LMFDB - Embedded newform 1027.2.a.c.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1027,2,Mod(1,1027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1027, 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("1027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1027 = 13 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1027.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:	$8.20063628759$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 8 x^{16} + 106 x^{15} - 57 x^{14} - 715 x^{13} + 859 x^{12} + 2323 x^{11} - 3741 x^{10} + \cdots + 8 $ x^18 - 6x^17 - 8x^16 + 106x^15 - 57x^14 - 715x^13 + 859x^12 + 2323x^11 - 3741x^10 - 3768x^9 + 7603x^8 + 2785x^7 - 7585x^6 - 510x^5 + 3292x^4 - 241x^3 - 361x^2 + 32*x + 8
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			1.10
Root			$0.264851$ of defining polynomial
Character	$\chi$	$=$	1027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.264851 q^{2} -0.551693 q^{3} -1.92985 q^{4} -2.56001 q^{5} +0.146116 q^{6} +4.55874 q^{7} +1.04083 q^{8} -2.69564 q^{9} +O(q^{10})$	\(q-0.264851 q^{2} -0.551693 q^{3} -1.92985 q^{4} -2.56001 q^{5} +0.146116 q^{6} +4.55874 q^{7} +1.04083 q^{8} -2.69564 q^{9} +0.678021 q^{10} +1.88114 q^{11} +1.06469 q^{12} -1.00000 q^{13} -1.20739 q^{14} +1.41234 q^{15} +3.58404 q^{16} +1.49827 q^{17} +0.713942 q^{18} +0.653648 q^{19} +4.94044 q^{20} -2.51502 q^{21} -0.498221 q^{22} -3.71277 q^{23} -0.574216 q^{24} +1.55364 q^{25} +0.264851 q^{26} +3.14224 q^{27} -8.79770 q^{28} +2.77024 q^{29} -0.374059 q^{30} -7.56657 q^{31} -3.03089 q^{32} -1.03781 q^{33} -0.396819 q^{34} -11.6704 q^{35} +5.20218 q^{36} +0.453727 q^{37} -0.173119 q^{38} +0.551693 q^{39} -2.66452 q^{40} -6.43134 q^{41} +0.666107 q^{42} -2.03819 q^{43} -3.63032 q^{44} +6.90085 q^{45} +0.983331 q^{46} -1.21535 q^{47} -1.97729 q^{48} +13.7821 q^{49} -0.411484 q^{50} -0.826585 q^{51} +1.92985 q^{52} -10.0911 q^{53} -0.832226 q^{54} -4.81573 q^{55} +4.74485 q^{56} -0.360613 q^{57} -0.733701 q^{58} -7.98972 q^{59} -2.72561 q^{60} -6.26169 q^{61} +2.00401 q^{62} -12.2887 q^{63} -6.36535 q^{64} +2.56001 q^{65} +0.274865 q^{66} -8.93104 q^{67} -2.89144 q^{68} +2.04831 q^{69} +3.09092 q^{70} -12.1265 q^{71} -2.80569 q^{72} +7.89146 q^{73} -0.120170 q^{74} -0.857134 q^{75} -1.26145 q^{76} +8.57561 q^{77} -0.146116 q^{78} -1.00000 q^{79} -9.17518 q^{80} +6.35335 q^{81} +1.70335 q^{82} -5.63045 q^{83} +4.85363 q^{84} -3.83559 q^{85} +0.539817 q^{86} -1.52832 q^{87} +1.95794 q^{88} -5.39142 q^{89} -1.82770 q^{90} -4.55874 q^{91} +7.16510 q^{92} +4.17442 q^{93} +0.321886 q^{94} -1.67335 q^{95} +1.67212 q^{96} +12.4943 q^{97} -3.65020 q^{98} -5.07086 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 6 q^{2} - 8 q^{3} + 16 q^{4} - 7 q^{5} + 2 q^{6} - 6 q^{7} - 18 q^{8} + 10 q^{9}+O(q^{10}) $ 18 * q - 6 * q^2 - 8 * q^3 + 16 * q^4 - 7 * q^5 + 2 * q^6 - 6 * q^7 - 18 * q^8 + 10 * q^9	\( 18 q - 6 q^{2} - 8 q^{3} + 16 q^{4} - 7 q^{5} + 2 q^{6} - 6 q^{7} - 18 q^{8} + 10 q^{9} - 8 q^{10} - 2 q^{11} - 25 q^{12} - 18 q^{13} - 16 q^{14} - 8 q^{15} + 20 q^{16} - 25 q^{17} - 15 q^{18} - 3 q^{19} - 5 q^{20} - 14 q^{21} - 14 q^{22} - 21 q^{23} + 18 q^{24} + 9 q^{25} + 6 q^{26} - 35 q^{27} - q^{28} - 50 q^{29} - 8 q^{30} + 19 q^{31} - 37 q^{32} - 4 q^{33} + 26 q^{34} - 26 q^{35} + 14 q^{36} - 40 q^{37} - 3 q^{38} + 8 q^{39} - 36 q^{40} - q^{41} + 49 q^{42} - 17 q^{43} + 11 q^{44} - 12 q^{45} + 4 q^{46} - 15 q^{47} - 59 q^{48} + 24 q^{49} - 34 q^{50} + 10 q^{51} - 16 q^{52} - 79 q^{53} + 58 q^{54} + 12 q^{55} - 37 q^{56} - 3 q^{57} - 14 q^{58} + 7 q^{59} + 30 q^{60} - 30 q^{61} - 52 q^{62} - 3 q^{63} + 38 q^{64} + 7 q^{65} - 56 q^{66} + 8 q^{67} - 21 q^{68} - 22 q^{69} + 39 q^{70} - 20 q^{71} - 46 q^{72} - 9 q^{73} - 4 q^{74} + 10 q^{75} - 46 q^{76} - 75 q^{77} - 2 q^{78} - 18 q^{79} + 36 q^{80} - 18 q^{81} - 16 q^{82} - 13 q^{83} - 61 q^{84} - 21 q^{85} + 19 q^{86} - 8 q^{87} - 10 q^{88} + 18 q^{89} + 58 q^{90} + 6 q^{91} - 76 q^{92} - 41 q^{93} + 58 q^{94} - 25 q^{95} + 96 q^{96} + 24 q^{97} - 35 q^{98} + 26 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 - 8 * q^3 + 16 * q^4 - 7 * q^5 + 2 * q^6 - 6 * q^7 - 18 * q^8 + 10 * q^9 - 8 * q^10 - 2 * q^11 - 25 * q^12 - 18 * q^13 - 16 * q^14 - 8 * q^15 + 20 * q^16 - 25 * q^17 - 15 * q^18 - 3 * q^19 - 5 * q^20 - 14 * q^21 - 14 * q^22 - 21 * q^23 + 18 * q^24 + 9 * q^25 + 6 * q^26 - 35 * q^27 - q^28 - 50 * q^29 - 8 * q^30 + 19 * q^31 - 37 * q^32 - 4 * q^33 + 26 * q^34 - 26 * q^35 + 14 * q^36 - 40 * q^37 - 3 * q^38 + 8 * q^39 - 36 * q^40 - q^41 + 49 * q^42 - 17 * q^43 + 11 * q^44 - 12 * q^45 + 4 * q^46 - 15 * q^47 - 59 * q^48 + 24 * q^49 - 34 * q^50 + 10 * q^51 - 16 * q^52 - 79 * q^53 + 58 * q^54 + 12 * q^55 - 37 * q^56 - 3 * q^57 - 14 * q^58 + 7 * q^59 + 30 * q^60 - 30 * q^61 - 52 * q^62 - 3 * q^63 + 38 * q^64 + 7 * q^65 - 56 * q^66 + 8 * q^67 - 21 * q^68 - 22 * q^69 + 39 * q^70 - 20 * q^71 - 46 * q^72 - 9 * q^73 - 4 * q^74 + 10 * q^75 - 46 * q^76 - 75 * q^77 - 2 * q^78 - 18 * q^79 + 36 * q^80 - 18 * q^81 - 16 * q^82 - 13 * q^83 - 61 * q^84 - 21 * q^85 + 19 * q^86 - 8 * q^87 - 10 * q^88 + 18 * q^89 + 58 * q^90 + 6 * q^91 - 76 * q^92 - 41 * q^93 + 58 * q^94 - 25 * q^95 + 96 * q^96 + 24 * q^97 - 35 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.264851	−0.187278	−0.0936390	−	0.995606i	$-0.529850\pi$
$2$	−0.264851	−0.187278	−0.0936390	+	0.995606i	$0.529850\pi$
$3$	−0.551693	−0.318520	−0.159260	−	0.987237i	$-0.550911\pi$
$3$	−0.551693	−0.318520	−0.159260	+	0.987237i	$0.550911\pi$
$4$	−1.92985	−0.964927
$5$	−2.56001	−1.14487	−0.572435	−	0.819950i	$-0.694001\pi$
$5$	−2.56001	−1.14487	−0.572435	+	0.819950i	$0.694001\pi$
$6$	0.146116	0.0596518
$7$	4.55874	1.72304	0.861520	−	0.507723i	$-0.169513\pi$
$7$	4.55874	1.72304	0.861520	+	0.507723i	$0.169513\pi$
$8$	1.04083	0.367988
$9$	−2.69564	−0.898545
$10$	0.678021	0.214409
$11$	1.88114	0.567184	0.283592	−	0.958945i	$-0.408474\pi$
$11$	1.88114	0.567184	0.283592	+	0.958945i	$0.408474\pi$
$12$	1.06469	0.307349
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.20739	−0.322688
$15$	1.41234	0.364664
$16$	3.58404	0.896011
$17$	1.49827	0.363384	0.181692	−	0.983355i	$-0.441843\pi$
$17$	1.49827	0.363384	0.181692	+	0.983355i	$0.441843\pi$
$18$	0.713942	0.168278
$19$	0.653648	0.149957	0.0749786	−	0.997185i	$-0.476111\pi$
