LMFDB - Embedded newform 8030.2.a.z.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8030,2,Mod(1,8030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8030, 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("8030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8030 = 2 \cdot 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8030.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:	$64.1198728231$
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} - 2x^{6} - 11x^{5} + 17x^{4} + 25x^{3} - 9x^{2} - 14x - 3 $ x^7 - 2x^6 - 11x^5 + 17x^4 + 25x^3 - 9x^2 - 14x - 3
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			1.5
Root			$-0.496547$ of defining polynomial
Character	$\chi$	$=$	8030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.496547 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.496547 q^{6} +0.154508 q^{7} -1.00000 q^{8} -2.75344 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.496547 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.496547 q^{6} +0.154508 q^{7} -1.00000 q^{8} -2.75344 q^{9} -1.00000 q^{10} -1.00000 q^{11} +0.496547 q^{12} +3.41609 q^{13} -0.154508 q^{14} +0.496547 q^{15} +1.00000 q^{16} +0.773230 q^{17} +2.75344 q^{18} +6.71997 q^{19} +1.00000 q^{20} +0.0767206 q^{21} +1.00000 q^{22} -6.55692 q^{23} -0.496547 q^{24} +1.00000 q^{25} -3.41609 q^{26} -2.85686 q^{27} +0.154508 q^{28} +8.44775 q^{29} -0.496547 q^{30} -5.89121 q^{31} -1.00000 q^{32} -0.496547 q^{33} -0.773230 q^{34} +0.154508 q^{35} -2.75344 q^{36} -4.82608 q^{37} -6.71997 q^{38} +1.69625 q^{39} -1.00000 q^{40} -12.3234 q^{41} -0.0767206 q^{42} -8.81100 q^{43} -1.00000 q^{44} -2.75344 q^{45} +6.55692 q^{46} +6.60623 q^{47} +0.496547 q^{48} -6.97613 q^{49} -1.00000 q^{50} +0.383945 q^{51} +3.41609 q^{52} -3.65129 q^{53} +2.85686 q^{54} -1.00000 q^{55} -0.154508 q^{56} +3.33679 q^{57} -8.44775 q^{58} -12.8313 q^{59} +0.496547 q^{60} -5.52844 q^{61} +5.89121 q^{62} -0.425429 q^{63} +1.00000 q^{64} +3.41609 q^{65} +0.496547 q^{66} +1.64732 q^{67} +0.773230 q^{68} -3.25582 q^{69} -0.154508 q^{70} +13.7245 q^{71} +2.75344 q^{72} +1.00000 q^{73} +4.82608 q^{74} +0.496547 q^{75} +6.71997 q^{76} -0.154508 q^{77} -1.69625 q^{78} -7.30211 q^{79} +1.00000 q^{80} +6.84176 q^{81} +12.3234 q^{82} +3.90548 q^{83} +0.0767206 q^{84} +0.773230 q^{85} +8.81100 q^{86} +4.19471 q^{87} +1.00000 q^{88} +0.0565942 q^{89} +2.75344 q^{90} +0.527814 q^{91} -6.55692 q^{92} -2.92527 q^{93} -6.60623 q^{94} +6.71997 q^{95} -0.496547 q^{96} -10.2614 q^{97} +6.97613 q^{98} +2.75344 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} - 2 q^{3} + 7 q^{4} + 7 q^{5} + 2 q^{6} - 3 q^{7} - 7 q^{8} + 5 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 - 2 * q^3 + 7 * q^4 + 7 * q^5 + 2 * q^6 - 3 * q^7 - 7 * q^8 + 5 * q^9	\( 7 q - 7 q^{2} - 2 q^{3} + 7 q^{4} + 7 q^{5} + 2 q^{6} - 3 q^{7} - 7 q^{8} + 5 q^{9} - 7 q^{10} - 7 q^{11} - 2 q^{12} - 3 q^{13} + 3 q^{14} - 2 q^{15} + 7 q^{16} - 11 q^{17} - 5 q^{18} - 8 q^{19} + 7 q^{20} - 3 q^{21} + 7 q^{22} + 8 q^{23} + 2 q^{24} + 7 q^{25} + 3 q^{26} - 11 q^{27} - 3 q^{28} - 9 q^{29} + 2 q^{30} - 9 q^{31} - 7 q^{32} + 2 q^{33} + 11 q^{34} - 3 q^{35} + 5 q^{36} + 21 q^{37} + 8 q^{38} + 39 q^{39} - 7 q^{40} - 10 q^{41} + 3 q^{42} - 5 q^{43} - 7 q^{44} + 5 q^{45} - 8 q^{46} + 19 q^{47} - 2 q^{48} - 14 q^{49} - 7 q^{50} + 37 q^{51} - 3 q^{52} - 13 q^{53} + 11 q^{54} - 7 q^{55} + 3 q^{56} - 13 q^{57} + 9 q^{58} + 5 q^{59} - 2 q^{60} - 12 q^{61} + 9 q^{62} - 12 q^{63} + 7 q^{64} - 3 q^{65} - 2 q^{66} - 23 q^{67} - 11 q^{68} - 24 q^{69} + 3 q^{70} + 22 q^{71} - 5 q^{72} + 7 q^{73} - 21 q^{74} - 2 q^{75} - 8 q^{76} + 3 q^{77} - 39 q^{78} - 32 q^{79} + 7 q^{80} + 27 q^{81} + 10 q^{82} + q^{83} - 3 q^{84} - 11 q^{85} + 5 q^{86} - 13 q^{87} + 7 q^{88} + 20 q^{89} - 5 q^{90} - 2 q^{91} + 8 q^{92} - 25 q^{93} - 19 q^{94} - 8 q^{95} + 2 q^{96} - 2 q^{97} + 14 q^{98} - 5 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - 2 * q^3 + 7 * q^4 + 7 * q^5 + 2 * q^6 - 3 * q^7 - 7 * q^8 + 5 * q^9 - 7 * q^10 - 7 * q^11 - 2 * q^12 - 3 * q^13 + 3 * q^14 - 2 * q^15 + 7 * q^16 - 11 * q^17 - 5 * q^18 - 8 * q^19 + 7 * q^20 - 3 * q^21 + 7 * q^22 + 8 * q^23 + 2 * q^24 + 7 * q^25 + 3 * q^26 - 11 * q^27 - 3 * q^28 - 9 * q^29 + 2 * q^30 - 9 * q^31 - 7 * q^32 + 2 * q^33 + 11 * q^34 - 3 * q^35 + 5 * q^36 + 21 * q^37 + 8 * q^38 + 39 * q^39 - 7 * q^40 - 10 * q^41 + 3 * q^42 - 5 * q^43 - 7 * q^44 + 5 * q^45 - 8 * q^46 + 19 * q^47 - 2 * q^48 - 14 * q^49 - 7 * q^50 + 37 * q^51 - 3 * q^52 - 13 * q^53 + 11 * q^54 - 7 * q^55 + 3 * q^56 - 13 * q^57 + 9 * q^58 + 5 * q^59 - 2 * q^60 - 12 * q^61 + 9 * q^62 - 12 * q^63 + 7 * q^64 - 3 * q^65 - 2 * q^66 - 23 * q^67 - 11 * q^68 - 24 * q^69 + 3 * q^70 + 22 * q^71 - 5 * q^72 + 7 * q^73 - 21 * q^74 - 2 * q^75 - 8 * q^76 + 3 * q^77 - 39 * q^78 - 32 * q^79 + 7 * q^80 + 27 * q^81 + 10 * q^82 + q^83 - 3 * q^84 - 11 * q^85 + 5 * q^86 - 13 * q^87 + 7 * q^88 + 20 * q^89 - 5 * q^90 - 2 * q^91 + 8 * q^92 - 25 * q^93 - 19 * q^94 - 8 * q^95 + 2 * q^96 - 2 * q^97 + 14 * q^98 - 5 * 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
$3$	0.496547	0.286682	0.143341	−	0.989673i	$-0.454215\pi$
$3$	0.496547	0.286682	0.143341	+	0.989673i	$0.454215\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.496547	−0.202715
$7$	0.154508	0.0583986	0.0291993	−	0.999574i	$-0.490704\pi$
$7$	0.154508	0.0583986	0.0291993	+	0.999574i	$0.490704\pi$
$8$	−1.00000	−0.353553
$9$	−2.75344	−0.917814
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.496547	0.143341
$13$	3.41609	0.947454	0.473727	−	0.880672i	$-0.342908\pi$
$13$	3.41609	0.947454	0.473727	+	0.880672i	$0.342908\pi$
$14$	−0.154508	−0.0412940
$15$	0.496547	0.128208
$16$	1.00000	0.250000
$17$	0.773230	0.187536	0.0937679	−	0.995594i	$-0.470109\pi$
$17$	0.773230	0.187536	0.0937679	+	0.995594i	$0.470109\pi$
$18$	2.75344	0.648992
$19$	6.71997	1.54167	0.770834	−	0.637036i	$-0.219840\pi$
$19$	6.71997	1.54167	0.770834	+	0.637036i	$0.219840\pi$
$20$	1.00000	0.223607
$21$	0.0767206	0.0167418
$22$	1.00000	0.213201
$23$	−6.55692	−1.36721	−0.683607	−	0.729851i	$-0.739590\pi$
$23$	−6.55692	−1.36721	−0.683607	+	0.729851i	$0.739590\pi$
$24$	−0.496547	−0.101357
$25$	1.00000	0.200000
$26$	−3.41609	−0.669951
$27$	−2.85686	−0.549802
$28$	0.154508	0.0291993
