LMFDB - Embedded newform 4030.2.a.j.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4030,2,Mod(1,4030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4030, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4030 = 2 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4030.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:	$32.1797120146$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 6x^{5} + 20x^{4} + 9x^{3} - 37x^{2} - 3x + 20 $ x^7 - 3x^6 - 6x^5 + 20x^4 + 9x^3 - 37x^2 - 3x + 20
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-1.98668$ of defining polynomial
Character	$\chi$	$=$	4030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.820963 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.820963 q^{6} +2.40836 q^{7} +1.00000 q^{8} -2.32602 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.820963 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.820963 q^{6} +2.40836 q^{7} +1.00000 q^{8} -2.32602 q^{9} -1.00000 q^{10} -0.643884 q^{11} +0.820963 q^{12} -1.00000 q^{13} +2.40836 q^{14} -0.820963 q^{15} +1.00000 q^{16} -7.01761 q^{17} -2.32602 q^{18} -4.17256 q^{19} -1.00000 q^{20} +1.97717 q^{21} -0.643884 q^{22} -2.44939 q^{23} +0.820963 q^{24} +1.00000 q^{25} -1.00000 q^{26} -4.37246 q^{27} +2.40836 q^{28} -7.99422 q^{29} -0.820963 q^{30} +1.00000 q^{31} +1.00000 q^{32} -0.528605 q^{33} -7.01761 q^{34} -2.40836 q^{35} -2.32602 q^{36} +4.60774 q^{37} -4.17256 q^{38} -0.820963 q^{39} -1.00000 q^{40} +5.00986 q^{41} +1.97717 q^{42} -10.6353 q^{43} -0.643884 q^{44} +2.32602 q^{45} -2.44939 q^{46} +7.08296 q^{47} +0.820963 q^{48} -1.19981 q^{49} +1.00000 q^{50} -5.76120 q^{51} -1.00000 q^{52} +0.0598965 q^{53} -4.37246 q^{54} +0.643884 q^{55} +2.40836 q^{56} -3.42552 q^{57} -7.99422 q^{58} -3.54904 q^{59} -0.820963 q^{60} -12.2448 q^{61} +1.00000 q^{62} -5.60189 q^{63} +1.00000 q^{64} +1.00000 q^{65} -0.528605 q^{66} -6.35346 q^{67} -7.01761 q^{68} -2.01086 q^{69} -2.40836 q^{70} +5.07826 q^{71} -2.32602 q^{72} -12.8377 q^{73} +4.60774 q^{74} +0.820963 q^{75} -4.17256 q^{76} -1.55070 q^{77} -0.820963 q^{78} +11.0105 q^{79} -1.00000 q^{80} +3.38843 q^{81} +5.00986 q^{82} +15.7904 q^{83} +1.97717 q^{84} +7.01761 q^{85} -10.6353 q^{86} -6.56296 q^{87} -0.643884 q^{88} -12.0033 q^{89} +2.32602 q^{90} -2.40836 q^{91} -2.44939 q^{92} +0.820963 q^{93} +7.08296 q^{94} +4.17256 q^{95} +0.820963 q^{96} +15.2953 q^{97} -1.19981 q^{98} +1.49769 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 7 q^{2} - 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 4 q^{7} + 7 q^{8} + 4 q^{9}+O(q^{10}) $ 7 * q + 7 * q^2 - 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 4 * q^7 + 7 * q^8 + 4 * q^9	\( 7 q + 7 q^{2} - 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 4 q^{7} + 7 q^{8} + 4 q^{9} - 7 q^{10} - 10 q^{11} - 3 q^{12} - 7 q^{13} + 4 q^{14} + 3 q^{15} + 7 q^{16} - 6 q^{17} + 4 q^{18} - 5 q^{19} - 7 q^{20} - 15 q^{21} - 10 q^{22} - 11 q^{23} - 3 q^{24} + 7 q^{25} - 7 q^{26} - 21 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 7 q^{31} + 7 q^{32} + 4 q^{33} - 6 q^{34} - 4 q^{35} + 4 q^{36} - 8 q^{37} - 5 q^{38} + 3 q^{39} - 7 q^{40} - 12 q^{41} - 15 q^{42} - 5 q^{43} - 10 q^{44} - 4 q^{45} - 11 q^{46} - 10 q^{47} - 3 q^{48} + 7 q^{49} + 7 q^{50} - 29 q^{51} - 7 q^{52} - 18 q^{53} - 21 q^{54} + 10 q^{55} + 4 q^{56} + 13 q^{57} - 18 q^{58} - 11 q^{59} + 3 q^{60} - 25 q^{61} + 7 q^{62} + 17 q^{63} + 7 q^{64} + 7 q^{65} + 4 q^{66} - 22 q^{67} - 6 q^{68} - 18 q^{69} - 4 q^{70} - 22 q^{71} + 4 q^{72} + 19 q^{73} - 8 q^{74} - 3 q^{75} - 5 q^{76} - 47 q^{77} + 3 q^{78} - 20 q^{79} - 7 q^{80} + 7 q^{81} - 12 q^{82} - 8 q^{83} - 15 q^{84} + 6 q^{85} - 5 q^{86} + 29 q^{87} - 10 q^{88} - 4 q^{89} - 4 q^{90} - 4 q^{91} - 11 q^{92} - 3 q^{93} - 10 q^{94} + 5 q^{95} - 3 q^{96} + 13 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 - 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 4 * q^7 + 7 * q^8 + 4 * q^9 - 7 * q^10 - 10 * q^11 - 3 * q^12 - 7 * q^13 + 4 * q^14 + 3 * q^15 + 7 * q^16 - 6 * q^17 + 4 * q^18 - 5 * q^19 - 7 * q^20 - 15 * q^21 - 10 * q^22 - 11 * q^23 - 3 * q^24 + 7 * q^25 - 7 * q^26 - 21 * q^27 + 4 * q^28 - 18 * q^29 + 3 * q^30 + 7 * q^31 + 7 * q^32 + 4 * q^33 - 6 * q^34 - 4 * q^35 + 4 * q^36 - 8 * q^37 - 5 * q^38 + 3 * q^39 - 7 * q^40 - 12 * q^41 - 15 * q^42 - 5 * q^43 - 10 * q^44 - 4 * q^45 - 11 * q^46 - 10 * q^47 - 3 * q^48 + 7 * q^49 + 7 * q^50 - 29 * q^51 - 7 * q^52 - 18 * q^53 - 21 * q^54 + 10 * q^55 + 4 * q^56 + 13 * q^57 - 18 * q^58 - 11 * q^59 + 3 * q^60 - 25 * q^61 + 7 * q^62 + 17 * q^63 + 7 * q^64 + 7 * q^65 + 4 * q^66 - 22 * q^67 - 6 * q^68 - 18 * q^69 - 4 * q^70 - 22 * q^71 + 4 * q^72 + 19 * q^73 - 8 * q^74 - 3 * q^75 - 5 * q^76 - 47 * q^77 + 3 * q^78 - 20 * q^79 - 7 * q^80 + 7 * q^81 - 12 * q^82 - 8 * q^83 - 15 * q^84 + 6 * q^85 - 5 * q^86 + 29 * q^87 - 10 * q^88 - 4 * q^89 - 4 * q^90 - 4 * q^91 - 11 * q^92 - 3 * q^93 - 10 * q^94 + 5 * q^95 - 3 * q^96 + 13 * q^97 + 7 * q^98 - 27 * 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
$3$	0.820963	0.473983	0.236992	−	0.971512i	$-0.423839\pi$
$3$	0.820963	0.473983	0.236992	+	0.971512i	$0.423839\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.820963	0.335157
$7$	2.40836	0.910274	0.455137	−	0.890422i	$-0.349590\pi$
$7$	2.40836	0.910274	0.455137	+	0.890422i	$0.349590\pi$
$8$	1.00000	0.353553
$9$	−2.32602	−0.775340
$10$	−1.00000	−0.316228
$11$	−0.643884	−0.194138	−0.0970692	−	0.995278i	$-0.530947\pi$
$11$	−0.643884	−0.194138	−0.0970692	+	0.995278i	$0.530947\pi$
$12$	0.820963	0.236992
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	2.40836	0.643661
$15$	−0.820963	−0.211972
$16$	1.00000	0.250000
$17$	−7.01761	−1.70202	−0.851011	−	0.525148i	$-0.824010\pi$
$17$	−7.01761	−1.70202	−0.851011	+	0.525148i	$0.824010\pi$
$18$	−2.32602	−0.548248
$19$	−4.17256	−0.957251	−0.478625	−	0.878019i	$-0.658865\pi$
$19$	−4.17256	−0.957251	−0.478625	+	0.878019i	$0.658865\pi$
$20$	−1.00000	−0.223607
$21$	1.97717	0.431454
$22$	−0.643884	−0.137277
$23$	−2.44939	−0.510733	−0.255366	−	0.966844i	$-0.582196\pi$
$23$	−2.44939	−0.510733	−0.255366	+	0.966844i	$0.582196\pi$
$24$	0.820963	0.167578
$25$	1.00000	0.200000
$26$	−1.00000	−0.196116
$27$	−4.37246	−0.841481