$19$	0.653648	0.149957	0.0749786	+	0.997185i	$0.476111\pi$
$20$	4.94044	1.10472
$21$	−2.51502	−0.548823
$22$	−0.498221	−0.106221
$23$	−3.71277	−0.774166	−0.387083	−	0.922045i	$-0.626517\pi$
$23$	−3.71277	−0.774166	−0.387083	+	0.922045i	$0.626517\pi$
$24$	−0.574216	−0.117211
$25$	1.55364	0.310729
$26$	0.264851	0.0519416
$27$	3.14224	0.604725
$28$	−8.79770	−1.66261
$29$	2.77024	0.514420	0.257210	−	0.966355i	$-0.417197\pi$
$29$	2.77024	0.514420	0.257210	+	0.966355i	$0.417197\pi$
$30$	−0.374059	−0.0682936
$31$	−7.56657	−1.35900	−0.679498	−	0.733678i	$-0.737802\pi$
$31$	−7.56657	−1.35900	−0.679498	+	0.733678i	$0.737802\pi$
$32$	−3.03089	−0.535791
$33$	−1.03781	−0.180660
$34$	−0.396819	−0.0680538
$35$	−11.6704	−1.97266
$36$	5.20218	0.867030
$37$	0.453727	0.0745922	0.0372961	−	0.999304i	$-0.488126\pi$
$37$	0.453727	0.0745922	0.0372961	+	0.999304i	$0.488126\pi$
$38$	−0.173119	−0.0280837
$39$	0.551693	0.0883416
$40$	−2.66452	−0.421298
$41$	−6.43134	−1.00441	−0.502203	−	0.864750i	$-0.667477\pi$
$41$	−6.43134	−1.00441	−0.502203	+	0.864750i	$0.667477\pi$
$42$	0.666107	0.102782
$43$	−2.03819	−0.310821	−0.155411	−	0.987850i	$-0.549670\pi$
$43$	−2.03819	−0.310821	−0.155411	+	0.987850i	$0.549670\pi$
$44$	−3.63032	−0.547291
$45$	6.90085	1.02872
$46$	0.983331	0.144984
$47$	−1.21535	−0.177277	−0.0886384	−	0.996064i	$-0.528252\pi$
$47$	−1.21535	−0.177277	−0.0886384	+	0.996064i	$0.528252\pi$
$48$	−1.97729	−0.285397
$49$	13.7821	1.96887
$50$	−0.411484	−0.0581926
$51$	−0.826585	−0.115745
$52$	1.92985	0.267623
$53$	−10.0911	−1.38612	−0.693059	−	0.720881i	$-0.743737\pi$
$53$	−10.0911	−1.38612	−0.693059	+	0.720881i	$0.743737\pi$
$54$	−0.832226	−0.113252
$55$	−4.81573	−0.649353
$56$	4.74485	0.634058
$57$	−0.360613	−0.0477644
$58$	−0.733701	−0.0963396
$59$	−7.98972	−1.04017	−0.520087	−	0.854114i	$-0.674100\pi$
$59$	−7.98972	−1.04017	−0.520087	+	0.854114i	$0.674100\pi$
$60$	−2.72561	−0.351874
$61$	−6.26169	−0.801728	−0.400864	−	0.916138i	$-0.631290\pi$
$61$	−6.26169	−0.801728	−0.400864	+	0.916138i	$0.631290\pi$
$62$	2.00401	0.254510
$63$	−12.2887	−1.54823
$64$	−6.36535	−0.795669
$65$	2.56001	0.317530
$66$	0.274865	0.0338336
$67$	−8.93104	−1.09110	−0.545550	−	0.838078i	$-0.683679\pi$
$67$	−8.93104	−1.09110	−0.545550	+	0.838078i	$0.683679\pi$
$68$	−2.89144	−0.350639
$69$	2.04831	0.246587
$70$	3.09092	0.369436
$71$	−12.1265	−1.43915	−0.719575	−	0.694414i	$-0.755664\pi$
$71$	−12.1265	−1.43915	−0.719575	+	0.694414i	$0.755664\pi$
$72$	−2.80569	−0.330653
$73$	7.89146	0.923626	0.461813	−	0.886977i	$-0.347199\pi$
$73$	7.89146	0.923626	0.461813	+	0.886977i	$0.347199\pi$
$74$	−0.120170	−0.0139695
$75$	−0.857134	−0.0989733
$76$	−1.26145	−0.144698
$77$	8.57561	0.977282
$78$	−0.146116	−0.0165444
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	−9.17518	−1.02582
$81$	6.35335	0.705928
$82$	1.70335	0.188103
$83$	−5.63045	−0.618023	−0.309011	−	0.951058i	$-0.599998\pi$
$83$	−5.63045	−0.618023	−0.309011	+	0.951058i	$0.599998\pi$
$84$	4.85363	0.529574
$85$	−3.83559	−0.416028
$86$	0.539817	0.0582100
$87$	−1.52832	−0.163853
$88$	1.95794	0.208717
$89$	−5.39142	−0.571489	−0.285744	−	0.958306i	$-0.592241\pi$
$89$	−5.39142	−0.571489	−0.285744	+	0.958306i	$0.592241\pi$
$90$	−1.82770	−0.192656
$91$	−4.55874	−0.477886
$92$	7.16510	0.747014
$93$	4.17442	0.432867
$94$	0.321886	0.0332000
$95$	−1.67335	−0.171682
$96$	1.67212	0.170660
$97$	12.4943	1.26861	0.634304	−	0.773084i	$-0.281287\pi$
$97$	12.4943	1.26861	0.634304	+	0.773084i	$0.281287\pi$
$98$	−3.65020	−0.368726
$99$	−5.07086	−0.509641
$100$	−2.99830	−0.299830
$101$	−14.0174	−1.39479	−0.697394	−	0.716688i	$-0.745657\pi$
$101$	−14.0174	−1.39479	−0.697394	+	0.716688i	$0.745657\pi$
$102$	0.218922	0.0216765
$103$	13.7904	1.35881	0.679405	−	0.733763i	$-0.262238\pi$
$103$	13.7904	1.35881	0.679405	+	0.733763i	$0.262238\pi$
$104$	−1.04083	−0.102061
$105$	6.43848	0.628331
$106$	2.67264	0.259589
$107$	−2.58395	−0.249800	−0.124900	−	0.992169i	$-0.539861\pi$
$107$	−2.58395	−0.249800	−0.124900	+	0.992169i	$0.539861\pi$
$108$	−6.06407	−0.583515
$109$	−12.3180	−1.17985	−0.589927	−	0.807457i	$-0.700844\pi$
$109$	−12.3180	−1.17985	−0.589927	+	0.807457i	$0.700844\pi$
$110$	1.27545	0.121609
$111$	−0.250318	−0.0237591
$112$	16.3387	1.54386
$113$	6.69211	0.629540	0.314770	−	0.949168i	$-0.398073\pi$
$113$	6.69211	0.629540	0.314770	+	0.949168i	$0.398073\pi$
$114$	0.0955088	0.00894522
$115$	9.50472	0.886320
$116$	−5.34615	−0.496378
$117$	2.69564	0.249212
$118$	2.11609	0.194802
$119$	6.83022	0.626126
$120$	1.47000	0.134192
$121$	−7.46132	−0.678302
$122$	1.65842	0.150146
$123$	3.54812	0.319923
$124$	14.6024	1.31133
$125$	8.82270	0.789127
$126$	3.25467	0.289949
$127$	12.0996	1.07367	0.536834	−	0.843688i	$-0.319620\pi$
$127$	12.0996	1.07367	0.536834	+	0.843688i	$0.319620\pi$
$128$	7.74765	0.684802
$129$	1.12446	0.0990028
$130$	−0.678021	−0.0594664
$131$	−15.4064	−1.34606	−0.673031	−	0.739614i	$-0.735008\pi$
$131$	−15.4064	−1.34606	−0.673031	+	0.739614i	$0.735008\pi$
$132$	2.00282	0.174323
$133$	2.97981	0.258382
$134$	2.36540	0.204339
$135$	−8.04416	−0.692331
$136$	1.55944	0.133721
$137$	5.92279	0.506018	0.253009	−	0.967464i	$-0.418580\pi$
$137$	5.92279	0.506018	0.253009	+	0.967464i	$0.418580\pi$
$138$	−0.542497	−0.0461804
$139$	19.1073	1.62066	0.810328	−	0.585977i	$-0.199289\pi$
$139$	19.1073	1.62066	0.810328	+	0.585977i	$0.199289\pi$
$140$	22.5222	1.90347
$141$	0.670499	0.0564662
$142$	3.21172	0.269521
$143$	−1.88114	−0.157309
$144$	−9.66127	−0.805106
$145$	−7.09183	−0.588945
$146$	−2.09006	−0.172975
$147$	−7.60348	−0.627124
$148$	−0.875627	−0.0719761
$149$	8.89899	0.729033	0.364517	−	0.931197i	$-0.381234\pi$
$149$	8.89899	0.729033	0.364517	+	0.931197i	$0.381234\pi$
$150$	0.227013	0.0185355
$151$	−7.35920	−0.598883	−0.299441	−	0.954115i	$-0.596800\pi$
$151$	−7.35920	−0.598883	−0.299441	+	0.954115i	$0.596800\pi$
$152$	0.680334	0.0551824
$153$	−4.03879	−0.326517
$154$	−2.27126	−0.183023
$155$	19.3705	1.55587
$156$	−1.06469	−0.0852431
$157$	10.7064	0.854461	0.427230	−	0.904143i	$-0.359489\pi$
$157$	10.7064	0.854461	0.427230	+	0.904143i	$0.359489\pi$
$158$	0.264851	0.0210704
$159$	5.56718	0.441506
$160$	7.75910	0.613411
$161$	−16.9255	−1.33392
$162$	−1.68269	−0.132205
$163$	−7.57269	−0.593139	−0.296569	−	0.955011i	$-0.595843\pi$
