LMFDB - Embedded newform 8035.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.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:	$64.1597980241$
Analytic rank:	$1$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.82578 q^{2} +1.42747 q^{3} +5.98503 q^{4} -1.00000 q^{5} -4.03370 q^{6} +3.78558 q^{7} -11.2608 q^{8} -0.962340 q^{9} +O(q^{10})$	\(q-2.82578 q^{2} +1.42747 q^{3} +5.98503 q^{4} -1.00000 q^{5} -4.03370 q^{6} +3.78558 q^{7} -11.2608 q^{8} -0.962340 q^{9} +2.82578 q^{10} -3.96953 q^{11} +8.54342 q^{12} -5.38707 q^{13} -10.6972 q^{14} -1.42747 q^{15} +19.8505 q^{16} +0.0181827 q^{17} +2.71936 q^{18} +1.94830 q^{19} -5.98503 q^{20} +5.40379 q^{21} +11.2170 q^{22} +1.92214 q^{23} -16.0744 q^{24} +1.00000 q^{25} +15.2227 q^{26} -5.65611 q^{27} +22.6568 q^{28} +7.74485 q^{29} +4.03370 q^{30} -0.113993 q^{31} -33.5715 q^{32} -5.66637 q^{33} -0.0513802 q^{34} -3.78558 q^{35} -5.75963 q^{36} +3.28405 q^{37} -5.50546 q^{38} -7.68986 q^{39} +11.2608 q^{40} -5.69503 q^{41} -15.2699 q^{42} +0.809225 q^{43} -23.7577 q^{44} +0.962340 q^{45} -5.43154 q^{46} -0.271503 q^{47} +28.3359 q^{48} +7.33061 q^{49} -2.82578 q^{50} +0.0259551 q^{51} -32.2418 q^{52} -3.05962 q^{53} +15.9829 q^{54} +3.96953 q^{55} -42.6287 q^{56} +2.78113 q^{57} -21.8852 q^{58} +12.9955 q^{59} -8.54342 q^{60} -11.6526 q^{61} +0.322120 q^{62} -3.64302 q^{63} +55.1646 q^{64} +5.38707 q^{65} +16.0119 q^{66} +15.7420 q^{67} +0.108824 q^{68} +2.74379 q^{69} +10.6972 q^{70} -7.77707 q^{71} +10.8367 q^{72} +6.78930 q^{73} -9.27999 q^{74} +1.42747 q^{75} +11.6606 q^{76} -15.0270 q^{77} +21.7298 q^{78} +5.48537 q^{79} -19.8505 q^{80} -5.18688 q^{81} +16.0929 q^{82} +2.71169 q^{83} +32.3418 q^{84} -0.0181827 q^{85} -2.28669 q^{86} +11.0555 q^{87} +44.7001 q^{88} +2.70711 q^{89} -2.71936 q^{90} -20.3932 q^{91} +11.5040 q^{92} -0.162722 q^{93} +0.767207 q^{94} -1.94830 q^{95} -47.9221 q^{96} +6.26479 q^{97} -20.7147 q^{98} +3.82004 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9}+O(q^{10}) $ 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9} + 20 q^{10} - 26 q^{11} - 31 q^{12} - 32 q^{13} - 37 q^{14} + 12 q^{15} + 152 q^{16} - 69 q^{17} - 64 q^{18} + 37 q^{19} - 144 q^{20} - 43 q^{21} - 25 q^{22} - 63 q^{23} - 5 q^{24} + 140 q^{25} - 16 q^{26} - 48 q^{27} - 52 q^{28} - 136 q^{29} + 25 q^{31} - 151 q^{32} - 48 q^{33} + 29 q^{34} + 15 q^{35} + 120 q^{36} - 82 q^{37} - 69 q^{38} - 26 q^{39} + 63 q^{40} - 11 q^{41} - 35 q^{42} - 54 q^{43} - 83 q^{44} - 134 q^{45} + 25 q^{46} - 39 q^{47} - 83 q^{48} + 215 q^{49} - 20 