LMFDB - Embedded newform 8030.2.a.bc.1.6

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:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 5 x^{10} - 10 x^{9} + 71 x^{8} + 28 x^{7} - 360 x^{6} - 60 x^{5} + 788 x^{4} + 309 x^{3} + \cdots - 95 $ x^11 - 5x^10 - 10x^9 + 71x^8 + 28x^7 - 360x^6 - 60x^5 + 788x^4 + 309x^3 - 632x^2 - 503x - 95
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			1.6
Root			$-0.328152$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +0.328152 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.328152 q^{6} -2.28236 q^{7} -1.00000 q^{8} -2.89232 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.328152 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.328152 q^{6} -2.28236 q^{7} -1.00000 q^{8} -2.89232 q^{9} -1.00000 q^{10} +1.00000 q^{11} +0.328152 q^{12} -1.97229 q^{13} +2.28236 q^{14} +0.328152 q^{15} +1.00000 q^{16} -2.34990 q^{17} +2.89232 q^{18} +6.58377 q^{19} +1.00000 q^{20} -0.748960 q^{21} -1.00000 q^{22} +1.49683 q^{23} -0.328152 q^{24} +1.00000 q^{25} +1.97229 q^{26} -1.93357 q^{27} -2.28236 q^{28} +3.81089 q^{29} -0.328152 q^{30} +1.07682 q^{31} -1.00000 q^{32} +0.328152 q^{33} +2.34990 q^{34} -2.28236 q^{35} -2.89232 q^{36} -0.561834 q^{37} -6.58377 q^{38} -0.647212 q^{39} -1.00000 q^{40} +2.80300 q^{41} +0.748960 q^{42} -3.31581 q^{43} +1.00000 q^{44} -2.89232 q^{45} -1.49683 q^{46} -6.28808 q^{47} +0.328152 q^{48} -1.79083 q^{49} -1.00000 q^{50} -0.771125 q^{51} -1.97229 q^{52} +2.99806 q^{53} +1.93357 q^{54} +1.00000 q^{55} +2.28236 q^{56} +2.16047 q^{57} -3.81089 q^{58} -12.6396 q^{59} +0.328152 q^{60} +3.60188 q^{61} -1.07682 q^{62} +6.60131 q^{63} +1.00000 q^{64} -1.97229 q^{65} -0.328152 q^{66} +8.22788 q^{67} -2.34990 q^{68} +0.491188 q^{69} +2.28236 q^{70} +8.15439 q^{71} +2.89232 q^{72} -1.00000 q^{73} +0.561834 q^{74} +0.328152 q^{75} +6.58377 q^{76} -2.28236 q^{77} +0.647212 q^{78} -6.79545 q^{79} +1.00000 q^{80} +8.04244 q^{81} -2.80300 q^{82} +5.33620 q^{83} -0.748960 q^{84} -2.34990 q^{85} +3.31581 q^{86} +1.25055 q^{87} -1.00000 q^{88} +12.2085 q^{89} +2.89232 q^{90} +4.50148 q^{91} +1.49683 q^{92} +0.353362 q^{93} +6.28808 q^{94} +6.58377 q^{95} -0.328152 q^{96} +6.86339 q^{97} +1.79083 q^{98} -2.89232 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9} - 11 q^{10} + 11 q^{11} - 5 q^{12} - 8 q^{13} + q^{14} - 5 q^{15} + 11 q^{16} - 15 q^{17} - 12 q^{18} + 5 q^{19} + 11 q^{20} - 11 q^{22} - 24 q^{23} + 5 q^{24} + 11 q^{25} + 8 q^{26} - 32 q^{27} - q^{28} + 10 q^{29} + 5 q^{30} + 7 q^{31} - 11 q^{32} - 5 q^{33} + 15 q^{34} - q^{35} + 12 q^{36} - 24 q^{37} - 5 q^{38} + 3 q^{39} - 11 q^{40} + 10 q^{41} - 14 q^{43} + 11 q^{44} + 12 q^{45} + 24 q^{46} - 8 q^{47} - 5 q^{48} - 18 q^{49} - 11 q^{50} + 22 q^{51} - 8 q^{52} - 30 q^{53} + 32 q^{54} + 11 q^{55} + q^{56} - 32 q^{57} - 10 q^{58} + 8 q^{59} - 5 q^{60} - 26 q^{61} - 7 q^{62} - 5 q^{63} + 11 q^{64} - 8 q^{65} + 5 q^{66} - 24 q^{67} - 15 q^{68} - 25 q^{69} + q^{70} + 16 q^{71} - 12 q^{72} - 11 q^{73} + 24 q^{74} - 5 q^{75} + 5 q^{76} - q^{77} - 3 q^{78} + 4 q^{79} + 11 q^{80} - 13 q^{81} - 10 q^{82} - 2 q^{83} - 15 q^{85} + 14 q^{86} - 17 q^{87} - 11 q^{88} - 11 q^{89} - 12 q^{90} - 41 q^{91} - 24 q^{92} - 15 q^{93} + 8 q^{94} + 5 q^{95} + 5 q^{96} - 37 q^{97} + 18 q^{98} + 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9 - 11 * q^10 + 11 * q^11 - 5 * q^12 - 8 * q^13 + q^14 - 5 * q^15 + 11 * q^16 - 15 * q^17 - 12 * q^18 + 5 * q^19 + 11 * q^20 - 11 * q^22 - 24 * q^23 + 5 * q^24 + 11 * q^25 + 8 * q^26 - 32 * q^27 - q^28 + 10 * q^29 + 5 * q^30 + 7 * q^31 - 11 * q^32 - 5 * q^33 + 15 * q^34 - q^35 + 12 * q^36 - 24 * q^37 - 5 * q^38 + 3 * q^39 - 11 * q^40 + 10 * q^41 - 14 * q^43 + 11 * q^44 + 12 * q^45 + 24 * q^46 - 8 * q^47 - 5 * q^48 - 18 * q^49 - 11 * q^50 + 22 * q^51 - 8 * q^52 - 30 * q^53 + 32 * q^54 + 11 * q^55 + q^56 - 32 * q^57 - 10 * q^58 + 8 * q^59 - 5 * q^60 - 26 * q^61 - 7 * q^62 - 5 * q^63 + 11 * q^64 - 8 * q^65 + 5 * q^66 - 24 * q^67 - 15 * q^68 - 25 * q^69 + q^70 + 16 * q^71 - 12 * q^72 - 11 * q^73 + 24 * q^74 - 5 * q^75 + 5 * q^76 - q^77 - 3 * q^78 + 4 * q^79 + 11 * q^80 - 13 * q^81 - 10 * q^82 - 2 * q^83 - 15 * q^85 + 14 * q^86 - 17 * q^87 - 11 * q^88 - 11 * q^89 - 12 * q^90 - 41 * q^91 - 24 * q^92 - 15 * q^93 + 8 * q^94 + 5 * q^95 + 5 * q^96 - 37 * q^97 + 18 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.328152	0.189459	0.0947293	−	0.995503i	$-0.469801\pi$
$3$	0.328152	0.189459	0.0947293	+	0.995503i	$0.469801\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.328152	−0.133967
$7$	−2.28236	−0.862651	−0.431325	−	0.902196i	$-0.641954\pi$
$7$	−2.28236	−0.862651	−0.431325	+	0.902196i	$0.641954\pi$
$8$	−1.00000	−0.353553
$9$	−2.89232	−0.964105
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.328152	0.0947293
$13$	−1.97229	−0.547016	−0.273508	−	0.961870i	$-0.588184\pi$
$13$	−1.97229	−0.547016	−0.273508	+	0.961870i	$0.588184\pi$
$14$	2.28236	0.609986
$15$	0.328152	0.0847284
$16$	1.00000	0.250000
$17$	−2.34990	−0.569935	−0.284968	−	0.958537i	$-0.591983\pi$
$17$	−2.34990	−0.569935	−0.284968	+	0.958537i	$0.591983\pi$
$18$	2.89232	0.681726
$19$	6.58377	1.51042	0.755210	−	0.655483i	$-0.227535\pi$
$19$	6.58377	1.51042	0.755210	+	0.655483i	$0.227535\pi$
$20$	1.00000	0.223607
$21$	−0.748960	−0.163437
$22$	−1.00000	−0.213201
$23$	1.49683	0.312111	0.156055	−	0.987748i	$-0.450122\pi$
$23$	1.49683	0.312111	0.156055	+	0.987748i	$0.450122\pi$
$24$	−0.328152	−0.0669837
$25$	1.00000	0.200000
$26$	1.97229	0.386799
$27$	−1.93357	−0.372117
$28$	−2.28236	−0.431325
$29$	3.81089	0.707665	0.353833	−	0.935309i	$-0.384878\pi$
$29$	3.81089	0.707665	0.353833	+	0.935309i	$0.384878\pi$
$30$	−0.328152	−0.0599120
$31$	1.07682	0.193403	0.0967016	−	0.995313i	$-0.469171\pi$
$31$	1.07682	0.193403	0.0967016	+	0.995313i	$0.469171\pi$
$32$	−1.00000	−0.176777
$33$	0.328152	0.0571239
$34$	2.34990	0.403005
$35$	−2.28236	−0.385789
$36$	−2.89232	−0.482053
$37$	−0.561834	−0.0923649	−0.0461825	−	0.998933i	$-0.514706\pi$
$37$	−0.561834	−0.0923649	−0.0461825	+	0.998933i	$0.514706\pi$
$38$	−6.58377	−1.06803
$39$	−0.647212	−0.103637
