$	64.3970	3.41784
$356$	−10.1689	−0.538948
$357$	22.8418	1.20892
$358$	10.2202	0.540156
$359$	−24.3249	−1.28382	−0.641910	−	0.766780i	$-0.721858\pi$
$359$	−24.3249	−1.28382	−0.641910	+	0.766780i	$0.721858\pi$
$360$	−7.14560	−0.376606
$361$	6.17417	0.324956
$362$	11.2021	0.588769
$363$	2.18116	0.114481
$364$	11.2538	0.589860
$365$	20.7875	1.08807
$366$	14.8523	0.776342
$367$	0.766009	0.0399853	0.0199927	−	0.999800i	$-0.493636\pi$
$367$	0.766009	0.0399853	0.0199927	+	0.999800i	$0.493636\pi$
$368$	−3.23213	−0.168486
$369$	17.3386	0.902612
$370$	10.4636	0.543976
$371$	3.94267	0.204693
$372$	−17.5305	−0.908913
$373$	−9.04186	−0.468170	−0.234085	−	0.972216i	$-0.575209\pi$
$373$	−9.04186	−0.468170	−0.234085	+	0.972216i	$0.575209\pi$
$374$	−5.58917	−0.289009
$375$	57.9235	2.99116
$376$	−3.79248	−0.195582
$377$	29.7176	1.53053
$378$	−5.07804	−0.261186
$379$	−16.9857	−0.872499	−0.436249	−	0.899826i	$-0.643693\pi$
$379$	−16.9857	−0.872499	−0.436249	+	0.899826i	$0.643693\pi$
$380$	−20.4002	−1.04651
$381$	−19.3091	−0.989236
$382$	−4.70127	−0.240538
$383$	−3.65359	−0.186690	−0.0933449	−	0.995634i	$-0.529756\pi$
$383$	−3.65359	−0.186690	−0.0933449	+	0.995634i	$0.529756\pi$
$384$	−2.18116	−0.111307
$385$	7.61818	0.388259
$386$	23.3245	1.18719
$387$	13.5883	0.690734
$388$	−2.42584	−0.123154
$389$	−14.6928	−0.744956	−0.372478	−	0.928041i	$-0.621492\pi$
$389$	−14.6928	−0.744956	−0.372478	+	0.928041i	$0.621492\pi$
$390$	53.2657	2.69721
$391$	18.0649	0.913583
$392$	3.48932	0.176237
$393$	−45.6393	−2.30220
$394$	1.00000	0.0503793
$395$	67.1938	3.38088
$396$	−1.75745	−0.0883152
$397$	−7.21915	−0.362319	−0.181159	−	0.983454i	$-0.557985\pi$
$397$	−7.21915	−0.362319	−0.181159	+	0.983454i	$0.557985\pi$
$398$	4.61639	0.231399
$399$	20.5050	1.02653
$400$	11.5315	0.576574
$401$	−26.7889	−1.33777	−0.668887	−	0.743364i	$-0.733229\pi$
$401$	−26.7889	−1.33777	−0.668887	+	0.743364i	$0.733229\pi$
$402$	−18.9027	−0.942779
$403$	48.2737	2.40469
$404$	7.22896	0.359654
$405$	−45.4718	−2.25951
$406$	−9.27053	−0.460089
$407$	2.57350	0.127564
$408$	12.1909	0.603538
$409$	24.0498	1.18918	0.594592	−	0.804027i	$-0.297314\pi$
$409$	24.0498	1.18918	0.594592	+	0.804027i	$0.297314\pi$
$410$	−40.1132	−1.98105
$411$	36.8133	1.81587
$412$	−1.53845	−0.0757942
$413$	25.2295	1.24146
$414$	5.68031	0.279172
$415$	−7.04963	−0.346053
$416$	6.00627	0.294481
$417$	44.1352	2.16131
$418$	−5.01739	−0.245408
$419$	−31.3519	−1.53164	−0.765821	−	0.643054i	$-0.777667\pi$
$419$	−31.3519	−1.53164	−0.765821	+	0.643054i	$0.777667\pi$
$420$	−16.6165	−0.810800
$421$	−10.8632	−0.529438	−0.264719	−	0.964326i	$-0.585279\pi$
$421$	−10.8632	−0.529438	−0.264719	+	0.964326i	$0.585279\pi$
$422$	7.40084	0.360267
$423$	6.66509	0.324068
$424$	2.10424	0.102191
$425$	−64.4515	−3.12636
$426$	−34.5459	−1.67376
$427$	12.7586	0.617431
$428$	−7.74471	−0.374355
$429$	13.1006	0.632504
$430$	−31.4369	−1.51602
$431$	9.13949	0.440234	0.220117	−	0.975473i	$-0.429356\pi$
$431$	9.13949	0.440234	0.220117	+	0.975473i	$0.429356\pi$
$432$	−2.71020	−0.130394
$433$	−14.3588	−0.690042	−0.345021	−	0.938595i	$-0.612128\pi$
$433$	−14.3588	−0.690042	−0.345021	+	0.938595i	$0.612128\pi$
$434$	−15.0592	−0.722865
$435$	−43.8786	−2.10382
$436$	−1.90203	−0.0910906
$437$	16.2168	0.775757
$438$	−11.1515	−0.532841
$439$	−14.8707	−0.709739	−0.354870	−	0.934916i	$-0.615475\pi$
$439$	−14.8707	−0.709739	−0.354870	+	0.934916i	$0.615475\pi$
$440$	4.06589	0.193834
$441$	−6.13231	−0.292015
$442$	−33.5701	−1.59677
$443$	−4.42144	−0.210069	−0.105034	−	0.994469i	$-0.533495\pi$
$443$	−4.42144	−0.210069	−0.105034	+	0.994469i	$0.533495\pi$
$444$	−5.61321	−0.266391