$163$	−7.57269	−0.593139	−0.296569	+	0.955011i	$0.595843\pi$
$164$	12.4115	0.969178
$165$	2.65680	0.206832
$166$	1.49123	0.115742
$167$	−2.83372	−0.219280	−0.109640	−	0.993971i	$-0.534970\pi$
$167$	−2.83372	−0.219280	−0.109640	+	0.993971i	$0.534970\pi$
$168$	−2.61770	−0.201960
$169$	1.00000	0.0769231
$170$	1.01586	0.0779128
$171$	−1.76200	−0.134743
$172$	3.93341	0.299920
$173$	−9.44910	−0.718401	−0.359201	−	0.933260i	$-0.616951\pi$
$173$	−9.44910	−0.718401	−0.359201	+	0.933260i	$0.616951\pi$
$174$	0.404777	0.0306861
$175$	7.08265	0.535398
$176$	6.74208	0.508203
$177$	4.40787	0.331316
$178$	1.42792	0.107027
$179$	−2.13523	−0.159595	−0.0797974	−	0.996811i	$-0.525427\pi$
$179$	−2.13523	−0.159595	−0.0797974	+	0.996811i	$0.525427\pi$
$180$	−13.3176	−0.992637
$181$	6.75232	0.501896	0.250948	−	0.968001i	$-0.419258\pi$
$181$	6.75232	0.501896	0.250948	+	0.968001i	$0.419258\pi$
$182$	1.20739	0.0894975
$183$	3.45453	0.255366
$184$	−3.86435	−0.284884
$185$	−1.16154	−0.0853985
$186$	−1.10560	−0.0810665
$187$	2.81845	0.206106
$188$	2.34544	0.171059
$189$	14.3247	1.04197
$190$	0.443187	0.0321522
$191$	−14.0930	−1.01974	−0.509868	−	0.860252i	$-0.670306\pi$
$191$	−14.0930	−1.01974	−0.509868	+	0.860252i	$0.670306\pi$
$192$	3.51172	0.253437
$193$	−19.3495	−1.39281	−0.696403	−	0.717651i	$-0.745218\pi$
$193$	−19.3495	−1.39281	−0.696403	+	0.717651i	$0.745218\pi$
$194$	−3.30914	−0.237582
$195$	−1.41234	−0.101140
$196$	−26.5974	−1.89982
$197$	−1.89309	−0.134877	−0.0674387	−	0.997723i	$-0.521483\pi$
$197$	−1.89309	−0.134877	−0.0674387	+	0.997723i	$0.521483\pi$
$198$	1.34302	0.0954445
$199$	−23.4206	−1.66024	−0.830122	−	0.557582i	$-0.811729\pi$
$199$	−23.4206	−1.66024	−0.830122	+	0.557582i	$0.811729\pi$
$200$	1.61707	0.114344
$201$	4.92719	0.347537
$202$	3.71254	0.261213
$203$	12.6288	0.886367
$204$	1.59519	0.111686
$205$	16.4643	1.14991
$206$	−3.65241	−0.254475
$207$	10.0083	0.695623
$208$	−3.58404	−0.248509
$209$	1.22960	0.0850534
$210$	−1.70524	−0.117673
$211$	−10.1839	−0.701090	−0.350545	−	0.936546i	$-0.614004\pi$
$211$	−10.1839	−0.701090	−0.350545	+	0.936546i	$0.614004\pi$
$212$	19.4743	1.33750
$213$	6.69010	0.458398
$214$	0.684361	0.0467820
$215$	5.21778	0.355850
$216$	3.27053	0.222531
$217$	−34.4940	−2.34160
$218$	3.26245	0.220961
$219$	−4.35366	−0.294193
$220$	9.29365	0.626578
$221$	−1.49827	−0.100785
$222$	0.0662970	0.00444956
$223$	−6.92619	−0.463812	−0.231906	−	0.972738i	$-0.574496\pi$
$223$	−6.92619	−0.463812	−0.231906	+	0.972738i	$0.574496\pi$
$224$	−13.8170	−0.923189
$225$	−4.18805	−0.279204
$226$	−1.77241	−0.117899
$227$	−0.841559	−0.0558562	−0.0279281	−	0.999610i	$-0.508891\pi$
$227$	−0.841559	−0.0558562	−0.0279281	+	0.999610i	$0.508891\pi$
$228$	0.695931	0.0460891
$229$	7.41968	0.490307	0.245153	−	0.969484i	$-0.421162\pi$
$229$	7.41968	0.490307	0.245153	+	0.969484i	$0.421162\pi$
$230$	−2.51734	−0.165988
$231$	−4.73110	−0.311284
$232$	2.88334	0.189300
$233$	5.66286	0.370986	0.185493	−	0.982646i	$-0.440612\pi$
$233$	5.66286	0.370986	0.185493	+	0.982646i	$0.440612\pi$
$234$	−0.713942	−0.0466718
$235$	3.11130	0.202959
$236$	15.4190	1.00369
$237$	0.551693	0.0358363
$238$	−1.80899	−0.117260
$239$	27.0073	1.74696	0.873480	−	0.486861i	$-0.161858\pi$
$239$	27.0073	1.74696	0.873480	+	0.486861i	$0.161858\pi$
$240$	5.06188	0.326743
$241$	8.49546	0.547241	0.273620	−	0.961838i	$-0.411779\pi$
$241$	8.49546	0.547241	0.273620	+	0.961838i	$0.411779\pi$
$242$	1.97614	0.127031
$243$	−12.9318	−0.829577
$244$	12.0842	0.773609
$245$	−35.2823	−2.25410
$246$	−0.939724	−0.0599146
$247$	−0.653648	−0.0415906
$248$	−7.87548	−0.500094
$249$	3.10628	0.196853
$250$	−2.33670	−0.147786
$251$	2.11313	0.133379	0.0666897	−	0.997774i	$-0.478756\pi$
$251$	2.11313	0.133379	0.0666897	+	0.997774i	$0.478756\pi$
$252$	23.7154	1.49393
$253$	−6.98423	−0.439095
$254$	−3.20460	−0.201074
$255$	2.11607	0.132513
$256$	10.6787	0.667421
$257$	−27.9889	−1.74590	−0.872949	−	0.487811i	$-0.837795\pi$
$257$	−27.9889	−1.74590	−0.872949	+	0.487811i	$0.837795\pi$
$258$	−0.297813	−0.0185410
$259$	2.06842	0.128525
$260$	−4.94044	−0.306393
$261$	−7.46755	−0.462230
$262$	4.08040	0.252088
$263$	−6.65025	−0.410072	−0.205036	−	0.978754i	$-0.565731\pi$
$263$	−6.65025	−0.410072	−0.205036	+	0.978754i	$0.565731\pi$
$264$	−1.08018	−0.0664805
$265$	25.8333	1.58693
$266$	−0.789206	−0.0483893
$267$	2.97441	0.182031
$268$	17.2356	1.05283
$269$	−15.0128	−0.915349	−0.457675	−	0.889120i	$-0.651317\pi$
$269$	−15.0128	−0.915349	−0.457675	+	0.889120i	$0.651317\pi$
$270$	2.13051	0.129658
$271$	23.5498	1.43055	0.715276	−	0.698842i	$-0.246301\pi$
$271$	23.5498	1.43055	0.715276	+	0.698842i	$0.246301\pi$
$272$	5.36987	0.325596
$273$	2.51502	0.152216
$274$	−1.56866	−0.0947660
$275$	2.92262	0.176240
$276$	−3.95294	−0.237939
$277$	−5.14408	−0.309078	−0.154539	−	0.987987i	$-0.549389\pi$
$277$	−5.14408	−0.309078	−0.154539	+	0.987987i	$0.549389\pi$
$278$	−5.06058	−0.303513
$279$	20.3967	1.22112
$280$	−12.1469	−0.725914
$281$	−2.16104	−0.128917	−0.0644584	−	0.997920i	$-0.520532\pi$
$281$	−2.16104	−0.128917	−0.0644584	+	0.997920i	$0.520532\pi$
$282$	−0.177582	−0.0105749
$283$	−15.6722	−0.931613	−0.465806	−	0.884887i	$-0.654236\pi$
$283$	−15.6722	−0.931613	−0.465806	+	0.884887i	$0.654236\pi$
$284$	23.4024	1.38868
$285$	0.923173	0.0546840
$286$	0.498221	0.0294605
$287$	−29.3188	−1.73063
$288$	8.17017	0.481432
$289$	−14.7552	−0.867952
$290$	1.87828	0.110296
$291$	−6.89304	−0.404077
$292$	−15.2294	−0.891232
$293$	−25.5964	−1.49536	−0.747680	−	0.664060i	$-0.768832\pi$
$293$	−25.5964	−1.49536	−0.747680	+	0.664060i	$0.768832\pi$
$294$	2.01379	0.117447
$295$	20.4538	1.19086
$296$	0.472251	0.0274490
$297$	5.91099	0.342990
$298$	−2.35691	−0.136532
$299$	3.71277	0.214715
$300$	1.65414	0.0955020
$301$	−9.29158	−0.535557
$302$	1.94909	0.112158
$303$	7.73332	0.444268
$304$	2.34270	0.134363
$305$	16.0300	0.917874
$306$	1.06968	0.0611494
$307$	−0.444149	−0.0253489	−0.0126745	−	0.999920i	$-0.504035\pi$
$307$	−0.444149	−0.0253489	−0.0126745	+	0.999920i	$0.504035\pi$
$308$	−16.5497	−0.943006
$309$	−7.60808	−0.432808
$310$	−5.13029	−0.291381
$311$	31.6834	1.79660	0.898300	−	0.439382i	$-0.144802\pi$
$311$	31.6834	1.79660	0.898300	+	0.439382i	$0.144802\pi$
$312$	0.574216	0.0325086
$313$	27.7235	1.56703	0.783514	−	0.621375i	$-0.213426\pi$
$313$	27.7235	1.56703	0.783514	+	0.621375i	$0.213426\pi$