$28$	2.40836	0.455137
$29$	−7.99422	−1.48449	−0.742245	−	0.670129i	$-0.766239\pi$
$29$	−7.99422	−1.48449	−0.742245	+	0.670129i	$0.766239\pi$
$30$	−0.820963	−0.149887
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	−0.528605	−0.0920183
$34$	−7.01761	−1.20351
$35$	−2.40836	−0.407087
$36$	−2.32602	−0.387670
$37$	4.60774	0.757507	0.378754	−	0.925498i	$-0.376353\pi$
$37$	4.60774	0.757507	0.378754	+	0.925498i	$0.376353\pi$
$38$	−4.17256	−0.676878
$39$	−0.820963	−0.131459
$40$	−1.00000	−0.158114
$41$	5.00986	0.782409	0.391205	−	0.920304i	$-0.372059\pi$
$41$	5.00986	0.782409	0.391205	+	0.920304i	$0.372059\pi$
$42$	1.97717	0.305084
$43$	−10.6353	−1.62187	−0.810933	−	0.585139i	$-0.801040\pi$
$43$	−10.6353	−1.62187	−0.810933	+	0.585139i	$0.801040\pi$
$44$	−0.643884	−0.0970692
$45$	2.32602	0.346743
$46$	−2.44939	−0.361143
$47$	7.08296	1.03316	0.516578	−	0.856240i	$-0.327206\pi$
$47$	7.08296	1.03316	0.516578	+	0.856240i	$0.327206\pi$
$48$	0.820963	0.118496
$49$	−1.19981	−0.171402
$50$	1.00000	0.141421
$51$	−5.76120	−0.806730
$52$	−1.00000	−0.138675
$53$	0.0598965	0.00822742	0.00411371	−	0.999992i	$-0.498691\pi$
$53$	0.0598965	0.00822742	0.00411371	+	0.999992i	$0.498691\pi$
$54$	−4.37246	−0.595017
$55$	0.643884	0.0868213
$56$	2.40836	0.321830
$57$	−3.42552	−0.453721
$58$	−7.99422	−1.04969
$59$	−3.54904	−0.462046	−0.231023	−	0.972948i	$-0.574207\pi$
$59$	−3.54904	−0.462046	−0.231023	+	0.972948i	$0.574207\pi$
$60$	−0.820963	−0.105986
$61$	−12.2448	−1.56778	−0.783892	−	0.620897i	$-0.786769\pi$
$61$	−12.2448	−1.56778	−0.783892	+	0.620897i	$0.786769\pi$
$62$	1.00000	0.127000
$63$	−5.60189	−0.705771
$64$	1.00000	0.125000
$65$	1.00000	0.124035
$66$	−0.528605	−0.0650668
$67$	−6.35346	−0.776199	−0.388099	−	0.921618i	$-0.626868\pi$
$67$	−6.35346	−0.776199	−0.388099	+	0.921618i	$0.626868\pi$
$68$	−7.01761	−0.851011
$69$	−2.01086	−0.242079
$70$	−2.40836	−0.287854
$71$	5.07826	0.602678	0.301339	−	0.953517i	$-0.402566\pi$
$71$	5.07826	0.602678	0.301339	+	0.953517i	$0.402566\pi$
$72$	−2.32602	−0.274124
$73$	−12.8377	−1.50254	−0.751272	−	0.659993i	$-0.770559\pi$
$73$	−12.8377	−1.50254	−0.751272	+	0.659993i	$0.770559\pi$
$74$	4.60774	0.535638
$75$	0.820963	0.0947966
$76$	−4.17256	−0.478625
$77$	−1.55070	−0.176719
$78$	−0.820963	−0.0929557
$79$	11.0105	1.23878	0.619392	−	0.785082i	$-0.287379\pi$
$79$	11.0105	1.23878	0.619392	+	0.785082i	$0.287379\pi$
$80$	−1.00000	−0.111803
$81$	3.38843	0.376492
$82$	5.00986	0.553247
$83$	15.7904	1.73322	0.866612	−	0.498982i	$-0.166293\pi$
$83$	15.7904	1.73322	0.866612	+	0.498982i	$0.166293\pi$
$84$	1.97717	0.215727
$85$	7.01761	0.761167
$86$	−10.6353	−1.14683
$87$	−6.56296	−0.703623
$88$	−0.643884	−0.0686383
$89$	−12.0033	−1.27234	−0.636172	−	0.771547i	$-0.719483\pi$
$89$	−12.0033	−1.27234	−0.636172	+	0.771547i	$0.719483\pi$
$90$	2.32602	0.245184
$91$	−2.40836	−0.252464
$92$	−2.44939	−0.255366
$93$	0.820963	0.0851299
$94$	7.08296	0.730552
$95$	4.17256	0.428095
$96$	0.820963	0.0837892
$97$	15.2953	1.55300	0.776501	−	0.630116i	$-0.216992\pi$
$97$	15.2953	1.55300	0.776501	+	0.630116i	$0.216992\pi$
$98$	−1.19981	−0.121200
$99$	1.49769	0.150523
$100$	1.00000	0.100000
$101$	1.52397	0.151641	0.0758204	−	0.997121i	$-0.475842\pi$
$101$	1.52397	0.151641	0.0758204	+	0.997121i	$0.475842\pi$
$102$	−5.76120	−0.570444
$103$	12.7867	1.25991	0.629956	−	0.776631i	$-0.283073\pi$
$103$	12.7867	1.25991	0.629956	+	0.776631i	$0.283073\pi$
$104$	−1.00000	−0.0980581
$105$	−1.97717	−0.192952
$106$	0.0598965	0.00581766
$107$	−6.93658	−0.670584	−0.335292	−	0.942114i	$-0.608835\pi$
$107$	−6.93658	−0.670584	−0.335292	+	0.942114i	$0.608835\pi$
$108$	−4.37246	−0.420741
$109$	19.4420	1.86221	0.931105	−	0.364751i	$-0.118846\pi$
$109$	19.4420	1.86221	0.931105	+	0.364751i	$0.118846\pi$
$110$	0.643884	0.0613920
$111$	3.78278	0.359046
$112$	2.40836	0.227568
$113$	−3.95134	−0.371710	−0.185855	−	0.982577i	$-0.559506\pi$
$113$	−3.95134	−0.371710	−0.185855	+	0.982577i	$0.559506\pi$
$114$	−3.42552	−0.320829
$115$	2.44939	0.228407
$116$	−7.99422	−0.742245
$117$	2.32602	0.215041
$118$	−3.54904	−0.326716
$119$	−16.9009	−1.54931
$120$	−0.820963	−0.0749433
$121$	−10.5854	−0.962310
$122$	−12.2448	−1.10859
$123$	4.11291	0.370849
$124$	1.00000	0.0898027
$125$	−1.00000	−0.0894427
$126$	−5.60189	−0.499056
$127$	−0.179879	−0.0159617	−0.00798085	−	0.999968i	$-0.502540\pi$
$127$	−0.179879	−0.0159617	−0.00798085	+	0.999968i	$0.502540\pi$
$128$	1.00000	0.0883883
$129$	−8.73117	−0.768737
$130$	1.00000	0.0877058
$131$	1.65437	0.144543	0.0722714	−	0.997385i	$-0.476975\pi$
$131$	1.65437	0.144543	0.0722714	+	0.997385i	$0.476975\pi$
$132$	−0.528605	−0.0460092
$133$	−10.0490	−0.871360
$134$	−6.35346	−0.548855
$135$	4.37246	0.376322
$136$	−7.01761	−0.601755
$137$	−20.7976	−1.77686	−0.888430	−	0.459011i	$-0.848204\pi$
$137$	−20.7976	−1.77686	−0.888430	+	0.459011i	$0.848204\pi$
$138$	−2.01086	−0.171176
$139$	−7.83871	−0.664871	−0.332435	−	0.943126i	$-0.607870\pi$
$139$	−7.83871	−0.664871	−0.332435	+	0.943126i	$0.607870\pi$
$140$	−2.40836	−0.203543
$141$	5.81485	0.489699
$142$	5.07826	0.426158
$143$	0.643884	0.0538443
$144$	−2.32602	−0.193835
$145$	7.99422	0.663884
$146$	−12.8377	−1.06246
$147$	−0.985003	−0.0812417
$148$	4.60774	0.378754
$149$	3.08367	0.252624	0.126312	−	0.991991i	$-0.459686\pi$
$149$	3.08367	0.252624	0.126312	+	0.991991i	$0.459686\pi$
$150$	0.820963	0.0670313
$151$	21.8936	1.78167	0.890837	−	0.454322i	$-0.150119\pi$
$151$	21.8936	1.78167	0.890837	+	0.454322i	$0.150119\pi$
$152$	−4.17256	−0.338439
$153$	16.3231	1.31965
$154$	−1.55070	−0.124959
$155$	−1.00000	−0.0803219
$156$	−0.820963	−0.0657296
$157$	2.95439	0.235786	0.117893	−	0.993026i	$-0.462386\pi$
$157$	2.95439	0.235786	0.117893	+	0.993026i	$0.462386\pi$
$158$	11.0105	0.875952
$159$	0.0491728	0.00389966
$160$	−1.00000	−0.0790569
$161$	−5.89900	−0.464907
$162$	3.38843	0.266220
$163$	1.37660	0.107824	0.0539118	−	0.998546i	$-0.482831\pi$
$163$	1.37660	0.107824	0.0539118	+	0.998546i	$0.482831\pi$
$164$	5.00986	0.391205
$165$	0.528605	0.0411519
$166$	15.7904	1.22557
$167$	3.48207	0.269451	0.134726	−	0.990883i	$-0.456985\pi$
$167$	3.48207	0.269451	0.134726	+	0.990883i	$0.456985\pi$
$168$	1.97717	0.152542
$169$	1.00000	0.0769231
$170$	7.01761	0.538226