$445$	−41.3455	−1.95996
$446$	−22.2940	−1.05565
$447$	−34.7963	−1.64581
$448$	−1.87368	−0.0885231
$449$	−17.9042	−0.844954	−0.422477	−	0.906374i	$-0.638839\pi$
$449$	−17.9042	−0.844954	−0.422477	+	0.906374i	$0.638839\pi$
$450$	−20.2660	−0.955349
$451$	−9.86578	−0.464561
$452$	−17.3199	−0.814657
$453$	29.8984	1.40475
$454$	−16.5920	−0.778702
$455$	45.7568	2.14511
$456$	10.9437	0.512486
$457$	−39.1112	−1.82954	−0.914772	−	0.403970i	$-0.867630\pi$
$457$	−39.1112	−1.82954	−0.914772	+	0.403970i	$0.867630\pi$
$458$	4.84592	0.226435
$459$	15.1478	0.707037
$460$	−13.1415	−0.612725
$461$	6.42637	0.299306	0.149653	−	0.988739i	$-0.452184\pi$
$461$	6.42637	0.299306	0.149653	+	0.988739i	$0.452184\pi$
$462$	−4.08679	−0.190135
$463$	−36.9404	−1.71677	−0.858384	−	0.513008i	$-0.828531\pi$
$463$	−36.9404	−1.71677	−0.858384	+	0.513008i	$0.828531\pi$
$464$	−4.94777	−0.229694
$465$	−71.2770	−3.30539
$466$	13.6461	0.632143
$467$	28.3737	1.31298	0.656490	−	0.754335i	$-0.272040\pi$
$467$	28.3737	1.31298	0.656490	+	0.754335i	$0.272040\pi$
$468$	−10.5557	−0.487938
$469$	−16.2379	−0.749799
$470$	−15.4198	−0.711263
$471$	8.72308	0.401938
$472$	13.4652	0.619786
$473$	−7.73185	−0.355511
$474$	−36.0462	−1.65566
$475$	−57.8579	−2.65470
$476$	10.4723	0.479998
$477$	−3.69809	−0.169324
$478$	−5.72010	−0.261631
$479$	−40.2392	−1.83858	−0.919288	−	0.393585i	$-0.871235\pi$
$479$	−40.2392	−1.83858	−0.919288	+	0.393585i	$0.871235\pi$
$480$	−8.86835	−0.404783
$481$	15.4571	0.704785
$482$	−7.80759	−0.355626
$483$	13.2090	0.601032
$484$	1.00000	0.0454545
$485$	−9.86322	−0.447866
$486$	16.2629	0.737699
$487$	12.8422	0.581938	0.290969	−	0.956733i	$-0.406022\pi$
$487$	12.8422	0.581938	0.290969	+	0.956733i	$0.406022\pi$
$488$	6.80937	0.308246
$489$	0.662123	0.0299422
$490$	14.1872	0.640913
$491$	19.1974	0.866368	0.433184	−	0.901306i	$-0.357390\pi$
$491$	19.1974	0.866368	0.433184	+	0.901306i	$0.357390\pi$
$492$	21.5188	0.970143
$493$	27.6539	1.24547
$494$	−30.1358	−1.35587
$495$	−7.14560	−0.321171
$496$	−8.03723	−0.360882
$497$	−29.6760	−1.33115
$498$	3.78179	0.169466
$499$	35.2555	1.57825	0.789126	−	0.614232i	$-0.210534\pi$
$499$	35.2555	1.57825	0.789126	+	0.614232i	$0.210534\pi$
$500$	26.5563	1.18763
$501$	14.2364	0.636034
$502$	−27.4196	−1.22380
$503$	−6.90510	−0.307883	−0.153942	−	0.988080i	$-0.549197\pi$
$503$	−6.90510	−0.307883	−0.153942	+	0.988080i	$0.549197\pi$
$504$	3.29290	0.146677
$505$	29.3922	1.30793
$506$	−3.23213	−0.143686
$507$	50.3307	2.23527
$508$	−8.85269	−0.392774
$509$	−35.4256	−1.57021	−0.785105	−	0.619362i	$-0.787391\pi$
$509$	−35.4256	−1.57021	−0.785105	+	0.619362i	$0.787391\pi$
$510$	49.5668	2.19485
$511$	−9.57950	−0.423772
$512$	−1.00000	−0.0441942
$513$	13.5981	0.600371
$514$	6.12661	0.270233
$515$	−6.25519	−0.275637
$516$	16.8644	0.742413
$517$	−3.79248	−0.166793
$518$	−4.82192	−0.211863
$519$	42.5513	1.86779
$520$	24.4208	1.07092
$521$	17.9532	0.786543	0.393271	−	0.919422i	$-0.371343\pi$
$521$	17.9532	0.786543	0.393271	+	0.919422i	$0.371343\pi$
$522$	8.69545	0.380590
$523$	−39.5232	−1.72823	−0.864115	−	0.503294i	$-0.832121\pi$
$523$	−39.5232	−1.72823	−0.864115	+	0.503294i	$0.832121\pi$
$524$	−20.9243	−0.914084
$525$	−47.1268	−2.05678
$526$	−3.14555	−0.137152
$527$	44.9215	1.95681
$528$	−2.18116	−0.0949227
$529$	−12.5533	−0.545797
$530$	8.55561	0.371632
$531$	−23.6644	−1.02695
$532$	9.40098	0.407584
$533$	−59.2565	−2.56668
$534$	22.1799	0.959817
$535$	−31.4892	−1.36139
$536$	−8.66634	−0.374329
$537$	−22.2920	−0.961969
$538$	7.80341	0.336429
$539$	3.48932	0.150296
$540$	−11.0194	−0.474198
$541$	−21.7403	−0.934690	−0.467345	−	0.884075i	$-0.654789\pi$