$314$	−2.83559	−0.160022
$315$	31.4592	1.77252
$316$	1.92985	0.108563
$317$	1.26479	0.0710379	0.0355190	−	0.999369i	$-0.488692\pi$
$317$	1.26479	0.0710379	0.0355190	+	0.999369i	$0.488692\pi$
$318$	−1.47447	−0.0826844
$319$	5.21120	0.291771
$320$	16.2954	0.910938
$321$	1.42555	0.0795662
$322$	4.48275	0.249814
$323$	0.979342	0.0544921
$324$	−12.2610	−0.681169
$325$	−1.55364	−0.0861806
$326$	2.00564	0.111082
$327$	6.79577	0.375807
$328$	−6.69390	−0.369609
$329$	−5.54045	−0.305455
$330$	−0.703657	−0.0387351
$331$	8.38237	0.460737	0.230368	−	0.973103i	$-0.426007\pi$
$331$	8.38237	0.460737	0.230368	+	0.973103i	$0.426007\pi$
$332$	10.8660	0.596347
$333$	−1.22308	−0.0670245
$334$	0.750514	0.0410663
$335$	22.8635	1.24917
$336$	−9.01395	−0.491751
$337$	14.1689	0.771829	0.385915	−	0.922535i	$-0.373886\pi$
$337$	14.1689	0.771829	0.385915	+	0.922535i	$0.373886\pi$
$338$	−0.264851	−0.0144060
$339$	−3.69199	−0.200521
$340$	7.40212	0.401436
$341$	−14.2338	−0.770801
$342$	0.466667	0.0252345
$343$	30.9177	1.66940
$344$	−2.12140	−0.114378
$345$	−5.24369	−0.282311
$346$	2.50260	0.134541
$347$	20.9096	1.12249	0.561243	−	0.827651i	$-0.310323\pi$
$347$	20.9096	1.12249	0.561243	+	0.827651i	$0.310323\pi$
$348$	2.94944	0.158106
$349$	−3.38637	−0.181268	−0.0906341	−	0.995884i	$-0.528889\pi$
$349$	−3.38637	−0.181268	−0.0906341	+	0.995884i	$0.528889\pi$
$350$	−1.87585	−0.100268
$351$	−3.14224	−0.167720
$352$	−5.70152	−0.303892
$353$	31.8203	1.69363	0.846813	−	0.531891i	$-0.178518\pi$
$353$	31.8203	1.69363	0.846813	+	0.531891i	$0.178518\pi$
$354$	−1.16743	−0.0620482
$355$	31.0439	1.64764
$356$	10.4046	0.551445
$357$	−3.76819	−0.199434
$358$	0.565519	0.0298886
$359$	−2.84610	−0.150211	−0.0751056	−	0.997176i	$-0.523929\pi$
$359$	−2.84610	−0.150211	−0.0751056	+	0.997176i	$0.523929\pi$
$360$	7.18258	0.378555
$361$	−18.5727	−0.977513
$362$	−1.78836	−0.0939941
$363$	4.11636	0.216053
$364$	8.79770	0.461125
$365$	−20.2022	−1.05743
$366$	−0.914936	−0.0478245
$367$	14.4730	0.755486	0.377743	−	0.925911i	$-0.376700\pi$
$367$	14.4730	0.755486	0.377743	+	0.925911i	$0.376700\pi$
$368$	−13.3067	−0.693661
$369$	17.3365	0.902504
$370$	0.307636	0.0159933
$371$	−46.0026	−2.38834
$372$	−8.05602	−0.417685
$373$	8.06190	0.417429	0.208715	−	0.977977i	$-0.433072\pi$
$373$	8.06190	0.417429	0.208715	+	0.977977i	$0.433072\pi$
$374$	−0.746471	−0.0385991
$375$	−4.86742	−0.251353
$376$	−1.26497	−0.0652356
$377$	−2.77024	−0.142675
$378$	−3.79390	−0.195137
$379$	−0.237880	−0.0122191	−0.00610953	−	0.999981i	$-0.501945\pi$
$379$	−0.237880	−0.0122191	−0.00610953	+	0.999981i	$0.501945\pi$
$380$	3.22931	0.165660
$381$	−6.67527	−0.341985
$382$	3.73256	0.190974
$383$	−3.00931	−0.153769	−0.0768843	−	0.997040i	$-0.524497\pi$
$383$	−3.00931	−0.153769	−0.0768843	+	0.997040i	$0.524497\pi$
$384$	−4.27432	−0.218123
$385$	−21.9536	−1.11886
$386$	5.12473	0.260842
$387$	5.49422	0.279287
$388$	−24.1123	−1.22411
$389$	−35.2594	−1.78772	−0.893861	−	0.448344i	$-0.852014\pi$
$389$	−35.2594	−1.78772	−0.893861	+	0.448344i	$0.852014\pi$
$390$	0.374059	0.0189412
$391$	−5.56273	−0.281320
$392$	14.3448	0.724520
$393$	8.49959	0.428748
$394$	0.501388	0.0252596
$395$	2.56001	0.128808
$396$	9.78602	0.491766
$397$	−23.3614	−1.17247	−0.586237	−	0.810140i	$-0.699391\pi$
$397$	−23.3614	−1.17247	−0.586237	+	0.810140i	$0.699391\pi$
$398$	6.20298	0.310927
$399$	−1.64394	−0.0823000
$400$	5.56832	0.278416
$401$	−12.2140	−0.609936	−0.304968	−	0.952363i	$-0.598646\pi$
$401$	−12.2140	−0.609936	−0.304968	+	0.952363i	$0.598646\pi$
$402$	−1.30497	−0.0650861
$403$	7.56657	0.376918
$404$	27.0516	1.34587
$405$	−16.2646	−0.808196
$406$	−3.34475	−0.165997
$407$	0.853523	0.0423076
$408$	−0.860332	−0.0425928
$409$	7.02814	0.347519	0.173760	−	0.984788i	$-0.444408\pi$
$409$	7.02814	0.347519	0.173760	+	0.984788i	$0.444408\pi$
$410$	−4.36058	−0.215354
$411$	−3.26756	−0.161177
$412$	−26.6135	−1.31115
$413$	−36.4230	−1.79226
$414$	−2.65070	−0.130275
$415$	14.4140	0.707556
$416$	3.03089	0.148602
$417$	−10.5413	−0.516211
$418$	−0.325662	−0.0159286
$419$	−25.9098	−1.26578	−0.632889	−	0.774243i	$-0.718131\pi$
$419$	−25.9098	−1.26578	−0.632889	+	0.774243i	$0.718131\pi$
$420$	−12.4253	−0.606294
$421$	19.9856	0.974039	0.487019	−	0.873391i	$-0.338084\pi$
$421$	19.9856	0.974039	0.487019	+	0.873391i	$0.338084\pi$
$422$	2.69722	0.131299
$423$	3.27613	0.159291
$424$	−10.5031	−0.510074
$425$	2.32778	0.112914
$426$	−1.77188	−0.0858479
$427$	−28.5454	−1.38141
$428$	4.98664	0.241038
$429$	1.03781	0.0501059
$430$	−1.38194	−0.0666429
$431$	6.09978	0.293816	0.146908	−	0.989150i	$-0.453068\pi$
$431$	6.09978	0.293816	0.146908	+	0.989150i	$0.453068\pi$
$432$	11.2619	0.541840
$433$	−40.8972	−1.96539	−0.982697	−	0.185219i	$-0.940700\pi$
$433$	−40.8972	−1.96539	−0.982697	+	0.185219i	$0.940700\pi$
$434$	9.13577	0.438531
$435$	3.91251	0.187591
$436$	23.7720	1.13847
$437$	−2.42685	−0.116092
$438$	1.15307	0.0550959
$439$	−9.54307	−0.455466	−0.227733	−	0.973724i	$-0.573131\pi$
$439$	−9.54307	−0.455466	−0.227733	+	0.973724i	$0.573131\pi$
$440$	−5.01234	−0.238954
$441$	−37.1515	−1.76912
$442$	0.396819	0.0188747
$443$	−17.1582	−0.815209	−0.407604	−	0.913159i	$-0.633636\pi$
$443$	−17.1582	−0.815209	−0.407604	+	0.913159i	$0.633636\pi$
$444$	0.483077	0.0229258
$445$	13.8021	0.654281
$446$	1.83441	0.0868618
$447$	−4.90951	−0.232212
$448$	−29.0180	−1.37097
$449$	21.0845	0.995038	0.497519	−	0.867453i	$-0.334244\pi$
$449$	21.0845	0.995038	0.497519	+	0.867453i	$0.334244\pi$
$450$	1.10921	0.0522887
$451$	−12.0982	−0.569683
$452$	−12.9148	−0.607460
$453$	4.06002	0.190756
$454$	0.222888	0.0104606
$455$	11.6704	0.547117
$456$	−0.375336	−0.0175767
$457$	8.90806	0.416701	0.208351	−	0.978054i	$-0.433190\pi$
$457$	8.90806	0.416701	0.208351	+	0.978054i	$0.433190\pi$
$458$	−1.96511	−0.0918236
$459$	4.70793	0.219747
$460$	−18.3427	−0.855234
$461$	20.5340	0.956365	0.478183	−	0.878260i	$-0.341296\pi$
$461$	20.5340	0.956365	0.478183	+	0.878260i	$0.341296\pi$
$462$	1.25304	0.0582966
$463$	−12.2349	−0.568603	−0.284302	−	0.958735i	$-0.591762\pi$
$463$	−12.2349	−0.568603	−0.284302	+	0.958735i	$0.591762\pi$
$464$	9.92865	0.460926
$465$	−10.6866	−0.495577
$466$	−1.49981	−0.0694775
$467$	−6.65827	−0.308108	−0.154054	−	0.988062i	$-0.549233\pi$
$467$	−6.65827	−0.308108	−0.154054	+	0.988062i	$0.549233\pi$