$29$	8.44775	1.56871	0.784354	−	0.620314i	$-0.212995\pi$
$29$	8.44775	1.56871	0.784354	+	0.620314i	$0.212995\pi$
$30$	−0.496547	−0.0906567
$31$	−5.89121	−1.05809	−0.529047	−	0.848593i	$-0.677450\pi$
$31$	−5.89121	−1.05809	−0.529047	+	0.848593i	$0.677450\pi$
$32$	−1.00000	−0.176777
$33$	−0.496547	−0.0864378
$34$	−0.773230	−0.132608
$35$	0.154508	0.0261167
$36$	−2.75344	−0.458907
$37$	−4.82608	−0.793402	−0.396701	−	0.917948i	$-0.629845\pi$
$37$	−4.82608	−0.793402	−0.396701	+	0.917948i	$0.629845\pi$
$38$	−6.71997	−1.09012
$39$	1.69625	0.271618
$40$	−1.00000	−0.158114
$41$	−12.3234	−1.92459	−0.962293	−	0.272015i	$-0.912310\pi$
$41$	−12.3234	−1.92459	−0.962293	+	0.272015i	$0.912310\pi$
$42$	−0.0767206	−0.0118383
$43$	−8.81100	−1.34366	−0.671832	−	0.740703i	$-0.734492\pi$
$43$	−8.81100	−1.34366	−0.671832	+	0.740703i	$0.734492\pi$
$44$	−1.00000	−0.150756
$45$	−2.75344	−0.410459
$46$	6.55692	0.966766
$47$	6.60623	0.963617	0.481808	−	0.876277i	$-0.339980\pi$
$47$	6.60623	0.963617	0.481808	+	0.876277i	$0.339980\pi$
$48$	0.496547	0.0716704
$49$	−6.97613	−0.996590
$50$	−1.00000	−0.141421
$51$	0.383945	0.0537631
$52$	3.41609	0.473727
$53$	−3.65129	−0.501543	−0.250772	−	0.968046i	$-0.580684\pi$
$53$	−3.65129	−0.501543	−0.250772	+	0.968046i	$0.580684\pi$
$54$	2.85686	0.388769
$55$	−1.00000	−0.134840
$56$	−0.154508	−0.0206470
$57$	3.33679	0.441968
$58$	−8.44775	−1.10924
$59$	−12.8313	−1.67049	−0.835245	−	0.549878i	$-0.814674\pi$
$59$	−12.8313	−1.67049	−0.835245	+	0.549878i	$0.814674\pi$
$60$	0.496547	0.0641040
$61$	−5.52844	−0.707844	−0.353922	−	0.935275i	$-0.615152\pi$
$61$	−5.52844	−0.707844	−0.353922	+	0.935275i	$0.615152\pi$
$62$	5.89121	0.748185
$63$	−0.425429	−0.0535990
$64$	1.00000	0.125000
$65$	3.41609	0.423714
$66$	0.496547	0.0611208
$67$	1.64732	0.201252	0.100626	−	0.994924i	$-0.467915\pi$
$67$	1.64732	0.201252	0.100626	+	0.994924i	$0.467915\pi$
$68$	0.773230	0.0937679
$69$	−3.25582	−0.391955
$70$	−0.154508	−0.0184673
$71$	13.7245	1.62880	0.814402	−	0.580301i	$-0.197065\pi$
$71$	13.7245	1.62880	0.814402	+	0.580301i	$0.197065\pi$
$72$	2.75344	0.324496
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	4.82608	0.561020
$75$	0.496547	0.0573363
$76$	6.71997	0.770834
$77$	−0.154508	−0.0176078
$78$	−1.69625	−0.192063
$79$	−7.30211	−0.821552	−0.410776	−	0.911736i	$-0.634742\pi$
$79$	−7.30211	−0.821552	−0.410776	+	0.911736i	$0.634742\pi$
$80$	1.00000	0.111803
$81$	6.84176	0.760195
$82$	12.3234	1.36089
$83$	3.90548	0.428682	0.214341	−	0.976759i	$-0.431240\pi$
$83$	3.90548	0.428682	0.214341	+	0.976759i	$0.431240\pi$
$84$	0.0767206	0.00837091
$85$	0.773230	0.0838686
$86$	8.81100	0.950114
$87$	4.19471	0.449720
$88$	1.00000	0.106600
$89$	0.0565942	0.00599897	0.00299948	−	0.999996i	$-0.499045\pi$
$89$	0.0565942	0.00599897	0.00299948	+	0.999996i	$0.499045\pi$
$90$	2.75344	0.290238
$91$	0.527814	0.0553300
$92$	−6.55692	−0.683607
$93$	−2.92527	−0.303336
$94$	−6.60623	−0.681380
$95$	6.71997	0.689455
$96$	−0.496547	−0.0506787
$97$	−10.2614	−1.04189	−0.520945	−	0.853590i	$-0.674420\pi$
$97$	−10.2614	−1.04189	−0.520945	+	0.853590i	$0.674420\pi$
$98$	6.97613	0.704695
$99$	2.75344	0.276731
$100$	1.00000	0.100000
$101$	−3.92034	−0.390089	−0.195044	−	0.980794i	$-0.562485\pi$
$101$	−3.92034	−0.390089	−0.195044	+	0.980794i	$0.562485\pi$
$102$	−0.383945	−0.0380162
$103$	−9.09142	−0.895805	−0.447902	−	0.894083i	$-0.647829\pi$
$103$	−9.09142	−0.895805	−0.447902	+	0.894083i	$0.647829\pi$
$104$	−3.41609	−0.334975
$105$	0.0767206	0.00748717
$106$	3.65129	0.354645
$107$	17.6794	1.70913	0.854566	−	0.519343i	$-0.173823\pi$
$107$	17.6794	1.70913	0.854566	+	0.519343i	$0.173823\pi$
$108$	−2.85686	−0.274901
$109$	7.08049	0.678188	0.339094	−	0.940752i	$-0.389880\pi$
$109$	7.08049	0.678188	0.339094	+	0.940752i	$0.389880\pi$
$110$	1.00000	0.0953463
$111$	−2.39638	−0.227454
$112$	0.154508	0.0145997
$113$	1.52962	0.143895	0.0719474	−	0.997408i	$-0.477079\pi$
$113$	1.52962	0.143895	0.0719474	+	0.997408i	$0.477079\pi$
$114$	−3.33679	−0.312519
$115$	−6.55692	−0.611436
$116$	8.44775	0.784354
$117$	−9.40601	−0.869586
$118$	12.8313	1.18121
$119$	0.119470	0.0109518
$120$	−0.496547	−0.0453284
$121$	1.00000	0.0909091
$122$	5.52844	0.500521
$123$	−6.11913	−0.551744
$124$	−5.89121	−0.529047
$125$	1.00000	0.0894427
$126$	0.425429	0.0379002
$127$	−3.07293	−0.272678	−0.136339	−	0.990662i	$-0.543534\pi$
$127$	−3.07293	−0.272678	−0.136339	+	0.990662i	$0.543534\pi$
$128$	−1.00000	−0.0883883
$129$	−4.37508	−0.385204
$130$	−3.41609	−0.299611
$131$	13.6925	1.19632	0.598158	−	0.801378i	$-0.295899\pi$
$131$	13.6925	1.19632	0.598158	+	0.801378i	$0.295899\pi$
$132$	−0.496547	−0.0432189
$133$	1.03829	0.0900313
$134$	−1.64732	−0.142307
$135$	−2.85686	−0.245879
$136$	−0.773230	−0.0663039
$137$	20.6051	1.76041	0.880207	−	0.474589i	$-0.157403\pi$
$137$	20.6051	1.76041	0.880207	+	0.474589i	$0.157403\pi$
$138$	3.25582	0.277154
$139$	3.51973	0.298539	0.149270	−	0.988797i	$-0.452308\pi$
$139$	3.51973	0.298539	0.149270	+	0.988797i	$0.452308\pi$
$140$	0.154508	0.0130583
$141$	3.28030	0.276251
$142$	−13.7245	−1.15174
$143$	−3.41609	−0.285668
$144$	−2.75344	−0.229453
$145$	8.44775	0.701548
$146$	−1.00000	−0.0827606
$147$	−3.46398	−0.285704
$148$	−4.82608	−0.396701
$149$	−0.462165	−0.0378620	−0.0189310	−	0.999821i	$-0.506026\pi$
$149$	−0.462165	−0.0378620	−0.0189310	+	0.999821i	$0.506026\pi$
$150$	−0.496547	−0.0405429
$151$	10.9058	0.887499	0.443750	−	0.896151i	$-0.353648\pi$
$151$	10.9058	0.887499	0.443750	+	0.896151i	$0.353648\pi$
$152$	−6.71997	−0.545062
$153$	−2.12904	−0.172123
$154$	0.154508	0.0124506
$155$	−5.89121	−0.473194
$156$	1.69625	0.135809
$157$	−20.4633	−1.63315	−0.816574	−	0.577241i	$-0.804129\pi$
$157$	−20.4633	−1.63315	−0.816574	+	0.577241i	$0.804129\pi$
$158$	7.30211	0.580925
$159$	−1.81304	−0.143783
$160$	−1.00000	−0.0790569
$161$	−1.01310	−0.0798433
$162$	−6.84176	−0.537539
$163$	−10.2743	−0.804744	−0.402372	−	0.915476i	$-0.631814\pi$
$163$	−10.2743	−0.804744	−0.402372	+	0.915476i	$0.631814\pi$
$164$	−12.3234	−0.962293
$165$	−0.496547	−0.0386562
$166$	−3.90548	−0.303124
$167$	−24.5275	−1.89800	−0.948999	−	0.315280i	$-0.897902\pi$
$167$	−24.5275	−1.89800	−0.948999	+	0.315280i	$0.897902\pi$
$168$	−0.0767206	−0.00591913
$169$	−1.33031	−0.102331
$170$	−0.773230	−0.0593040