$541$	−21.7403	−0.934690	−0.467345	+	0.884075i	$0.654789\pi$
$542$	25.2844	1.08606
$543$	−24.4335	−1.04854
$544$	5.58917	0.239634
$545$	−7.73344	−0.331264
$546$	−24.5464	−1.05049
$547$	23.7056	1.01358	0.506789	−	0.862070i	$-0.330832\pi$
$547$	23.7056	1.01358	0.506789	+	0.862070i	$0.330832\pi$
$548$	16.8779	0.720987
$549$	−11.9671	−0.510744
$550$	11.5315	0.491704
$551$	24.8249	1.05757
$552$	7.04978	0.300059
$553$	−30.9648	−1.31676
$554$	−23.3902	−0.993753
$555$	−22.8227	−0.968771
$556$	20.2348	0.858145
$557$	−23.3826	−0.990751	−0.495375	−	0.868679i	$-0.664969\pi$
$557$	−23.3826	−0.990751	−0.495375	+	0.868679i	$0.664969\pi$
$558$	14.1250	0.597960
$559$	−46.4396	−1.96418
$560$	−7.61818	−0.321927
$561$	12.1909	0.514699
$562$	7.05567	0.297625
$563$	2.72365	0.114788	0.0573941	−	0.998352i	$-0.481721\pi$
$563$	2.72365	0.114788	0.0573941	+	0.998352i	$0.481721\pi$
$564$	8.27199	0.348314
$565$	−70.4207	−2.96262
$566$	−0.310870	−0.0130668
$567$	20.9547	0.880015
$568$	−15.8383	−0.664562
$569$	29.0501	1.21784	0.608921	−	0.793231i	$-0.291602\pi$
$569$	29.0501	1.21784	0.608921	+	0.793231i	$0.291602\pi$
$570$	44.4960	1.86373
$571$	−13.0227	−0.544982	−0.272491	−	0.962158i	$-0.587847\pi$
$571$	−13.0227	−0.544982	−0.272491	+	0.962158i	$0.587847\pi$
$572$	6.00627	0.251135
$573$	10.2542	0.428376
$574$	18.4853	0.771562
$575$	−37.2712	−1.55432
$576$	1.75745	0.0732271
$577$	3.64794	0.151866	0.0759328	−	0.997113i	$-0.475807\pi$
$577$	3.64794	0.151866	0.0759328	+	0.997113i	$0.475807\pi$
$578$	−14.2389	−0.592259
$579$	−50.8745	−2.11427
$580$	−20.1171	−0.835317
$581$	3.24867	0.134778
$582$	5.29115	0.219325
$583$	2.10424	0.0871487
$584$	−5.11266	−0.211564
$585$	−42.9184	−1.77446
$586$	−26.6602	−1.10132
$587$	−11.5470	−0.476594	−0.238297	−	0.971192i	$-0.576589\pi$
$587$	−11.5470	−0.476594	−0.238297	+	0.971192i	$0.576589\pi$
$588$	−7.61077	−0.313863
$589$	40.3259	1.66160
$590$	54.7481	2.25394
$591$	−2.18116	−0.0897208
$592$	−2.57350	−0.105770
$593$	−28.1824	−1.15731	−0.578657	−	0.815571i	$-0.696423\pi$
$593$	−28.1824	−1.15731	−0.578657	+	0.815571i	$0.696423\pi$
$594$	−2.71020	−0.111201
$595$	42.5793	1.74558
$596$	−15.9531	−0.653465
$597$	−10.0691	−0.412100
$598$	−19.4130	−0.793858
$599$	−18.4198	−0.752614	−0.376307	−	0.926495i	$-0.622806\pi$
$599$	−18.4198	−0.752614	−0.376307	+	0.926495i	$0.622806\pi$
$600$	−25.1520	−1.02683
$601$	−31.9562	−1.30352	−0.651760	−	0.758425i	$-0.725969\pi$
$601$	−31.9562	−1.30352	−0.651760	+	0.758425i	$0.725969\pi$
$602$	14.4870	0.590447
$603$	15.2307	0.620240
$604$	13.7076	0.557754
$605$	4.06589	0.165302
$606$	−15.7675	−0.640511
$607$	35.4105	1.43727	0.718633	−	0.695390i	$-0.244768\pi$
$607$	35.4105	1.43727	0.718633	+	0.695390i	$0.244768\pi$
$608$	5.01739	0.203482
$609$	20.2205	0.819376
$610$	27.6862	1.12098
$611$	−22.7786	−0.921524
$612$	−9.82269	−0.397059
$613$	−5.97164	−0.241192	−0.120596	−	0.992702i	$-0.538481\pi$
$613$	−5.97164	−0.241192	−0.120596	+	0.992702i	$0.538481\pi$
$614$	−10.5098	−0.424139
$615$	87.4932	3.52807
$616$	−1.87368	−0.0754927
$617$	−0.516703	−0.0208017	−0.0104008	−	0.999946i	$-0.503311\pi$
$617$	−0.516703	−0.0208017	−0.0104008	+	0.999946i	$0.503311\pi$
$618$	3.35561	0.134983
$619$	−1.55593	−0.0625381	−0.0312691	−	0.999511i	$-0.509955\pi$
$619$	−1.55593	−0.0625381	−0.0312691	+	0.999511i	$0.509955\pi$
$620$	−32.6785	−1.31240
$621$	8.75971	0.351515
$622$	22.1835	0.889479
$623$	19.0532	0.763350
$624$	−13.1006	−0.524444
$625$	50.3177	2.01271
$626$	−6.56662	−0.262455
$627$	10.9437	0.437050
$628$	3.99929	0.159589
$629$	14.3837	0.573518
$630$	13.3886	0.533414
$631$	−24.4518	−0.973410	−0.486705	−	0.873566i	$-0.661801\pi$