$171$	9.70545	0.742195
$172$	−10.6353	−0.810933
$173$	−16.5437	−1.25780	−0.628898	−	0.777488i	$-0.716494\pi$
$173$	−16.5437	−1.25780	−0.628898	+	0.777488i	$0.716494\pi$
$174$	−6.56296	−0.497537
$175$	2.40836	0.182055
$176$	−0.643884	−0.0485346
$177$	−2.91363	−0.219002
$178$	−12.0033	−0.899684
$179$	−7.43548	−0.555754	−0.277877	−	0.960617i	$-0.589631\pi$
$179$	−7.43548	−0.555754	−0.277877	+	0.960617i	$0.589631\pi$
$180$	2.32602	0.173371
$181$	−4.29620	−0.319334	−0.159667	−	0.987171i	$-0.551042\pi$
$181$	−4.29620	−0.319334	−0.159667	+	0.987171i	$0.551042\pi$
$182$	−2.40836	−0.178519
$183$	−10.0525	−0.743103
$184$	−2.44939	−0.180571
$185$	−4.60774	−0.338768
$186$	0.820963	0.0601959
$187$	4.51853	0.330428
$188$	7.08296	0.516578
$189$	−10.5305	−0.765978
$190$	4.17256	0.302709
$191$	2.48512	0.179817	0.0899086	−	0.995950i	$-0.471343\pi$
$191$	2.48512	0.179817	0.0899086	+	0.995950i	$0.471343\pi$
$192$	0.820963	0.0592479
$193$	7.92818	0.570683	0.285341	−	0.958426i	$-0.407893\pi$
$193$	7.92818	0.570683	0.285341	+	0.958426i	$0.407893\pi$
$194$	15.2953	1.09814
$195$	0.820963	0.0587904
$196$	−1.19981	−0.0857010
$197$	−25.9816	−1.85111	−0.925556	−	0.378611i	$-0.876402\pi$
$197$	−25.9816	−1.85111	−0.925556	+	0.378611i	$0.876402\pi$
$198$	1.49769	0.106436
$199$	7.00475	0.496554	0.248277	−	0.968689i	$-0.420136\pi$
$199$	7.00475	0.496554	0.248277	+	0.968689i	$0.420136\pi$
$200$	1.00000	0.0707107
$201$	−5.21596	−0.367905
$202$	1.52397	0.107226
$203$	−19.2529	−1.35129
$204$	−5.76120	−0.403365
$205$	−5.00986	−0.349904
$206$	12.7867	0.890892
$207$	5.69733	0.395992
$208$	−1.00000	−0.0693375
$209$	2.68664	0.185839
$210$	−1.97717	−0.136438
$211$	6.97125	0.479920	0.239960	−	0.970783i	$-0.422866\pi$
$211$	6.97125	0.479920	0.239960	+	0.970783i	$0.422866\pi$
$212$	0.0598965	0.00411371
$213$	4.16906	0.285659
$214$	−6.93658	−0.474175
$215$	10.6353	0.725320
$216$	−4.37246	−0.297509
$217$	2.40836	0.163490
$218$	19.4420	1.31678
$219$	−10.5393	−0.712181
$220$	0.643884	0.0434107
$221$	7.01761	0.472056
$222$	3.78278	0.253884
$223$	16.8234	1.12658	0.563289	−	0.826260i	$-0.309536\pi$
$223$	16.8234	1.12658	0.563289	+	0.826260i	$0.309536\pi$
$224$	2.40836	0.160915
$225$	−2.32602	−0.155068
$226$	−3.95134	−0.262839
$227$	2.12305	0.140912	0.0704559	−	0.997515i	$-0.477555\pi$
$227$	2.12305	0.140912	0.0704559	+	0.997515i	$0.477555\pi$
$228$	−3.42552	−0.226860
$229$	−22.8085	−1.50723	−0.753614	−	0.657317i	$-0.771691\pi$
$229$	−22.8085	−1.50723	−0.753614	+	0.657317i	$0.771691\pi$
$230$	2.44939	0.161508
$231$	−1.27307	−0.0837619
$232$	−7.99422	−0.524846
$233$	−29.0445	−1.90277	−0.951383	−	0.308011i	$-0.900337\pi$
$233$	−29.0445	−1.90277	−0.951383	+	0.308011i	$0.900337\pi$
$234$	2.32602	0.152057
$235$	−7.08296	−0.462041
$236$	−3.54904	−0.231023
$237$	9.03925	0.587162
$238$	−16.9009	−1.09552
$239$	−2.39758	−0.155087	−0.0775433	−	0.996989i	$-0.524708\pi$
$239$	−2.39758	−0.155087	−0.0775433	+	0.996989i	$0.524708\pi$
$240$	−0.820963	−0.0529929
$241$	13.1175	0.844972	0.422486	−	0.906369i	$-0.361158\pi$
$241$	13.1175	0.844972	0.422486	+	0.906369i	$0.361158\pi$
$242$	−10.5854	−0.680456
$243$	15.8992	1.01993
$244$	−12.2448	−0.783892
$245$	1.19981	0.0766533
$246$	4.11291	0.262230
$247$	4.17256	0.265494
$248$	1.00000	0.0635001
$249$	12.9634	0.821519
$250$	−1.00000	−0.0632456
$251$	19.9569	1.25967	0.629834	−	0.776730i	$-0.283123\pi$
$251$	19.9569	1.25967	0.629834	+	0.776730i	$0.283123\pi$
$252$	−5.60189	−0.352886
$253$	1.57712	0.0991529
$254$	−0.179879	−0.0112866
$255$	5.76120	0.360780
$256$	1.00000	0.0625000
$257$	−1.28584	−0.0802088	−0.0401044	−	0.999195i	$-0.512769\pi$
$257$	−1.28584	−0.0802088	−0.0401044	+	0.999195i	$0.512769\pi$
$258$	−8.73117	−0.543579
$259$	11.0971	0.689539
$260$	1.00000	0.0620174
$261$	18.5947	1.15098
$262$	1.65437	0.102207
$263$	−30.5276	−1.88241	−0.941205	−	0.337836i	$-0.890305\pi$
$263$	−30.5276	−1.88241	−0.941205	+	0.337836i	$0.890305\pi$
$264$	−0.528605	−0.0325334
$265$	−0.0598965	−0.00367941
$266$	−10.0490	−0.616145
$267$	−9.85425	−0.603070
$268$	−6.35346	−0.388099
$269$	−20.0665	−1.22348	−0.611738	−	0.791061i	$-0.709529\pi$
$269$	−20.0665	−1.22348	−0.611738	+	0.791061i	$0.709529\pi$
$270$	4.37246	0.266100
$271$	10.9743	0.666642	0.333321	−	0.942813i	$-0.391831\pi$
$271$	10.9743	0.666642	0.333321	+	0.942813i	$0.391831\pi$
$272$	−7.01761	−0.425505
$273$	−1.97717	−0.119664
$274$	−20.7976	−1.25643
$275$	−0.643884	−0.0388277
$276$	−2.01086	−0.121039
$277$	−25.1434	−1.51072	−0.755361	−	0.655309i	$-0.772538\pi$
$277$	−25.1434	−1.51072	−0.755361	+	0.655309i	$0.772538\pi$
$278$	−7.83871	−0.470135
$279$	−2.32602	−0.139255
$280$	−2.40836	−0.143927
$281$	−18.6989	−1.11548	−0.557740	−	0.830016i	$-0.688331\pi$
$281$	−18.6989	−1.11548	−0.557740	+	0.830016i	$0.688331\pi$
$282$	5.81485	0.346269
$283$	−26.3485	−1.56625	−0.783127	−	0.621861i	$-0.786377\pi$
$283$	−26.3485	−1.56625	−0.783127	+	0.621861i	$0.786377\pi$
$284$	5.07826	0.301339
$285$	3.42552	0.202910
$286$	0.643884	0.0380737
$287$	12.0655	0.712206
$288$	−2.32602	−0.137062
$289$	32.2469	1.89688
$290$	7.99422	0.469437
$291$	12.5569	0.736097
$292$	−12.8377	−0.751272
$293$	9.35109	0.546296	0.273148	−	0.961972i	$-0.411935\pi$
$293$	9.35109	0.546296	0.273148	+	0.961972i	$0.411935\pi$
$294$	−0.985003	−0.0574465
$295$	3.54904	0.206633
$296$	4.60774	0.267819
$297$	2.81536	0.163364
$298$	3.08367	0.178632
$299$	2.44939	0.141652
$300$	0.820963	0.0473983
$301$	−25.6136	−1.47634
$302$	21.8936	1.25983
$303$	1.25112	0.0718752
$304$	−4.17256	−0.239313
$305$	12.2448	0.701135
$306$	16.3231	0.933130
$307$	−29.1880	−1.66585	−0.832924	−	0.553387i	$-0.813335\pi$
$307$	−29.1880	−1.66585	−0.832924	+	0.553387i	$0.813335\pi$
$308$	−1.55070	−0.0883595
$309$	10.4974	0.597177
$310$	−1.00000	−0.0567962
$311$	20.1624	1.14331	0.571653	−	0.820496i	$-0.306302\pi$
$311$	20.1624	1.14331	0.571653	+	0.820496i	$0.306302\pi$
$312$	−0.820963	−0.0464779
$313$	16.4985	0.932549	0.466275	−	0.884640i	$-0.345596\pi$
$313$	16.4985	0.932549	0.466275	+	0.884640i	$0.345596\pi$
$314$	2.95439	0.166726
$315$	5.60189	0.315631
$316$	11.0105	0.619392
$317$	16.2193	0.910967	0.455484	−	0.890244i	$-0.349466\pi$
$317$	16.2193	0.910967	0.455484	+	0.890244i	$0.349466\pi$
$318$	0.0491728	0.00275747