$171$	−18.5031	−1.41496
$172$	−8.81100	−0.671832
$173$	−2.57656	−0.195892	−0.0979460	−	0.995192i	$-0.531227\pi$
$173$	−2.57656	−0.195892	−0.0979460	+	0.995192i	$0.531227\pi$
$174$	−4.19471	−0.318000
$175$	0.154508	0.0116797
$176$	−1.00000	−0.0753778
$177$	−6.37133	−0.478899
$178$	−0.0565942	−0.00424191
$179$	12.9133	0.965184	0.482592	−	0.875845i	$-0.339695\pi$
$179$	12.9133	0.965184	0.482592	+	0.875845i	$0.339695\pi$
$180$	−2.75344	−0.205229
$181$	13.2663	0.986077	0.493039	−	0.870007i	$-0.335886\pi$
$181$	13.2663	0.986077	0.493039	+	0.870007i	$0.335886\pi$
$182$	−0.527814	−0.0391242
$183$	−2.74513	−0.202926
$184$	6.55692	0.483383
$185$	−4.82608	−0.354820
$186$	2.92527	0.214491
$187$	−0.773230	−0.0565442
$188$	6.60623	0.481808
$189$	−0.441408	−0.0321077
$190$	−6.71997	−0.487518
$191$	3.61447	0.261534	0.130767	−	0.991413i	$-0.458256\pi$
$191$	3.61447	0.261534	0.130767	+	0.991413i	$0.458256\pi$
$192$	0.496547	0.0358352
$193$	−11.7801	−0.847953	−0.423976	−	0.905673i	$-0.639366\pi$
$193$	−11.7801	−0.847953	−0.423976	+	0.905673i	$0.639366\pi$
$194$	10.2614	0.736727
$195$	1.69625	0.121471
$196$	−6.97613	−0.498295
$197$	−19.2189	−1.36929	−0.684644	−	0.728877i	$-0.740042\pi$
$197$	−19.2189	−1.36929	−0.684644	+	0.728877i	$0.740042\pi$
$198$	−2.75344	−0.195679
$199$	−20.3987	−1.44602	−0.723012	−	0.690835i	$-0.757243\pi$
$199$	−20.3987	−1.44602	−0.723012	+	0.690835i	$0.757243\pi$
$200$	−1.00000	−0.0707107
$201$	0.817973	0.0576954
$202$	3.92034	0.275834
$203$	1.30525	0.0916104
$204$	0.383945	0.0268815
$205$	−12.3234	−0.860701
$206$	9.09142	0.633429
$207$	18.0541	1.25485
$208$	3.41609	0.236863
$209$	−6.71997	−0.464830
$210$	−0.0767206	−0.00529423
$211$	−14.9954	−1.03232	−0.516161	−	0.856491i	$-0.672640\pi$
$211$	−14.9954	−1.03232	−0.516161	+	0.856491i	$0.672640\pi$
$212$	−3.65129	−0.250772
$213$	6.81489	0.466948
$214$	−17.6794	−1.20854
$215$	−8.81100	−0.600905
$216$	2.85686	0.194384
$217$	−0.910241	−0.0617912
$218$	−7.08049	−0.479551
$219$	0.496547	0.0335536
$220$	−1.00000	−0.0674200
$221$	2.64142	0.177681
$222$	2.39638	0.160834
$223$	26.2141	1.75543	0.877713	−	0.479187i	$-0.159068\pi$
$223$	26.2141	1.75543	0.877713	+	0.479187i	$0.159068\pi$
$224$	−0.154508	−0.0103235
$225$	−2.75344	−0.183563
$226$	−1.52962	−0.101749
$227$	12.6044	0.836584	0.418292	−	0.908313i	$-0.362629\pi$
$227$	12.6044	0.836584	0.418292	+	0.908313i	$0.362629\pi$
$228$	3.33679	0.220984
$229$	−22.6294	−1.49539	−0.747697	−	0.664040i	$-0.768840\pi$
$229$	−22.6294	−1.49539	−0.747697	+	0.664040i	$0.768840\pi$
$230$	6.55692	0.432351
$231$	−0.0767206	−0.00504785
$232$	−8.44775	−0.554622
$233$	8.36957	0.548309	0.274154	−	0.961686i	$-0.411602\pi$
$233$	8.36957	0.548309	0.274154	+	0.961686i	$0.411602\pi$
$234$	9.40601	0.614890
$235$	6.60623	0.430943
$236$	−12.8313	−0.835245
$237$	−3.62584	−0.235524
$238$	−0.119470	−0.00774411
$239$	0.499926	0.0323375	0.0161688	−	0.999869i	$-0.494853\pi$
$239$	0.499926	0.0323375	0.0161688	+	0.999869i	$0.494853\pi$
$240$	0.496547	0.0320520
$241$	−29.7244	−1.91472	−0.957359	−	0.288901i	$-0.906710\pi$
$241$	−29.7244	−1.91472	−0.957359	+	0.288901i	$0.906710\pi$
$242$	−1.00000	−0.0642824
$243$	11.9678	0.767736
$244$	−5.52844	−0.353922
$245$	−6.97613	−0.445688
$246$	6.11913	0.390142
$247$	22.9561	1.46066
$248$	5.89121	0.374092
$249$	1.93926	0.122895
$250$	−1.00000	−0.0632456
$251$	−2.85815	−0.180405	−0.0902025	−	0.995923i	$-0.528751\pi$
$251$	−2.85815	−0.180405	−0.0902025	+	0.995923i	$0.528751\pi$
$252$	−0.425429	−0.0267995
$253$	6.55692	0.412230
$254$	3.07293	0.192813
$255$	0.383945	0.0240436
$256$	1.00000	0.0625000
$257$	−22.1330	−1.38062	−0.690308	−	0.723515i	$-0.742525\pi$
$257$	−22.1330	−1.38062	−0.690308	+	0.723515i	$0.742525\pi$
$258$	4.37508	0.272380
$259$	−0.745669	−0.0463336
$260$	3.41609	0.211857
$261$	−23.2604	−1.43978
$262$	−13.6925	−0.845923
$263$	11.9201	0.735024	0.367512	−	0.930019i	$-0.380210\pi$
$263$	11.9201	0.735024	0.367512	+	0.930019i	$0.380210\pi$
$264$	0.496547	0.0305604
$265$	−3.65129	−0.224297
$266$	−1.03829	−0.0636617
$267$	0.0281017	0.00171979
$268$	1.64732	0.100626
$269$	18.2114	1.11037	0.555183	−	0.831728i	$-0.312648\pi$
$269$	18.2114	1.11037	0.555183	+	0.831728i	$0.312648\pi$
$270$	2.85686	0.173863
$271$	−19.7262	−1.19828	−0.599140	−	0.800644i	$-0.704491\pi$
$271$	−19.7262	−1.19828	−0.599140	+	0.800644i	$0.704491\pi$
$272$	0.773230	0.0468839
$273$	0.262085	0.0158621
$274$	−20.6051	−1.24480
$275$	−1.00000	−0.0603023
$276$	−3.25582	−0.195978
$277$	−1.25507	−0.0754096	−0.0377048	−	0.999289i	$-0.512005\pi$
$277$	−1.25507	−0.0754096	−0.0377048	+	0.999289i	$0.512005\pi$
$278$	−3.51973	−0.211099
$279$	16.2211	0.971132
$280$	−0.154508	−0.00923363
$281$	14.5688	0.869104	0.434552	−	0.900647i	$-0.356907\pi$
$281$	14.5688	0.869104	0.434552	+	0.900647i	$0.356907\pi$
$282$	−3.28030	−0.195339
$283$	18.7543	1.11483	0.557414	−	0.830234i	$-0.311794\pi$
$283$	18.7543	1.11483	0.557414	+	0.830234i	$0.311794\pi$
$284$	13.7245	0.814402
$285$	3.33679	0.197654
$286$	3.41609	0.201998
$287$	−1.90406	−0.112393
$288$	2.75344	0.162248
$289$	−16.4021	−0.964830
$290$	−8.44775	−0.496069
$291$	−5.09528	−0.298691
$292$	1.00000	0.0585206
$293$	−8.70241	−0.508400	−0.254200	−	0.967152i	$-0.581812\pi$
$293$	−8.70241	−0.508400	−0.254200	+	0.967152i	$0.581812\pi$
$294$	3.46398	0.202023
$295$	−12.8313	−0.747066
$296$	4.82608	0.280510
$297$	2.85686	0.165772
$298$	0.462165	0.0267725
$299$	−22.3991	−1.29537
$300$	0.496547	0.0286682
$301$	−1.36137	−0.0784681
$302$	−10.9058	−0.627557
$303$	−1.94664	−0.111831
$304$	6.71997	0.385417
$305$	−5.52844	−0.316557
$306$	2.12904	0.121709
$307$	−22.2080	−1.26748	−0.633739	−	0.773547i	$-0.718481\pi$
$307$	−22.2080	−1.26748	−0.633739	+	0.773547i	$0.718481\pi$
$308$	−0.154508	−0.00880392
$309$	−4.51432	−0.256811
$310$	5.89121	0.334598
$311$	−32.4555	−1.84038	−0.920192	−	0.391466i	$-0.871968\pi$
$311$	−32.4555	−1.84038	−0.920192	+	0.391466i	$0.871968\pi$
$312$	−1.69625	−0.0960314
$313$	−8.82579	−0.498863	−0.249432	−	0.968392i	$-0.580244\pi$
$313$	−8.82579	−0.498863	−0.249432	+	0.968392i	$0.580244\pi$
$314$	20.4633	1.15481
$315$	−0.425429	−0.0239702
$316$	−7.30211	−0.410776
$317$	−28.1281	−1.57983	−0.789917	−	0.613214i	$-0.789876\pi$
$317$	−28.1281	−1.57983	−0.789917	+	0.613214i	$0.789876\pi$