$468$	−5.20218	−0.240471
$469$	−40.7143	−1.88001
$470$	−0.824032	−0.0380097
$471$	−5.90662	−0.272163
$472$	−8.31591	−0.382771
$473$	−3.83412	−0.176293
$474$	−0.146116	−0.00671135
$475$	1.01554	0.0465960
$476$	−13.1813	−0.604165
$477$	27.2019	1.24549
$478$	−7.15292	−0.327167
$479$	−9.48308	−0.433293	−0.216647	−	0.976250i	$-0.569512\pi$
$479$	−9.48308	−0.433293	−0.216647	+	0.976250i	$0.569512\pi$
$480$	−4.28064	−0.195384
$481$	−0.453727	−0.0206882
$482$	−2.25003	−0.102486
$483$	9.33770	0.424880
$484$	14.3993	0.654512
$485$	−31.9856	−1.45239
$486$	3.42501	0.155361
$487$	−22.5759	−1.02301	−0.511505	−	0.859280i	$-0.670912\pi$
$487$	−22.5759	−1.02301	−0.511505	+	0.859280i	$0.670912\pi$
$488$	−6.51733	−0.295026
$489$	4.17780	0.188927
$490$	9.34454	0.422143
$491$	−1.69848	−0.0766514	−0.0383257	−	0.999265i	$-0.512202\pi$
$491$	−1.69848	−0.0766514	−0.0383257	+	0.999265i	$0.512202\pi$
$492$	−6.84736	−0.308703
$493$	4.15057	0.186932
$494$	0.173119	0.00778901
$495$	12.9814	0.583473
$496$	−27.1189	−1.21767
$497$	−55.2815	−2.47972
$498$	−0.822702	−0.0368662
$499$	−4.21656	−0.188759	−0.0943796	−	0.995536i	$-0.530087\pi$
$499$	−4.21656	−0.188759	−0.0943796	+	0.995536i	$0.530087\pi$
$500$	−17.0265	−0.761449
$501$	1.56334	0.0698450
$502$	−0.559664	−0.0249790
$503$	19.7828	0.882072	0.441036	−	0.897489i	$-0.354611\pi$
$503$	19.7828	0.882072	0.441036	+	0.897489i	$0.354611\pi$
$504$	−12.7904	−0.569729
$505$	35.8848	1.59685
$506$	1.84978	0.0822328
$507$	−0.551693	−0.0245015
$508$	−23.3505	−1.03601
$509$	2.08584	0.0924531	0.0462265	−	0.998931i	$-0.485280\pi$
$509$	2.08584	0.0924531	0.0462265	+	0.998931i	$0.485280\pi$
$510$	−0.560442	−0.0248168
$511$	35.9751	1.59145
$512$	−18.3236	−0.809795
$513$	2.05392	0.0906828
$514$	7.41289	0.326968
$515$	−35.3036	−1.55566
$516$	−2.17003	−0.0955304
$517$	−2.28624	−0.100549
$518$	−0.547824	−0.0240700
$519$	5.21300	0.228825
$520$	2.66452	0.116847
$521$	35.8524	1.57072	0.785362	−	0.619037i	$-0.212477\pi$
$521$	35.8524	1.57072	0.785362	+	0.619037i	$0.212477\pi$
$522$	1.97779	0.0865655
$523$	−1.02729	−0.0449204	−0.0224602	−	0.999748i	$-0.507150\pi$
$523$	−1.02729	−0.0449204	−0.0224602	+	0.999748i	$0.507150\pi$
$524$	29.7321	1.29885
$525$	−3.90745	−0.170535
$526$	1.76133	0.0767975
$527$	−11.3368	−0.493837
$528$	−3.71956	−0.161873
$529$	−9.21534	−0.400667
$530$	−6.84197	−0.297196
$531$	21.5374	0.934642
$532$	−5.75060	−0.249320
$533$	6.43134	0.278572
$534$	−0.787775	−0.0340903
$535$	6.61493	0.285988
$536$	−9.29566	−0.401511
$537$	1.17799	0.0508341
$538$	3.97617	0.171425
$539$	25.9260	1.11671
$540$	15.5241	0.668049
$541$	26.1538	1.12444	0.562221	−	0.826987i	$-0.309947\pi$
$541$	26.1538	1.12444	0.562221	+	0.826987i	$0.309947\pi$
$542$	−6.23720	−0.267911
$543$	−3.72521	−0.159864
$544$	−4.54109	−0.194698
$545$	31.5343	1.35078
$546$	−0.666107	−0.0285067
$547$	25.9928	1.11137	0.555686	−	0.831392i	$-0.312456\pi$
$547$	25.9928	1.11137	0.555686	+	0.831392i	$0.312456\pi$
$548$	−11.4301	−0.488270
$549$	16.8792	0.720388
$550$	−0.774058	−0.0330059
$551$	1.81076	0.0771410
$552$	2.13193	0.0907411
$553$	−4.55874	−0.193857
$554$	1.36242	0.0578835
$555$	0.640816	0.0272011
$556$	−36.8742	−1.56381
$557$	−47.0222	−1.99240	−0.996198	−	0.0871194i	$-0.972234\pi$
$557$	−47.0222	−1.99240	−0.996198	+	0.0871194i	$0.972234\pi$
$558$	−5.40209	−0.228689
$559$	2.03819	0.0862063
$560$	−41.8272	−1.76752
$561$	−1.55492	−0.0656488
$562$	0.572353	0.0241433
$563$	29.9301	1.26140	0.630702	−	0.776025i	$-0.282767\pi$
$563$	29.9301	1.26140	0.630702	+	0.776025i	$0.282767\pi$
$564$	−1.29396	−0.0544857
$565$	−17.1318	−0.720742
$566$	4.15079	0.174471
$567$	28.9633	1.21634
$568$	−12.6216	−0.529590
$569$	−26.5799	−1.11429	−0.557144	−	0.830416i	$-0.688103\pi$
$569$	−26.5799	−1.11429	−0.557144	+	0.830416i	$0.688103\pi$
$570$	−0.244503	−0.0102411
$571$	38.2618	1.60121	0.800603	−	0.599195i	$-0.204513\pi$
$571$	38.2618	1.60121	0.800603	+	0.599195i	$0.204513\pi$
$572$	3.63032	0.151791
$573$	7.77503	0.324807
$574$	7.76511	0.324109
$575$	−5.76832	−0.240555
$576$	17.1587	0.714945
$577$	28.1797	1.17314	0.586569	−	0.809899i	$-0.300478\pi$
$577$	28.1797	1.17314	0.586569	+	0.809899i	$0.300478\pi$
$578$	3.90793	0.162548
$579$	10.6750	0.443637
$580$	13.6862	0.568289
$581$	−25.6678	−1.06488
$582$	1.82563	0.0756748
$583$	−18.9827	−0.786184
$584$	8.21364	0.339883
$585$	−6.90085	−0.285315
$586$	6.77924	0.280048
$587$	−3.19149	−0.131727	−0.0658635	−	0.997829i	$-0.520980\pi$
$587$	−3.19149	−0.131727	−0.0658635	+	0.997829i	$0.520980\pi$
$588$	14.6736	0.605129
$589$	−4.94587	−0.203791
$590$	−5.41720	−0.223023
$591$	1.04441	0.0429612
$592$	1.62618	0.0668355
$593$	31.7102	1.30218	0.651092	−	0.758999i	$-0.274311\pi$
$593$	31.7102	1.30218	0.651092	+	0.758999i	$0.274311\pi$
$594$	−1.56553	−0.0642345
$595$	−17.4854	−0.716833
$596$	−17.1737	−0.703464
$597$	12.9210	0.528821
$598$	−0.983331	−0.0402114
$599$	−20.0519	−0.819299	−0.409649	−	0.912243i	$-0.634349\pi$
$599$	−20.0519	−0.819299	−0.409649	+	0.912243i	$0.634349\pi$
$600$	−0.892127	−0.0364209
$601$	−16.4503	−0.671023	−0.335512	−	0.942036i	$-0.608909\pi$
$601$	−16.4503	−0.671023	−0.335512	+	0.942036i	$0.608909\pi$
$602$	2.46088	0.100298
$603$	24.0748	0.980403
$604$	14.2022	0.577878
$605$	19.1010	0.776568
$606$	−2.04818	−0.0832016
$607$	40.0849	1.62700	0.813498	−	0.581567i	$-0.197560\pi$
$607$	40.0849	1.62700	0.813498	+	0.581567i	$0.197560\pi$
$608$	−1.98114	−0.0803457
$609$	−6.96721	−0.282326
$610$	−4.24556	−0.171898
$611$	1.21535	0.0491677
$612$	7.79428	0.315065
$613$	−1.52546	−0.0616128	−0.0308064	−	0.999525i	$-0.509808\pi$
$613$	−1.52546	−0.0616128	−0.0308064	+	0.999525i	$0.509808\pi$
$614$	0.117633	0.00474730
$615$	−9.08322	−0.366271
$616$	8.92572	0.359628
$617$	−24.4186	−0.983055	−0.491528	−	0.870862i	$-0.663561\pi$
$617$	−24.4186	−0.983055	−0.491528	+	0.870862i	$0.663561\pi$
$618$	2.01501	0.0810555
$619$	40.2338	1.61713	0.808567	−	0.588404i	$-0.200244\pi$
$619$	40.2338	1.61713	0.808567	+	0.588404i	$0.200244\pi$
$620$	−37.3822	−1.50130
$621$	−11.6664	−0.468157
$622$	−8.39138	−0.336464
$623$	−24.5780	−0.984699
$624$	1.97729	0.0791550
$625$	−30.3544	−1.21418
$626$	−7.34261	−0.293470
$627$	−0.678363	−0.0270912
$628$	−20.6617	−0.824492
$629$	0.679806	0.0271056
$630$	−8.33199	−0.331955
$631$	44.3338	1.76490	0.882450	−	0.470407i	$-0.155893\pi$