q^{50} - 75 q^{51} - 56 q^{52} - 196 q^{53} - 29 q^{54} + 26 q^{55} - 132 q^{56} - 110 q^{57} - 29 q^{58} - 31 q^{59} + 31 q^{60} - 18 q^{61} - 107 q^{62} - 67 q^{63} + 165 q^{64} + 32 q^{65} - 16 q^{66} - 50 q^{67} - 201 q^{68} - 46 q^{69} + 37 q^{70} - 84 q^{71} - 200 q^{72} - 70 q^{73} - 101 q^{74} - 12 q^{75} + 118 q^{76} - 166 q^{77} - 106 q^{78} - 35 q^{79} - 152 q^{80} + 116 q^{81} - 72 q^{82} - 66 q^{83} - 60 q^{84} + 69 q^{85} - 66 q^{86} - 75 q^{87} - 101 q^{88} + 8 q^{89} + 64 q^{90} + 2 q^{91} - 197 q^{92} - 134 q^{93} + 65 q^{94} - 37 q^{95} + 6 q^{96} - 73 q^{97} - 151 q^{98} - 51 q^{99}+O(q^{100}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9 + 20 * q^10 - 26 * q^11 - 31 * q^12 - 32 * q^13 - 37 * q^14 + 12 * q^15 + 152 * q^16 - 69 * q^17 - 64 * q^18 + 37 * q^19 - 144 * q^20 - 43 * q^21 - 25 * q^22 - 63 * q^23 - 5 * q^24 + 140 * q^25 - 16 * q^26 - 48 * q^27 - 52 * q^28 - 136 * q^29 + 25 * q^31 - 151 * q^32 - 48 * q^33 + 29 * q^34 + 15 * q^35 + 120 * q^36 - 82 * q^37 - 69 * q^38 - 26 * q^39 + 63 * q^40 - 11 * q^41 - 35 * q^42 - 54 * q^43 - 83 * q^44 - 134 * q^45 + 25 * q^46 - 39 * q^47 - 83 * q^48 + 215 * q^49 - 20 * q^50 - 75 * q^51 - 56 * q^52 - 196 * q^53 - 29 * q^54 + 26 * q^55 - 132 * q^56 - 110 * q^57 - 29 * q^58 - 31 * q^59 + 31 * q^60 - 18 * q^61 - 107 * q^62 - 67 * q^63 + 165 * q^64 + 32 * q^65 - 16 * q^66 - 50 * q^67 - 201 * q^68 - 46 * q^69 + 37 * q^70 - 84 * q^71 - 200 * q^72 - 70 * q^73 - 101 * q^74 - 12 * q^75 + 118 * q^76 - 166 * q^77 - 106 * q^78 - 35 * q^79 - 152 * q^80 + 116 * q^81 - 72 * q^82 - 66 * q^83 - 60 * q^84 + 69 * q^85 - 66 * q^86 - 75 * q^87 - 101 * q^88 + 8 * q^89 + 64 * q^90 + 2 * q^91 - 197 * q^92 - 134 * q^93 + 65 * q^94 - 37 * q^95 + 6 * q^96 - 73 * q^97 - 151 * q^98 - 51 * 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 $

$2$	−2.82578	−1.99813	−0.999064	−	0.0432639i	$-0.986224\pi$
$2$	−2.82578	−1.99813	−0.999064	+	0.0432639i	$0.986224\pi$
$3$	1.42747	0.824148	0.412074	−	0.911150i	$-0.364805\pi$
$3$	1.42747	0.824148	0.412074	+	0.911150i	$0.364805\pi$
$4$	5.98503	2.99251
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−4.03370	−1.64675
$7$	3.78558	1.43081	0.715407	−	0.698708i	$-0.246241\pi$
$7$	3.78558	1.43081	0.715407	+	0.698708i	$0.246241\pi$
$8$	−11.2608	−3.98129
$9$	−0.962340	−0.320780
$10$	2.82578	0.893590
$11$	−3.96953	−1.19686	−0.598429	−	0.801176i	$-0.704208\pi$
$11$	−3.96953	−1.19686	−0.598429	+	0.801176i	$0.704208\pi$
$12$	8.54342	2.46627
$13$	−5.38707	−1.49410	−0.747052	−	0.664765i	$-0.768531\pi$