$631$	−24.4518	−0.973410	−0.486705	+	0.873566i	$0.661801\pi$
$632$	−16.5262	−0.657377
$633$	−16.1424	−0.641602
$634$	−26.5182	−1.05317
$635$	−35.9941	−1.42838
$636$	−4.58968	−0.181993
$637$	20.9578	0.830378
$638$	−4.94777	−0.195884
$639$	27.8351	1.10114
$640$	−4.06589	−0.160719
$641$	22.6081	0.892965	0.446483	−	0.894792i	$-0.352676\pi$
$641$	22.6081	0.892965	0.446483	+	0.894792i	$0.352676\pi$
$642$	16.8924	0.666691
$643$	−34.0180	−1.34154	−0.670770	−	0.741666i	$-0.734036\pi$
$643$	−34.0180	−1.34154	−0.670770	+	0.741666i	$0.734036\pi$
$644$	6.05598	0.238639
$645$	68.5688	2.69989
$646$	−28.0430	−1.10334
$647$	−28.2683	−1.11134	−0.555671	−	0.831402i	$-0.687539\pi$
$647$	−28.2683	−1.11134	−0.555671	+	0.831402i	$0.687539\pi$
$648$	11.1837	0.439338
$649$	13.4652	0.528555
$650$	69.2612	2.71665
$651$	32.8465	1.28736
$652$	0.303565	0.0118885
$653$	−41.6550	−1.63009	−0.815043	−	0.579401i	$-0.803287\pi$
$653$	−41.6550	−1.63009	−0.815043	+	0.579401i	$0.803287\pi$
$654$	4.14862	0.162224
$655$	−85.0762	−3.32420
$656$	9.86578	0.385194
$657$	8.98525	0.350548
$658$	7.10589	0.277016
$659$	27.0930	1.05539	0.527697	−	0.849433i	$-0.323056\pi$
$659$	27.0930	1.05539	0.527697	+	0.849433i	$0.323056\pi$
$660$	−8.86835	−0.345200
$661$	26.9290	1.04742	0.523708	−	0.851898i	$-0.324548\pi$
$661$	26.9290	1.04742	0.523708	+	0.851898i	$0.324548\pi$
$662$	−13.6354	−0.529955
$663$	73.2216	2.84369
$664$	1.73384	0.0672862
$665$	38.2234	1.48224
$666$	4.52280	0.175255
$667$	15.9918	0.619206
$668$	6.52698	0.252536
$669$	48.6268	1.88002
$670$	−35.2364	−1.36130
$671$	6.80937	0.262873
$672$	4.08679	0.157651
$673$	−27.3846	−1.05560	−0.527800	−	0.849369i	$-0.676983\pi$
$673$	−27.3846	−1.05560	−0.527800	+	0.849369i	$0.676983\pi$
$674$	−8.34144	−0.321300
$675$	−31.2526	−1.20291
$676$	23.0752	0.887509
$677$	23.5336	0.904469	0.452235	−	0.891899i	$-0.350627\pi$
$677$	23.5336	0.904469	0.452235	+	0.891899i	$0.350627\pi$
$678$	37.7773	1.45083
$679$	4.54525	0.174431
$680$	22.7250	0.871463
$681$	36.1898	1.38680
$682$	−8.03723	−0.307761
$683$	39.7735	1.52189	0.760945	−	0.648816i	$-0.224736\pi$
$683$	39.7735	1.52189	0.760945	+	0.648816i	$0.224736\pi$
$684$	−8.81781	−0.337157
$685$	68.6237	2.62198
$686$	−19.6536	−0.750379
$687$	−10.5697	−0.403260
$688$	7.73185	0.294774
$689$	12.6386	0.481493
$690$	28.6637	1.09121
$691$	−47.5208	−1.80778	−0.903888	−	0.427769i	$-0.859300\pi$
$691$	−47.5208	−1.80778	−0.903888	+	0.427769i	$0.859300\pi$
$692$	19.5086	0.741605
$693$	3.29290	0.125087
$694$	−9.90408	−0.375954
$695$	82.2724	3.12077
$696$	10.7919	0.409064
$697$	−55.1415	−2.08864
$698$	25.9365	0.981710
$699$	−29.7643	−1.12579
$700$	−21.6063	−0.816642
$701$	48.2342	1.82178	0.910891	−	0.412647i	$-0.135396\pi$
$701$	48.2342	1.82178	0.910891	+	0.412647i	$0.135396\pi$
$702$	−16.2782	−0.614380
$703$	12.9123	0.486995
$704$	−1.00000	−0.0376889
$705$	33.6330	1.26669
$706$	22.3697	0.841893
$707$	−13.5448	−0.509403
$708$	−29.3697	−1.10378
$709$	−8.53838	−0.320665	−0.160333	−	0.987063i	$-0.551257\pi$
$709$	−8.53838	−0.320665	−0.160333	+	0.987063i	$0.551257\pi$
$710$	−64.3970	−2.41678
$711$	29.0440	1.08923
$712$	10.1689	0.381094
$713$	25.9774	0.972860
$714$	−22.8418	−0.854833
$715$	24.4208	0.913287
$716$	−10.2202	−0.381948
$717$	12.4764	0.465941
$718$	24.3249	0.907797
$719$	−14.2309	−0.530724	−0.265362	−	0.964149i	$-0.585492\pi$
$719$	−14.2309	−0.530724	−0.265362	+	0.964149i	$0.585492\pi$
$720$	7.14560	0.266301
$721$	2.88257	0.107353
$722$	−6.17417	−0.229779
$723$	17.0296	0.633337
$724$	−11.2021	−0.416322
$725$	−57.0551	−2.11897
$726$	−2.18116	−0.0809504
$727$	−26.7954	−0.993785	−0.496893	−	0.867812i	$-0.665526\pi$
$727$	−26.7954	−0.993785	−0.496893	+	0.867812i	$0.665526\pi$