$40$	−1.00000	−0.158114
$41$	2.80300	0.437755	0.218877	−	0.975752i	$-0.429760\pi$
$41$	2.80300	0.437755	0.218877	+	0.975752i	$0.429760\pi$
$42$	0.748960	0.115567
$43$	−3.31581	−0.505656	−0.252828	−	0.967511i	$-0.581361\pi$
$43$	−3.31581	−0.505656	−0.252828	+	0.967511i	$0.581361\pi$
$44$	1.00000	0.150756
$45$	−2.89232	−0.431161
$46$	−1.49683	−0.220696
$47$	−6.28808	−0.917211	−0.458606	−	0.888640i	$-0.651651\pi$
$47$	−6.28808	−0.917211	−0.458606	+	0.888640i	$0.651651\pi$
$48$	0.328152	0.0473646
$49$	−1.79083	−0.255833
$50$	−1.00000	−0.141421
$51$	−0.771125	−0.107979
$52$	−1.97229	−0.273508
$53$	2.99806	0.411816	0.205908	−	0.978571i	$-0.433985\pi$
$53$	2.99806	0.411816	0.205908	+	0.978571i	$0.433985\pi$
$54$	1.93357	0.263126
$55$	1.00000	0.134840
$56$	2.28236	0.304993
$57$	2.16047	0.286162
$58$	−3.81089	−0.500395
$59$	−12.6396	−1.64554	−0.822768	−	0.568378i	$-0.807571\pi$
$59$	−12.6396	−1.64554	−0.822768	+	0.568378i	$0.807571\pi$
$60$	0.328152	0.0423642
$61$	3.60188	0.461173	0.230586	−	0.973052i	$-0.425936\pi$
$61$	3.60188	0.461173	0.230586	+	0.973052i	$0.425936\pi$
$62$	−1.07682	−0.136757
$63$	6.60131	0.831686
$64$	1.00000	0.125000
$65$	−1.97229	−0.244633
$66$	−0.328152	−0.0403927
$67$	8.22788	1.00519	0.502597	−	0.864521i	$-0.332378\pi$
$67$	8.22788	1.00519	0.502597	+	0.864521i	$0.332378\pi$
$68$	−2.34990	−0.284968
$69$	0.491188	0.0591320
$70$	2.28236	0.272794
$71$	8.15439	0.967748	0.483874	−	0.875138i	$-0.339229\pi$
$71$	8.15439	0.967748	0.483874	+	0.875138i	$0.339229\pi$
$72$	2.89232	0.340863
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	0.561834	0.0653119
$75$	0.328152	0.0378917
$76$	6.58377	0.755210
$77$	−2.28236	−0.260099
$78$	0.647212	0.0732823
$79$	−6.79545	−0.764548	−0.382274	−	0.924049i	$-0.624859\pi$
$79$	−6.79545	−0.764548	−0.382274	+	0.924049i	$0.624859\pi$
$80$	1.00000	0.111803
$81$	8.04244	0.893605
$82$	−2.80300	−0.309539
$83$	5.33620	0.585724	0.292862	−	0.956155i	$-0.405392\pi$
$83$	5.33620	0.585724	0.292862	+	0.956155i	$0.405392\pi$
$84$	−0.748960	−0.0817183
$85$	−2.34990	−0.254883
$86$	3.31581	0.357553
$87$	1.25055	0.134073
$88$	−1.00000	−0.106600
$89$	12.2085	1.29410	0.647051	−	0.762447i	$-0.276002\pi$
$89$	12.2085	1.29410	0.647051	+	0.762447i	$0.276002\pi$
$90$	2.89232	0.304877
$91$	4.50148	0.471884
$92$	1.49683	0.156055
$93$	0.353362	0.0366419
$94$	6.28808	0.648566
$95$	6.58377	0.675480
$96$	−0.328152	−0.0334919
$97$	6.86339	0.696872	0.348436	−	0.937333i	$-0.386713\pi$
$97$	6.86339	0.696872	0.348436	+	0.937333i	$0.386713\pi$
$98$	1.79083	0.180902
$99$	−2.89232	−0.290689
$100$	1.00000	0.100000
$101$	9.24740	0.920151	0.460075	−	0.887880i	$-0.347822\pi$
$101$	9.24740	0.920151	0.460075	+	0.887880i	$0.347822\pi$
$102$	0.771125	0.0763528
$103$	−16.4216	−1.61806	−0.809032	−	0.587764i	$-0.800008\pi$
$103$	−16.4216	−1.61806	−0.809032	+	0.587764i	$0.800008\pi$
$104$	1.97229	0.193399
$105$	−0.748960	−0.0730911
$106$	−2.99806	−0.291198
$107$	−7.02829	−0.679450	−0.339725	−	0.940525i	$-0.610334\pi$
$107$	−7.02829	−0.679450	−0.339725	+	0.940525i	$0.610334\pi$
$108$	−1.93357	−0.186058
$109$	−11.5207	−1.10348	−0.551742	−	0.834015i	$-0.686037\pi$
$109$	−11.5207	−1.10348	−0.551742	+	0.834015i	$0.686037\pi$
$110$	−1.00000	−0.0953463
$111$	−0.184367	−0.0174993
$112$	−2.28236	−0.215663
$113$	−19.3274	−1.81817	−0.909084	−	0.416613i	$-0.863217\pi$
$113$	−19.3274	−1.81817	−0.909084	+	0.416613i	$0.863217\pi$
$114$	−2.16047	−0.202347
$115$	1.49683	0.139580
$116$	3.81089	0.353833
$117$	5.70450	0.527381
$118$	12.6396	1.16357
$119$	5.36333	0.491655
$120$	−0.328152	−0.0299560
$121$	1.00000	0.0909091
$122$	−3.60188	−0.326099
$123$	0.919809	0.0829364
$124$	1.07682	0.0967016
$125$	1.00000	0.0894427
$126$	−6.60131	−0.588091
$127$	3.88201	0.344472	0.172236	−	0.985056i	$-0.444901\pi$
$127$	3.88201	0.344472	0.172236	+	0.985056i	$0.444901\pi$
$128$	−1.00000	−0.0883883
$129$	−1.08809	−0.0958008
$130$	1.97229	0.172982
$131$	16.3870	1.43174	0.715869	−	0.698235i	$-0.246031\pi$
$131$	16.3870	1.43174	0.715869	+	0.698235i	$0.246031\pi$
$132$	0.328152	0.0285619
$133$	−15.0265	−1.30296
$134$	−8.22788	−0.710780
$135$	−1.93357	−0.166416
$136$	2.34990	0.201503
$137$	−15.0481	−1.28564	−0.642821	−	0.766017i	$-0.722236\pi$
$137$	−15.0481	−1.28564	−0.642821	+	0.766017i	$0.722236\pi$
$138$	−0.491188	−0.0418127
$139$	0.895362	0.0759436	0.0379718	−	0.999279i	$-0.487910\pi$
$139$	0.895362	0.0759436	0.0379718	+	0.999279i	$0.487910\pi$
$140$	−2.28236	−0.192895
$141$	−2.06345	−0.173773
$142$	−8.15439	−0.684301
$143$	−1.97229	−0.164931
$144$	−2.89232	−0.241026
$145$	3.81089	0.316478
$146$	1.00000	0.0827606
$147$	−0.587665	−0.0484698
$148$	−0.561834	−0.0461825
$149$	−15.7380	−1.28931	−0.644654	−	0.764475i	$-0.722998\pi$
$149$	−15.7380	−1.28931	−0.644654	+	0.764475i	$0.722998\pi$
$150$	−0.328152	−0.0267935
$151$	−0.678960	−0.0552530	−0.0276265	−	0.999618i	$-0.508795\pi$
$151$	−0.678960	−0.0552530	−0.0276265	+	0.999618i	$0.508795\pi$
$152$	−6.58377	−0.534014
$153$	6.79667	0.549478
$154$	2.28236	0.183918
$155$	1.07682	0.0864925
$156$	−0.647212	−0.0518184
$157$	8.78150	0.700840	0.350420	−	0.936593i	$-0.386039\pi$
$157$	8.78150	0.700840	0.350420	+	0.936593i	$0.386039\pi$
$158$	6.79545	0.540617
$159$	0.983820	0.0780220
$160$	−1.00000	−0.0790569
$161$	−3.41631	−0.269243
$162$	−8.04244	−0.631874
$163$	−13.5923	−1.06463	−0.532317	−	0.846545i	$-0.678679\pi$
$163$	−13.5923	−1.06463	−0.532317	+	0.846545i	$0.678679\pi$
$164$	2.80300	0.218877
$165$	0.328152	0.0255466
$166$	−5.33620	−0.414170
$167$	−10.4003	−0.804799	−0.402399	−	0.915464i	$-0.631824\pi$
$167$	−10.4003	−0.804799	−0.402399	+	0.915464i	$0.631824\pi$
$168$	0.748960	0.0577836
$169$	−9.11006	−0.700774
$170$	2.34990	0.180229
$171$	−19.0423	−1.45620
$172$	−3.31581	−0.252828
$173$	13.6483	1.03766	0.518831	−	0.854877i	$-0.326367\pi$
$173$	13.6483	1.03766	0.518831	+	0.854877i	$0.326367\pi$
$174$	−1.25055	−0.0948041
$175$	−2.28236	−0.172530
$176$	1.00000	0.0753778
$177$	−4.14771	−0.311761
$178$	−12.2085	−0.915068
$179$	−4.79284	−0.358234	−0.179117	−	0.983828i	$-0.557324\pi$
$179$	−4.79284	−0.358234	−0.179117	+	0.983828i	$0.557324\pi$