$13$	−5.38707	−1.49410	−0.747052	+	0.664765i	$0.768531\pi$
$14$	−10.6972	−2.85895
$15$	−1.42747	−0.368570
$16$	19.8505	4.96262
$17$	0.0181827	0.00440994	0.00220497	−	0.999998i	$-0.499298\pi$
$17$	0.0181827	0.00440994	0.00220497	+	0.999998i	$0.499298\pi$
$18$	2.71936	0.640959
$19$	1.94830	0.446970	0.223485	−	0.974707i	$-0.428257\pi$
$19$	1.94830	0.446970	0.223485	+	0.974707i	$0.428257\pi$
$20$	−5.98503	−1.33829
$21$	5.40379	1.17920
$22$	11.2170	2.39148
$23$	1.92214	0.400793	0.200397	−	0.979715i	$-0.435777\pi$
$23$	1.92214	0.400793	0.200397	+	0.979715i	$0.435777\pi$
$24$	−16.0744	−3.28118
$25$	1.00000	0.200000
$26$	15.2227	2.98541
$27$	−5.65611	−1.08852
$28$	22.6568	4.28173
$29$	7.74485	1.43818	0.719091	−	0.694916i	$-0.244558\pi$
$29$	7.74485	1.43818	0.719091	+	0.694916i	$0.244558\pi$
$30$	4.03370	0.736450
$31$	−0.113993	−0.0204738	−0.0102369	−	0.999948i	$-0.503259\pi$
$31$	−0.113993	−0.0204738	−0.0102369	+	0.999948i	$0.503259\pi$
$32$	−33.5715	−5.93465
$33$	−5.66637	−0.986388
$34$	−0.0513802	−0.00881163
$35$	−3.78558	−0.639880
$36$	−5.75963	−0.959939
$37$	3.28405	0.539894	0.269947	−	0.962875i	$-0.412994\pi$
$37$	3.28405	0.539894	0.269947	+	0.962875i	$0.412994\pi$
$38$	−5.50546	−0.893104
$39$	−7.68986	−1.23136
$40$	11.2608	1.78049
$41$	−5.69503	−0.889414	−0.444707	−	0.895676i	$-0.646692\pi$
$41$	−5.69503	−0.889414	−0.444707	+	0.895676i	$0.646692\pi$
$42$	−15.2699	−2.35620
$43$	0.809225	0.123406	0.0617028	−	0.998095i	$-0.480347\pi$
$43$	0.809225	0.123406	0.0617028	+	0.998095i	$0.480347\pi$
$44$	−23.7577	−3.58161
$45$	0.962340	0.143457
$46$	−5.43154	−0.800836
$47$	−0.271503	−0.0396028	−0.0198014	−	0.999804i	$-0.506303\pi$
$47$	−0.271503	−0.0396028	−0.0198014	+	0.999804i	$0.506303\pi$
$48$	28.3359	4.08993
$49$	7.33061	1.04723
$50$	−2.82578	−0.399625
$51$	0.0259551	0.00363445
$52$	−32.2418	−4.47113
$53$	−3.05962	−0.420271	−0.210135	−	0.977672i	$-0.567390\pi$
$53$	−3.05962	−0.420271	−0.210135	+	0.977672i	$0.567390\pi$
$54$	15.9829	2.17500
$55$	3.96953	0.535251
$56$	−42.6287	−5.69649
$57$	2.78113	0.368370
$58$	−21.8852	−2.87367
$59$	12.9955	1.69187	0.845934	−	0.533288i	$-0.179044\pi$
$59$	12.9955	1.69187	0.845934	+	0.533288i	$0.179044\pi$
$60$	−8.54342	−1.10295
$61$	−11.6526	−1.49196	−0.745978	−	0.665970i	$-0.768018\pi$
$61$	−11.6526	−1.49196	−0.745978	+	0.665970i	$0.768018\pi$
$62$	0.322120	0.0409092
$63$	−3.64302	−0.458977
$64$	55.1646	6.89557
$65$	5.38707	0.668184
$66$	16.0119	1.97093
$67$	15.7420	1.92320	0.961598	−	0.274463i	$-0.0885000\pi$
$67$	15.7420	1.92320	0.961598	+	0.274463i	$0.0885000\pi$