$319$	5.14735	0.288196
$320$	−1.00000	−0.0559017
$321$	−5.69467	−0.317846
$322$	−5.89900	−0.328739
$323$	29.2814	1.62926
$324$	3.38843	0.188246
$325$	−1.00000	−0.0554700
$326$	1.37660	0.0762427
$327$	15.9612	0.882656
$328$	5.00986	0.276623
$329$	17.0583	0.940455
$330$	0.528605	0.0290988
$331$	−14.3034	−0.786187	−0.393094	−	0.919498i	$-0.628595\pi$
$331$	−14.3034	−0.786187	−0.393094	+	0.919498i	$0.628595\pi$
$332$	15.7904	0.866612
$333$	−10.7177	−0.587326
$334$	3.48207	0.190531
$335$	6.35346	0.347127
$336$	1.97717	0.107864
$337$	−14.9418	−0.813929	−0.406965	−	0.913444i	$-0.633413\pi$
$337$	−14.9418	−0.813929	−0.406965	+	0.913444i	$0.633413\pi$
$338$	1.00000	0.0543928
$339$	−3.24390	−0.176184
$340$	7.01761	0.380584
$341$	−0.643884	−0.0348683
$342$	9.70545	0.524811
$343$	−19.7481	−1.06630
$344$	−10.6353	−0.573416
$345$	2.01086	0.108261
$346$	−16.5437	−0.889396
$347$	31.1437	1.67188	0.835941	−	0.548820i	$-0.184923\pi$
$347$	31.1437	1.67188	0.835941	+	0.548820i	$0.184923\pi$
$348$	−6.56296	−0.351812
$349$	−8.40270	−0.449786	−0.224893	−	0.974383i	$-0.572203\pi$
$349$	−8.40270	−0.449786	−0.224893	+	0.974383i	$0.572203\pi$
$350$	2.40836	0.128732
$351$	4.37246	0.233385
$352$	−0.643884	−0.0343191
$353$	11.0951	0.590533	0.295266	−	0.955415i	$-0.404592\pi$
$353$	11.0951	0.590533	0.295266	+	0.955415i	$0.404592\pi$
$354$	−2.91363	−0.154858
$355$	−5.07826	−0.269526
$356$	−12.0033	−0.636172
$357$	−13.8750	−0.734345
$358$	−7.43548	−0.392977
$359$	−27.0433	−1.42729	−0.713645	−	0.700507i	$-0.752957\pi$
$359$	−27.0433	−1.42729	−0.713645	+	0.700507i	$0.752957\pi$
$360$	2.32602	0.122592
$361$	−1.58975	−0.0836713
$362$	−4.29620	−0.225803
$363$	−8.69023	−0.456119
$364$	−2.40836	−0.126232
$365$	12.8377	0.671958
$366$	−10.0525	−0.525453
$367$	3.46841	0.181050	0.0905248	−	0.995894i	$-0.471146\pi$
$367$	3.46841	0.181050	0.0905248	+	0.995894i	$0.471146\pi$
$368$	−2.44939	−0.127683
$369$	−11.6530	−0.606633
$370$	−4.60774	−0.239545
$371$	0.144252	0.00748920
$372$	0.820963	0.0425649
$373$	29.0667	1.50502	0.752508	−	0.658583i	$-0.228844\pi$
$373$	29.0667	1.50502	0.752508	+	0.658583i	$0.228844\pi$
$374$	4.51853	0.233648
$375$	−0.820963	−0.0423943
$376$	7.08296	0.365276
$377$	7.99422	0.411723
$378$	−10.5305	−0.541628
$379$	−7.24702	−0.372255	−0.186127	−	0.982526i	$-0.559594\pi$
$379$	−7.24702	−0.372255	−0.186127	+	0.982526i	$0.559594\pi$
$380$	4.17256	0.214048
$381$	−0.147674	−0.00756558
$382$	2.48512	0.127150
$383$	−19.4409	−0.993381	−0.496691	−	0.867928i	$-0.665452\pi$
$383$	−19.4409	−0.993381	−0.496691	+	0.867928i	$0.665452\pi$
$384$	0.820963	0.0418946
$385$	1.55070	0.0790312
$386$	7.92818	0.403534
$387$	24.7379	1.25750
$388$	15.2953	0.776501
$389$	28.2823	1.43397	0.716986	−	0.697088i	$-0.245521\pi$
$389$	28.2823	1.43397	0.716986	+	0.697088i	$0.245521\pi$
$390$	0.820963	0.0415711
$391$	17.1889	0.869278
$392$	−1.19981	−0.0605998
$393$	1.35817	0.0685108
$394$	−25.9816	−1.30893
$395$	−11.0105	−0.554001
$396$	1.49769	0.0752616
$397$	33.4229	1.67745	0.838723	−	0.544558i	$-0.183302\pi$
$397$	33.4229	1.67745	0.838723	+	0.544558i	$0.183302\pi$
$398$	7.00475	0.351116
$399$	−8.24987	−0.413010
$400$	1.00000	0.0500000
$401$	−22.4102	−1.11911	−0.559555	−	0.828793i	$-0.689028\pi$
$401$	−22.4102	−1.11911	−0.559555	+	0.828793i	$0.689028\pi$
$402$	−5.21596	−0.260148
$403$	−1.00000	−0.0498135
$404$	1.52397	0.0758204
$405$	−3.38843	−0.168372
$406$	−19.2529	−0.955507
$407$	−2.96685	−0.147061
$408$	−5.76120	−0.285222
$409$	35.5030	1.75551	0.877756	−	0.479107i	$-0.159040\pi$
$409$	35.5030	1.75551	0.877756	+	0.479107i	$0.159040\pi$
$410$	−5.00986	−0.247419
$411$	−17.0741	−0.842202
$412$	12.7867	0.629956
$413$	−8.54736	−0.420588
$414$	5.69733	0.280008
$415$	−15.7904	−0.775122
$416$	−1.00000	−0.0490290
$417$	−6.43529	−0.315138
$418$	2.68664	0.131408
$419$	−33.9792	−1.65999	−0.829997	−	0.557768i	$-0.811658\pi$
$419$	−33.9792	−1.65999	−0.829997	+	0.557768i	$0.811658\pi$
$420$	−1.97717	−0.0964761
$421$	22.0199	1.07318	0.536592	−	0.843842i	$-0.319711\pi$
$421$	22.0199	1.07318	0.536592	+	0.843842i	$0.319711\pi$
$422$	6.97125	0.339355
$423$	−16.4751	−0.801047
$424$	0.0598965	0.00290883
$425$	−7.01761	−0.340404
$426$	4.16906	0.201992
$427$	−29.4898	−1.42711
$428$	−6.93658	−0.335292
$429$	0.528605	0.0255213
$430$	10.6353	0.512879
$431$	−10.3826	−0.500111	−0.250055	−	0.968232i	$-0.580449\pi$
$431$	−10.3826	−0.500111	−0.250055	+	0.968232i	$0.580449\pi$
$432$	−4.37246	−0.210370
$433$	−20.4374	−0.982157	−0.491079	−	0.871115i	$-0.663397\pi$
$433$	−20.4374	−0.982157	−0.491079	+	0.871115i	$0.663397\pi$
$434$	2.40836	0.115605
$435$	6.56296	0.314670
$436$	19.4420	0.931105
$437$	10.2202	0.488899
$438$	−10.5393	−0.503588
$439$	30.8175	1.47084	0.735419	−	0.677613i	$-0.236985\pi$
$439$	30.8175	1.47084	0.735419	+	0.677613i	$0.236985\pi$
$440$	0.643884	0.0306960
$441$	2.79079	0.132895
$442$	7.01761	0.333794
$443$	5.72789	0.272140	0.136070	−	0.990699i	$-0.456553\pi$
$443$	5.72789	0.272140	0.136070	+	0.990699i	$0.456553\pi$
$444$	3.78278	0.179523
$445$	12.0033	0.569010
$446$	16.8234	0.796612
$447$	2.53158	0.119740
$448$	2.40836	0.113784
$449$	−2.78384	−0.131378	−0.0656888	−	0.997840i	$-0.520924\pi$
$449$	−2.78384	−0.131378	−0.0656888	+	0.997840i	$0.520924\pi$
$450$	−2.32602	−0.109650
$451$	−3.22577	−0.151896
$452$	−3.95134	−0.185855
$453$	17.9738	0.844484
$454$	2.12305	0.0996398
$455$	2.40836	0.112906
$456$	−3.42552	−0.160414
$457$	12.1524	0.568465	0.284233	−	0.958755i	$-0.408261\pi$
$457$	12.1524	0.568465	0.284233	+	0.958755i	$0.408261\pi$
$458$	−22.8085	−1.06577
$459$	30.6843	1.43222
$460$	2.44939	0.114203
$461$	−31.4073	−1.46278	−0.731392	−	0.681957i	$-0.761129\pi$
$461$	−31.4073	−1.46278	−0.731392	+	0.681957i	$0.761129\pi$
$462$	−1.27307	−0.0592286
$463$	8.34823	0.387975	0.193988	−	0.981004i	$-0.437858\pi$
$463$	8.34823	0.387975	0.193988	+	0.981004i	$0.437858\pi$
$464$	−7.99422	−0.371122
$465$	−0.820963	−0.0380712
$466$	−29.0445	−1.34546
$467$	24.4055	1.12935	0.564677	−	0.825312i	$-0.309001\pi$
$467$	24.4055	1.12935	0.564677	+	0.825312i	$0.309001\pi$
$468$	2.32602	0.107520
$469$	−15.3014	−0.706553
$470$	−7.08296	−0.326713
$471$	2.42545	0.111759
$472$	−3.54904	−0.163358
$473$	6.84789	0.314866
$474$	9.03925	0.415187