$728$	−11.2538	−0.417094
$729$	−1.92072	−0.0711378
$730$	−20.7875	−0.769382
$731$	−43.2147	−1.59835
$732$	−14.8523	−0.548957
$733$	−9.80216	−0.362051	−0.181026	−	0.983478i	$-0.557942\pi$
$733$	−9.80216	−0.362051	−0.181026	+	0.983478i	$0.557942\pi$
$734$	−0.766009	−0.0282739
$735$	−30.9446	−1.14141
$736$	3.23213	0.119138
$737$	−8.66634	−0.319229
$738$	−17.3386	−0.638243
$739$	−6.21175	−0.228503	−0.114251	−	0.993452i	$-0.536447\pi$
$739$	−6.21175	−0.228503	−0.114251	+	0.993452i	$0.536447\pi$
$740$	−10.4636	−0.384649
$741$	65.7308	2.41468
$742$	−3.94267	−0.144740
$743$	−11.7126	−0.429692	−0.214846	−	0.976648i	$-0.568925\pi$
$743$	−11.7126	−0.429692	−0.214846	+	0.976648i	$0.568925\pi$
$744$	17.5305	0.642698
$745$	−64.8637	−2.37642
$746$	9.04186	0.331046
$747$	−3.04715	−0.111489
$748$	5.58917	0.204360
$749$	14.5111	0.530224
$750$	−57.9235	−2.11507
$751$	−3.93235	−0.143494	−0.0717468	−	0.997423i	$-0.522857\pi$
$751$	−3.93235	−0.143494	−0.0717468	+	0.997423i	$0.522857\pi$
$752$	3.79248	0.138297
$753$	59.8064	2.17947
$754$	−29.7176	−1.08225
$755$	55.7336	2.02835
$756$	5.07804	0.184687
$757$	−16.3320	−0.593596	−0.296798	−	0.954940i	$-0.595919\pi$
$757$	−16.3320	−0.593596	−0.296798	+	0.954940i	$0.595919\pi$
$758$	16.9857	0.616950
$759$	7.04978	0.255891
$760$	20.4002	0.739991
$761$	15.2370	0.552341	0.276170	−	0.961109i	$-0.410935\pi$
$761$	15.2370	0.552341	0.276170	+	0.961109i	$0.410935\pi$
$762$	19.3091	0.699495
$763$	3.56379	0.129018
$764$	4.70127	0.170086
$765$	−39.9380	−1.44396
$766$	3.65359	0.132010
$767$	80.8756	2.92025
$768$	2.18116	0.0787058
$769$	−16.2075	−0.584457	−0.292228	−	0.956349i	$-0.594397\pi$
$769$	−16.2075	−0.584457	−0.292228	+	0.956349i	$0.594397\pi$
$770$	−7.61818	−0.274540
$771$	−13.3631	−0.481260
$772$	−23.3245	−0.839469
$773$	28.7655	1.03462	0.517311	−	0.855797i	$-0.326933\pi$
$773$	28.7655	1.03462	0.517311	+	0.855797i	$0.326933\pi$
$774$	−13.5883	−0.488423
$775$	−92.6812	−3.32921
$776$	2.42584	0.0870827
$777$	10.5174	0.377308
$778$	14.6928	0.526764
$779$	−49.5004	−1.77354
$780$	−53.2657	−1.90722
$781$	−15.8383	−0.566741
$782$	−18.0649	−0.646001
$783$	13.4094	0.479214
$784$	−3.48932	−0.124619
$785$	16.2607	0.580369
$786$	45.6393	1.62790
$787$	15.1880	0.541393	0.270696	−	0.962665i	$-0.412746\pi$
$787$	15.1880	0.541393	0.270696	+	0.962665i	$0.412746\pi$
$788$	−1.00000	−0.0356235
$789$	6.86093	0.244256
$790$	−67.1938	−2.39065
$791$	32.4519	1.15386
$792$	1.75745	0.0624483
$793$	40.8989	1.45236
$794$	7.21915	0.256198
$795$	−18.6611	−0.661842
$796$	−4.61639	−0.163624
$797$	−6.46372	−0.228957	−0.114478	−	0.993426i	$-0.536520\pi$
$797$	−6.46372	−0.228957	−0.114478	+	0.993426i	$0.536520\pi$
$798$	−20.5050	−0.725870
$799$	−21.1968	−0.749889
$800$	−11.5315	−0.407700
$801$	−17.8713	−0.631450
$802$	26.7889	0.945949
$803$	−5.11266	−0.180422
$804$	18.9027	0.666645
$805$	24.6229	0.867845
$806$	−48.2737	−1.70037
$807$	−17.0205	−0.599149
$808$	−7.22896	−0.254314
$809$	−1.40023	−0.0492294	−0.0246147	−	0.999697i	$-0.507836\pi$
$809$	−1.40023	−0.0492294	−0.0246147	+	0.999697i	$0.507836\pi$
$810$	45.4718	1.59772
$811$	−48.0215	−1.68626	−0.843131	−	0.537708i	$-0.819290\pi$
$811$	−48.0215	−1.68626	−0.843131	+	0.537708i	$0.819290\pi$
$812$	9.27053	0.325332
$813$	−55.1492	−1.93417
$814$	−2.57350	−0.0902012
$815$	1.23426	0.0432343
$816$	−12.1909	−0.426766
$817$	−38.7937	−1.35722
$818$	−24.0498	−0.840880
$819$	19.7780	0.691100
$820$	40.1132	1.40081
$821$	−31.0656	−1.08420	−0.542099	−	0.840315i	$-0.682370\pi$
$821$	−31.0656	−1.08420	−0.542099	+	0.840315i	$0.682370\pi$
$822$	−36.8133	−1.28401
$823$	17.4208	0.607251	0.303625	−	0.952791i	$-0.401803\pi$