$180$	−2.89232	−0.215581
$181$	−20.2447	−1.50478	−0.752389	−	0.658720i	$-0.771098\pi$
$181$	−20.2447	−1.50478	−0.752389	+	0.658720i	$0.771098\pi$
$182$	−4.50148	−0.333672
$183$	1.18196	0.0873732
$184$	−1.49683	−0.110348
$185$	−0.561834	−0.0413069
$186$	−0.353362	−0.0259097
$187$	−2.34990	−0.171842
$188$	−6.28808	−0.458606
$189$	4.41311	0.321007
$190$	−6.58377	−0.477637
$191$	−14.0176	−1.01428	−0.507140	−	0.861864i	$-0.669297\pi$
$191$	−14.0176	−1.01428	−0.507140	+	0.861864i	$0.669297\pi$
$192$	0.328152	0.0236823
$193$	−9.83450	−0.707903	−0.353951	−	0.935264i	$-0.615162\pi$
$193$	−9.83450	−0.707903	−0.353951	+	0.935264i	$0.615162\pi$
$194$	−6.86339	−0.492763
$195$	−0.647212	−0.0463478
$196$	−1.79083	−0.127917
$197$	12.1967	0.868977	0.434488	−	0.900677i	$-0.356929\pi$
$197$	12.1967	0.868977	0.434488	+	0.900677i	$0.356929\pi$
$198$	2.89232	0.205548
$199$	18.6771	1.32399	0.661993	−	0.749510i	$-0.269711\pi$
$199$	18.6771	1.32399	0.661993	+	0.749510i	$0.269711\pi$
$200$	−1.00000	−0.0707107
$201$	2.69999	0.190443
$202$	−9.24740	−0.650645
$203$	−8.69783	−0.610468
$204$	−0.771125	−0.0539896
$205$	2.80300	0.195770
$206$	16.4216	1.14414
$207$	−4.32931	−0.300908
$208$	−1.97229	−0.136754
$209$	6.58377	0.455409
$210$	0.748960	0.0516832
$211$	−2.04691	−0.140915	−0.0704574	−	0.997515i	$-0.522446\pi$
$211$	−2.04691	−0.140915	−0.0704574	+	0.997515i	$0.522446\pi$
$212$	2.99806	0.205908
$213$	2.67588	0.183348
$214$	7.02829	0.480444
$215$	−3.31581	−0.226136
$216$	1.93357	0.131563
$217$	−2.45770	−0.166839
$218$	11.5207	0.780281
$219$	−0.328152	−0.0221744
$220$	1.00000	0.0674200
$221$	4.63470	0.311764
$222$	0.184367	0.0123739
$223$	−8.10658	−0.542857	−0.271428	−	0.962459i	$-0.587496\pi$
$223$	−8.10658	−0.542857	−0.271428	+	0.962459i	$0.587496\pi$
$224$	2.28236	0.152497
$225$	−2.89232	−0.192821
$226$	19.3274	1.28564
$227$	−23.3851	−1.55212	−0.776062	−	0.630657i	$-0.782786\pi$
$227$	−23.3851	−1.55212	−0.776062	+	0.630657i	$0.782786\pi$
$228$	2.16047	0.143081
$229$	7.57436	0.500528	0.250264	−	0.968178i	$-0.419483\pi$
$229$	7.57436	0.500528	0.250264	+	0.968178i	$0.419483\pi$
$230$	−1.49683	−0.0986981
$231$	−0.748960	−0.0492780
$232$	−3.81089	−0.250197
$233$	−2.16173	−0.141619	−0.0708097	−	0.997490i	$-0.522558\pi$
$233$	−2.16173	−0.141619	−0.0708097	+	0.997490i	$0.522558\pi$
$234$	−5.70450	−0.372915
$235$	−6.28808	−0.410189
$236$	−12.6396	−0.822768
$237$	−2.22994	−0.144850
$238$	−5.36333	−0.347653
$239$	−25.1190	−1.62481	−0.812405	−	0.583093i	$-0.801842\pi$
$239$	−25.1190	−1.62481	−0.812405	+	0.583093i	$0.801842\pi$
$240$	0.328152	0.0211821
$241$	24.2649	1.56304	0.781519	−	0.623881i	$-0.214445\pi$
$241$	24.2649	1.56304	0.781519	+	0.623881i	$0.214445\pi$
$242$	−1.00000	−0.0642824
$243$	8.43986	0.541418
$244$	3.60188	0.230586
$245$	−1.79083	−0.114412
$246$	−0.919809	−0.0586449
$247$	−12.9851	−0.826223
$248$	−1.07682	−0.0683784
$249$	1.75108	0.110970
$250$	−1.00000	−0.0632456
$251$	−9.54127	−0.602239	−0.301120	−	0.953586i	$-0.597360\pi$
$251$	−9.54127	−0.602239	−0.301120	+	0.953586i	$0.597360\pi$
$252$	6.60131	0.415843
$253$	1.49683	0.0941049
$254$	−3.88201	−0.243579
$255$	−0.771125	−0.0482897
$256$	1.00000	0.0625000
$257$	−10.2051	−0.636578	−0.318289	−	0.947994i	$-0.603108\pi$
$257$	−10.2051	−0.636578	−0.318289	+	0.947994i	$0.603108\pi$
$258$	1.08809	0.0677414
$259$	1.28231	0.0796787
$260$	−1.97229	−0.122316
$261$	−11.0223	−0.682264
$262$	−16.3870	−1.01239
$263$	15.9546	0.983803	0.491902	−	0.870651i	$-0.336302\pi$
$263$	15.9546	0.983803	0.491902	+	0.870651i	$0.336302\pi$
$264$	−0.328152	−0.0201963
$265$	2.99806	0.184170
$266$	15.0265	0.921335
$267$	4.00625	0.245179
$268$	8.22788	0.502597
$269$	−7.07273	−0.431232	−0.215616	−	0.976478i	$-0.569176\pi$
$269$	−7.07273	−0.431232	−0.215616	+	0.976478i	$0.569176\pi$
$270$	1.93357	0.117674
$271$	−0.755276	−0.0458797	−0.0229399	−	0.999737i	$-0.507303\pi$
$271$	−0.755276	−0.0458797	−0.0229399	+	0.999737i	$0.507303\pi$
$272$	−2.34990	−0.142484
$273$	1.47717	0.0894024
$274$	15.0481	0.909086
$275$	1.00000	0.0603023
$276$	0.491188	0.0295660
$277$	−14.0090	−0.841719	−0.420860	−	0.907126i	$-0.638271\pi$
$277$	−14.0090	−0.841719	−0.420860	+	0.907126i	$0.638271\pi$
$278$	−0.895362	−0.0537002
$279$	−3.11451	−0.186461
$280$	2.28236	0.136397
$281$	−21.0804	−1.25755	−0.628775	−	0.777588i	$-0.716443\pi$
$281$	−21.0804	−1.25755	−0.628775	+	0.777588i	$0.716443\pi$
$282$	2.06345	0.122876
$283$	−14.2393	−0.846441	−0.423221	−	0.906027i	$-0.639101\pi$
$283$	−14.2393	−0.846441	−0.423221	+	0.906027i	$0.639101\pi$
$284$	8.15439	0.483874
$285$	2.16047	0.127975
$286$	1.97229	0.116624
$287$	−6.39745	−0.377630
$288$	2.89232	0.170431
$289$	−11.4780	−0.675174
$290$	−3.81089	−0.223783
$291$	2.25223	0.132028
$292$	−1.00000	−0.0585206
$293$	0.507727	0.0296617	0.0148309	−	0.999890i	$-0.495279\pi$
$293$	0.507727	0.0296617	0.0148309	+	0.999890i	$0.495279\pi$
$294$	0.587665	0.0342733
$295$	−12.6396	−0.735906
$296$	0.561834	0.0326559
$297$	−1.93357	−0.112197
$298$	15.7380	0.911678
$299$	−2.95219	−0.170730
$300$	0.328152	0.0189459
$301$	7.56786	0.436204
$302$	0.678960	0.0390698
$303$	3.03455	0.174330
$304$	6.58377	0.377605
$305$	3.60188	0.206243
$306$	−6.79667	−0.388540
$307$	−2.90838	−0.165990	−0.0829950	−	0.996550i	$-0.526449\pi$
$307$	−2.90838	−0.165990	−0.0829950	+	0.996550i	$0.526449\pi$
$308$	−2.28236	−0.130050
$309$	−5.38876	−0.306556
$310$	−1.07682	−0.0611595
$311$	−26.3683	−1.49521	−0.747606	−	0.664143i	$-0.768797\pi$
$311$	−26.3683	−1.49521	−0.747606	+	0.664143i	$0.768797\pi$
$312$	0.647212	0.0366411
$313$	15.7646	0.891071	0.445535	−	0.895264i	$-0.353013\pi$
$313$	15.7646	0.891071	0.445535	+	0.895264i	$0.353013\pi$
$314$	−8.78150	−0.495569
$315$	6.60131	0.371941
$316$	−6.79545	−0.382274
$317$	3.51741	0.197557	0.0987787	−	0.995109i	$-0.468506\pi$
$317$	3.51741	0.197557	0.0987787	+	0.995109i	$0.468506\pi$
$318$	−0.983820	−0.0551699
$319$	3.81089	0.213369
$320$	1.00000	0.0559017
$321$	−2.30635	−0.128728
$322$	3.41631	0.190383
$323$	−15.4712	−0.860842
$324$	8.04244	0.446802
$325$	−1.97229	−0.109403
$326$	13.5923	0.752810
$327$	−3.78054	−0.209065