$475$	−4.17256	−0.191450
$476$	−16.9009	−0.774653
$477$	−0.139320	−0.00637905
$478$	−2.39758	−0.109663
$479$	−27.7061	−1.26592	−0.632961	−	0.774184i	$-0.718161\pi$
$479$	−27.7061	−1.26592	−0.632961	+	0.774184i	$0.718161\pi$
$480$	−0.820963	−0.0374717
$481$	−4.60774	−0.210095
$482$	13.1175	0.597486
$483$	−4.84286	−0.220358
$484$	−10.5854	−0.481155
$485$	−15.2953	−0.694524
$486$	15.8992	0.721201
$487$	−11.1682	−0.506079	−0.253040	−	0.967456i	$-0.581430\pi$
$487$	−11.1682	−0.506079	−0.253040	+	0.967456i	$0.581430\pi$
$488$	−12.2448	−0.554295
$489$	1.13014	0.0511065
$490$	1.19981	0.0542021
$491$	9.78508	0.441594	0.220797	−	0.975320i	$-0.429134\pi$
$491$	9.78508	0.441594	0.220797	+	0.975320i	$0.429134\pi$
$492$	4.11291	0.185424
$493$	56.1004	2.52663
$494$	4.17256	0.187732
$495$	−1.49769	−0.0673161
$496$	1.00000	0.0449013
$497$	12.2303	0.548602
$498$	12.9634	0.580902
$499$	23.9219	1.07089	0.535445	−	0.844570i	$-0.320144\pi$
$499$	23.9219	1.07089	0.535445	+	0.844570i	$0.320144\pi$
$500$	−1.00000	−0.0447214
$501$	2.85865	0.127715
$502$	19.9569	0.890720
$503$	42.6814	1.90307	0.951534	−	0.307544i	$-0.0995071\pi$
$503$	42.6814	1.90307	0.951534	+	0.307544i	$0.0995071\pi$
$504$	−5.60189	−0.249528
$505$	−1.52397	−0.0678158
$506$	1.57712	0.0701117
$507$	0.820963	0.0364602
$508$	−0.179879	−0.00798085
$509$	−34.6065	−1.53391	−0.766954	−	0.641702i	$-0.778229\pi$
$509$	−34.6065	−1.53391	−0.766954	+	0.641702i	$0.778229\pi$
$510$	5.76120	0.255110
$511$	−30.9179	−1.36773
$512$	1.00000	0.0441942
$513$	18.2444	0.805508
$514$	−1.28584	−0.0567162
$515$	−12.7867	−0.563450
$516$	−8.73117	−0.384369
$517$	−4.56061	−0.200575
$518$	11.0971	0.487578
$519$	−13.5818	−0.596174
$520$	1.00000	0.0438529
$521$	−14.9304	−0.654112	−0.327056	−	0.945005i	$-0.606056\pi$
$521$	−14.9304	−0.654112	−0.327056	+	0.945005i	$0.606056\pi$
$522$	18.5947	0.813869
$523$	−7.09954	−0.310441	−0.155221	−	0.987880i	$-0.549609\pi$
$523$	−7.09954	−0.310441	−0.155221	+	0.987880i	$0.549609\pi$
$524$	1.65437	0.0722714
$525$	1.97717	0.0862909
$526$	−30.5276	−1.33106
$527$	−7.01761	−0.305692
$528$	−0.528605	−0.0230046
$529$	−17.0005	−0.739152
$530$	−0.0598965	−0.00260174
$531$	8.25514	0.358242
$532$	−10.0490	−0.435680
$533$	−5.00986	−0.217001
$534$	−9.85425	−0.426435
$535$	6.93658	0.299894
$536$	−6.35346	−0.274428
$537$	−6.10425	−0.263418
$538$	−20.0665	−0.865128
$539$	0.772541	0.0332757
$540$	4.37246	0.188161
$541$	30.2998	1.30269	0.651345	−	0.758782i	$-0.274205\pi$
$541$	30.2998	1.30269	0.651345	+	0.758782i	$0.274205\pi$
$542$	10.9743	0.471387
$543$	−3.52702	−0.151359
$544$	−7.01761	−0.300878
$545$	−19.4420	−0.832806
$546$	−1.97717	−0.0846152
$547$	−7.11141	−0.304062	−0.152031	−	0.988376i	$-0.548581\pi$
$547$	−7.11141	−0.304062	−0.152031	+	0.988376i	$0.548581\pi$
$548$	−20.7976	−0.888430
$549$	28.4816	1.21557
$550$	−0.643884	−0.0274553
$551$	33.3564	1.42103
$552$	−2.01086	−0.0855878
$553$	26.5173	1.12763
$554$	−25.1434	−1.06824
$555$	−3.78278	−0.160570
$556$	−7.83871	−0.332435
$557$	25.0335	1.06070	0.530351	−	0.847778i	$-0.322060\pi$
$557$	25.0335	1.06070	0.530351	+	0.847778i	$0.322060\pi$
$558$	−2.32602	−0.0984683
$559$	10.6353	0.449825
$560$	−2.40836	−0.101772
$561$	3.70955	0.156617
$562$	−18.6989	−0.788764
$563$	−34.8964	−1.47071	−0.735355	−	0.677682i	$-0.762984\pi$
$563$	−34.8964	−1.47071	−0.735355	+	0.677682i	$0.762984\pi$
$564$	5.81485	0.244849
$565$	3.95134	0.166234
$566$	−26.3485	−1.10751
$567$	8.16055	0.342711
$568$	5.07826	0.213079
$569$	26.3023	1.10265	0.551326	−	0.834290i	$-0.314122\pi$
$569$	26.3023	1.10265	0.551326	+	0.834290i	$0.314122\pi$
$570$	3.42552	0.143479
$571$	21.8860	0.915900	0.457950	−	0.888978i	$-0.348584\pi$
$571$	21.8860	0.915900	0.457950	+	0.888978i	$0.348584\pi$
$572$	0.643884	0.0269222
$573$	2.04019	0.0852303
$574$	12.0655	0.503606
$575$	−2.44939	−0.102147
$576$	−2.32602	−0.0969175
$577$	26.0889	1.08610	0.543048	−	0.839701i	$-0.317270\pi$
$577$	26.0889	1.08610	0.543048	+	0.839701i	$0.317270\pi$
$578$	32.2469	1.34129
$579$	6.50874	0.270494
$580$	7.99422	0.331942
$581$	38.0290	1.57771
$582$	12.5569	0.520499
$583$	−0.0385664	−0.00159726
$584$	−12.8377	−0.531230
$585$	−2.32602	−0.0961691
$586$	9.35109	0.386290
$587$	25.0237	1.03284	0.516418	−	0.856336i	$-0.327265\pi$
$587$	25.0237	1.03284	0.516418	+	0.856336i	$0.327265\pi$
$588$	−0.985003	−0.0406208
$589$	−4.17256	−0.171927
$590$	3.54904	0.146112
$591$	−21.3299	−0.877396
$592$	4.60774	0.189377
$593$	5.36722	0.220405	0.110203	−	0.993909i	$-0.464850\pi$
$593$	5.36722	0.220405	0.110203	+	0.993909i	$0.464850\pi$
$594$	2.81536	0.115516
$595$	16.9009	0.692870
$596$	3.08367	0.126312
$597$	5.75064	0.235358
$598$	2.44939	0.100163
$599$	−16.6823	−0.681619	−0.340809	−	0.940132i	$-0.610701\pi$
$599$	−16.6823	−0.681619	−0.340809	+	0.940132i	$0.610701\pi$
$600$	0.820963	0.0335157
$601$	−37.2275	−1.51854	−0.759270	−	0.650776i	$-0.774444\pi$
$601$	−37.2275	−1.51854	−0.759270	+	0.650776i	$0.774444\pi$
$602$	−25.6136	−1.04393
$603$	14.7783	0.601818
$604$	21.8936	0.890837
$605$	10.5854	0.430358
$606$	1.25112	0.0508234
$607$	−16.3804	−0.664861	−0.332431	−	0.943128i	$-0.607869\pi$
$607$	−16.3804	−0.664861	−0.332431	+	0.943128i	$0.607869\pi$
$608$	−4.17256	−0.169220
$609$	−15.8060	−0.640489
$610$	12.2448	0.495777
$611$	−7.08296	−0.286546
$612$	16.3231	0.659823
$613$	6.73399	0.271983	0.135992	−	0.990710i	$-0.456578\pi$
$613$	6.73399	0.271983	0.135992	+	0.990710i	$0.456578\pi$
$614$	−29.1880	−1.17793
$615$	−4.11291	−0.165849
$616$	−1.55070	−0.0624796
$617$	−9.70960	−0.390894	−0.195447	−	0.980714i	$-0.562616\pi$
$617$	−9.70960	−0.390894	−0.195447	+	0.980714i	$0.562616\pi$
$618$	10.4974	0.422268
$619$	11.7367	0.471738	0.235869	−	0.971785i	$-0.424206\pi$
$619$	11.7367	0.471738	0.235869	+	0.971785i	$0.424206\pi$
$620$	−1.00000	−0.0401610
$621$	10.7099	0.429772
$622$	20.1624	0.808439
$623$	−28.9082	−1.15818
$624$	−0.820963	−0.0328648
$625$	1.00000	0.0400000
$626$	16.4985	0.659412
$627$	2.20564	0.0880846
$628$	2.95439	0.117893
$629$	−32.3353	−1.28929
$630$	5.60189	0.223185
$631$	29.6954	1.18216	0.591078	−	0.806614i	$-0.298702\pi$
$631$	29.6954	1.18216	0.591078	+	0.806614i	$0.298702\pi$
$632$	11.0105	0.437976
$633$	5.72314	0.227474
$634$	16.2193	0.644151
$635$	0.179879	0.00713829