$823$	17.4208	0.607251	0.303625	+	0.952791i	$0.401803\pi$
$824$	1.53845	0.0535946
$825$	−25.1520	−0.875680
$826$	−25.2295	−0.877846
$827$	1.15147	0.0400406	0.0200203	−	0.999800i	$-0.493627\pi$
$827$	1.15147	0.0400406	0.0200203	+	0.999800i	$0.493627\pi$
$828$	−5.68031	−0.197404
$829$	−8.28442	−0.287730	−0.143865	−	0.989597i	$-0.545953\pi$
$829$	−8.28442	−0.287730	−0.143865	+	0.989597i	$0.545953\pi$
$830$	7.04963	0.244696
$831$	51.0176	1.76978
$832$	−6.00627	−0.208230
$833$	19.5024	0.675719
$834$	−44.1352	−1.52828
$835$	26.5380	0.918386
$836$	5.01739	0.173530
$837$	21.7825	0.752913
$838$	31.3519	1.08303
$839$	12.1293	0.418749	0.209374	−	0.977836i	$-0.432857\pi$
$839$	12.1293	0.418749	0.209374	+	0.977836i	$0.432857\pi$
$840$	16.6165	0.573322
$841$	−4.51960	−0.155848
$842$	10.8632	0.374369
$843$	−15.3895	−0.530043
$844$	−7.40084	−0.254747
$845$	93.8214	3.22755
$846$	−6.66509	−0.229150
$847$	−1.87368	−0.0643804
$848$	−2.10424	−0.0722599
$849$	0.678056	0.0232708
$850$	64.4515	2.21067
$851$	8.31789	0.285134
$852$	34.5459	1.18352
$853$	−2.19334	−0.0750984	−0.0375492	−	0.999295i	$-0.511955\pi$
$853$	−2.19334	−0.0750984	−0.0375492	+	0.999295i	$0.511955\pi$
$854$	−12.7586	−0.436589
$855$	−35.8523	−1.22612
$856$	7.74471	0.264709
$857$	−48.8090	−1.66729	−0.833643	−	0.552304i	$-0.813749\pi$
$857$	−48.8090	−1.66729	−0.833643	+	0.552304i	$0.813749\pi$
$858$	−13.1006	−0.447248
$859$	−34.7065	−1.18417	−0.592086	−	0.805875i	$-0.701695\pi$
$859$	−34.7065	−1.18417	−0.592086	+	0.805875i	$0.701695\pi$
$860$	31.4369	1.07199
$861$	−40.3194	−1.37408
$862$	−9.13949	−0.311292
$863$	28.9821	0.986561	0.493281	−	0.869870i	$-0.335798\pi$
$863$	28.9821	0.986561	0.493281	+	0.869870i	$0.335798\pi$
$864$	2.71020	0.0922028
$865$	79.3198	2.69695
$866$	14.3588	0.487933
$867$	31.0572	1.05476
$868$	15.0592	0.511143
$869$	−16.5262	−0.560613
$870$	43.8786	1.48762
$871$	−52.0523	−1.76373
$872$	1.90203	0.0644107
$873$	−4.26330	−0.144291
$874$	−16.2168	−0.548543
$875$	−49.7580	−1.68213
$876$	11.1515	0.376775
$877$	−6.81757	−0.230213	−0.115106	−	0.993353i	$-0.536721\pi$
$877$	−6.81757	−0.230213	−0.115106	+	0.993353i	$0.536721\pi$
$878$	14.8707	0.501862
$879$	58.1502	1.96136
$880$	−4.06589	−0.137061
$881$	40.0600	1.34966	0.674829	−	0.737974i	$-0.264218\pi$
$881$	40.0600	1.34966	0.674829	+	0.737974i	$0.264218\pi$
$882$	6.13231	0.206486
$883$	−16.5210	−0.555975	−0.277987	−	0.960585i	$-0.589667\pi$
$883$	−16.5210	−0.555975	−0.277987	+	0.960585i	$0.589667\pi$
$884$	33.5701	1.12908
$885$	−119.414	−4.01406
$886$	4.42144	0.148541
$887$	43.8098	1.47099	0.735494	−	0.677531i	$-0.236950\pi$
$887$	43.8098	1.47099	0.735494	+	0.677531i	$0.236950\pi$
$888$	5.61321	0.188367
$889$	16.5871	0.556314
$890$	41.3455	1.38590
$891$	11.1837	0.374669
$892$	22.2940	0.746459
$893$	−19.0283	−0.636759
$894$	34.7963	1.16376
$895$	−41.5544	−1.38901
$896$	1.87368	0.0625953
$897$	42.3429	1.41379
$898$	17.9042	0.597473
$899$	39.7663	1.32628
$900$	20.2660	0.675534
$901$	11.7610	0.391814
$902$	9.86578	0.328494
$903$	−31.5985	−1.05153
$904$	17.3199	0.576050
$905$	−45.5465	−1.51402
$906$	−29.8984	−0.993308
$907$	12.7676	0.423942	0.211971	−	0.977276i	$-0.432012\pi$
$907$	12.7676	0.423942	0.211971	+	0.977276i	$0.432012\pi$
$908$	16.5920	0.550626
$909$	12.7045	0.421383
$910$	−45.7568	−1.51682
$911$	16.3134	0.540487	0.270244	−	0.962792i	$-0.412896\pi$
$911$	16.3134	0.540487	0.270244	+	0.962792i	$0.412896\pi$
$912$	−10.9437	−0.362383
$913$	1.73384	0.0573819
$914$	39.1112	1.29368
$915$	−60.3879	−1.99636
$916$	−4.84592	−0.160114
$917$	39.2055	1.29468
$918$	−15.1478	−0.499951
$919$	52.6914	1.73813	0.869065	−	0.494698i	$-0.164721\pi$