$328$	−2.80300	−0.154770
$329$	14.3517	0.791233
$330$	−0.328152	−0.0180642
$331$	−13.3230	−0.732300	−0.366150	−	0.930556i	$-0.619324\pi$
$331$	−13.3230	−0.732300	−0.366150	+	0.930556i	$0.619324\pi$
$332$	5.33620	0.292862
$333$	1.62500	0.0890496
$334$	10.4003	0.569079
$335$	8.22788	0.449537
$336$	−0.748960	−0.0408591
$337$	−4.52290	−0.246378	−0.123189	−	0.992383i	$-0.539312\pi$
$337$	−4.52290	−0.246378	−0.123189	+	0.992383i	$0.539312\pi$
$338$	9.11006	0.495522
$339$	−6.34232	−0.344467
$340$	−2.34990	−0.127441
$341$	1.07682	0.0583133
$342$	19.0423	1.02969
$343$	20.0638	1.08335
$344$	3.31581	0.178776
$345$	0.491188	0.0264447
$346$	−13.6483	−0.733738
$347$	13.3594	0.717171	0.358586	−	0.933497i	$-0.383259\pi$
$347$	13.3594	0.717171	0.358586	+	0.933497i	$0.383259\pi$
$348$	1.25055	0.0670366
$349$	−6.78258	−0.363063	−0.181532	−	0.983385i	$-0.558105\pi$
$349$	−6.78258	−0.363063	−0.181532	+	0.983385i	$0.558105\pi$
$350$	2.28236	0.121997
$351$	3.81358	0.203554
$352$	−1.00000	−0.0533002
$353$	−1.56515	−0.0833046	−0.0416523	−	0.999132i	$-0.513262\pi$
$353$	−1.56515	−0.0833046	−0.0416523	+	0.999132i	$0.513262\pi$
$354$	4.14771	0.220448
$355$	8.15439	0.432790
$356$	12.2085	0.647051
$357$	1.75999	0.0931483
$358$	4.79284	0.253309
$359$	−23.0096	−1.21440	−0.607201	−	0.794548i	$-0.707708\pi$
$359$	−23.0096	−1.21440	−0.607201	+	0.794548i	$0.707708\pi$
$360$	2.89232	0.152438
$361$	24.3460	1.28137
$362$	20.2447	1.06404
$363$	0.328152	0.0172235
$364$	4.50148	0.235942
$365$	−1.00000	−0.0523424
$366$	−1.18196	−0.0617821
$367$	−13.1310	−0.685430	−0.342715	−	0.939439i	$-0.611347\pi$
$367$	−13.1310	−0.685430	−0.342715	+	0.939439i	$0.611347\pi$
$368$	1.49683	0.0780277
$369$	−8.10716	−0.422042
$370$	0.561834	0.0292084
$371$	−6.84266	−0.355253
$372$	0.353362	0.0183209
$373$	−11.2266	−0.581291	−0.290646	−	0.956831i	$-0.593870\pi$
$373$	−11.2266	−0.581291	−0.290646	+	0.956831i	$0.593870\pi$
$374$	2.34990	0.121511
$375$	0.328152	0.0169457
$376$	6.28808	0.324283
$377$	−7.51620	−0.387104
$378$	−4.41311	−0.226986
$379$	8.63722	0.443664	0.221832	−	0.975085i	$-0.428796\pi$
$379$	8.63722	0.443664	0.221832	+	0.975085i	$0.428796\pi$
$380$	6.58377	0.337740
$381$	1.27389	0.0652632
$382$	14.0176	0.717204
$383$	21.9672	1.12247	0.561237	−	0.827655i	$-0.310326\pi$
$383$	21.9672	1.12247	0.561237	+	0.827655i	$0.310326\pi$
$384$	−0.328152	−0.0167459
$385$	−2.28236	−0.116320
$386$	9.83450	0.500563
$387$	9.59036	0.487505
$388$	6.86339	0.348436
$389$	−19.7444	−1.00108	−0.500540	−	0.865714i	$-0.666865\pi$
$389$	−19.7444	−1.00108	−0.500540	+	0.865714i	$0.666865\pi$
$390$	0.647212	0.0327728
$391$	−3.51741	−0.177883
$392$	1.79083	0.0904508
$393$	5.37742	0.271255
$394$	−12.1967	−0.614460
$395$	−6.79545	−0.341916
$396$	−2.89232	−0.145344
$397$	−31.0890	−1.56031	−0.780155	−	0.625586i	$-0.784860\pi$
$397$	−31.0890	−1.56031	−0.780155	+	0.625586i	$0.784860\pi$
$398$	−18.6771	−0.936200
$399$	−4.93098	−0.246858
$400$	1.00000	0.0500000
$401$	−28.9229	−1.44434	−0.722170	−	0.691715i	$-0.756855\pi$
$401$	−28.9229	−1.44434	−0.722170	+	0.691715i	$0.756855\pi$
$402$	−2.69999	−0.134663
$403$	−2.12381	−0.105795
$404$	9.24740	0.460075
$405$	8.04244	0.399632
$406$	8.69783	0.431666
$407$	−0.561834	−0.0278491
$408$	0.771125	0.0381764
$409$	−8.06610	−0.398843	−0.199421	−	0.979914i	$-0.563906\pi$
$409$	−8.06610	−0.398843	−0.199421	+	0.979914i	$0.563906\pi$
$410$	−2.80300	−0.138430
$411$	−4.93804	−0.243576
$412$	−16.4216	−0.809032
$413$	28.8481	1.41952
$414$	4.32931	0.212774
$415$	5.33620	0.261944
$416$	1.97229	0.0966996
$417$	0.293814	0.0143882
$418$	−6.58377	−0.322023
$419$	−18.2092	−0.889576	−0.444788	−	0.895636i	$-0.646721\pi$
$419$	−18.2092	−0.889576	−0.444788	+	0.895636i	$0.646721\pi$
$420$	−0.748960	−0.0365455
$421$	−1.53413	−0.0747691	−0.0373845	−	0.999301i	$-0.511903\pi$
$421$	−1.53413	−0.0747691	−0.0373845	+	0.999301i	$0.511903\pi$
$422$	2.04691	0.0996418
$423$	18.1871	0.884288
$424$	−2.99806	−0.145599
$425$	−2.34990	−0.113987
$426$	−2.67588	−0.129647
$427$	−8.22078	−0.397831
$428$	−7.02829	−0.339725
$429$	−0.647212	−0.0312477
$430$	3.31581	0.159902
$431$	40.8726	1.96877	0.984383	−	0.176042i	$-0.0563294\pi$
$431$	40.8726	1.96877	0.984383	+	0.176042i	$0.0563294\pi$
$432$	−1.93357	−0.0930291
$433$	−10.9933	−0.528304	−0.264152	−	0.964481i	$-0.585092\pi$
$433$	−10.9933	−0.528304	−0.264152	+	0.964481i	$0.585092\pi$
$434$	2.45770	0.117973
$435$	1.25055	0.0599594
$436$	−11.5207	−0.551742
$437$	9.85478	0.471418
$438$	0.328152	0.0156797
$439$	2.79299	0.133302	0.0666510	−	0.997776i	$-0.478769\pi$
$439$	2.79299	0.133302	0.0666510	+	0.997776i	$0.478769\pi$
$440$	−1.00000	−0.0476731
$441$	5.17966	0.246650
$442$	−4.63470	−0.220450
$443$	27.8572	1.32353	0.661767	−	0.749710i	$-0.269807\pi$
$443$	27.8572	1.32353	0.661767	+	0.749710i	$0.269807\pi$
$444$	−0.184367	−0.00874966
$445$	12.2085	0.578740
$446$	8.10658	0.383858
$447$	−5.16445	−0.244270
$448$	−2.28236	−0.107831
$449$	14.4839	0.683538	0.341769	−	0.939784i	$-0.388974\pi$
$449$	14.4839	0.683538	0.341769	+	0.939784i	$0.388974\pi$
$450$	2.89232	0.136345
$451$	2.80300	0.131988
$452$	−19.3274	−0.909084
$453$	−0.222802	−0.0104681
$454$	23.3851	1.09752
$455$	4.50148	0.211033
$456$	−2.16047	−0.101174
$457$	11.8795	0.555698	0.277849	−	0.960625i	$-0.410379\pi$
$457$	11.8795	0.555698	0.277849	+	0.960625i	$0.410379\pi$
$458$	−7.57436	−0.353927
$459$	4.54371	0.212082
$460$	1.49683	0.0697901
$461$	−2.54337	−0.118456	−0.0592282	−	0.998244i	$-0.518864\pi$
$461$	−2.54337	−0.118456	−0.0592282	+	0.998244i	$0.518864\pi$
$462$	0.748960	0.0348448
$463$	−17.3789	−0.807667	−0.403834	−	0.914832i	$-0.632323\pi$
$463$	−17.3789	−0.807667	−0.403834	+	0.914832i	$0.632323\pi$
$464$	3.81089	0.176916
$465$	0.353362	0.0163868
$466$	2.16173	0.100140
$467$	−26.9517	−1.24718	−0.623588	−	0.781753i	$-0.714326\pi$
$467$	−26.9517	−1.24718	−0.623588	+	0.781753i	$0.714326\pi$
$468$	5.70450	0.263690
$469$	−18.7790	−0.867132
$470$	6.28808	0.290048
$471$	2.88167	0.132780
$472$	12.6396	0.581785
$473$	−3.31581	−0.152461
$474$	2.22994	0.102425
$475$	6.58377	0.302084
$476$	5.36333	0.245828
$477$	−8.67135	−0.397034