$318$	1.81304	0.101670
$319$	−8.44775	−0.472983
$320$	1.00000	0.0559017
$321$	8.77866	0.489977
$322$	1.01310	0.0564578
$323$	5.19608	0.289118
$324$	6.84176	0.380098
$325$	3.41609	0.189491
$326$	10.2743	0.569040
$327$	3.51580	0.194424
$328$	12.3234	0.680444
$329$	1.02072	0.0562739
$330$	0.496547	0.0273340
$331$	4.56671	0.251009	0.125504	−	0.992093i	$-0.459945\pi$
$331$	4.56671	0.251009	0.125504	+	0.992093i	$0.459945\pi$
$332$	3.90548	0.214341
$333$	13.2883	0.728195
$334$	24.5275	1.34209
$335$	1.64732	0.0900028
$336$	0.0767206	0.00418545
$337$	−16.9095	−0.921117	−0.460559	−	0.887629i	$-0.652351\pi$
$337$	−16.9095	−0.921117	−0.460559	+	0.887629i	$0.652351\pi$
$338$	1.33031	0.0723593
$339$	0.759530	0.0412520
$340$	0.773230	0.0419343
$341$	5.89121	0.319027
$342$	18.5031	1.00053
$343$	−2.15943	−0.116598
$344$	8.81100	0.475057
$345$	−3.25582	−0.175288
$346$	2.57656	0.138517
$347$	−23.8720	−1.28152	−0.640758	−	0.767743i	$-0.721380\pi$
$347$	−23.8720	−1.28152	−0.640758	+	0.767743i	$0.721380\pi$
$348$	4.19471	0.224860
$349$	−9.39377	−0.502837	−0.251419	−	0.967878i	$-0.580897\pi$
$349$	−9.39377	−0.502837	−0.251419	+	0.967878i	$0.580897\pi$
$350$	−0.154508	−0.00825881
$351$	−9.75928	−0.520912
$352$	1.00000	0.0533002
$353$	−8.50430	−0.452638	−0.226319	−	0.974053i	$-0.572669\pi$
$353$	−8.50430	−0.452638	−0.226319	+	0.974053i	$0.572669\pi$
$354$	6.37133	0.338633
$355$	13.7245	0.728423
$356$	0.0565942	0.00299948
$357$	0.0593227	0.00313969
$358$	−12.9133	−0.682488
$359$	25.4132	1.34126	0.670629	−	0.741793i	$-0.266024\pi$
$359$	25.4132	1.34126	0.670629	+	0.741793i	$0.266024\pi$
$360$	2.75344	0.145119
$361$	26.1581	1.37674
$362$	−13.2663	−0.697262
$363$	0.496547	0.0260620
$364$	0.527814	0.0276650
$365$	1.00000	0.0523424
$366$	2.74513	0.143490
$367$	−5.97189	−0.311730	−0.155865	−	0.987778i	$-0.549816\pi$
$367$	−5.97189	−0.311730	−0.155865	+	0.987778i	$0.549816\pi$
$368$	−6.55692	−0.341803
$369$	33.9316	1.76641
$370$	4.82608	0.250896
$371$	−0.564154	−0.0292894
$372$	−2.92527	−0.151668
$373$	21.1182	1.09346	0.546730	−	0.837309i	$-0.315872\pi$
$373$	21.1182	1.09346	0.546730	+	0.837309i	$0.315872\pi$
$374$	0.773230	0.0399828
$375$	0.496547	0.0256416
$376$	−6.60623	−0.340690
$377$	28.8583	1.48628
$378$	0.441408	0.0227036
$379$	−23.1503	−1.18915	−0.594574	−	0.804041i	$-0.702679\pi$
$379$	−23.1503	−1.18915	−0.594574	+	0.804041i	$0.702679\pi$
$380$	6.71997	0.344727
$381$	−1.52585	−0.0781718
$382$	−3.61447	−0.184932
$383$	−15.4593	−0.789931	−0.394966	−	0.918696i	$-0.629243\pi$
$383$	−15.4593	−0.789931	−0.394966	+	0.918696i	$0.629243\pi$
$384$	−0.496547	−0.0253393
$385$	−0.154508	−0.00787447
$386$	11.7801	0.599593
$387$	24.2606	1.23323
$388$	−10.2614	−0.520945
$389$	13.0258	0.660436	0.330218	−	0.943905i	$-0.392878\pi$
$389$	13.0258	0.660436	0.330218	+	0.943905i	$0.392878\pi$
$390$	−1.69625	−0.0858931
$391$	−5.07001	−0.256401
$392$	6.97613	0.352348
$393$	6.79896	0.342962
$394$	19.2189	0.968233
$395$	−7.30211	−0.367409
$396$	2.75344	0.138366
$397$	−12.8032	−0.642575	−0.321288	−	0.946982i	$-0.604116\pi$
$397$	−12.8032	−0.642575	−0.321288	+	0.946982i	$0.604116\pi$
$398$	20.3987	1.02249
$399$	0.515561	0.0258103
$400$	1.00000	0.0500000
$401$	11.5399	0.576276	0.288138	−	0.957589i	$-0.406964\pi$
$401$	11.5399	0.576276	0.288138	+	0.957589i	$0.406964\pi$
$402$	−0.817973	−0.0407968
$403$	−20.1249	−1.00249
$404$	−3.92034	−0.195044
$405$	6.84176	0.339970
$406$	−1.30525	−0.0647783
$407$	4.82608	0.239220
$408$	−0.383945	−0.0190081
$409$	12.7927	0.632556	0.316278	−	0.948666i	$-0.397567\pi$
$409$	12.7927	0.632556	0.316278	+	0.948666i	$0.397567\pi$
$410$	12.3234	0.608607
$411$	10.2314	0.504679
$412$	−9.09142	−0.447902
$413$	−1.98254	−0.0975543
$414$	−18.0541	−0.887311
$415$	3.90548	0.191713
$416$	−3.41609	−0.167488
$417$	1.74771	0.0855858
$418$	6.71997	0.328685
$419$	−38.1110	−1.86185	−0.930923	−	0.365215i	$-0.880996\pi$
$419$	−38.1110	−1.86185	−0.930923	+	0.365215i	$0.880996\pi$
$420$	0.0767206	0.00374358
$421$	10.6154	0.517363	0.258681	−	0.965963i	$-0.416712\pi$
$421$	10.6154	0.517363	0.258681	+	0.965963i	$0.416712\pi$
$422$	14.9954	0.729963
$423$	−18.1898	−0.884421
$424$	3.65129	0.177322
$425$	0.773230	0.0375072
$426$	−6.81489	−0.330182
$427$	−0.854189	−0.0413371
$428$	17.6794	0.854566
$429$	−1.69625	−0.0818958
$430$	8.81100	0.424904
$431$	5.96373	0.287263	0.143631	−	0.989631i	$-0.454122\pi$
$431$	5.96373	0.287263	0.143631	+	0.989631i	$0.454122\pi$
$432$	−2.85686	−0.137451
$433$	26.6656	1.28146	0.640732	−	0.767764i	$-0.278631\pi$
$433$	26.6656	1.28146	0.640732	+	0.767764i	$0.278631\pi$
$434$	0.910241	0.0436930
$435$	4.19471	0.201121
$436$	7.08049	0.339094
$437$	−44.0624	−2.10779
$438$	−0.496547	−0.0237260
$439$	−10.4215	−0.497390	−0.248695	−	0.968582i	$-0.580002\pi$
$439$	−10.4215	−0.497390	−0.248695	+	0.968582i	$0.580002\pi$
$440$	1.00000	0.0476731
$441$	19.2084	0.914683
$442$	−2.64142	−0.125640
$443$	−20.8608	−0.991127	−0.495564	−	0.868572i	$-0.665038\pi$
$443$	−20.8608	−0.991127	−0.495564	+	0.868572i	$0.665038\pi$
$444$	−2.39638	−0.113727
$445$	0.0565942	0.00268282
$446$	−26.2141	−1.24127
$447$	−0.229487	−0.0108544
$448$	0.154508	0.00729983
$449$	11.3053	0.533529	0.266765	−	0.963762i	$-0.414045\pi$
$449$	11.3053	0.533529	0.266765	+	0.963762i	$0.414045\pi$
$450$	2.75344	0.129798
$451$	12.3234	0.580284
$452$	1.52962	0.0719474
$453$	5.41523	0.254430
$454$	−12.6044	−0.591554
$455$	0.527814	0.0247443
$456$	−3.33679	−0.156259
$457$	−0.172061	−0.00804869	−0.00402435	−	0.999992i	$-0.501281\pi$
$457$	−0.172061	−0.00804869	−0.00402435	+	0.999992i	$0.501281\pi$
$458$	22.6294	1.05740
$459$	−2.20901	−0.103108
$460$	−6.55692	−0.305718
$461$	−19.2996	−0.898870	−0.449435	−	0.893313i	$-0.648375\pi$
$461$	−19.2996	−0.898870	−0.449435	+	0.893313i	$0.648375\pi$
$462$	0.0767206	0.00356937
$463$	8.83723	0.410701	0.205350	−	0.978689i	$-0.434167\pi$
$463$	8.83723	0.410701	0.205350	+	0.978689i	$0.434167\pi$
$464$	8.44775	0.392177
$465$	−2.92527	−0.135656
$466$	−8.36957	−0.387713
$467$	24.9863	1.15623	0.578114	−	0.815956i	$-0.303789\pi$
$467$	24.9863	1.15623	0.578114	+	0.815956i	$0.303789\pi$
$468$	−9.40601	−0.434793
$469$	0.254525	0.0117529
$470$	−6.60623	−0.304722
$471$	−10.1610	−0.468194
$472$	12.8313	0.590607
$473$	8.81100	0.405130
$474$	3.62584	0.166541