$919$	52.6914	1.73813	0.869065	+	0.494698i	$0.164721\pi$
$920$	13.1415	0.433262
$921$	22.9234	0.755353
$922$	−6.42637	−0.211641
$923$	−95.1293	−3.13122
$924$	4.08679	0.134446
$925$	−29.6763	−0.975750
$926$	36.9404	1.21394
$927$	−2.70376	−0.0888030
$928$	4.94777	0.162418
$929$	−32.1342	−1.05429	−0.527144	−	0.849776i	$-0.676737\pi$
$929$	−32.1342	−1.05429	−0.527144	+	0.849776i	$0.676737\pi$
$930$	71.2770	2.33727
$931$	17.5073	0.573778
$932$	−13.6461	−0.446993
$933$	−48.3858	−1.58408
$934$	−28.3737	−0.928417
$935$	22.7250	0.743186
$936$	10.5557	0.345024
$937$	32.0618	1.04741	0.523706	−	0.851899i	$-0.324549\pi$
$937$	32.0618	1.04741	0.523706	+	0.851899i	$0.324549\pi$
$938$	16.2379	0.530188
$939$	14.3228	0.467408
$940$	15.4198	0.502939
$941$	7.11274	0.231869	0.115934	−	0.993257i	$-0.463014\pi$
$941$	7.11274	0.231869	0.115934	+	0.993257i	$0.463014\pi$
$942$	−8.72308	−0.284213
$943$	−31.8875	−1.03840
$944$	−13.4652	−0.438255
$945$	20.6468	0.671640
$946$	7.73185	0.251384
$947$	39.8666	1.29549	0.647745	−	0.761857i	$-0.275712\pi$
$947$	39.8666	1.29549	0.647745	+	0.761857i	$0.275712\pi$
$948$	36.0462	1.17073
$949$	−30.7080	−0.996824
$950$	57.8579	1.87716
$951$	57.8403	1.87560
$952$	−10.4723	−0.339410
$953$	−6.30740	−0.204317	−0.102158	−	0.994768i	$-0.532575\pi$
$953$	−6.30740	−0.204317	−0.102158	+	0.994768i	$0.532575\pi$
$954$	3.69809	0.119730
$955$	19.1148	0.618542
$956$	5.72010	0.185001
$957$	10.7919	0.348851
$958$	40.2392	1.30007
$959$	−31.6237	−1.02118
$960$	8.86835	0.286225
$961$	33.5971	1.08378
$962$	−15.4571	−0.498358
$963$	−13.6109	−0.438606
$964$	7.80759	0.251465
$965$	−94.8351	−3.05285
$966$	−13.2090	−0.424994
$967$	21.7824	0.700476	0.350238	−	0.936661i	$-0.386101\pi$
$967$	21.7824	0.700476	0.350238	+	0.936661i	$0.386101\pi$
$968$	−1.00000	−0.0321412
$969$	61.1663	1.96495
$970$	9.86322	0.316689
$971$	39.9215	1.28114	0.640571	−	0.767899i	$-0.278698\pi$
$971$	39.9215	1.28114	0.640571	+	0.767899i	$0.278698\pi$
$972$	−16.2629	−0.521632
$973$	−37.9135	−1.21545
$974$	−12.8422	−0.411492
$975$	−151.070	−4.83810
$976$	−6.80937	−0.217963
$977$	41.8855	1.34004	0.670018	−	0.742345i	$-0.266286\pi$
$977$	41.8855	1.34004	0.670018	+	0.742345i	$0.266286\pi$
$978$	−0.662123	−0.0211724
$979$	10.1689	0.324998
$980$	−14.1872	−0.453194
$981$	−3.34272	−0.106725
$982$	−19.1974	−0.612615
$983$	11.4123	0.363995	0.181998	−	0.983299i	$-0.441744\pi$
$983$	11.4123	0.363995	0.181998	+	0.983299i	$0.441744\pi$
$984$	−21.5188	−0.685995
$985$	−4.06589	−0.129550
$986$	−27.6539	−0.880681
$987$	−15.4991	−0.493341
$988$	30.1358	0.958746
$989$	−24.9903	−0.794647
$990$	7.14560	0.227102
$991$	−48.4451	−1.53891	−0.769454	−	0.638702i	$-0.779472\pi$
$991$	−48.4451	−1.53891	−0.769454	+	0.638702i	$0.779472\pi$
$992$	8.03723	0.255182
$993$	29.7410	0.943802
$994$	29.6760	0.941265
$995$	−18.7697	−0.595041
$996$	−3.78179	−0.119831
$997$	−55.8372	−1.76838	−0.884190	−	0.467127i	$-0.845289\pi$
$997$	−55.8372	−1.76838	−0.884190	+	0.467127i	$0.845289\pi$
$998$	−35.2555	−1.11599
$999$	6.97470	0.220670

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.c.1.14	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.c.