$478$	25.1190	1.14891
$479$	32.8825	1.50244	0.751220	−	0.660052i	$-0.229466\pi$
$479$	32.8825	1.50244	0.751220	+	0.660052i	$0.229466\pi$
$480$	−0.328152	−0.0149780
$481$	1.10810	0.0505251
$482$	−24.2649	−1.10524
$483$	−1.12107	−0.0510103
$484$	1.00000	0.0454545
$485$	6.86339	0.311651
$486$	−8.43986	−0.382840
$487$	4.63865	0.210197	0.105099	−	0.994462i	$-0.466484\pi$
$487$	4.63865	0.210197	0.105099	+	0.994462i	$0.466484\pi$
$488$	−3.60188	−0.163049
$489$	−4.46035	−0.201704
$490$	1.79083	0.0809016
$491$	13.0338	0.588208	0.294104	−	0.955773i	$-0.404979\pi$
$491$	13.0338	0.588208	0.294104	+	0.955773i	$0.404979\pi$
$492$	0.919809	0.0414682
$493$	−8.95524	−0.403324
$494$	12.9851	0.584228
$495$	−2.89232	−0.130000
$496$	1.07682	0.0483508
$497$	−18.6112	−0.834829
$498$	−1.75108	−0.0784680
$499$	0.314585	0.0140827	0.00704137	−	0.999975i	$-0.497759\pi$
$499$	0.314585	0.0140827	0.00704137	+	0.999975i	$0.497759\pi$
$500$	1.00000	0.0447214
$501$	−3.41287	−0.152476
$502$	9.54127	0.425848
$503$	−16.0979	−0.717772	−0.358886	−	0.933381i	$-0.616843\pi$
$503$	−16.0979	−0.717772	−0.358886	+	0.933381i	$0.616843\pi$
$504$	−6.60131	−0.294046
$505$	9.24740	0.411504
$506$	−1.49683	−0.0665422
$507$	−2.98948	−0.132768
$508$	3.88201	0.172236
$509$	5.95599	0.263994	0.131997	−	0.991250i	$-0.457861\pi$
$509$	5.95599	0.263994	0.131997	+	0.991250i	$0.457861\pi$
$510$	0.771125	0.0341460
$511$	2.28236	0.100966
$512$	−1.00000	−0.0441942
$513$	−12.7302	−0.562052
$514$	10.2051	0.450129
$515$	−16.4216	−0.723620
$516$	−1.08809	−0.0479004
$517$	−6.28808	−0.276550
$518$	−1.28231	−0.0563414
$519$	4.47872	0.196594
$520$	1.97229	0.0864908
$521$	−26.3402	−1.15399	−0.576993	−	0.816749i	$-0.695774\pi$
$521$	−26.3402	−1.15399	−0.576993	+	0.816749i	$0.695774\pi$
$522$	11.0223	0.482434
$523$	32.1625	1.40637	0.703184	−	0.711008i	$-0.251761\pi$
$523$	32.1625	1.40637	0.703184	+	0.711008i	$0.251761\pi$
$524$	16.3870	0.715869
$525$	−0.748960	−0.0326873
$526$	−15.9546	−0.695654
$527$	−2.53043	−0.110227
$528$	0.328152	0.0142810
$529$	−20.7595	−0.902587
$530$	−2.99806	−0.130228
$531$	36.5577	1.58647
$532$	−15.0265	−0.651482
$533$	−5.52834	−0.239459
$534$	−4.00625	−0.173367
$535$	−7.02829	−0.303859
$536$	−8.22788	−0.355390
$537$	−1.57278	−0.0678704
$538$	7.07273	0.304927
$539$	−1.79083	−0.0771367
$540$	−1.93357	−0.0832078
$541$	1.18579	0.0509810	0.0254905	−	0.999675i	$-0.491885\pi$
$541$	1.18579	0.0509810	0.0254905	+	0.999675i	$0.491885\pi$
$542$	0.755276	0.0324419
$543$	−6.64334	−0.285093
$544$	2.34990	0.100751
$545$	−11.5207	−0.493493
$546$	−1.47717	−0.0632170
$547$	18.8405	0.805563	0.402782	−	0.915296i	$-0.368043\pi$
$547$	18.8405	0.805563	0.402782	+	0.915296i	$0.368043\pi$
$548$	−15.0481	−0.642821
$549$	−10.4178	−0.444619
$550$	−1.00000	−0.0426401
$551$	25.0900	1.06887
$552$	−0.491188	−0.0209063
$553$	15.5097	0.659538
$554$	14.0090	0.595185
$555$	−0.184367	−0.00782594
$556$	0.895362	0.0379718
$557$	16.1611	0.684770	0.342385	−	0.939560i	$-0.388765\pi$
$557$	16.1611	0.684770	0.342385	+	0.939560i	$0.388765\pi$
$558$	3.11451	0.131848
$559$	6.53974	0.276602
$560$	−2.28236	−0.0964473
$561$	−0.771125	−0.0325569
$562$	21.0804	0.889222
$563$	−22.1489	−0.933466	−0.466733	−	0.884398i	$-0.654569\pi$
$563$	−22.1489	−0.933466	−0.466733	+	0.884398i	$0.654569\pi$
$564$	−2.06345	−0.0868867
$565$	−19.3274	−0.813110
$566$	14.2393	0.598524
$567$	−18.3557	−0.770869
$568$	−8.15439	−0.342151
$569$	36.9083	1.54728	0.773638	−	0.633628i	$-0.218435\pi$
$569$	36.9083	1.54728	0.773638	+	0.633628i	$0.218435\pi$
$570$	−2.16047	−0.0904923
$571$	5.02507	0.210293	0.105146	−	0.994457i	$-0.466469\pi$
$571$	5.02507	0.210293	0.105146	+	0.994457i	$0.466469\pi$
$572$	−1.97229	−0.0824657
$573$	−4.59991	−0.192164
$574$	6.39745	0.267025
$575$	1.49683	0.0624222
$576$	−2.89232	−0.120513
$577$	−17.8548	−0.743303	−0.371652	−	0.928372i	$-0.621208\pi$
$577$	−17.8548	−0.743303	−0.371652	+	0.928372i	$0.621208\pi$
$578$	11.4780	0.477420
$579$	−3.22721	−0.134118
$580$	3.81089	0.158239
$581$	−12.1791	−0.505276
$582$	−2.25223	−0.0933581
$583$	2.99806	0.124167
$584$	1.00000	0.0413803
$585$	5.70450	0.235852
$586$	−0.507727	−0.0209740
$587$	−11.0903	−0.457744	−0.228872	−	0.973457i	$-0.573504\pi$
$587$	−11.0903	−0.457744	−0.228872	+	0.973457i	$0.573504\pi$
$588$	−0.587665	−0.0242349
$589$	7.08956	0.292120
$590$	12.6396	0.520364
$591$	4.00236	0.164635
$592$	−0.561834	−0.0230912
$593$	−8.02214	−0.329430	−0.164715	−	0.986341i	$-0.552670\pi$
$593$	−8.02214	−0.329430	−0.164715	+	0.986341i	$0.552670\pi$
$594$	1.93357	0.0793355
$595$	5.36333	0.219875
$596$	−15.7380	−0.644654
$597$	6.12893	0.250840
$598$	2.95219	0.120724
$599$	37.9132	1.54909	0.774545	−	0.632519i	$-0.217979\pi$
$599$	37.9132	1.54909	0.774545	+	0.632519i	$0.217979\pi$
$600$	−0.328152	−0.0133967
$601$	39.5674	1.61399	0.806995	−	0.590559i	$-0.201093\pi$
$601$	39.5674	1.61399	0.806995	+	0.590559i	$0.201093\pi$
$602$	−7.56786	−0.308443
$603$	−23.7976	−0.969114
$604$	−0.678960	−0.0276265
$605$	1.00000	0.0406558
$606$	−3.03455	−0.123270
$607$	1.92175	0.0780013	0.0390007	−	0.999239i	$-0.487583\pi$
$607$	1.92175	0.0780013	0.0390007	+	0.999239i	$0.487583\pi$
$608$	−6.58377	−0.267007
$609$	−2.85421	−0.115658
$610$	−3.60188	−0.145836
$611$	12.4019	0.501729
$612$	6.79667	0.274739
$613$	−37.6992	−1.52266	−0.761329	−	0.648366i	$-0.775453\pi$
$613$	−37.6992	−1.52266	−0.761329	+	0.648366i	$0.775453\pi$
$614$	2.90838	0.117373
$615$	0.919809	0.0370903
$616$	2.28236	0.0919589
$617$	4.95597	0.199520	0.0997599	−	0.995012i	$-0.468193\pi$
$617$	4.95597	0.199520	0.0997599	+	0.995012i	$0.468193\pi$
$618$	5.38876	0.216768
$619$	−35.5386	−1.42842	−0.714209	−	0.699932i	$-0.753214\pi$
$619$	−35.5386	−1.42842	−0.714209	+	0.699932i	$0.753214\pi$
$620$	1.07682	0.0432463
$621$	−2.89423	−0.116142
$622$	26.3683	1.05727
$623$	−27.8643	−1.11636
$624$	−0.647212	−0.0259092
$625$	1.00000	0.0400000
$626$	−15.7646	−0.630082
$627$	2.16047	0.0862811
$628$	8.78150	0.350420
$629$	1.32026	0.0526421
$630$	−6.60131	−0.263002
$631$	−14.3427	−0.570975	−0.285487	−	0.958382i	$-0.592155\pi$
$631$	−14.3427	−0.570975	−0.285487	+	0.958382i	$0.592155\pi$