$475$	6.71997	0.308334
$476$	0.119470	0.00547591
$477$	10.0536	0.460323
$478$	−0.499926	−0.0228661
$479$	4.34749	0.198642	0.0993210	−	0.995055i	$-0.468333\pi$
$479$	4.34749	0.198642	0.0993210	+	0.995055i	$0.468333\pi$
$480$	−0.496547	−0.0226642
$481$	−16.4863	−0.751712
$482$	29.7244	1.35391
$483$	−0.503051	−0.0228896
$484$	1.00000	0.0454545
$485$	−10.2614	−0.465947
$486$	−11.9678	−0.542872
$487$	−19.5164	−0.884372	−0.442186	−	0.896923i	$-0.645797\pi$
$487$	−19.5164	−0.884372	−0.442186	+	0.896923i	$0.645797\pi$
$488$	5.52844	0.250261
$489$	−5.10167	−0.230706
$490$	6.97613	0.315149
$491$	33.5016	1.51191	0.755953	−	0.654626i	$-0.227174\pi$
$491$	33.5016	1.51191	0.755953	+	0.654626i	$0.227174\pi$
$492$	−6.11913	−0.275872
$493$	6.53205	0.294189
$494$	−22.9561	−1.03284
$495$	2.75344	0.123758
$496$	−5.89121	−0.264523
$497$	2.12055	0.0951199
$498$	−1.93926	−0.0869001
$499$	24.0042	1.07458	0.537288	−	0.843399i	$-0.319449\pi$
$499$	24.0042	1.07458	0.537288	+	0.843399i	$0.319449\pi$
$500$	1.00000	0.0447214
$501$	−12.1791	−0.544121
$502$	2.85815	0.127566
$503$	1.05682	0.0471212	0.0235606	−	0.999722i	$-0.492500\pi$
$503$	1.05682	0.0471212	0.0235606	+	0.999722i	$0.492500\pi$
$504$	0.425429	0.0189501
$505$	−3.92034	−0.174453
$506$	−6.55692	−0.291491
$507$	−0.660561	−0.0293366
$508$	−3.07293	−0.136339
$509$	−27.0669	−1.19972	−0.599860	−	0.800105i	$-0.704777\pi$
$509$	−27.0669	−1.19972	−0.599860	+	0.800105i	$0.704777\pi$
$510$	−0.383945	−0.0170014
$511$	0.154508	0.00683504
$512$	−1.00000	−0.0441942
$513$	−19.1980	−0.847612
$514$	22.1330	0.976243
$515$	−9.09142	−0.400616
$516$	−4.37508	−0.192602
$517$	−6.60623	−0.290541
$518$	0.745669	0.0327628
$519$	−1.27938	−0.0561587
$520$	−3.41609	−0.149806
$521$	−26.3986	−1.15654	−0.578272	−	0.815844i	$-0.696273\pi$
$521$	−26.3986	−1.15654	−0.578272	+	0.815844i	$0.696273\pi$
$522$	23.2604	1.01808
$523$	−2.77253	−0.121234	−0.0606171	−	0.998161i	$-0.519307\pi$
$523$	−2.77253	−0.121234	−0.0606171	+	0.998161i	$0.519307\pi$
$524$	13.6925	0.598158
$525$	0.0767206	0.00334836
$526$	−11.9201	−0.519740
$527$	−4.55526	−0.198430
$528$	−0.496547	−0.0216094
$529$	19.9933	0.869272
$530$	3.65129	0.158602
$531$	35.3302	1.53320
$532$	1.03829	0.0450156
$533$	−42.0978	−1.82346
$534$	−0.0281017	−0.00121608
$535$	17.6794	0.764347
$536$	−1.64732	−0.0711535
$537$	6.41205	0.276701
$538$	−18.2114	−0.785147
$539$	6.97613	0.300483
$540$	−2.85686	−0.122939
$541$	27.1651	1.16792	0.583960	−	0.811782i	$-0.301502\pi$
$541$	27.1651	1.16792	0.583960	+	0.811782i	$0.301502\pi$
$542$	19.7262	0.847312
$543$	6.58735	0.282690
$544$	−0.773230	−0.0331520
$545$	7.08049	0.303295
$546$	−0.262085	−0.0112162
$547$	−45.4309	−1.94248	−0.971242	−	0.238093i	$-0.923478\pi$
$547$	−45.4309	−1.94248	−0.971242	+	0.238093i	$0.923478\pi$
$548$	20.6051	0.880207
$549$	15.2222	0.649669
$550$	1.00000	0.0426401
$551$	56.7687	2.41843
$552$	3.25582	0.138577
$553$	−1.12824	−0.0479775
$554$	1.25507	0.0533226
$555$	−2.39638	−0.101720
$556$	3.51973	0.149270
$557$	0.252819	0.0107123	0.00535614	−	0.999986i	$-0.498295\pi$
$557$	0.252819	0.0107123	0.00535614	+	0.999986i	$0.498295\pi$
$558$	−16.2211	−0.686694
$559$	−30.0992	−1.27306
$560$	0.154508	0.00652916
$561$	−0.383945	−0.0162102
$562$	−14.5688	−0.614549
$563$	−23.5827	−0.993892	−0.496946	−	0.867782i	$-0.665545\pi$
$563$	−23.5827	−0.993892	−0.496946	+	0.867782i	$0.665545\pi$
$564$	3.28030	0.138126
$565$	1.52962	0.0643517
$566$	−18.7543	−0.788303
$567$	1.05711	0.0443943
$568$	−13.7245	−0.575869
$569$	9.03243	0.378659	0.189330	−	0.981914i	$-0.439369\pi$
$569$	9.03243	0.378659	0.189330	+	0.981914i	$0.439369\pi$
$570$	−3.33679	−0.139763
$571$	−13.4101	−0.561195	−0.280598	−	0.959825i	$-0.590533\pi$
$571$	−13.4101	−0.561195	−0.280598	+	0.959825i	$0.590533\pi$
$572$	−3.41609	−0.142834
$573$	1.79476	0.0749770
$574$	1.90406	0.0794739
$575$	−6.55692	−0.273443
$576$	−2.75344	−0.114727
$577$	33.7496	1.40502	0.702508	−	0.711676i	$-0.252064\pi$
$577$	33.7496	1.40502	0.702508	+	0.711676i	$0.252064\pi$
$578$	16.4021	0.682238
$579$	−5.84939	−0.243093
$580$	8.44775	0.350774
$581$	0.603429	0.0250344
$582$	5.09528	0.211206
$583$	3.65129	0.151221
$584$	−1.00000	−0.0413803
$585$	−9.40601	−0.388891
$586$	8.70241	0.359493
$587$	−16.0436	−0.662192	−0.331096	−	0.943597i	$-0.607418\pi$
$587$	−16.0436	−0.662192	−0.331096	+	0.943597i	$0.607418\pi$
$588$	−3.46398	−0.142852
$589$	−39.5888	−1.63123
$590$	12.8313	0.528255
$591$	−9.54309	−0.392550
$592$	−4.82608	−0.198351
$593$	−19.1004	−0.784357	−0.392179	−	0.919889i	$-0.628279\pi$
$593$	−19.1004	−0.784357	−0.392179	+	0.919889i	$0.628279\pi$
$594$	−2.85686	−0.117218
$595$	0.119470	0.00489781
$596$	−0.462165	−0.0189310
$597$	−10.1289	−0.414549
$598$	22.3991	0.915966
$599$	16.9838	0.693939	0.346969	−	0.937876i	$-0.387211\pi$
$599$	16.9838	0.693939	0.346969	+	0.937876i	$0.387211\pi$
$600$	−0.496547	−0.0202715
$601$	−15.0908	−0.615566	−0.307783	−	0.951457i	$-0.599587\pi$
$601$	−15.0908	−0.615566	−0.307783	+	0.951457i	$0.599587\pi$
$602$	1.36137	0.0554853
$603$	−4.53580	−0.184712
$604$	10.9058	0.443750
$605$	1.00000	0.0406558
$606$	1.94664	0.0790767
$607$	−20.8585	−0.846621	−0.423310	−	0.905985i	$-0.639132\pi$
$607$	−20.8585	−0.846621	−0.423310	+	0.905985i	$0.639132\pi$
$608$	−6.71997	−0.272531
$609$	0.648117	0.0262630
$610$	5.52844	0.223840
$611$	22.5675	0.912983
$612$	−2.12904	−0.0860614
$613$	−21.2587	−0.858633	−0.429316	−	0.903154i	$-0.641245\pi$
$613$	−21.2587	−0.858633	−0.429316	+	0.903154i	$0.641245\pi$
$614$	22.2080	0.896243
$615$	−6.11913	−0.246747
$616$	0.154508	0.00622531
$617$	15.8027	0.636193	0.318096	−	0.948058i	$-0.396956\pi$
$617$	15.8027	0.636193	0.318096	+	0.948058i	$0.396956\pi$
$618$	4.51432	0.181593
$619$	−11.7684	−0.473013	−0.236506	−	0.971630i	$-0.576002\pi$
$619$	−11.7684	−0.473013	−0.236506	+	0.971630i	$0.576002\pi$
$620$	−5.89121	−0.236597
$621$	18.7322	0.751697
$622$	32.4555	1.30135
$623$	0.00874426	0.000350331 0
$624$	1.69625	0.0679044
$625$	1.00000	0.0400000
$626$	8.82579	0.352749
$627$	−3.33679	−0.133258
$628$	−20.4633	−0.816574
$629$	−3.73167	−0.148791
$630$	0.425429	0.0169495
$631$	48.7384	1.94025	0.970123	−	0.242613i	$-0.0780046\pi$
$631$	48.7384	1.94025	0.970123	+	0.242613i	$0.0780046\pi$
$632$	7.30211	0.290462
$633$	−7.44590	−0.295948
$634$	28.1281	1.11711