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.18116 q^{3} +1.00000 q^{4} +4.06589 q^{5} -2.18116 q^{6} -1.87368 q^{7} -1.00000 q^{8} +1.75745 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.18116 q^{3} +1.00000 q^{4} +4.06589 q^{5} -2.18116 q^{6} -1.87368 q^{7} -1.00000 q^{8} +1.75745 q^{9} -4.06589 q^{10} -1.00000 q^{11} +2.18116 q^{12} -6.00627 q^{13} +1.87368 q^{14} +8.86835 q^{15} +1.00000 q^{16} -5.58917 q^{17} -1.75745 q^{18} -5.01739 q^{19} +4.06589 q^{20} -4.08679 q^{21} +1.00000 q^{22} -3.23213 q^{23} -2.18116 q^{24} +11.5315 q^{25} +6.00627 q^{26} -2.71020 q^{27} -1.87368 q^{28} -4.94777 q^{29} -8.86835 q^{30} -8.03723 q^{31} -1.00000 q^{32} -2.18116 q^{33} +5.58917 q^{34} -7.61818 q^{35} +1.75745 q^{36} -2.57350 q^{37} +5.01739 q^{38} -13.1006 q^{39} -4.06589 q^{40} +9.86578 q^{41} +4.08679 q^{42} +7.73185 q^{43} -1.00000 q^{44} +7.14560 q^{45} +3.23213 q^{46} +3.79248 q^{47} +2.18116 q^{48} -3.48932 q^{49} -11.5315 q^{50} -12.1909 q^{51} -6.00627 q^{52} -2.10424 q^{53} +2.71020 q^{54} -4.06589 q^{55} +1.87368 q^{56} -10.9437 q^{57} +4.94777 q^{58} -13.4652 q^{59} +8.86835 q^{60} -6.80937 q^{61} +8.03723 q^{62} -3.29290 q^{63} +1.00000 q^{64} -24.4208 q^{65} +2.18116 q^{66} +8.66634 q^{67} -5.58917 q^{68} -7.04978 q^{69} +7.61818 q^{70} +15.8383 q^{71} -1.75745 q^{72} +5.11266 q^{73} +2.57350 q^{74} +25.1520 q^{75} -5.01739 q^{76} +1.87368 q^{77} +13.1006 q^{78} +16.5262 q^{79} +4.06589 q^{80} -11.1837 q^{81} -9.86578 q^{82} -1.73384 q^{83} -4.08679 q^{84} -22.7250 q^{85} -7.73185 q^{86} -10.7919 q^{87} +1.00000 q^{88} -10.1689 q^{89} -7.14560 q^{90} +11.2538 q^{91} -3.23213 q^{92} -17.5305 q^{93} -3.79248 q^{94} -20.4002 q^{95} -2.18116 q^{96} -2.42584 q^{97} +3.48932 q^{98} -1.75745 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9}+O(q^{10}) \) 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9	\( 17 q - 17 q^{2} + 5 q^{3} + 17 q^{4} + 6 q^{5} - 5 q^{6} - 9 q^{7} - 17 q^{8} + 12 q^{9} - 6 q^{10} - 17 q^{11} + 5 q^{12} - 16 q^{13} + 9 q^{14} + 17 q^{16} - 8 q^{17} - 12 q^{18} - 23 q^{19} + 6 q^{20} - 15 q^{21} + 17 q^{22} + 12 q^{23} - 5 q^{24} + 11 q^{25} + 16 q^{26} + 17 q^{27} - 9 q^{28} - 8 q^{31} - 17 q^{32} - 5 q^{33} + 8 q^{34} + 6 q^{35} + 12 q^{36} - 7 q^{37} + 23 q^{38} - 9 q^{39} - 6 q^{40} - 27 q^{41} + 15 q^{42} - 13 q^{43} - 17 q^{44} - 11 q^{45} - 12 q^{46} + 23 q^{47} + 5 q^{48} - 8 q^{49} - 11 q^{50} - 40 q^{51} - 16 q^{52} + 14 q^{53} - 17 q^{54} - 6 q^{55} + 9 q^{56} - 18 q^{57} + 2 q^{59} - 49 q^{61} + 8 q^{62} - 42 q^{63} + 17 q^{64} - 57 q^{65} + 5 q^{66} - 5 q^{67} - 8 q^{68} - 9 q^{69} - 6 q^{70} - 5 q^{71} - 12 q^{72} - 54 q^{73} + 7 q^{74} + 7 q^{75} - 23 q^{76} + 9 q^{77} + 9 q^{78} - 11 q^{79} + 6 q^{80} - 35 q^{81} + 27 q^{82} - 8 q^{83} - 15 q^{84} - 65 q^{85} + 13 q^{86} - 20 q^{87} + 17 q^{88} - 9 q^{89} + 11 q^{90} - 9 q^{91} + 12 q^{92} - 50 q^{93} - 23 q^{94} - 27 q^{95} - 5 q^{96} - 42 q^{97} + 8 q^{98} - 12 q^{99}+O(q^{100}) \) 17 * q - 17 * q^2 + 5 * q^3 + 17 * q^4 + 6 * q^5 - 5 * q^6 - 9 * q^7 - 17 * q^8 + 12 * q^9 - 6 * q^10 - 17 * q^11 + 5 * q^12 - 16 * q^13 + 9 * q^14 + 17 * q^16 - 8 * q^17 - 12 * q^18 - 23 * q^19 + 6 * q^20 - 15 * q^21 + 17 * q^22 + 12 * q^23 - 5 * q^24 + 11 * q^25 + 16 * q^26 + 17 * q^27 - 9 * q^28 - 8 * q^31 - 17 * q^32 - 5 * q^33 + 8 * q^34 + 6 * q^35 + 12 * q^36 - 7 * q^37 + 23 * q^38 - 9 * q^39 - 6 * q^40 - 27 * q^41 + 15 * q^42 - 13 * q^43 - 17 * q^44 - 11 * q^45 - 12 * q^46 + 23 * q^47 + 5 * q^48 - 8 * q^49 - 11 * q^50 - 40 * q^51 - 16 * q^52 + 14 * q^53 - 17 * q^54 - 6 * q^55 + 9 * q^56 - 18 * q^57 + 2 * q^59 - 49 * q^61 + 8 * q^62 - 42 * q^63 + 17 * q^64 - 57 * q^65 + 5 * q^66 - 5 * q^67 - 8 * q^68 - 9 * q^69 - 6 * q^70 - 5 * q^71 - 12 * q^72 - 54 * q^73 + 7 * q^74 + 7 * q^75 - 23 * q^76 + 9 * q^77 + 9 * q^78 - 11 * q^79 + 6 * q^80 - 35 * q^81 + 27 * q^82 - 8 * q^83 - 15 * q^84 - 65 * q^85 + 13 * q^86 - 20 * q^87 + 17 * q^88 - 9 * q^89 + 11 * q^90 - 9 * q^91 + 12 * q^92 - 50 * q^93 - 23 * q^94 - 27 * q^95 - 5 * q^96 - 42 * q^97 + 8 * q^98 - 12 * q^99

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