$632$	6.79545	0.270309
$633$	−0.671696	−0.0266975
$634$	−3.51741	−0.139694
$635$	3.88201	0.154053
$636$	0.983820	0.0390110
$637$	3.53205	0.139945
$638$	−3.81089	−0.150875
$639$	−23.5851	−0.933011
$640$	−1.00000	−0.0395285
$641$	21.6232	0.854065	0.427032	−	0.904236i	$-0.359559\pi$
$641$	21.6232	0.854065	0.427032	+	0.904236i	$0.359559\pi$
$642$	2.30635	0.0910242
$643$	1.44919	0.0571503	0.0285751	−	0.999592i	$-0.490903\pi$
$643$	1.44919	0.0571503	0.0285751	+	0.999592i	$0.490903\pi$
$644$	−3.41631	−0.134621
$645$	−1.08809	−0.0428434
$646$	15.4712	0.608707
$647$	−10.0460	−0.394949	−0.197474	−	0.980308i	$-0.563274\pi$
$647$	−10.0460	−0.394949	−0.197474	+	0.980308i	$0.563274\pi$
$648$	−8.04244	−0.315937
$649$	−12.6396	−0.496148
$650$	1.97229	0.0773597
$651$	−0.806498	−0.0316092
$652$	−13.5923	−0.532317
$653$	−12.6050	−0.493270	−0.246635	−	0.969108i	$-0.579325\pi$
$653$	−12.6050	−0.493270	−0.246635	+	0.969108i	$0.579325\pi$
$654$	3.78054	0.147831
$655$	16.3870	0.640292
$656$	2.80300	0.109439
$657$	2.89232	0.112840
$658$	−14.3517	−0.559486
$659$	25.6854	1.00056	0.500281	−	0.865863i	$-0.333230\pi$
$659$	25.6854	1.00056	0.500281	+	0.865863i	$0.333230\pi$
$660$	0.328152	0.0127733
$661$	−41.2079	−1.60280	−0.801400	−	0.598128i	$-0.795911\pi$
$661$	−41.2079	−1.60280	−0.801400	+	0.598128i	$0.795911\pi$
$662$	13.3230	0.517814
$663$	1.52089	0.0590663
$664$	−5.33620	−0.207085
$665$	−15.0265	−0.582704
$666$	−1.62500	−0.0629675
$667$	5.70426	0.220870
$668$	−10.4003	−0.402399
$669$	−2.66019	−0.102849
$670$	−8.22788	−0.317871
$671$	3.60188	0.139049
$672$	0.748960	0.0288918
$673$	−42.6841	−1.64535	−0.822675	−	0.568512i	$-0.807519\pi$
$673$	−42.6841	−1.64535	−0.822675	+	0.568512i	$0.807519\pi$
$674$	4.52290	0.174216
$675$	−1.93357	−0.0744233
$676$	−9.11006	−0.350387
$677$	−23.2676	−0.894245	−0.447122	−	0.894473i	$-0.647551\pi$
$677$	−23.2676	−0.894245	−0.447122	+	0.894473i	$0.647551\pi$
$678$	6.34232	0.243575
$679$	−15.6647	−0.601157
$680$	2.34990	0.0901147
$681$	−7.67386	−0.294063
$682$	−1.07682	−0.0412337
$683$	−4.58209	−0.175329	−0.0876645	−	0.996150i	$-0.527940\pi$
$683$	−4.58209	−0.175329	−0.0876645	+	0.996150i	$0.527940\pi$
$684$	−19.0423	−0.728102
$685$	−15.0481	−0.574956
$686$	−20.0638	−0.766041
$687$	2.48554	0.0948293
$688$	−3.31581	−0.126414
$689$	−5.91306	−0.225270
$690$	−0.491188	−0.0186992
$691$	−8.51289	−0.323846	−0.161923	−	0.986803i	$-0.551770\pi$
$691$	−8.51289	−0.323846	−0.161923	+	0.986803i	$0.551770\pi$
$692$	13.6483	0.518831
$693$	6.60131	0.250763
$694$	−13.3594	−0.507117
$695$	0.895362	0.0339630
$696$	−1.25055	−0.0474020
$697$	−6.58678	−0.249492
$698$	6.78258	0.256725
$699$	−0.709375	−0.0268310
$700$	−2.28236	−0.0862651
$701$	36.7650	1.38860	0.694298	−	0.719688i	$-0.255715\pi$
$701$	36.7650	1.38860	0.694298	+	0.719688i	$0.255715\pi$
$702$	−3.81358	−0.143934
$703$	−3.69898	−0.139510
$704$	1.00000	0.0376889
$705$	−2.06345	−0.0777139
$706$	1.56515	0.0589052
$707$	−21.1059	−0.793769
$708$	−4.14771	−0.155880
$709$	2.67487	0.100457	0.0502284	−	0.998738i	$-0.484005\pi$
$709$	2.67487	0.100457	0.0502284	+	0.998738i	$0.484005\pi$
$710$	−8.15439	−0.306029
$711$	19.6546	0.737105
$712$	−12.2085	−0.457534
$713$	1.61182	0.0603632
$714$	−1.75999	−0.0658658
$715$	−1.97229	−0.0737596
$716$	−4.79284	−0.179117
$717$	−8.24283	−0.307834
$718$	23.0096	0.858712
$719$	−26.9130	−1.00369	−0.501844	−	0.864958i	$-0.667345\pi$
$719$	−26.9130	−1.00369	−0.501844	+	0.864958i	$0.667345\pi$
$720$	−2.89232	−0.107790
$721$	37.4799	1.39582
$722$	−24.3460	−0.906064
$723$	7.96257	0.296131
$724$	−20.2447	−0.752389
$725$	3.81089	0.141533
$726$	−0.328152	−0.0121789
$727$	10.4780	0.388606	0.194303	−	0.980942i	$-0.437756\pi$
$727$	10.4780	0.388606	0.194303	+	0.980942i	$0.437756\pi$
$728$	−4.50148	−0.166836
$729$	−21.3578	−0.791029
$730$	1.00000	0.0370117
$731$	7.79183	0.288191
$732$	1.18196	0.0436866
$733$	−15.3430	−0.566705	−0.283353	−	0.959016i	$-0.591447\pi$
$733$	−15.3430	−0.566705	−0.283353	+	0.959016i	$0.591447\pi$
$734$	13.1310	0.484672
$735$	−0.587665	−0.0216764
$736$	−1.49683	−0.0551739
$737$	8.22788	0.303078
$738$	8.10716	0.298429
$739$	−40.2030	−1.47889	−0.739446	−	0.673216i	$-0.764912\pi$
$739$	−40.2030	−1.47889	−0.739446	+	0.673216i	$0.764912\pi$
$740$	−0.561834	−0.0206534
$741$	−4.26109	−0.156535
$742$	6.84266	0.251202
$743$	38.2486	1.40321	0.701603	−	0.712568i	$-0.252468\pi$
$743$	38.2486	1.40321	0.701603	+	0.712568i	$0.252468\pi$
$744$	−0.353362	−0.0129549
$745$	−15.7380	−0.576596
$746$	11.2266	0.411035
$747$	−15.4340	−0.564700
$748$	−2.34990	−0.0859210
$749$	16.0411	0.586129
$750$	−0.328152	−0.0119824
$751$	25.7010	0.937842	0.468921	−	0.883240i	$-0.344643\pi$
$751$	25.7010	0.937842	0.468921	+	0.883240i	$0.344643\pi$
$752$	−6.28808	−0.229303
$753$	−3.13098	−0.114099
$754$	7.51620	0.273724
$755$	−0.678960	−0.0247099
$756$	4.41311	0.160503
$757$	−21.8585	−0.794462	−0.397231	−	0.917719i	$-0.630029\pi$
$757$	−21.8585	−0.794462	−0.397231	+	0.917719i	$0.630029\pi$
$758$	−8.63722	−0.313718
$759$	0.491188	0.0178290
$760$	−6.58377	−0.238818
$761$	15.6800	0.568401	0.284200	−	0.958765i	$-0.408272\pi$
$761$	15.6800	0.568401	0.284200	+	0.958765i	$0.408272\pi$
$762$	−1.27389	−0.0461481
$763$	26.2944	0.951922
$764$	−14.0176	−0.507140
$765$	6.79667	0.245734
$766$	−21.9672	−0.793709
$767$	24.9290	0.900134
$768$	0.328152	0.0118412
$769$	37.6771	1.35867	0.679335	−	0.733828i	$-0.262268\pi$
$769$	37.6771	1.35867	0.679335	+	0.733828i	$0.262268\pi$
$770$	2.28236	0.0822505
$771$	−3.34883	−0.120605
$772$	−9.83450	−0.353951
$773$	12.4479	0.447719	0.223859	−	0.974621i	$-0.428134\pi$
$773$	12.4479	0.447719	0.223859	+	0.974621i	$0.428134\pi$
$774$	−9.59036	−0.344718
$775$	1.07682	0.0386806
$776$	−6.86339	−0.246381
$777$	0.420791	0.0150958
$778$	19.7444	0.707870
$779$	18.4543	0.661194
$780$	−0.647212	−0.0231739
$781$	8.15439	0.291787
$782$	3.51741	0.125782
$783$	−7.36865	−0.263334
$784$	−1.79083	−0.0639584
$785$	8.78150	0.313425
$786$	−5.37742	−0.191806
$787$	−55.3135	−1.97171	−0.985857	−	0.167587i	$-0.946403\pi$
$787$	−55.3135	−1.97171	−0.985857	+	0.167587i	$0.946403\pi$
$788$	12.1967	0.434488