$636$	0.0491728	0.00194983
$637$	1.19981	0.0475384
$638$	5.14735	0.203786
$639$	−11.8121	−0.467281
$640$	−1.00000	−0.0395285
$641$	−1.09197	−0.0431301	−0.0215650	−	0.999767i	$-0.506865\pi$
$641$	−1.09197	−0.0431301	−0.0215650	+	0.999767i	$0.506865\pi$
$642$	−5.69467	−0.224751
$643$	35.7387	1.40940	0.704698	−	0.709508i	$-0.251083\pi$
$643$	35.7387	1.40940	0.704698	+	0.709508i	$0.251083\pi$
$644$	−5.89900	−0.232453
$645$	8.73117	0.343790
$646$	29.2814	1.15206
$647$	9.33703	0.367077	0.183538	−	0.983013i	$-0.441245\pi$
$647$	9.33703	0.367077	0.183538	+	0.983013i	$0.441245\pi$
$648$	3.38843	0.133110
$649$	2.28517	0.0897008
$650$	−1.00000	−0.0392232
$651$	1.97717	0.0774915
$652$	1.37660	0.0539118
$653$	11.3273	0.443270	0.221635	−	0.975130i	$-0.428861\pi$
$653$	11.3273	0.443270	0.221635	+	0.975130i	$0.428861\pi$
$654$	15.9612	0.624132
$655$	−1.65437	−0.0646415
$656$	5.00986	0.195602
$657$	29.8608	1.16498
$658$	17.0583	0.665002
$659$	−0.884394	−0.0344511	−0.0172255	−	0.999852i	$-0.505483\pi$
$659$	−0.884394	−0.0344511	−0.0172255	+	0.999852i	$0.505483\pi$
$660$	0.528605	0.0205759
$661$	−22.3835	−0.870616	−0.435308	−	0.900282i	$-0.643361\pi$
$661$	−22.3835	−0.870616	−0.435308	+	0.900282i	$0.643361\pi$
$662$	−14.3034	−0.555918
$663$	5.76120	0.223747
$664$	15.7904	0.612787
$665$	10.0490	0.389684
$666$	−10.7177	−0.415302
$667$	19.5810	0.758178
$668$	3.48207	0.134726
$669$	13.8114	0.533979
$670$	6.35346	0.245456
$671$	7.88423	0.304367
$672$	1.97717	0.0762711
$673$	−23.6100	−0.910099	−0.455049	−	0.890466i	$-0.650378\pi$
$673$	−23.6100	−0.910099	−0.455049	+	0.890466i	$0.650378\pi$
$674$	−14.9418	−0.575535
$675$	−4.37246	−0.168296
$676$	1.00000	0.0384615
$677$	19.6745	0.756152	0.378076	−	0.925775i	$-0.376586\pi$
$677$	19.6745	0.756152	0.378076	+	0.925775i	$0.376586\pi$
$678$	−3.24390	−0.124581
$679$	36.8366	1.41366
$680$	7.01761	0.269113
$681$	1.74295	0.0667899
$682$	−0.643884	−0.0246556
$683$	−9.21730	−0.352690	−0.176345	−	0.984328i	$-0.556427\pi$
$683$	−9.21730	−0.352690	−0.176345	+	0.984328i	$0.556427\pi$
$684$	9.70545	0.371097
$685$	20.7976	0.794636
$686$	−19.7481	−0.753985
$687$	−18.7249	−0.714401
$688$	−10.6353	−0.405466
$689$	−0.0598965	−0.00228188
$690$	2.01086	0.0765520
$691$	−19.0419	−0.724387	−0.362194	−	0.932103i	$-0.617972\pi$
$691$	−19.0419	−0.724387	−0.362194	+	0.932103i	$0.617972\pi$
$692$	−16.5437	−0.628898
$693$	3.60697	0.137017
$694$	31.1437	1.18220
$695$	7.83871	0.297339
$696$	−6.56296	−0.248768
$697$	−35.1573	−1.33168
$698$	−8.40270	−0.318047
$699$	−23.8444	−0.901879
$700$	2.40836	0.0910274
$701$	−23.6449	−0.893056	−0.446528	−	0.894770i	$-0.647340\pi$
$701$	−23.6449	−0.893056	−0.446528	+	0.894770i	$0.647340\pi$
$702$	4.37246	0.165028
$703$	−19.2261	−0.725124
$704$	−0.643884	−0.0242673
$705$	−5.81485	−0.219000
$706$	11.0951	0.417570
$707$	3.67027	0.138035
$708$	−2.91363	−0.109501
$709$	−27.6475	−1.03832	−0.519162	−	0.854676i	$-0.673756\pi$
$709$	−27.6475	−1.03832	−0.519162	+	0.854676i	$0.673756\pi$
$710$	−5.07826	−0.190584
$711$	−25.6107	−0.960478
$712$	−12.0033	−0.449842
$713$	−2.44939	−0.0917303
$714$	−13.8750	−0.519260
$715$	−0.643884	−0.0240799
$716$	−7.43548	−0.277877
$717$	−1.96832	−0.0735084
$718$	−27.0433	−1.00925
$719$	19.4272	0.724514	0.362257	−	0.932078i	$-0.382006\pi$
$719$	19.4272	0.724514	0.362257	+	0.932078i	$0.382006\pi$
$720$	2.32602	0.0866856
$721$	30.7950	1.14686
$722$	−1.58975	−0.0591645
$723$	10.7690	0.400503
$724$	−4.29620	−0.159667
$725$	−7.99422	−0.296898
$726$	−8.69023	−0.322525
$727$	41.0911	1.52399	0.761993	−	0.647586i	$-0.224221\pi$
$727$	41.0911	1.52399	0.761993	+	0.647586i	$0.224221\pi$
$728$	−2.40836	−0.0892597
$729$	2.88735	0.106939
$730$	12.8377	0.475146
$731$	74.6343	2.76045
$732$	−10.0525	−0.371552
$733$	−10.6593	−0.393711	−0.196855	−	0.980433i	$-0.563073\pi$
$733$	−10.6593	−0.393711	−0.196855	+	0.980433i	$0.563073\pi$
$734$	3.46841	0.128021
$735$	0.985003	0.0363324
$736$	−2.44939	−0.0902857
$737$	4.09089	0.150690
$738$	−11.6530	−0.428954
$739$	2.96238	0.108973	0.0544864	−	0.998515i	$-0.482648\pi$
$739$	2.96238	0.108973	0.0544864	+	0.998515i	$0.482648\pi$
$740$	−4.60774	−0.169384
$741$	3.42552	0.125839
$742$	0.144252	0.00529566
$743$	−19.7481	−0.724487	−0.362244	−	0.932083i	$-0.617989\pi$
$743$	−19.7481	−0.724487	−0.362244	+	0.932083i	$0.617989\pi$
$744$	0.820963	0.0300980
$745$	−3.08367	−0.112977
$746$	29.0667	1.06421
$747$	−36.7289	−1.34384
$748$	4.51853	0.165214
$749$	−16.7058	−0.610415
$750$	−0.820963	−0.0299773
$751$	−18.2753	−0.666877	−0.333438	−	0.942772i	$-0.608209\pi$
$751$	−18.2753	−0.666877	−0.333438	+	0.942772i	$0.608209\pi$
$752$	7.08296	0.258289
$753$	16.3839	0.597061
$754$	7.99422	0.291132
$755$	−21.8936	−0.796789
$756$	−10.5305	−0.382989
$757$	40.6524	1.47754	0.738768	−	0.673960i	$-0.235408\pi$
$757$	40.6524	1.47754	0.738768	+	0.673960i	$0.235408\pi$
$758$	−7.24702	−0.263224
$759$	1.29476	0.0469968
$760$	4.17256	0.151355
$761$	21.5730	0.782021	0.391010	−	0.920386i	$-0.372126\pi$
$761$	21.5730	0.782021	0.391010	+	0.920386i	$0.372126\pi$
$762$	−0.147674	−0.00534967
$763$	46.8234	1.69512
$764$	2.48512	0.0899086
$765$	−16.3231	−0.590163
$766$	−19.4409	−0.702427
$767$	3.54904	0.128148
$768$	0.820963	0.0296239
$769$	−50.8507	−1.83372	−0.916861	−	0.399206i	$-0.869286\pi$
$769$	−50.8507	−1.83372	−0.916861	+	0.399206i	$0.869286\pi$
$770$	1.55070	0.0558835
$771$	−1.05563	−0.0380176
$772$	7.92818	0.285341
$773$	27.2138	0.978813	0.489407	−	0.872056i	$-0.337213\pi$
$773$	27.2138	0.978813	0.489407	+	0.872056i	$0.337213\pi$
$774$	24.7379	0.889185
$775$	1.00000	0.0359211
$776$	15.2953	0.549069
$777$	9.11029	0.326830
$778$	28.2823	1.01397
$779$	−20.9039	−0.748961
$780$	0.820963	0.0293952
$781$	−3.26981	−0.117003
$782$	17.1889	0.614673
$783$	34.9544	1.24917
$784$	−1.19981	−0.0428505
$785$	−2.95439	−0.105447
$786$	1.35817	0.0484445
$787$	17.3519	0.618527	0.309263	−	0.950976i	$-0.399918\pi$
$787$	17.3519	0.618527	0.309263	+	0.950976i	$0.399918\pi$
$788$	−25.9816	−0.925556
$789$	−25.0620	−0.892231
$790$	−11.0105	−0.391738
$791$	−9.51623	−0.338358
$792$	1.49769	0.0532180
$793$	12.2448	0.434825
$794$	33.4229	1.18613
$795$	−0.0491728	−0.00174398
$796$	7.00475	0.248277
$797$	32.3559	1.14611	0.573053	−	0.819518i	$-0.305759\pi$