$635$	−3.07293	−0.121945
$636$	−1.81304	−0.0718917
$637$	−23.8311	−0.944223
$638$	8.44775	0.334450
$639$	−37.7897	−1.49494
$640$	−1.00000	−0.0395285
$641$	31.8051	1.25623	0.628114	−	0.778121i	$-0.283827\pi$
$641$	31.8051	1.25623	0.628114	+	0.778121i	$0.283827\pi$
$642$	−8.77866	−0.346466
$643$	7.78364	0.306957	0.153478	−	0.988152i	$-0.450952\pi$
$643$	7.78364	0.306957	0.153478	+	0.988152i	$0.450952\pi$
$644$	−1.01310	−0.0399217
$645$	−4.37508	−0.172268
$646$	−5.19608	−0.204437
$647$	21.6983	0.853049	0.426524	−	0.904476i	$-0.359738\pi$
$647$	21.6983	0.853049	0.426524	+	0.904476i	$0.359738\pi$
$648$	−6.84176	−0.268770
$649$	12.8313	0.503672
$650$	−3.41609	−0.133990
$651$	−0.451978	−0.0177144
$652$	−10.2743	−0.402372
$653$	−38.8027	−1.51847	−0.759233	−	0.650819i	$-0.774426\pi$
$653$	−38.8027	−1.51847	−0.759233	+	0.650819i	$0.774426\pi$
$654$	−3.51580	−0.137479
$655$	13.6925	0.535009
$656$	−12.3234	−0.481146
$657$	−2.75344	−0.107422
$658$	−1.02072	−0.0397916
$659$	−50.6025	−1.97119	−0.985597	−	0.169113i	$-0.945910\pi$
$659$	−50.6025	−1.97119	−0.985597	+	0.169113i	$0.945910\pi$
$660$	−0.496547	−0.0193281
$661$	32.8414	1.27738	0.638692	−	0.769463i	$-0.279476\pi$
$661$	32.8414	1.27738	0.638692	+	0.769463i	$0.279476\pi$
$662$	−4.56671	−0.177490
$663$	1.31159	0.0509380
$664$	−3.90548	−0.151562
$665$	1.03829	0.0402632
$666$	−13.2883	−0.514912
$667$	−55.3913	−2.14476
$668$	−24.5275	−0.948999
$669$	13.0165	0.503248
$670$	−1.64732	−0.0636416
$671$	5.52844	0.213423
$672$	−0.0767206	−0.00295956
$673$	3.42526	0.132034	0.0660171	−	0.997818i	$-0.478971\pi$
$673$	3.42526	0.132034	0.0660171	+	0.997818i	$0.478971\pi$
$674$	16.9095	0.651328
$675$	−2.85686	−0.109960
$676$	−1.33031	−0.0511657
$677$	−31.6436	−1.21616	−0.608082	−	0.793874i	$-0.708061\pi$
$677$	−31.6436	−1.21616	−0.608082	+	0.793874i	$0.708061\pi$
$678$	−0.759530	−0.0291696
$679$	−1.58547	−0.0608449
$680$	−0.773230	−0.0296520
$681$	6.25869	0.239833
$682$	−5.89121	−0.225586
$683$	48.7216	1.86428	0.932140	−	0.362097i	$-0.117939\pi$
$683$	48.7216	1.86428	0.932140	+	0.362097i	$0.117939\pi$
$684$	−18.5031	−0.707482
$685$	20.6051	0.787281
$686$	2.15943	0.0824473
$687$	−11.2366	−0.428702
$688$	−8.81100	−0.335916
$689$	−12.4732	−0.475189
$690$	3.25582	0.123947
$691$	24.3634	0.926827	0.463413	−	0.886142i	$-0.346625\pi$
$691$	24.3634	0.926827	0.463413	+	0.886142i	$0.346625\pi$
$692$	−2.57656	−0.0979460
$693$	0.425429	0.0161607
$694$	23.8720	0.906168
$695$	3.51973	0.133511
$696$	−4.19471	−0.159000
$697$	−9.52879	−0.360929
$698$	9.39377	0.355560
$699$	4.15589	0.157190
$700$	0.154508	0.00583986
$701$	26.0343	0.983302	0.491651	−	0.870792i	$-0.336394\pi$
$701$	26.0343	0.983302	0.491651	+	0.870792i	$0.336394\pi$
$702$	9.75928	0.368340
$703$	−32.4311	−1.22316
$704$	−1.00000	−0.0376889
$705$	3.28030	0.123543
$706$	8.50430	0.320064
$707$	−0.605725	−0.0227806
$708$	−6.37133	−0.239449
$709$	−8.48390	−0.318620	−0.159310	−	0.987229i	$-0.550927\pi$
$709$	−8.48390	−0.318620	−0.159310	+	0.987229i	$0.550927\pi$
$710$	−13.7245	−0.515073
$711$	20.1059	0.754031
$712$	−0.0565942	−0.00212096
$713$	38.6282	1.44664
$714$	−0.0593227	−0.00222010
$715$	−3.41609	−0.127755
$716$	12.9133	0.482592
$717$	0.248237	0.00927059
$718$	−25.4132	−0.948413
$719$	39.8133	1.48478	0.742392	−	0.669965i	$-0.233691\pi$
$719$	39.8133	1.48478	0.742392	+	0.669965i	$0.233691\pi$
$720$	−2.75344	−0.102615
$721$	−1.40470	−0.0523137
$722$	−26.1581	−0.973502
$723$	−14.7596	−0.548915
$724$	13.2663	0.493039
$725$	8.44775	0.313742
$726$	−0.496547	−0.0184286
$727$	−10.8848	−0.403694	−0.201847	−	0.979417i	$-0.564694\pi$
$727$	−10.8848	−0.403694	−0.201847	+	0.979417i	$0.564694\pi$
$728$	−0.527814	−0.0195621
$729$	−14.5827	−0.540099
$730$	−1.00000	−0.0370117
$731$	−6.81292	−0.251985
$732$	−2.74513	−0.101463
$733$	−34.8639	−1.28773	−0.643864	−	0.765140i	$-0.722670\pi$
$733$	−34.8639	−1.28773	−0.643864	+	0.765140i	$0.722670\pi$
$734$	5.97189	0.220426
$735$	−3.46398	−0.127771
$736$	6.55692	0.241691
$737$	−1.64732	−0.0606799
$738$	−33.9316	−1.24904
$739$	−15.7283	−0.578575	−0.289287	−	0.957242i	$-0.593418\pi$
$739$	−15.7283	−0.578575	−0.289287	+	0.957242i	$0.593418\pi$
$740$	−4.82608	−0.177410
$741$	11.3988	0.418744
$742$	0.564154	0.0207108
$743$	−27.6991	−1.01618	−0.508090	−	0.861304i	$-0.669648\pi$
$743$	−27.6991	−1.01618	−0.508090	+	0.861304i	$0.669648\pi$
$744$	2.92527	0.107245
$745$	−0.462165	−0.0169324
$746$	−21.1182	−0.773193
$747$	−10.7535	−0.393450
$748$	−0.773230	−0.0282721
$749$	2.73161	0.0998109
$750$	−0.496547	−0.0181313
$751$	−8.76199	−0.319730	−0.159865	−	0.987139i	$-0.551106\pi$
$751$	−8.76199	−0.319730	−0.159865	+	0.987139i	$0.551106\pi$
$752$	6.60623	0.240904
$753$	−1.41921	−0.0517188
$754$	−28.8583	−1.05096
$755$	10.9058	0.396902
$756$	−0.441408	−0.0160538
$757$	−52.4654	−1.90689	−0.953443	−	0.301573i	$-0.902488\pi$
$757$	−52.4654	−1.90689	−0.953443	+	0.301573i	$0.902488\pi$
$758$	23.1503	0.840855
$759$	3.25582	0.118179
$760$	−6.71997	−0.243759
$761$	−51.4937	−1.86664	−0.933322	−	0.359041i	$-0.883104\pi$
$761$	−51.4937	−1.86664	−0.933322	+	0.359041i	$0.883104\pi$
$762$	1.52585	0.0552758
$763$	1.09399	0.0396052
$764$	3.61447	0.130767
$765$	−2.12904	−0.0769757
$766$	15.4593	0.558566
$767$	−43.8328	−1.58271
$768$	0.496547	0.0179176
$769$	−18.5263	−0.668076	−0.334038	−	0.942560i	$-0.608411\pi$
$769$	−18.5263	−0.668076	−0.334038	+	0.942560i	$0.608411\pi$
$770$	0.154508	0.00556809
$771$	−10.9901	−0.395798
$772$	−11.7801	−0.423976
$773$	−38.5313	−1.38587	−0.692937	−	0.720998i	$-0.743684\pi$
$773$	−38.5313	−1.38587	−0.692937	+	0.720998i	$0.743684\pi$
$774$	−24.2606	−0.872028
$775$	−5.89121	−0.211619
$776$	10.2614	0.368364
$777$	−0.370260	−0.0132830
$778$	−13.0258	−0.466999
$779$	−82.8127	−2.96707
$780$	1.69625	0.0607356
$781$	−13.7245	−0.491103
$782$	5.07001	0.181303
$783$	−24.1340	−0.862479
$784$	−6.97613	−0.249147
$785$	−20.4633	−0.730366
$786$	−6.79896	−0.242511
$787$	4.86365	0.173370	0.0866852	−	0.996236i	$-0.472373\pi$
$787$	4.86365	0.173370	0.0866852	+	0.996236i	$0.472373\pi$
$788$	−19.2189	−0.684644
$789$	5.91889	0.210718
$790$	7.30211	0.259797
$791$	0.236339	0.00840325
$792$	−2.75344	−0.0978393
$793$	−18.8857	−0.670649
$794$	12.8032	0.454369
$795$	−1.81304	−0.0643019
$796$	−20.3987	−0.723012