$631$	44.3338	1.76490	0.882450	+	0.470407i	$0.155893\pi$
$632$	−1.04083	−0.0414018
$633$	5.61840	0.223311
$634$	−0.334982	−0.0133038
$635$	−30.9751	−1.22921
$636$	−10.7438	−0.426021
$637$	−13.7821	−0.546066
$638$	−1.38019	−0.0546423
$639$	32.6886	1.29314
$640$	−19.8341	−0.784010
$641$	46.2897	1.82833	0.914167	−	0.405338i	$-0.132846\pi$
$641$	46.2897	1.82833	0.914167	+	0.405338i	$0.132846\pi$
$642$	−0.377557	−0.0149010
$643$	8.95695	0.353227	0.176614	−	0.984280i	$-0.443486\pi$
$643$	8.95695	0.353227	0.176614	+	0.984280i	$0.443486\pi$
$644$	32.6638	1.28713
$645$	−2.87861	−0.113345
$646$	−0.259380	−0.0102052
$647$	−4.98533	−0.195994	−0.0979968	−	0.995187i	$-0.531243\pi$
$647$	−4.98533	−0.195994	−0.0979968	+	0.995187i	$0.531243\pi$
$648$	6.61274	0.259773
$649$	−15.0298	−0.589970
$650$	0.411484	0.0161397
$651$	19.0301	0.745848
$652$	14.6142	0.572336
$653$	0.635077	0.0248525	0.0124262	−	0.999923i	$-0.496045\pi$
$653$	0.635077	0.0248525	0.0124262	+	0.999923i	$0.496045\pi$
$654$	−1.79987	−0.0703804
$655$	39.4405	1.54107
$656$	−23.0502	−0.899959
$657$	−21.2725	−0.829919
$658$	1.46739	0.0572050
$659$	15.0392	0.585844	0.292922	−	0.956136i	$-0.405372\pi$
$659$	15.0392	0.585844	0.292922	+	0.956136i	$0.405372\pi$
$660$	−5.12724	−0.199578
$661$	−2.03059	−0.0789808	−0.0394904	−	0.999220i	$-0.512573\pi$
$661$	−2.03059	−0.0789808	−0.0394904	+	0.999220i	$0.512573\pi$
$662$	−2.22008	−0.0862859
$663$	0.826585	0.0321019
$664$	−5.86032	−0.227425
$665$	−7.62834	−0.295814
$666$	0.323935	0.0125522
$667$	−10.2853	−0.398247
$668$	5.46867	0.211589
$669$	3.82113	0.147733
$670$	−6.05543	−0.233942
$671$	−11.7791	−0.454727
$672$	7.62276	0.294054
$673$	−28.9199	−1.11478	−0.557391	−	0.830250i	$-0.688198\pi$
$673$	−28.9199	−1.11478	−0.557391	+	0.830250i	$0.688198\pi$
$674$	−3.75265	−0.144547
$675$	4.88192	0.187905
$676$	−1.92985	−0.0742251
$677$	−21.7757	−0.836908	−0.418454	−	0.908238i	$-0.637428\pi$
$677$	−21.7757	−0.836908	−0.418454	+	0.908238i	$0.637428\pi$
$678$	0.977827	0.0375532
$679$	56.9584	2.18586
$680$	−3.99218	−0.153093
$681$	0.464282	0.0177913
$682$	3.76983	0.144354
$683$	−48.8201	−1.86805	−0.934025	−	0.357208i	$-0.883729\pi$
$683$	−48.8201	−1.86805	−0.934025	+	0.357208i	$0.883729\pi$
$684$	3.40040	0.130017
$685$	−15.1624	−0.579325
$686$	−8.18860	−0.312642
$687$	−4.09339	−0.156172
$688$	−7.30496	−0.278499
$689$	10.0911	0.384440
$690$	1.38880	0.0528706
$691$	−39.3630	−1.49744	−0.748720	−	0.662887i	$-0.769331\pi$
$691$	−39.3630	−1.49744	−0.748720	+	0.662887i	$0.769331\pi$
$692$	18.2354	0.693205
$693$	−23.1167	−0.878132
$694$	−5.53793	−0.210217
$695$	−48.9147	−1.85544
$696$	−1.59072	−0.0602959
$697$	−9.63588	−0.364985
$698$	0.896884	0.0339476
$699$	−3.12416	−0.118166
$700$	−13.6685	−0.516620
$701$	10.9679	0.414251	0.207125	−	0.978314i	$-0.433589\pi$
$701$	10.9679	0.414251	0.207125	+	0.978314i	$0.433589\pi$
$702$	0.832226	0.0314103
$703$	0.296578	0.0111856
$704$	−11.9741	−0.451291
$705$	−1.71648	−0.0646465
$706$	−8.42765	−0.317179
$707$	−63.9019	−2.40328
$708$	−8.50655	−0.319696
$709$	4.26945	0.160342	0.0801712	−	0.996781i	$-0.474453\pi$
$709$	4.26945	0.160342	0.0801712	+	0.996781i	$0.474453\pi$
$710$	−8.22202	−0.308567
$711$	2.69564	0.101094
$712$	−5.61153	−0.210301
$713$	28.0929	1.05209
$714$	0.998008	0.0373495
$715$	4.81573	0.180098
$716$	4.12069	0.153997
$717$	−14.8998	−0.556442
$718$	0.753792	0.0281313
$719$	−33.6725	−1.25577	−0.627887	−	0.778305i	$-0.716080\pi$
$719$	−33.6725	−1.25577	−0.627887	+	0.778305i	$0.716080\pi$
$720$	24.7329	0.921742
$721$	62.8669	2.34129
$722$	4.91901	0.183067
$723$	−4.68689	−0.174307
$724$	−13.0310	−0.484293
$725$	4.30396	0.159845
$726$	−1.09022	−0.0404619
$727$	44.4795	1.64965	0.824827	−	0.565385i	$-0.191272\pi$
$727$	44.4795	1.64965	0.824827	+	0.565385i	$0.191272\pi$
$728$	−4.74485	−0.175856
$729$	−11.9257	−0.441691
$730$	5.35058	0.198034
$731$	−3.05376	−0.112947
$732$	−6.66674	−0.246410
$733$	−6.69469	−0.247274	−0.123637	−	0.992328i	$-0.539456\pi$
$733$	−6.69469	−0.247274	−0.123637	+	0.992328i	$0.539456\pi$
$734$	−3.83320	−0.141486
$735$	19.4650	0.717976
$736$	11.2530	0.414791
$737$	−16.8005	−0.618855
$738$	−4.59160	−0.169019
$739$	−1.66292	−0.0611717	−0.0305858	−	0.999532i	$-0.509737\pi$
$739$	−1.66292	−0.0611717	−0.0305858	+	0.999532i	$0.509737\pi$
$740$	2.24161	0.0824033
$741$	0.360613	0.0132475
$742$	12.1838	0.447283
$743$	50.1368	1.83934	0.919671	−	0.392691i	$-0.128456\pi$
$743$	50.1368	1.83934	0.919671	+	0.392691i	$0.128456\pi$
$744$	4.34485	0.159290
$745$	−22.7815	−0.834649
$746$	−2.13520	−0.0781754
$747$	15.1776	0.555321
$748$	−5.43920	−0.198877
$749$	−11.7795	−0.430415
$750$	1.28914	0.0470728
$751$	−32.5779	−1.18879	−0.594393	−	0.804175i	$-0.702608\pi$
$751$	−32.5779	−1.18879	−0.594393	+	0.804175i	$0.702608\pi$
$752$	−4.35586	−0.158842
$753$	−1.16580	−0.0424840
$754$	0.733701	0.0267198
$755$	18.8396	0.685643
$756$	−27.6445	−1.00542
$757$	−41.8694	−1.52177	−0.760885	−	0.648887i	$-0.775235\pi$
$757$	−41.8694	−1.52177	−0.760885	+	0.648887i	$0.775235\pi$
$758$	0.0630028	0.00228836
$759$	3.85315	0.139861
$760$	−1.74166	−0.0631767
$761$	−37.6002	−1.36300	−0.681502	−	0.731816i	$-0.738673\pi$
$761$	−37.6002	−1.36300	−0.681502	+	0.731816i	$0.738673\pi$
$762$	1.76795	0.0640462
$763$	−56.1547	−2.03294
$764$	27.1975	0.983971
$765$	10.3393	0.373820
$766$	0.797020	0.0287975
$767$	7.98972	0.288492
$768$	−5.89138	−0.212587
$769$	44.6033	1.60843	0.804217	−	0.594335i	$-0.202585\pi$
$769$	44.6033	1.60843	0.804217	+	0.594335i	$0.202585\pi$
$770$	5.81445	0.209538
$771$	15.4413	0.556104
$772$	37.3417	1.34396
$773$	0.711131	0.0255776	0.0127888	−	0.999918i	$-0.495929\pi$
$773$	0.711131	0.0255776	0.0127888	+	0.999918i	$0.495929\pi$
$774$	−1.45515	−0.0523043
$775$	−11.7557	−0.422279
$776$	13.0044	0.466832
$777$	−1.14113	−0.0409379
$778$	9.33849	0.334801
$779$	−4.20383	−0.150618
$780$	2.72561	0.0975924
$781$	−22.8116	−0.816264
$782$	1.47330	0.0526850
$783$	8.70476	0.311083
$784$	49.3956	1.76413
$785$	−27.4084	−0.978247
$786$	−2.25113	−0.0802950
$787$	47.1383	1.68030	0.840150	−	0.542355i	$-0.182467\pi$
$787$	47.1383	1.68030	0.840150	+	0.542355i	$0.182467\pi$
$788$	3.65340	0.130147
$789$	3.66890	0.130616
$790$	−0.678021	−0.0241229
$791$	30.5075	1.08472
$792$	−5.27788	−0.187541
$793$	6.26169	0.222359
$794$	6.18728	0.219579