$797$	32.3559	1.14611	0.573053	+	0.819518i	$0.305759\pi$
$798$	−8.24987	−0.292042
$799$	−49.7055	−1.75845
$800$	1.00000	0.0353553
$801$	27.9199	0.986500
$802$	−22.4102	−0.791331
$803$	8.26602	0.291701
$804$	−5.21596	−0.183953
$805$	5.89900	0.207913
$806$	−1.00000	−0.0352235
$807$	−16.4738	−0.579907
$808$	1.52397	0.0536131
$809$	−31.3472	−1.10211	−0.551054	−	0.834470i	$-0.685774\pi$
$809$	−31.3472	−1.10211	−0.551054	+	0.834470i	$0.685774\pi$
$810$	−3.38843	−0.119057
$811$	−34.7096	−1.21882	−0.609409	−	0.792856i	$-0.708593\pi$
$811$	−34.7096	−1.21882	−0.609409	+	0.792856i	$0.708593\pi$
$812$	−19.2529	−0.675646
$813$	9.00950	0.315977
$814$	−2.96685	−0.103988
$815$	−1.37660	−0.0482201
$816$	−5.76120	−0.201682
$817$	44.3763	1.55253
$818$	35.5030	1.24133
$819$	5.60189	0.195746
$820$	−5.00986	−0.174952
$821$	−5.42026	−0.189168	−0.0945841	−	0.995517i	$-0.530152\pi$
$821$	−5.42026	−0.189168	−0.0945841	+	0.995517i	$0.530152\pi$
$822$	−17.0741	−0.595527
$823$	−28.9159	−1.00795	−0.503973	−	0.863720i	$-0.668129\pi$
$823$	−28.9159	−1.00795	−0.503973	+	0.863720i	$0.668129\pi$
$824$	12.7867	0.445446
$825$	−0.528605	−0.0184037
$826$	−8.54736	−0.297401
$827$	−54.5358	−1.89640	−0.948198	−	0.317681i	$-0.897096\pi$
$827$	−54.5358	−1.89640	−0.948198	+	0.317681i	$0.897096\pi$
$828$	5.69733	0.197996
$829$	−49.8477	−1.73128	−0.865641	−	0.500665i	$-0.833089\pi$
$829$	−49.8477	−1.73128	−0.865641	+	0.500665i	$0.833089\pi$
$830$	−15.7904	−0.548094
$831$	−20.6418	−0.716057
$832$	−1.00000	−0.0346688
$833$	8.41983	0.291730
$834$	−6.43529	−0.222836
$835$	−3.48207	−0.120502
$836$	2.68664	0.0929196
$837$	−4.37246	−0.151134
$838$	−33.9792	−1.17379
$839$	19.0703	0.658378	0.329189	−	0.944264i	$-0.393225\pi$
$839$	19.0703	0.658378	0.329189	+	0.944264i	$0.393225\pi$
$840$	−1.97717	−0.0682189
$841$	34.9076	1.20371
$842$	22.0199	0.758856
$843$	−15.3511	−0.528719
$844$	6.97125	0.239960
$845$	−1.00000	−0.0344010
$846$	−16.4751	−0.566426
$847$	−25.4935	−0.875966
$848$	0.0598965	0.00205685
$849$	−21.6311	−0.742378
$850$	−7.01761	−0.240702
$851$	−11.2861	−0.386884
$852$	4.16906	0.142830
$853$	3.83301	0.131240	0.0656199	−	0.997845i	$-0.479098\pi$
$853$	3.83301	0.131240	0.0656199	+	0.997845i	$0.479098\pi$
$854$	−29.4898	−1.00912
$855$	−9.70545	−0.331920
$856$	−6.93658	−0.237087
$857$	−32.5710	−1.11260	−0.556302	−	0.830980i	$-0.687780\pi$
$857$	−32.5710	−1.11260	−0.556302	+	0.830980i	$0.687780\pi$
$858$	0.528605	0.0180463
$859$	−50.4183	−1.72025	−0.860124	−	0.510084i	$-0.829614\pi$
$859$	−50.4183	−1.72025	−0.860124	+	0.510084i	$0.829614\pi$
$860$	10.6353	0.362660
$861$	9.90536	0.337574
$862$	−10.3826	−0.353632
$863$	−41.9834	−1.42913	−0.714567	−	0.699567i	$-0.753376\pi$
$863$	−41.9834	−1.42913	−0.714567	+	0.699567i	$0.753376\pi$
$864$	−4.37246	−0.148754
$865$	16.5437	0.562503
$866$	−20.4374	−0.694490
$867$	26.4735	0.899088
$868$	2.40836	0.0817450
$869$	−7.08952	−0.240495
$870$	6.56296	0.222505
$871$	6.35346	0.215279
$872$	19.4420	0.658391
$873$	−35.5772	−1.20411
$874$	10.2202	0.345704
$875$	−2.40836	−0.0814173
$876$	−10.5393	−0.356090
$877$	41.0641	1.38664	0.693318	−	0.720632i	$-0.256148\pi$
$877$	41.0641	1.38664	0.693318	+	0.720632i	$0.256148\pi$
$878$	30.8175	1.04004
$879$	7.67690	0.258935
$880$	0.643884	0.0217053
$881$	27.6863	0.932777	0.466388	−	0.884580i	$-0.345555\pi$
$881$	27.6863	0.932777	0.466388	+	0.884580i	$0.345555\pi$
$882$	2.79079	0.0939708
$883$	−34.1921	−1.15066	−0.575328	−	0.817923i	$-0.695125\pi$
$883$	−34.1921	−1.15066	−0.575328	+	0.817923i	$0.695125\pi$
$884$	7.01761	0.236028
$885$	2.91363	0.0979406
$886$	5.72789	0.192432
$887$	8.19615	0.275200	0.137600	−	0.990488i	$-0.456061\pi$
$887$	8.19615	0.275200	0.137600	+	0.990488i	$0.456061\pi$
$888$	3.78278	0.126942
$889$	−0.433213	−0.0145295
$890$	12.0033	0.402351
$891$	−2.18176	−0.0730916
$892$	16.8234	0.563289
$893$	−29.5541	−0.988989
$894$	2.53158	0.0846688
$895$	7.43548	0.248541
$896$	2.40836	0.0804576
$897$	2.01086	0.0671406
$898$	−2.78384	−0.0928980
$899$	−7.99422	−0.266622
$900$	−2.32602	−0.0775340
$901$	−0.420331	−0.0140032
$902$	−3.22577	−0.107406
$903$	−21.0278	−0.699761
$904$	−3.95134	−0.131419
$905$	4.29620	0.142811
$906$	17.9738	0.597140
$907$	−19.7707	−0.656476	−0.328238	−	0.944595i	$-0.606455\pi$
$907$	−19.7707	−0.656476	−0.328238	+	0.944595i	$0.606455\pi$
$908$	2.12305	0.0704559
$909$	−3.54479	−0.117573
$910$	2.40836	0.0798363
$911$	36.3338	1.20379	0.601896	−	0.798574i	$-0.294412\pi$
$911$	36.3338	1.20379	0.601896	+	0.798574i	$0.294412\pi$
$912$	−3.42552	−0.113430
$913$	−10.1672	−0.336486
$914$	12.1524	0.401966
$915$	10.0525	0.332326
$916$	−22.8085	−0.753614
$917$	3.98431	0.131573
$918$	30.6843	1.01273
$919$	−50.5675	−1.66807	−0.834034	−	0.551713i	$-0.813975\pi$
$919$	−50.5675	−1.66807	−0.834034	+	0.551713i	$0.813975\pi$
$920$	2.44939	0.0807540
$921$	−23.9623	−0.789584
$922$	−31.4073	−1.03434
$923$	−5.07826	−0.167153
$924$	−1.27307	−0.0418809
$925$	4.60774	0.151501
$926$	8.34823	0.274340
$927$	−29.7421	−0.976860
$928$	−7.99422	−0.262423
$929$	41.7886	1.37104	0.685520	−	0.728054i	$-0.259575\pi$
$929$	41.7886	1.37104	0.685520	+	0.728054i	$0.259575\pi$
$930$	−0.820963	−0.0269204
$931$	5.00629	0.164075
$932$	−29.0445	−0.951383
$933$	16.5526	0.541908
$934$	24.4055	0.798574
$935$	−4.51853	−0.147772
$936$	2.32602	0.0760283
$937$	18.8829	0.616878	0.308439	−	0.951244i	$-0.400193\pi$
$937$	18.8829	0.616878	0.308439	+	0.951244i	$0.400193\pi$
$938$	−15.3014	−0.499609
$939$	13.5446	0.442013
$940$	−7.08296	−0.231021
$941$	−45.3445	−1.47819	−0.739095	−	0.673601i	$-0.764747\pi$
$941$	−45.3445	−1.47819	−0.739095	+	0.673601i	$0.764747\pi$
$942$	2.42545	0.0790254
$943$	−12.2711	−0.399602
$944$	−3.54904	−0.115511
$945$	10.5305	0.342556
$946$	6.84789	0.222644
$947$	−41.0527	−1.33403	−0.667017	−	0.745043i	$-0.732429\pi$
$947$	−41.0527	−1.33403	−0.667017	+	0.745043i	$0.732429\pi$
$948$	9.03925	0.293581
$949$	12.8377	0.416731
$950$	−4.17256	−0.135376
$951$	13.3155	0.431783
$952$	−16.9009	−0.547762
$953$	−44.9320	−1.45549	−0.727744	−	0.685848i	$-0.759431\pi$
$953$	−44.9320	−1.45549	−0.727744	+	0.685848i	$0.759431\pi$
$954$	−0.139320	−0.00451067
$955$	−2.48512	−0.0804167
$956$	−2.39758	−0.0775433
$957$	4.22579	0.136600