$797$	32.4303	1.14874	0.574370	−	0.818596i	$-0.305247\pi$
$797$	32.4303	1.14874	0.574370	+	0.818596i	$0.305247\pi$
$798$	−0.515561	−0.0182507
$799$	5.10813	0.180713
$800$	−1.00000	−0.0353553
$801$	−0.155829	−0.00550593
$802$	−11.5399	−0.407489
$803$	−1.00000	−0.0352892
$804$	0.817973	0.0288477
$805$	−1.01310	−0.0357070
$806$	20.1249	0.708871
$807$	9.04280	0.318322
$808$	3.92034	0.137917
$809$	−18.6787	−0.656708	−0.328354	−	0.944555i	$-0.606494\pi$
$809$	−18.6787	−0.656708	−0.328354	+	0.944555i	$0.606494\pi$
$810$	−6.84176	−0.240395
$811$	7.78760	0.273460	0.136730	−	0.990608i	$-0.456341\pi$
$811$	7.78760	0.273460	0.136730	+	0.990608i	$0.456341\pi$
$812$	1.30525	0.0458052
$813$	−9.79498	−0.343525
$814$	−4.82608	−0.169154
$815$	−10.2743	−0.359893
$816$	0.383945	0.0134408
$817$	−59.2097	−2.07148
$818$	−12.7927	−0.447285
$819$	−1.45331	−0.0507826
$820$	−12.3234	−0.430350
$821$	2.05965	0.0718822	0.0359411	−	0.999354i	$-0.488557\pi$
$821$	2.05965	0.0718822	0.0359411	+	0.999354i	$0.488557\pi$
$822$	−10.2314	−0.356862
$823$	25.0300	0.872493	0.436246	−	0.899827i	$-0.356308\pi$
$823$	25.0300	0.872493	0.436246	+	0.899827i	$0.356308\pi$
$824$	9.09142	0.316715
$825$	−0.496547	−0.0172876
$826$	1.98254	0.0689813
$827$	−5.56406	−0.193481	−0.0967406	−	0.995310i	$-0.530842\pi$
$827$	−5.56406	−0.193481	−0.0967406	+	0.995310i	$0.530842\pi$
$828$	18.0541	0.627423
$829$	45.7672	1.58956	0.794781	−	0.606896i	$-0.207586\pi$
$829$	45.7672	1.58956	0.794781	+	0.606896i	$0.207586\pi$
$830$	−3.90548	−0.135561
$831$	−0.623199	−0.0216185
$832$	3.41609	0.118432
$833$	−5.39415	−0.186896
$834$	−1.74771	−0.0605183
$835$	−24.5275	−0.848810
$836$	−6.71997	−0.232415
$837$	16.8303	0.581742
$838$	38.1110	1.31652
$839$	−13.6535	−0.471370	−0.235685	−	0.971829i	$-0.575733\pi$
$839$	−13.6535	−0.471370	−0.235685	+	0.971829i	$0.575733\pi$
$840$	−0.0767206	−0.00264711
$841$	42.3645	1.46084
$842$	−10.6154	−0.365831
$843$	7.23412	0.249156
$844$	−14.9954	−0.516161
$845$	−1.33031	−0.0457640
$846$	18.1898	0.625380
$847$	0.154508	0.00530896
$848$	−3.65129	−0.125386
$849$	9.31241	0.319601
$850$	−0.773230	−0.0265216
$851$	31.6442	1.08475
$852$	6.81489	0.233474
$853$	−39.6371	−1.35715	−0.678574	−	0.734532i	$-0.737402\pi$
$853$	−39.6371	−1.35715	−0.678574	+	0.734532i	$0.737402\pi$
$854$	0.854189	0.0292297
$855$	−18.5031	−0.632791
$856$	−17.6794	−0.604269
$857$	12.0190	0.410560	0.205280	−	0.978703i	$-0.434190\pi$
$857$	12.0190	0.410560	0.205280	+	0.978703i	$0.434190\pi$
$858$	1.69625	0.0579091
$859$	57.3076	1.95531	0.977655	−	0.210214i	$-0.0674162\pi$
$859$	57.3076	1.95531	0.977655	+	0.210214i	$0.0674162\pi$
$860$	−8.81100	−0.300452
$861$	−0.945456	−0.0322211
$862$	−5.96373	−0.203125
$863$	−50.1196	−1.70609	−0.853046	−	0.521836i	$-0.825247\pi$
$863$	−50.1196	−1.70609	−0.853046	+	0.521836i	$0.825247\pi$
$864$	2.85686	0.0971922
$865$	−2.57656	−0.0876056
$866$	−26.6656	−0.906132
$867$	−8.14443	−0.276599
$868$	−0.910241	−0.0308956
$869$	7.30211	0.247707
$870$	−4.19471	−0.142214
$871$	5.62740	0.190677
$872$	−7.08049	−0.239776
$873$	28.2542	0.956261
$874$	44.0624	1.49043
$875$	0.154508	0.00522333
$876$	0.496547	0.0167768
$877$	−20.5017	−0.692293	−0.346147	−	0.938180i	$-0.612510\pi$
$877$	−20.5017	−0.692293	−0.346147	+	0.938180i	$0.612510\pi$
$878$	10.4215	0.351708
$879$	−4.32116	−0.145749
$880$	−1.00000	−0.0337100
$881$	15.0845	0.508209	0.254104	−	0.967177i	$-0.418219\pi$
$881$	15.0845	0.508209	0.254104	+	0.967177i	$0.418219\pi$
$882$	−19.2084	−0.646779
$883$	21.1275	0.710995	0.355498	−	0.934677i	$-0.384311\pi$
$883$	21.1275	0.710995	0.355498	+	0.934677i	$0.384311\pi$
$884$	2.64142	0.0888407
$885$	−6.37133	−0.214170
$886$	20.8608	0.700833
$887$	5.68162	0.190770	0.0953851	−	0.995440i	$-0.469592\pi$
$887$	5.68162	0.190770	0.0953851	+	0.995440i	$0.469592\pi$
$888$	2.39638	0.0804171
$889$	−0.474792	−0.0159240
$890$	−0.0565942	−0.00189704
$891$	−6.84176	−0.229208
$892$	26.2141	0.877713
$893$	44.3937	1.48558
$894$	0.229487	0.00767519
$895$	12.9133	0.431643
$896$	−0.154508	−0.00516176
$897$	−11.1222	−0.371359
$898$	−11.3053	−0.377262
$899$	−49.7675	−1.65984
$900$	−2.75344	−0.0917814
$901$	−2.82329	−0.0940573
$902$	−12.3234	−0.410323
$903$	−0.675985	−0.0224954
$904$	−1.52962	−0.0508745
$905$	13.2663	0.440987
$906$	−5.41523	−0.179909
$907$	−23.6586	−0.785570	−0.392785	−	0.919630i	$-0.628488\pi$
$907$	−23.6586	−0.785570	−0.392785	+	0.919630i	$0.628488\pi$
$908$	12.6044	0.418292
$909$	10.7944	0.358029
$910$	−0.527814	−0.0174969
$911$	16.9804	0.562587	0.281294	−	0.959622i	$-0.409237\pi$
$911$	16.9804	0.562587	0.281294	+	0.959622i	$0.409237\pi$
$912$	3.33679	0.110492
$913$	−3.90548	−0.129253
$914$	0.172061	0.00569129
$915$	−2.74513	−0.0907512
$916$	−22.6294	−0.747697
$917$	2.11560	0.0698632
$918$	2.20901	0.0729081
$919$	2.89961	0.0956494	0.0478247	−	0.998856i	$-0.484771\pi$
$919$	2.89961	0.0956494	0.0478247	+	0.998856i	$0.484771\pi$
$920$	6.55692	0.216175
$921$	−11.0273	−0.363363
$922$	19.2996	0.635597
$923$	46.8843	1.54322
$924$	−0.0767206	−0.00252392
$925$	−4.82608	−0.158680
$926$	−8.83723	−0.290409
$927$	25.0327	0.822182
$928$	−8.44775	−0.277311
$929$	35.4395	1.16273	0.581365	−	0.813643i	$-0.302519\pi$
$929$	35.4395	1.16273	0.581365	+	0.813643i	$0.302519\pi$
$930$	2.92527	0.0959233
$931$	−46.8794	−1.53641
$932$	8.36957	0.274154
$933$	−16.1157	−0.527605
$934$	−24.9863	−0.817577
$935$	−0.773230	−0.0252873
$936$	9.40601	0.307445
$937$	33.3910	1.09084	0.545419	−	0.838164i	$-0.316371\pi$
$937$	33.3910	1.09084	0.545419	+	0.838164i	$0.316371\pi$
$938$	−0.254525	−0.00831053
$939$	−4.38242	−0.143015
$940$	6.60623	0.215471
$941$	4.32962	0.141142	0.0705708	−	0.997507i	$-0.477518\pi$
$941$	4.32962	0.141142	0.0705708	+	0.997507i	$0.477518\pi$
$942$	10.1610	0.331063
$943$	80.8033	2.63132
$944$	−12.8313	−0.417622
$945$	−0.441408	−0.0143590
$946$	−8.81100	−0.286470
$947$	−53.9075	−1.75176	−0.875879	−	0.482532i	$-0.839717\pi$
$947$	−53.9075	−1.75176	−0.875879	+	0.482532i	$0.839717\pi$
$948$	−3.62584	−0.117762
$949$	3.41609	0.110891
$950$	−6.71997	−0.218025
$951$	−13.9669	−0.452909
$952$	−0.119470	−0.00387206
$953$	−15.5987	−0.505292	−0.252646	−	0.967559i	$-0.581301\pi$
$953$	−15.5987	−0.505292	−0.252646	+	0.967559i	$0.581301\pi$
$954$	−10.0536	−0.325498
$955$	3.61447	0.116962
$956$	0.499926	0.0161688