$789$	5.23553	0.186390
$790$	6.79545	0.241771
$791$	44.1121	1.56844
$792$	2.89232	0.102774
$793$	−7.10396	−0.252269
$794$	31.0890	1.10331
$795$	0.983820	0.0348925
$796$	18.6771	0.661993
$797$	−43.7332	−1.54911	−0.774554	−	0.632508i	$-0.782026\pi$
$797$	−43.7332	−1.54911	−0.774554	+	0.632508i	$0.782026\pi$
$798$	4.93098	0.174555
$799$	14.7764	0.522751
$800$	−1.00000	−0.0353553
$801$	−35.3109	−1.24765
$802$	28.9229	1.02130
$803$	−1.00000	−0.0352892
$804$	2.69999	0.0952214
$805$	−3.41631	−0.120409
$806$	2.12381	0.0748081
$807$	−2.32093	−0.0817005
$808$	−9.24740	−0.325322
$809$	−9.08004	−0.319237	−0.159619	−	0.987179i	$-0.551026\pi$
$809$	−9.08004	−0.319237	−0.159619	+	0.987179i	$0.551026\pi$
$810$	−8.04244	−0.282583
$811$	0.871299	0.0305954	0.0152977	−	0.999883i	$-0.495130\pi$
$811$	0.871299	0.0305954	0.0152977	+	0.999883i	$0.495130\pi$
$812$	−8.69783	−0.305234
$813$	−0.247845	−0.00869231
$814$	0.561834	0.0196923
$815$	−13.5923	−0.476119
$816$	−0.771125	−0.0269948
$817$	−21.8305	−0.763752
$818$	8.06610	0.282024
$819$	−13.0197	−0.454946
$820$	2.80300	0.0978850
$821$	−10.8891	−0.380031	−0.190015	−	0.981781i	$-0.560854\pi$
$821$	−10.8891	−0.380031	−0.190015	+	0.981781i	$0.560854\pi$
$822$	4.93804	0.172234
$823$	35.3160	1.23104	0.615520	−	0.788122i	$-0.288946\pi$
$823$	35.3160	1.23104	0.615520	+	0.788122i	$0.288946\pi$
$824$	16.4216	0.572072
$825$	0.328152	0.0114248
$826$	−28.8481	−1.00375
$827$	15.0003	0.521611	0.260806	−	0.965391i	$-0.416012\pi$
$827$	15.0003	0.521611	0.260806	+	0.965391i	$0.416012\pi$
$828$	−4.32931	−0.150454
$829$	−25.0830	−0.871168	−0.435584	−	0.900148i	$-0.643458\pi$
$829$	−25.0830	−0.871168	−0.435584	+	0.900148i	$0.643458\pi$
$830$	−5.33620	−0.185222
$831$	−4.59708	−0.159471
$832$	−1.97229	−0.0683770
$833$	4.20829	0.145809
$834$	−0.293814	−0.0101740
$835$	−10.4003	−0.359917
$836$	6.58377	0.227704
$837$	−2.08212	−0.0719685
$838$	18.2092	0.629025
$839$	−40.3376	−1.39261	−0.696303	−	0.717748i	$-0.745173\pi$
$839$	−40.3376	−1.39261	−0.696303	+	0.717748i	$0.745173\pi$
$840$	0.748960	0.0258416
$841$	−14.4771	−0.499210
$842$	1.53413	0.0528697
$843$	−6.91756	−0.238253
$844$	−2.04691	−0.0704574
$845$	−9.11006	−0.313396
$846$	−18.1871	−0.625286
$847$	−2.28236	−0.0784228
$848$	2.99806	0.102954
$849$	−4.67267	−0.160366
$850$	2.34990	0.0806010
$851$	−0.840970	−0.0288281
$852$	2.67588	0.0916740
$853$	−42.4737	−1.45427	−0.727136	−	0.686493i	$-0.759149\pi$
$853$	−42.4737	−1.45427	−0.727136	+	0.686493i	$0.759149\pi$
$854$	8.22078	0.281309
$855$	−19.0423	−0.651234
$856$	7.02829	0.240222
$857$	−4.26676	−0.145750	−0.0728749	−	0.997341i	$-0.523217\pi$
$857$	−4.26676	−0.145750	−0.0728749	+	0.997341i	$0.523217\pi$
$858$	0.647212	0.0220954
$859$	−20.6256	−0.703735	−0.351868	−	0.936050i	$-0.614453\pi$
$859$	−20.6256	−0.703735	−0.351868	+	0.936050i	$0.614453\pi$
$860$	−3.31581	−0.113068
$861$	−2.09934	−0.0715452
$862$	−40.8726	−1.39213
$863$	25.1409	0.855807	0.427904	−	0.903824i	$-0.359252\pi$
$863$	25.1409	0.855807	0.427904	+	0.903824i	$0.359252\pi$
$864$	1.93357	0.0657815
$865$	13.6483	0.464057
$866$	10.9933	0.373568
$867$	−3.76651	−0.127917
$868$	−2.45770	−0.0834197
$869$	−6.79545	−0.230520
$870$	−1.25055	−0.0423977
$871$	−16.2278	−0.549857
$872$	11.5207	0.390141
$873$	−19.8511	−0.671858
$874$	−9.85478	−0.333343
$875$	−2.28236	−0.0771578
$876$	−0.328152	−0.0110872
$877$	−31.1585	−1.05215	−0.526074	−	0.850439i	$-0.676337\pi$
$877$	−31.1585	−1.05215	−0.526074	+	0.850439i	$0.676337\pi$
$878$	−2.79299	−0.0942588
$879$	0.166612	0.00561967
$880$	1.00000	0.0337100
$881$	30.0875	1.01367	0.506837	−	0.862042i	$-0.330814\pi$
$881$	30.0875	1.01367	0.506837	+	0.862042i	$0.330814\pi$
$882$	−5.17966	−0.174408
$883$	38.3488	1.29054	0.645270	−	0.763955i	$-0.276745\pi$
$883$	38.3488	1.29054	0.645270	+	0.763955i	$0.276745\pi$
$884$	4.63470	0.155882
$885$	−4.14771	−0.139424
$886$	−27.8572	−0.935880
$887$	−26.8721	−0.902276	−0.451138	−	0.892454i	$-0.648982\pi$
$887$	−26.8721	−0.902276	−0.451138	+	0.892454i	$0.648982\pi$
$888$	0.184367	0.00618695
$889$	−8.86013	−0.297159
$890$	−12.2085	−0.409231
$891$	8.04244	0.269432
$892$	−8.10658	−0.271428
$893$	−41.3993	−1.38537
$894$	5.16445	0.172725
$895$	−4.79284	−0.160207
$896$	2.28236	0.0762483
$897$	−0.968766	−0.0323462
$898$	−14.4839	−0.483335
$899$	4.10366	0.136865
$900$	−2.89232	−0.0964105
$901$	−7.04516	−0.234708
$902$	−2.80300	−0.0933297
$903$	2.48341	0.0826426
$904$	19.3274	0.642820
$905$	−20.2447	−0.672957
$906$	0.222802	0.00740210
$907$	28.9349	0.960768	0.480384	−	0.877058i	$-0.340497\pi$
$907$	28.9349	0.960768	0.480384	+	0.877058i	$0.340497\pi$
$908$	−23.3851	−0.776062
$909$	−26.7464	−0.887122
$910$	−4.50148	−0.149223
$911$	20.0240	0.663424	0.331712	−	0.943381i	$-0.392374\pi$
$911$	20.0240	0.663424	0.331712	+	0.943381i	$0.392374\pi$
$912$	2.16047	0.0715405
$913$	5.33620	0.176603
$914$	−11.8795	−0.392938
$915$	1.18196	0.0390745
$916$	7.57436	0.250264
$917$	−37.4010	−1.23509
$918$	−4.54371	−0.149965
$919$	−10.2489	−0.338079	−0.169040	−	0.985609i	$-0.554067\pi$
$919$	−10.2489	−0.338079	−0.169040	+	0.985609i	$0.554067\pi$
$920$	−1.49683	−0.0493490
$921$	−0.954390	−0.0314482
$922$	2.54337	0.0837614
$923$	−16.0828	−0.529373
$924$	−0.748960	−0.0246390
$925$	−0.561834	−0.0184730
$926$	17.3789	0.571107
$927$	47.4964	1.55998
$928$	−3.81089	−0.125099
$929$	24.5550	0.805622	0.402811	−	0.915283i	$-0.368033\pi$
$929$	24.5550	0.805622	0.402811	+	0.915283i	$0.368033\pi$
$930$	−0.353362	−0.0115872
$931$	−11.7904	−0.386416
$932$	−2.16173	−0.0708097
$933$	−8.65282	−0.283280
$934$	26.9517	0.881887
$935$	−2.34990	−0.0768501
$936$	−5.70450	−0.186457
$937$	−45.2814	−1.47928	−0.739639	−	0.673004i	$-0.765004\pi$
$937$	−45.2814	−1.47928	−0.739639	+	0.673004i	$0.765004\pi$
$938$	18.7790	0.613155
$939$	5.17320	0.168821
$940$	−6.28808	−0.205095
$941$	33.2982	1.08549	0.542745	−	0.839898i	$-0.317385\pi$
$941$	33.2982	1.08549	0.542745	+	0.839898i	$0.317385\pi$
$942$	−2.88167	−0.0938897
$943$	4.19562	0.136628
$944$	−12.6396	−0.411384
$945$	4.41311	0.143559
$946$	3.31581	0.107806
$947$	−8.55221	−0.277910	−0.138955	−	0.990299i	$-0.544374\pi$