$795$	−14.2520	−0.505467
$796$	45.1984	1.60201
$797$	1.49800	0.0530618	0.0265309	−	0.999648i	$-0.491554\pi$
$797$	1.49800	0.0530618	0.0265309	+	0.999648i	$0.491554\pi$
$798$	0.435399	0.0154130
$799$	−1.82092	−0.0644195
$800$	−4.70892	−0.166485
$801$	14.5333	0.513508
$802$	3.23488	0.114228
$803$	14.8449	0.523866
$804$	−9.50876	−0.335348
$805$	43.3295	1.52717
$806$	−2.00401	−0.0705884
$807$	8.28248	0.291557
$808$	−14.5897	−0.513265
$809$	25.1215	0.883224	0.441612	−	0.897206i	$-0.354407\pi$
$809$	25.1215	0.883224	0.441612	+	0.897206i	$0.354407\pi$
$810$	4.30771	0.151357
$811$	−15.5721	−0.546811	−0.273405	−	0.961899i	$-0.588150\pi$
$811$	−15.5721	−0.546811	−0.273405	+	0.961899i	$0.588150\pi$
$812$	−24.3717	−0.855280
$813$	−12.9923	−0.455659
$814$	−0.226056	−0.00792327
$815$	19.3862	0.679067
$816$	−2.96252	−0.103709
$817$	−1.33226	−0.0466099
$818$	−1.86141	−0.0650827
$819$	12.2887	0.429402
$820$	−31.7736	−1.10958
$821$	23.6501	0.825394	0.412697	−	0.910868i	$-0.364587\pi$
$821$	23.6501	0.825394	0.412697	+	0.910868i	$0.364587\pi$
$822$	0.865416	0.0301849
$823$	−17.8978	−0.623877	−0.311938	−	0.950102i	$-0.600978\pi$
$823$	−17.8978	−0.623877	−0.311938	+	0.950102i	$0.600978\pi$
$824$	14.3534	0.500025
$825$	−1.61239	−0.0561361
$826$	9.64668	0.335651
$827$	21.1670	0.736047	0.368024	−	0.929816i	$-0.380035\pi$
$827$	21.1670	0.736047	0.368024	+	0.929816i	$0.380035\pi$
$828$	−19.3145	−0.671225
$829$	45.5759	1.58292	0.791458	−	0.611224i	$-0.209323\pi$
$829$	45.5759	1.58292	0.791458	+	0.611224i	$0.209323\pi$
$830$	−3.81757	−0.132510
$831$	2.83795	0.0984475
$832$	6.36535	0.220679
$833$	20.6493	0.715456
$834$	2.79188	0.0966750
$835$	7.25435	0.251047
$836$	−2.37295	−0.0820703
$837$	−23.7760	−0.821818
$838$	6.86224	0.237052
$839$	17.6713	0.610081	0.305041	−	0.952339i	$-0.401330\pi$
$839$	17.6713	0.610081	0.305041	+	0.952339i	$0.401330\pi$
$840$	6.70134	0.231218
$841$	−21.3258	−0.735372
$842$	−5.29321	−0.182416
$843$	1.19223	0.0410626
$844$	19.6535	0.676501
$845$	−2.56001	−0.0880670
$846$	−0.867688	−0.0298317
$847$	−34.0142	−1.16874
$848$	−36.1669	−1.24198
$849$	8.64621	0.296737
$850$	−0.616514	−0.0211463
$851$	−1.68458	−0.0577468
$852$	−12.9109	−0.442321
$853$	37.4805	1.28331	0.641654	−	0.766994i	$-0.278248\pi$
$853$	37.4805	1.28331	0.641654	+	0.766994i	$0.278248\pi$
$854$	7.56028	0.258708
$855$	4.51073	0.154264
$856$	−2.68944	−0.0919232
$857$	16.1904	0.553054	0.276527	−	0.961006i	$-0.410816\pi$
$857$	16.1904	0.553054	0.276527	+	0.961006i	$0.410816\pi$
$858$	−0.274865	−0.00938374
$859$	2.12178	0.0723942	0.0361971	−	0.999345i	$-0.488476\pi$
$859$	2.12178	0.0723942	0.0361971	+	0.999345i	$0.488476\pi$
$860$	−10.0696	−0.343369
$861$	16.1750	0.551241
$862$	−1.61553	−0.0550253
$863$	7.56885	0.257647	0.128823	−	0.991668i	$-0.458880\pi$
$863$	7.56885	0.257647	0.128823	+	0.991668i	$0.458880\pi$
$864$	−9.52379	−0.324006
$865$	24.1898	0.822477
$866$	10.8317	0.368075
$867$	8.14033	0.276460
$868$	66.5684	2.25948
$869$	−1.88114	−0.0638132
$870$	−1.03623	−0.0351316
$871$	8.93104	0.302617
$872$	−12.8209	−0.434172
$873$	−33.6802	−1.13990
$874$	0.642753	0.0217414
$875$	40.2204	1.35970
$876$	8.40194	0.283875
$877$	−27.9289	−0.943093	−0.471546	−	0.881841i	$-0.656304\pi$
$877$	−27.9289	−0.943093	−0.471546	+	0.881841i	$0.656304\pi$
$878$	2.52749	0.0852988
$879$	14.1214	0.476302
$880$	−17.2598	−0.581827
$881$	−29.9278	−1.00829	−0.504147	−	0.863618i	$-0.668193\pi$
$881$	−29.9278	−1.00829	−0.504147	+	0.863618i	$0.668193\pi$
$882$	9.83961	0.331317
$883$	−16.1063	−0.542020	−0.271010	−	0.962577i	$-0.587358\pi$
$883$	−16.1063	−0.542020	−0.271010	+	0.962577i	$0.587358\pi$
$884$	2.89144	0.0972498
$885$	−11.2842	−0.379314
$886$	4.54436	0.152671
$887$	18.1405	0.609098	0.304549	−	0.952497i	$-0.401494\pi$
$887$	18.1405	0.609098	0.304549	+	0.952497i	$0.401494\pi$
$888$	−0.260537	−0.00874306
$889$	55.1590	1.84997
$890$	−3.65549	−0.122532
$891$	11.9515	0.400391
$892$	13.3665	0.447545
$893$	−0.794410	−0.0265839
$894$	1.30029	0.0434882
$895$	5.46621	0.182715
$896$	35.3195	1.17994
$897$	−2.04831	−0.0683910
$898$	−5.58425	−0.186349
$899$	−20.9612	−0.699095
$900$	8.08233	0.269411
$901$	−15.1192	−0.503693
$902$	3.20423	0.106689
$903$	5.12610	0.170586
$904$	6.96532	0.231663
$905$	−17.2860	−0.574606
$906$	−1.07530	−0.0357244
$907$	−33.0101	−1.09608	−0.548041	−	0.836452i	$-0.684626\pi$
$907$	−33.0101	−1.09608	−0.548041	+	0.836452i	$0.684626\pi$
$908$	1.62409	0.0538972
$909$	37.7859	1.25328
$910$	−3.09092	−0.102463
$911$	32.4875	1.07636	0.538179	−	0.842830i	$-0.319112\pi$
$911$	32.4875	1.07636	0.538179	+	0.842830i	$0.319112\pi$
$912$	−1.29245	−0.0427974
$913$	−10.5917	−0.350533
$914$	−2.35931	−0.0780390
$915$	−8.84363	−0.292361
$916$	−14.3189	−0.473110
$917$	−70.2336	−2.31932
$918$	−1.24690	−0.0411538
$919$	−47.9979	−1.58330	−0.791652	−	0.610973i	$-0.790778\pi$
$919$	−47.9979	−1.58330	−0.791652	+	0.610973i	$0.790778\pi$
$920$	9.89276	0.326155
$921$	0.245034	0.00807415
$922$	−5.43846	−0.179106
$923$	12.1265	0.399149
$924$	9.13034	0.300366
$925$	0.704929	0.0231779
$926$	3.24042	0.106487
$927$	−37.1739	−1.22095
$928$	−8.39629	−0.275622
$929$	40.8695	1.34089	0.670443	−	0.741961i	$-0.266104\pi$
$929$	40.8695	1.34089	0.670443	+	0.741961i	$0.266104\pi$
$930$	2.83035	0.0928107
$931$	9.00864	0.295246
$932$	−10.9285	−0.357974
$933$	−17.4795	−0.572253
$934$	1.76345	0.0577018
$935$	−7.21527	−0.235964
$936$	2.80569	0.0917068
$937$	36.2541	1.18437	0.592185	−	0.805802i	$-0.298266\pi$
$937$	36.2541	1.18437	0.592185	+	0.805802i	$0.298266\pi$
$938$	10.7832	0.352085
$939$	−15.2949	−0.499129
$940$	−6.00436	−0.195841
$941$	−60.8299	−1.98300	−0.991500	−	0.130110i	$-0.958467\pi$
$941$	−60.8299	−1.98300	−0.991500	+	0.130110i	$0.958467\pi$
$942$	1.56438	0.0509701
$943$	23.8781	0.777577
$944$	−28.6355	−0.932007
$945$	−36.6712	−1.19292
$946$	1.01547	0.0330158
$947$	−54.1111	−1.75838	−0.879188	−	0.476476i	$-0.841914\pi$
$947$	−54.1111	−1.75838	−0.879188	+	0.476476i	$0.841914\pi$
$948$	−1.06469	−0.0345794
$949$	−7.89146	−0.256168
$950$	−0.268966	−0.00872640
$951$	−0.697778	−0.0226270
$952$	7.10908	0.230406
$953$	44.3479	1.43657	0.718285	−	0.695749i	$-0.244928\pi$
$953$	44.3479	1.43657	0.718285	+	0.695749i	$0.244928\pi$
$954$	−7.20445	−0.233253
$955$	36.0783	1.16747
$956$	−52.1202	−1.68569
$957$	−2.87498	−0.0929349