$957$	−4.19471	−0.135596
$958$	−4.34749	−0.140461
$959$	3.18366	0.102806
$960$	0.496547	0.0160260
$961$	3.70640	0.119561
$962$	16.4863	0.531541
$963$	−48.6792	−1.56866
$964$	−29.7244	−0.957359
$965$	−11.7801	−0.379216
$966$	0.503051	0.0161854
$967$	30.3788	0.976916	0.488458	−	0.872588i	$-0.337560\pi$
$967$	30.3788	0.976916	0.488458	+	0.872588i	$0.337560\pi$
$968$	−1.00000	−0.0321412
$969$	2.58010	0.0828848
$970$	10.2614	0.329475
$971$	−44.2442	−1.41986	−0.709932	−	0.704270i	$-0.751275\pi$
$971$	−44.2442	−1.41986	−0.709932	+	0.704270i	$0.751275\pi$
$972$	11.9678	0.383868
$973$	0.543827	0.0174343
$974$	19.5164	0.625346
$975$	1.69625	0.0543235
$976$	−5.52844	−0.176961
$977$	−2.43377	−0.0778632	−0.0389316	−	0.999242i	$-0.512395\pi$
$977$	−2.43377	−0.0778632	−0.0389316	+	0.999242i	$0.512395\pi$
$978$	5.10167	0.163133
$979$	−0.0565942	−0.00180876
$980$	−6.97613	−0.222844
$981$	−19.4957	−0.622450
$982$	−33.5016	−1.06908
$983$	57.2537	1.82611	0.913054	−	0.407839i	$-0.133717\pi$
$983$	57.2537	1.82611	0.913054	+	0.407839i	$0.133717\pi$
$984$	6.11913	0.195071
$985$	−19.2189	−0.612365
$986$	−6.53205	−0.208023
$987$	0.506834	0.0161327
$988$	22.9561	0.730329
$989$	57.7730	1.83708
$990$	−2.75344	−0.0875101
$991$	51.8564	1.64727	0.823637	−	0.567118i	$-0.191942\pi$
$991$	51.8564	1.64727	0.823637	+	0.567118i	$0.191942\pi$
$992$	5.89121	0.187046
$993$	2.26759	0.0719597
$994$	−2.12055	−0.0672599
$995$	−20.3987	−0.646682
$996$	1.93926	0.0614477
$997$	−59.9704	−1.89928	−0.949641	−	0.313340i	$-0.898552\pi$
$997$	−59.9704	−1.89928	−0.949641	+	0.313340i	$0.898552\pi$
$998$	−24.0042	−0.759840
$999$	13.7874	0.436214

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.z.1.5	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.z.1.5	✓	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:	\( N \)	\(=\)	\( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8030.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.496547 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.496547 q^{6} +0.154508 q^{7} -1.00000 q^{8} -2.75344 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.496547 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.496547 q^{6} +0.154508 q^{7} -1.00000 q^{8} -2.75344 q^{9} -1.00000 q^{10} -1.00000 q^{11} +0.496547 q^{12} +3.41609 q^{13} -0.154508 q^{14} +0.496547 q^{15} +1.00000 q^{16} +0.773230 q^{17} +2.75344 q^{18} +6.71997 q^{19} +1.00000 q^{20} +0.0767206 q^{21} +1.00000 q^{22} -6.55692 q^{23} -0.496547 q^{24} +1.00000 q^{25} -3.41609 q^{26} -2.85686 q^{27} +0.154508 q^{28} +8.44775 q^{29} -0.496547 q^{30} -5.89121 q^{31} -1.00000 q^{32} -0.496547 q^{33} -0.773230 q^{34} +0.154508 q^{35} -2.75344 q^{36} -4.82608 q^{37} -6.71997 q^{38} +1.69625 q^{39} -1.00000 q^{40} -12.3234 q^{41} -0.0767206 q^{42} -8.81100 q^{43} -1.00000 q^{44} -2.75344 q^{45} +6.55692 q^{46} +6.60623 q^{47} +0.496547 q^{48} -6.97613 q^{49} -1.00000 q^{50} +0.383945 q^{51} +3.41609 q^{52} -3.65129 q^{53} +2.85686 q^{54} -1.00000 q^{55} -0.154508 q^{56} +3.33679 q^{57} -8.44775 q^{58} -12.8313 q^{59} +0.496547 q^{60} -5.52844 q^{61} +5.89121 q^{62} -0.425429 q^{63} +1.00000 q^{64} +3.41609 q^{65} +0.496547 q^{66} +1.64732 q^{67} +0.773230 q^{68} -3.25582 q^{69} -0.154508 q^{70} +13.7245 q^{71} +2.75344 q^{72} +1.00000 q^{73} +4.82608 q^{74} +0.496547 q^{75} +6.71997 q^{76} -0.154508 q^{77} -1.69625 q^{78} -7.30211 q^{79} +1.00000 q^{80} +6.84176 q^{81} +12.3234 q^{82} +3.90548 q^{83} +0.0767206 q^{84} +0.773230 q^{85} +8.81100 q^{86} +4.19471 q^{87} +1.00000 q^{88} +0.0565942 q^{89} +2.75344 q^{90} +0.527814 q^{91} -6.55692 q^{92} -2.92527 q^{93} -6.60623 q^{94} +6.71997 q^{95} -0.496547 q^{96} -10.2614 q^{97} +6.97613 q^{98} +2.75344 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} - 2 q^{3} + 7 q^{4} + 7 q^{5} + 2 q^{6} - 3 q^{7} - 7 q^{8} + 5 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 - 2 * q^3 + 7 * q^4 + 7 * q^5 + 2 * q^6 - 3 * q^7 - 7 * q^8 + 5 * q^9	\( 7 q - 7 q^{2} - 2 q^{3} + 7 q^{4} + 7 q^{5} + 2 q^{6} - 3 q^{7} - 7 q^{8} + 5 q^{9} - 7 q^{10} - 7 q^{11} - 2 q^{12} - 3 q^{13} + 3 q^{14} - 2 q^{15} + 7 q^{16} - 11 q^{17} - 5 q^{18} - 8 q^{19} + 7 q^{20} - 3 q^{21} + 7 q^{22} + 8 q^{23} + 2 q^{24} + 7 q^{25} + 3 q^{26} - 11 q^{27} - 3 q^{28} - 9 q^{29} + 2 q^{30} - 9 q^{31} - 7 q^{32} + 2 q^{33} + 11 q^{34} - 3 q^{35} + 5 q^{36} + 21 q^{37} + 8 q^{38} + 39 q^{39} - 7 q^{40} - 10 q^{41} + 3 q^{42} - 5 q^{43} - 7 q^{44} + 5 q^{45} - 8 q^{46} + 19 q^{47} - 2 q^{48} - 14 q^{49} - 7 q^{50} + 37 q^{51} - 3 q^{52} - 13 q^{53} + 11 q^{54} - 7 q^{55} + 3 q^{56} - 13 q^{57} + 9 q^{58} + 5 q^{59} - 2 q^{60} - 12 q^{61} + 9 q^{62} - 12 q^{63} + 7 q^{64} - 3 q^{65} - 2 q^{66} - 23 q^{67} - 11 q^{68} - 24 q^{69} + 3 q^{70} + 22 q^{71} - 5 q^{72} + 7 q^{73} - 21 q^{74} - 2 q^{75} - 8 q^{76} + 3 q^{77} - 39 q^{78} - 32 q^{79} + 7 q^{80} + 27 q^{81} + 10 q^{82} + q^{83} - 3 q^{84} - 11 q^{85} + 5 q^{86} - 13 q^{87} + 7 q^{88} + 20 q^{89} - 5 q^{90} - 2 q^{91} + 8 q^{92} - 25 q^{93} - 19 q^{94} - 8 q^{95} + 2 q^{96} - 2 q^{97} + 14 q^{98} - 5 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - 2 * q^3 + 7 * q^4 + 7 * q^5 + 2 * q^6 - 3 * q^7 - 7 * q^8 + 5 * q^9 - 7 * q^10 - 7 * q^11 - 2 * q^12 - 3 * q^13 + 3 * q^14 - 2 * q^15 + 7 * q^16 - 11 * q^17 - 5 * q^18 - 8 * q^19 + 7 * q^20 - 3 * q^21 + 7 * q^22 + 8 * q^23 + 2 * q^24 + 7 * q^25 + 3 * q^26 - 11 * q^27 - 3 * q^28 - 9 * q^29 + 2 * q^30 - 9 * q^31 - 7 * q^32 + 2 * q^33 + 11 * q^34 - 3 * q^35 + 5 * q^36 + 21 * q^37 + 8 * q^38 + 39 * q^39 - 7 * q^40 - 10 * q^41 + 3 * q^42 - 5 * q^43 - 7 * q^44 + 5 * q^45 - 8 * q^46 + 19 * q^47 - 2 * q^48 - 14 * q^49 - 7 * q^50 + 37 * q^51 - 3 * q^52 - 13 * q^53 + 11 * q^54 - 7 * q^55 + 3 * q^56 - 13 * q^57 + 9 * q^58 + 5 * q^59 - 2 * q^60 - 12 * q^61 + 9 * q^62 - 12 * q^63 + 7 * q^64 - 3 * q^65 - 2 * q^66 - 23 * q^67 - 11 * q^68 - 24 * q^69 + 3 * q^70 + 22 * q^71 - 5 * q^72 + 7 * q^73 - 21 * q^74 - 2 * q^75 - 8 * q^76 + 3 * q^77 - 39 * q^78 - 32 * q^79 + 7 * q^80 + 27 * q^81 + 10 * q^82 + q^83 - 3 * q^84 - 11 * q^85 + 5 * q^86 - 13 * q^87 + 7 * q^88 + 20 * q^89 - 5 * q^90 - 2 * q^91 + 8 * q^92 - 25 * q^93 - 19 * q^94 - 8 * q^95 + 2 * q^96 - 2 * q^97 + 14 * q^98 - 5 * q^99

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