$958$	−27.7061	−0.895142
$959$	−50.0881	−1.61743
$960$	−0.820963	−0.0264965
$961$	1.00000	0.0322581
$962$	−4.60774	−0.148559
$963$	16.1346	0.519931
$964$	13.1175	0.422486
$965$	−7.92818	−0.255217
$966$	−4.84286	−0.155817
$967$	48.4748	1.55884	0.779422	−	0.626499i	$-0.215513\pi$
$967$	48.4748	1.55884	0.779422	+	0.626499i	$0.215513\pi$
$968$	−10.5854	−0.340228
$969$	24.0389	0.772242
$970$	−15.2953	−0.491103
$971$	18.0215	0.578338	0.289169	−	0.957278i	$-0.406621\pi$
$971$	18.0215	0.578338	0.289169	+	0.957278i	$0.406621\pi$
$972$	15.8992	0.509966
$973$	−18.8784	−0.605214
$974$	−11.1682	−0.357852
$975$	−0.820963	−0.0262919
$976$	−12.2448	−0.391946
$977$	−11.8738	−0.379876	−0.189938	−	0.981796i	$-0.560829\pi$
$977$	−11.8738	−0.379876	−0.189938	+	0.981796i	$0.560829\pi$
$978$	1.13014	0.0361378
$979$	7.72872	0.247011
$980$	1.19981	0.0383267
$981$	−45.2226	−1.44385
$982$	9.78508	0.312254
$983$	53.7217	1.71346	0.856728	−	0.515769i	$-0.172494\pi$
$983$	53.7217	1.71346	0.856728	+	0.515769i	$0.172494\pi$
$984$	4.11291	0.131115
$985$	25.9816	0.827843
$986$	56.1004	1.78660
$987$	14.0042	0.445760
$988$	4.17256	0.132747
$989$	26.0499	0.828340
$990$	−1.49769	−0.0475996
$991$	−4.53843	−0.144168	−0.0720840	−	0.997399i	$-0.522965\pi$
$991$	−4.53843	−0.144168	−0.0720840	+	0.997399i	$0.522965\pi$
$992$	1.00000	0.0317500
$993$	−11.7426	−0.372640
$994$	12.2303	0.387920
$995$	−7.00475	−0.222065
$996$	12.9634	0.410760
$997$	52.9597	1.67725	0.838625	−	0.544709i	$-0.183360\pi$
$997$	52.9597	1.67725	0.838625	+	0.544709i	$0.183360\pi$
$998$	23.9219	0.757233
$999$	−20.1472	−0.637428

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4030.2.a.j.1.6	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4030.2.a.j.1.6	✓	7	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:	\( N \)	\(=\)	\( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4030.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.820963 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.820963 q^{6} +2.40836 q^{7} +1.00000 q^{8} -2.32602 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.820963 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.820963 q^{6} +2.40836 q^{7} +1.00000 q^{8} -2.32602 q^{9} -1.00000 q^{10} -0.643884 q^{11} +0.820963 q^{12} -1.00000 q^{13} +2.40836 q^{14} -0.820963 q^{15} +1.00000 q^{16} -7.01761 q^{17} -2.32602 q^{18} -4.17256 q^{19} -1.00000 q^{20} +1.97717 q^{21} -0.643884 q^{22} -2.44939 q^{23} +0.820963 q^{24} +1.00000 q^{25} -1.00000 q^{26} -4.37246 q^{27} +2.40836 q^{28} -7.99422 q^{29} -0.820963 q^{30} +1.00000 q^{31} +1.00000 q^{32} -0.528605 q^{33} -7.01761 q^{34} -2.40836 q^{35} -2.32602 q^{36} +4.60774 q^{37} -4.17256 q^{38} -0.820963 q^{39} -1.00000 q^{40} +5.00986 q^{41} +1.97717 q^{42} -10.6353 q^{43} -0.643884 q^{44} +2.32602 q^{45} -2.44939 q^{46} +7.08296 q^{47} +0.820963 q^{48} -1.19981 q^{49} +1.00000 q^{50} -5.76120 q^{51} -1.00000 q^{52} +0.0598965 q^{53} -4.37246 q^{54} +0.643884 q^{55} +2.40836 q^{56} -3.42552 q^{57} -7.99422 q^{58} -3.54904 q^{59} -0.820963 q^{60} -12.2448 q^{61} +1.00000 q^{62} -5.60189 q^{63} +1.00000 q^{64} +1.00000 q^{65} -0.528605 q^{66} -6.35346 q^{67} -7.01761 q^{68} -2.01086 q^{69} -2.40836 q^{70} +5.07826 q^{71} -2.32602 q^{72} -12.8377 q^{73} +4.60774 q^{74} +0.820963 q^{75} -4.17256 q^{76} -1.55070 q^{77} -0.820963 q^{78} +11.0105 q^{79} -1.00000 q^{80} +3.38843 q^{81} +5.00986 q^{82} +15.7904 q^{83} +1.97717 q^{84} +7.01761 q^{85} -10.6353 q^{86} -6.56296 q^{87} -0.643884 q^{88} -12.0033 q^{89} +2.32602 q^{90} -2.40836 q^{91} -2.44939 q^{92} +0.820963 q^{93} +7.08296 q^{94} +4.17256 q^{95} +0.820963 q^{96} +15.2953 q^{97} -1.19981 q^{98} +1.49769 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} - 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 4 q^{7} + 7 q^{8} + 4 q^{9}+O(q^{10}) \) 7 * q + 7 * q^2 - 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 4 * q^7 + 7 * q^8 + 4 * q^9	\( 7 q + 7 q^{2} - 3 q^{3} + 7 q^{4} - 7 q^{5} - 3 q^{6} + 4 q^{7} + 7 q^{8} + 4 q^{9} - 7 q^{10} - 10 q^{11} - 3 q^{12} - 7 q^{13} + 4 q^{14} + 3 q^{15} + 7 q^{16} - 6 q^{17} + 4 q^{18} - 5 q^{19} - 7 q^{20} - 15 q^{21} - 10 q^{22} - 11 q^{23} - 3 q^{24} + 7 q^{25} - 7 q^{26} - 21 q^{27} + 4 q^{28} - 18 q^{29} + 3 q^{30} + 7 q^{31} + 7 q^{32} + 4 q^{33} - 6 q^{34} - 4 q^{35} + 4 q^{36} - 8 q^{37} - 5 q^{38} + 3 q^{39} - 7 q^{40} - 12 q^{41} - 15 q^{42} - 5 q^{43} - 10 q^{44} - 4 q^{45} - 11 q^{46} - 10 q^{47} - 3 q^{48} + 7 q^{49} + 7 q^{50} - 29 q^{51} - 7 q^{52} - 18 q^{53} - 21 q^{54} + 10 q^{55} + 4 q^{56} + 13 q^{57} - 18 q^{58} - 11 q^{59} + 3 q^{60} - 25 q^{61} + 7 q^{62} + 17 q^{63} + 7 q^{64} + 7 q^{65} + 4 q^{66} - 22 q^{67} - 6 q^{68} - 18 q^{69} - 4 q^{70} - 22 q^{71} + 4 q^{72} + 19 q^{73} - 8 q^{74} - 3 q^{75} - 5 q^{76} - 47 q^{77} + 3 q^{78} - 20 q^{79} - 7 q^{80} + 7 q^{81} - 12 q^{82} - 8 q^{83} - 15 q^{84} + 6 q^{85} - 5 q^{86} + 29 q^{87} - 10 q^{88} - 4 q^{89} - 4 q^{90} - 4 q^{91} - 11 q^{92} - 3 q^{93} - 10 q^{94} + 5 q^{95} - 3 q^{96} + 13 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 - 3 * q^3 + 7 * q^4 - 7 * q^5 - 3 * q^6 + 4 * q^7 + 7 * q^8 + 4 * q^9 - 7 * q^10 - 10 * q^11 - 3 * q^12 - 7 * q^13 + 4 * q^14 + 3 * q^15 + 7 * q^16 - 6 * q^17 + 4 * q^18 - 5 * q^19 - 7 * q^20 - 15 * q^21 - 10 * q^22 - 11 * q^23 - 3 * q^24 + 7 * q^25 - 7 * q^26 - 21 * q^27 + 4 * q^28 - 18 * q^29 + 3 * q^30 + 7 * q^31 + 7 * q^32 + 4 * q^33 - 6 * q^34 - 4 * q^35 + 4 * q^36 - 8 * q^37 - 5 * q^38 + 3 * q^39 - 7 * q^40 - 12 * q^41 - 15 * q^42 - 5 * q^43 - 10 * q^44 - 4 * q^45 - 11 * q^46 - 10 * q^47 - 3 * q^48 + 7 * q^49 + 7 * q^50 - 29 * q^51 - 7 * q^52 - 18 * q^53 - 21 * q^54 + 10 * q^55 + 4 * q^56 + 13 * q^57 - 18 * q^58 - 11 * q^59 + 3 * q^60 - 25 * q^61 + 7 * q^62 + 17 * q^63 + 7 * q^64 + 7 * q^65 + 4 * q^66 - 22 * q^67 - 6 * q^68 - 18 * q^69 - 4 * q^70 - 22 * q^71 + 4 * q^72 + 19 * q^73 - 8 * q^74 - 3 * q^75 - 5 * q^76 - 47 * q^77 + 3 * q^78 - 20 * q^79 - 7 * q^80 + 7 * q^81 - 12 * q^82 - 8 * q^83 - 15 * q^84 + 6 * q^85 - 5 * q^86 + 29 * q^87 - 10 * q^88 - 4 * q^89 - 4 * q^90 - 4 * q^91 - 11 * q^92 - 3 * q^93 - 10 * q^94 + 5 * q^95 - 3 * q^96 + 13 * q^97 + 7 * q^98 - 27 * q^99

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