$958$	2.51160	0.0811463
$959$	27.0004	0.871889
$960$	−8.99003	−0.290152
$961$	26.2529	0.846869
$962$	0.120170	0.00387444
$963$	6.96538	0.224456
$964$	−16.3950	−0.528047
$965$	49.5349	1.59458
$966$	−2.47310	−0.0795707
$967$	24.6273	0.791962	0.395981	−	0.918259i	$-0.370405\pi$
$967$	24.6273	0.791962	0.395981	+	0.918259i	$0.370405\pi$
$968$	−7.76594	−0.249607
$969$	−0.540296	−0.0173568
$970$	8.47143	0.272001
$971$	−45.0275	−1.44500	−0.722500	−	0.691371i	$-0.757007\pi$
$971$	−45.0275	−1.44500	−0.722500	+	0.691371i	$0.757007\pi$
$972$	24.9565	0.800481
$973$	87.1049	2.79246
$974$	5.97924	0.191587
$975$	0.857134	0.0274502
$976$	−22.4422	−0.718357
$977$	36.4169	1.16508	0.582539	−	0.812803i	$-0.302059\pi$
$977$	36.4169	1.16508	0.582539	+	0.812803i	$0.302059\pi$
$978$	−1.10649	−0.0353818
$979$	−10.1420	−0.324140
$980$	68.0896	2.17504
$981$	33.2049	1.06015
$982$	0.449845	0.0143551
$983$	−8.00689	−0.255380	−0.127690	−	0.991814i	$-0.540756\pi$
$983$	−8.00689	−0.255380	−0.127690	+	0.991814i	$0.540756\pi$
$984$	3.69298	0.117728
$985$	4.84634	0.154417
$986$	−1.09928	−0.0350083
$987$	3.05663	0.0972935
$988$	1.26145	0.0401319
$989$	7.56733	0.240627
$990$	−3.43815	−0.109272
$991$	52.3068	1.66158	0.830790	−	0.556585i	$-0.187889\pi$
$991$	52.3068	1.66158	0.830790	+	0.556585i	$0.187889\pi$
$992$	22.9334	0.728137
$993$	−4.62450	−0.146754
$994$	14.6414	0.464396
$995$	59.9570	1.90076
$996$	−5.99467	−0.189948
$997$	−1.39557	−0.0441980	−0.0220990	−	0.999756i	$-0.507035\pi$
$997$	−1.39557	−0.0441980	−0.0220990	+	0.999756i	$0.507035\pi$
$998$	1.11676	0.0353504
$999$	1.42572	0.0451078

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1027.2.a.c.1.10	✓	18
3.2	odd	2		9243.2.a.m.1.9		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1027.2.a.c.1.10	✓	18	1.1	even	1	trivial
9243.2.a.m.1.9		18	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1027 = 13 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1027.a (trivial)

\(f(q)\)	\(=\)	\(q-0.264851 q^{2} -0.551693 q^{3} -1.92985 q^{4} -2.56001 q^{5} +0.146116 q^{6} +4.55874 q^{7} +1.04083 q^{8} -2.69564 q^{9} +O(q^{10})\)	\(q-0.264851 q^{2} -0.551693 q^{3} -1.92985 q^{4} -2.56001 q^{5} +0.146116 q^{6} +4.55874 q^{7} +1.04083 q^{8} -2.69564 q^{9} +0.678021 q^{10} +1.88114 q^{11} +1.06469 q^{12} -1.00000 q^{13} -1.20739 q^{14} +1.41234 q^{15} +3.58404 q^{16} +1.49827 q^{17} +0.713942 q^{18} +0.653648 q^{19} +4.94044 q^{20} -2.51502 q^{21} -0.498221 q^{22} -3.71277 q^{23} -0.574216 q^{24} +1.55364 q^{25} +0.264851 q^{26} +3.14224 q^{27} -8.79770 q^{28} +2.77024 q^{29} -0.374059 q^{30} -7.56657 q^{31} -3.03089 q^{32} -1.03781 q^{33} -0.396819 q^{34} -11.6704 q^{35} +5.20218 q^{36} +0.453727 q^{37} -0.173119 q^{38} +0.551693 q^{39} -2.66452 q^{40} -6.43134 q^{41} +0.666107 q^{42} -2.03819 q^{43} -3.63032 q^{44} +6.90085 q^{45} +0.983331 q^{46} -1.21535 q^{47} -1.97729 q^{48} +13.7821 q^{49} -0.411484 q^{50} -0.826585 q^{51} +1.92985 q^{52} -10.0911 q^{53} -0.832226 q^{54} -4.81573 q^{55} +4.74485 q^{56} -0.360613 q^{57} -0.733701 q^{58} -7.98972 q^{59} -2.72561 q^{60} -6.26169 q^{61} +2.00401 q^{62} -12.2887 q^{63} -6.36535 q^{64} +2.56001 q^{65} +0.274865 q^{66} -8.93104 q^{67} -2.89144 q^{68} +2.04831 q^{69} +3.09092 q^{70} -12.1265 q^{71} -2.80569 q^{72} +7.89146 q^{73} -0.120170 q^{74} -0.857134 q^{75} -1.26145 q^{76} +8.57561 q^{77} -0.146116 q^{78} -1.00000 q^{79} -9.17518 q^{80} +6.35335 q^{81} +1.70335 q^{82} -5.63045 q^{83} +4.85363 q^{84} -3.83559 q^{85} +0.539817 q^{86} -1.52832 q^{87} +1.95794 q^{88} -5.39142 q^{89} -1.82770 q^{90} -4.55874 q^{91} +7.16510 q^{92} +4.17442 q^{93} +0.321886 q^{94} -1.67335 q^{95} +1.67212 q^{96} +12.4943 q^{97} -3.65020 q^{98} -5.07086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 6 q^{2} - 8 q^{3} + 16 q^{4} - 7 q^{5} + 2 q^{6} - 6 q^{7} - 18 q^{8} + 10 q^{9}+O(q^{10}) \) 18 * q - 6 * q^2 - 8 * q^3 + 16 * q^4 - 7 * q^5 + 2 * q^6 - 6 * q^7 - 18 * q^8 + 10 * q^9	\( 18 q - 6 q^{2} - 8 q^{3} + 16 q^{4} - 7 q^{5} + 2 q^{6} - 6 q^{7} - 18 q^{8} + 10 q^{9} - 8 q^{10} - 2 q^{11} - 25 q^{12} - 18 q^{13} - 16 q^{14} - 8 q^{15} + 20 q^{16} - 25 q^{17} - 15 q^{18} - 3 q^{19} - 5 q^{20} - 14 q^{21} - 14 q^{22} - 21 q^{23} + 18 q^{24} + 9 q^{25} + 6 q^{26} - 35 q^{27} - q^{28} - 50 q^{29} - 8 q^{30} + 19 q^{31} - 37 q^{32} - 4 q^{33} + 26 q^{34} - 26 q^{35} + 14 q^{36} - 40 q^{37} - 3 q^{38} + 8 q^{39} - 36 q^{40} - q^{41} + 49 q^{42} - 17 q^{43} + 11 q^{44} - 12 q^{45} + 4 q^{46} - 15 q^{47} - 59 q^{48} + 24 q^{49} - 34 q^{50} + 10 q^{51} - 16 q^{52} - 79 q^{53} + 58 q^{54} + 12 q^{55} - 37 q^{56} - 3 q^{57} - 14 q^{58} + 7 q^{59} + 30 q^{60} - 30 q^{61} - 52 q^{62} - 3 q^{63} + 38 q^{64} + 7 q^{65} - 56 q^{66} + 8 q^{67} - 21 q^{68} - 22 q^{69} + 39 q^{70} - 20 q^{71} - 46 q^{72} - 9 q^{73} - 4 q^{74} + 10 q^{75} - 46 q^{76} - 75 q^{77} - 2 q^{78} - 18 q^{79} + 36 q^{80} - 18 q^{81} - 16 q^{82} - 13 q^{83} - 61 q^{84} - 21 q^{85} + 19 q^{86} - 8 q^{87} - 10 q^{88} + 18 q^{89} + 58 q^{90} + 6 q^{91} - 76 q^{92} - 41 q^{93} + 58 q^{94} - 25 q^{95} + 96 q^{96} + 24 q^{97} - 35 q^{98} + 26 q^{99}+O(q^{100}) \) 18 * q - 6 * q^2 - 8 * q^3 + 16 * q^4 - 7 * q^5 + 2 * q^6 - 6 * q^7 - 18 * q^8 + 10 * q^9 - 8 * q^10 - 2 * q^11 - 25 * q^12 - 18 * q^13 - 16 * q^14 - 8 * q^15 + 20 * q^16 - 25 * q^17 - 15 * q^18 - 3 * q^19 - 5 * q^20 - 14 * q^21 - 14 * q^22 - 21 * q^23 + 18 * q^24 + 9 * q^25 + 6 * q^26 - 35 * q^27 - q^28 - 50 * q^29 - 8 * q^30 + 19 * q^31 - 37 * q^32 - 4 * q^33 + 26 * q^34 - 26 * q^35 + 14 * q^36 - 40 * q^37 - 3 * q^38 + 8 * q^39 - 36 * q^40 - q^41 + 49 * q^42 - 17 * q^43 + 11 * q^44 - 12 * q^45 + 4 * q^46 - 15 * q^47 - 59 * q^48 + 24 * q^49 - 34 * q^50 + 10 * q^51 - 16 * q^52 - 79 * q^53 + 58 * q^54 + 12 * q^55 - 37 * q^56 - 3 * q^57 - 14 * q^58 + 7 * q^59 + 30 * q^60 - 30 * q^61 - 52 * q^62 - 3 * q^63 + 38 * q^64 + 7 * q^65 - 56 * q^66 + 8 * q^67 - 21 * q^68 - 22 * q^69 + 39 * q^70 - 20 * q^71 - 46 * q^72 - 9 * q^73 - 4 * q^74 + 10 * q^75 - 46 * q^76 - 75 * q^77 - 2 * q^78 - 18 * q^79 + 36 * q^80 - 18 * q^81 - 16 * q^82 - 13 * q^83 - 61 * q^84 - 21 * q^85 + 19 * q^86 - 8 * q^87 - 10 * q^88 + 18 * q^89 + 58 * q^90 + 6 * q^91 - 76 * q^92 - 41 * q^93 + 58 * q^94 - 25 * q^95 + 96 * q^96 + 24 * q^97 - 35 * q^98 + 26 * q^99

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