$947$	−8.55221	−0.277910	−0.138955	+	0.990299i	$0.544374\pi$
$948$	−2.22994	−0.0724251
$949$	1.97229	0.0640233
$950$	−6.58377	−0.213606
$951$	1.15424	0.0374289
$952$	−5.36333	−0.173826
$953$	−26.8726	−0.870488	−0.435244	−	0.900312i	$-0.643338\pi$
$953$	−26.8726	−0.870488	−0.435244	+	0.900312i	$0.643338\pi$
$954$	8.67135	0.280745
$955$	−14.0176	−0.453599
$956$	−25.1190	−0.812405
$957$	1.25055	0.0404246
$958$	−32.8825	−1.06239
$959$	34.3451	1.10906
$960$	0.328152	0.0105911
$961$	−29.8405	−0.962595
$962$	−1.10810	−0.0357266
$963$	20.3280	0.655062
$964$	24.2649	0.781519
$965$	−9.83450	−0.316584
$966$	1.12107	0.0360697
$967$	−24.5964	−0.790967	−0.395483	−	0.918473i	$-0.629423\pi$
$967$	−24.5964	−0.790967	−0.395483	+	0.918473i	$0.629423\pi$
$968$	−1.00000	−0.0321412
$969$	−5.07691	−0.163094
$970$	−6.86339	−0.220370
$971$	21.8539	0.701325	0.350663	−	0.936502i	$-0.385956\pi$
$971$	21.8539	0.701325	0.350663	+	0.936502i	$0.385956\pi$
$972$	8.43986	0.270709
$973$	−2.04354	−0.0655128
$974$	−4.63865	−0.148632
$975$	−0.647212	−0.0207274
$976$	3.60188	0.115293
$977$	−42.9252	−1.37330	−0.686649	−	0.726989i	$-0.740919\pi$
$977$	−42.9252	−1.37330	−0.686649	+	0.726989i	$0.740919\pi$
$978$	4.46035	0.142626
$979$	12.2085	0.390186
$980$	−1.79083	−0.0572061
$981$	33.3216	1.06388
$982$	−13.0338	−0.415926
$983$	27.2149	0.868021	0.434011	−	0.900908i	$-0.357098\pi$
$983$	27.2149	0.868021	0.434011	+	0.900908i	$0.357098\pi$
$984$	−0.919809	−0.0293224
$985$	12.1967	0.388618
$986$	8.95524	0.285193
$987$	4.70953	0.149906
$988$	−12.9851	−0.413112
$989$	−4.96320	−0.157821
$990$	2.89232	0.0919238
$991$	−3.86789	−0.122868	−0.0614338	−	0.998111i	$-0.519567\pi$
$991$	−3.86789	−0.122868	−0.0614338	+	0.998111i	$0.519567\pi$
$992$	−1.07682	−0.0341892
$993$	−4.37197	−0.138740
$994$	18.6112	0.590313
$995$	18.6771	0.592105
$996$	1.75108	0.0554852
$997$	26.5863	0.841995	0.420998	−	0.907062i	$-0.361680\pi$
$997$	26.5863	0.841995	0.420998	+	0.907062i	$0.361680\pi$
$998$	−0.314585	−0.00995800
$999$	1.08635	0.0343705

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bc.1.6	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bc.1.6	✓	11	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.328152 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.328152 q^{6} -2.28236 q^{7} -1.00000 q^{8} -2.89232 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.328152 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.328152 q^{6} -2.28236 q^{7} -1.00000 q^{8} -2.89232 q^{9} -1.00000 q^{10} +1.00000 q^{11} +0.328152 q^{12} -1.97229 q^{13} +2.28236 q^{14} +0.328152 q^{15} +1.00000 q^{16} -2.34990 q^{17} +2.89232 q^{18} +6.58377 q^{19} +1.00000 q^{20} -0.748960 q^{21} -1.00000 q^{22} +1.49683 q^{23} -0.328152 q^{24} +1.00000 q^{25} +1.97229 q^{26} -1.93357 q^{27} -2.28236 q^{28} +3.81089 q^{29} -0.328152 q^{30} +1.07682 q^{31} -1.00000 q^{32} +0.328152 q^{33} +2.34990 q^{34} -2.28236 q^{35} -2.89232 q^{36} -0.561834 q^{37} -6.58377 q^{38} -0.647212 q^{39} -1.00000 q^{40} +2.80300 q^{41} +0.748960 q^{42} -3.31581 q^{43} +1.00000 q^{44} -2.89232 q^{45} -1.49683 q^{46} -6.28808 q^{47} +0.328152 q^{48} -1.79083 q^{49} -1.00000 q^{50} -0.771125 q^{51} -1.97229 q^{52} +2.99806 q^{53} +1.93357 q^{54} +1.00000 q^{55} +2.28236 q^{56} +2.16047 q^{57} -3.81089 q^{58} -12.6396 q^{59} +0.328152 q^{60} +3.60188 q^{61} -1.07682 q^{62} +6.60131 q^{63} +1.00000 q^{64} -1.97229 q^{65} -0.328152 q^{66} +8.22788 q^{67} -2.34990 q^{68} +0.491188 q^{69} +2.28236 q^{70} +8.15439 q^{71} +2.89232 q^{72} -1.00000 q^{73} +0.561834 q^{74} +0.328152 q^{75} +6.58377 q^{76} -2.28236 q^{77} +0.647212 q^{78} -6.79545 q^{79} +1.00000 q^{80} +8.04244 q^{81} -2.80300 q^{82} +5.33620 q^{83} -0.748960 q^{84} -2.34990 q^{85} +3.31581 q^{86} +1.25055 q^{87} -1.00000 q^{88} +12.2085 q^{89} +2.89232 q^{90} +4.50148 q^{91} +1.49683 q^{92} +0.353362 q^{93} +6.28808 q^{94} +6.58377 q^{95} -0.328152 q^{96} +6.86339 q^{97} +1.79083 q^{98} -2.89232 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9} - 11 q^{10} + 11 q^{11} - 5 q^{12} - 8 q^{13} + q^{14} - 5 q^{15} + 11 q^{16} - 15 q^{17} - 12 q^{18} + 5 q^{19} + 11 q^{20} - 11 q^{22} - 24 q^{23} + 5 q^{24} + 11 q^{25} + 8 q^{26} - 32 q^{27} - q^{28} + 10 q^{29} + 5 q^{30} + 7 q^{31} - 11 q^{32} - 5 q^{33} + 15 q^{34} - q^{35} + 12 q^{36} - 24 q^{37} - 5 q^{38} + 3 q^{39} - 11 q^{40} + 10 q^{41} - 14 q^{43} + 11 q^{44} + 12 q^{45} + 24 q^{46} - 8 q^{47} - 5 q^{48} - 18 q^{49} - 11 q^{50} + 22 q^{51} - 8 q^{52} - 30 q^{53} + 32 q^{54} + 11 q^{55} + q^{56} - 32 q^{57} - 10 q^{58} + 8 q^{59} - 5 q^{60} - 26 q^{61} - 7 q^{62} - 5 q^{63} + 11 q^{64} - 8 q^{65} + 5 q^{66} - 24 q^{67} - 15 q^{68} - 25 q^{69} + q^{70} + 16 q^{71} - 12 q^{72} - 11 q^{73} + 24 q^{74} - 5 q^{75} + 5 q^{76} - q^{77} - 3 q^{78} + 4 q^{79} + 11 q^{80} - 13 q^{81} - 10 q^{82} - 2 q^{83} - 15 q^{85} + 14 q^{86} - 17 q^{87} - 11 q^{88} - 11 q^{89} - 12 q^{90} - 41 q^{91} - 24 q^{92} - 15 q^{93} + 8 q^{94} + 5 q^{95} + 5 q^{96} - 37 q^{97} + 18 q^{98} + 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9 - 11 * q^10 + 11 * q^11 - 5 * q^12 - 8 * q^13 + q^14 - 5 * q^15 + 11 * q^16 - 15 * q^17 - 12 * q^18 + 5 * q^19 + 11 * q^20 - 11 * q^22 - 24 * q^23 + 5 * q^24 + 11 * q^25 + 8 * q^26 - 32 * q^27 - q^28 + 10 * q^29 + 5 * q^30 + 7 * q^31 - 11 * q^32 - 5 * q^33 + 15 * q^34 - q^35 + 12 * q^36 - 24 * q^37 - 5 * q^38 + 3 * q^39 - 11 * q^40 + 10 * q^41 - 14 * q^43 + 11 * q^44 + 12 * q^45 + 24 * q^46 - 8 * q^47 - 5 * q^48 - 18 * q^49 - 11 * q^50 + 22 * q^51 - 8 * q^52 - 30 * q^53 + 32 * q^54 + 11 * q^55 + q^56 - 32 * q^57 - 10 * q^58 + 8 * q^59 - 5 * q^60 - 26 * q^61 - 7 * q^62 - 5 * q^63 + 11 * q^64 - 8 * q^65 + 5 * q^66 - 24 * q^67 - 15 * q^68 - 25 * q^69 + q^70 + 16 * q^71 - 12 * q^72 - 11 * q^73 + 24 * q^74 - 5 * q^75 + 5 * q^76 - q^77 - 3 * q^78 + 4 * q^79 + 11 * q^80 - 13 * q^81 - 10 * q^82 - 2 * q^83 - 15 * q^85 + 14 * q^86 - 17 * q^87 - 11 * q^88 - 11 * q^89 - 12 * q^90 - 41 * q^91 - 24 * q^92 - 15 * q^93 + 8 * q^94 + 5 * q^95 + 5 * q^96 - 37 * q^97 + 18 * q^98 + 12 * q^99

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