$68$	0.108824	0.0131968
$69$	2.74379	0.330313
$70$	10.6972	1.27856
$71$	−7.77707	−0.922968	−0.461484	−	0.887148i	$-0.652683\pi$
$71$	−7.77707	−0.922968	−0.461484	+	0.887148i	$0.652683\pi$
$72$	10.8367	1.27712
$73$	6.78930	0.794628	0.397314	−	0.917683i	$-0.369942\pi$
$73$	6.78930	0.794628	0.397314	+	0.917683i	$0.369942\pi$
$74$	−9.27999	−1.07878
$75$	1.42747	0.164830
$76$	11.6606	1.33756
$77$	−15.0270	−1.71248
$78$	21.7298	2.46042
$79$	5.48537	0.617152	0.308576	−	0.951200i	$-0.400148\pi$
$79$	5.48537	0.617152	0.308576	+	0.951200i	$0.400148\pi$
$80$	−19.8505	−2.21935
$81$	−5.18688	−0.576320
$82$	16.0929	1.77716
$83$	2.71169	0.297647	0.148823	−	0.988864i	$-0.452451\pi$
$83$	2.71169	0.297647	0.148823	+	0.988864i	$0.452451\pi$
$84$	32.3418	3.52878
$85$	−0.0181827	−0.00197219
$86$	−2.28669	−0.246580
$87$	11.0555	1.18528
$88$	44.7001	4.76505
$89$	2.70711	0.286953	0.143477	−	0.989654i	$-0.454172\pi$
$89$	2.70711	0.286953	0.143477	+	0.989654i	$0.454172\pi$
$90$	−2.71936	−0.286646
$91$	−20.3932	−2.13779
$92$	11.5040	1.19938
$93$	−0.162722	−0.0168734
$94$	0.767207	0.0791314
$95$	−1.94830	−0.199891
$96$	−47.9221	−4.89103
$97$	6.26479	0.636093	0.318046	−	0.948075i	$-0.396973\pi$
$97$	6.26479	0.636093	0.318046	+	0.948075i	$0.396973\pi$
$98$	−20.7147	−2.09250
$99$	3.82004	0.383928
$100$	5.98503	0.598503
$101$	8.74681	0.870340	0.435170	−	0.900348i	$-0.356688\pi$
$101$	8.74681	0.870340	0.435170	+	0.900348i	$0.356688\pi$
$102$	−0.0733435	−0.00726209
$103$	−9.88516	−0.974013	−0.487007	−	0.873398i	$-0.661911\pi$
$103$	−9.88516	−0.974013	−0.487007	+	0.873398i	$0.661911\pi$
$104$	60.6627	5.94847
$105$	−5.40379	−0.527356
$106$	8.64580	0.839754
$107$	−1.72476	−0.166739	−0.0833694	−	0.996519i	$-0.526568\pi$
$107$	−1.72476	−0.166739	−0.0833694	+	0.996519i	$0.526568\pi$
$108$	−33.8519	−3.25740
$109$	2.58611	0.247705	0.123852	−	0.992301i	$-0.460475\pi$
$109$	2.58611	0.247705	0.123852	+	0.992301i	$0.460475\pi$
$110$	−11.2170	−1.06950
$111$	4.68787	0.444952
$112$	75.1456	7.10059
$113$	−10.8511	−1.02078	−0.510392	−	0.859942i	$-0.670500\pi$
$113$	−10.8511	−1.02078	−0.510392	+	0.859942i	$0.670500\pi$
$114$	−7.85886	−0.736050
$115$	−1.92214	−0.179240
$116$	46.3531	4.30378
$117$	5.18419	0.479279
$118$	−36.7224	−3.38057
$119$	0.0688319	0.00630981
$120$	16.0744	1.46739
$121$	4.75717	0.432470
$122$	32.9275	2.98112
$123$	−8.12946	−0.733008
$124$	−0.682253	−0.0612681
$125$	−1.00000	−0.0894427
$126$	10.2944	0.917094
$127$	−17.3434	−1.53898	−0.769490	−	0.638659i	$-0.779489\pi$
$127$	−17.3434	−1.53898	−0.769490	+	0.638659i	$0.779489\pi$
$128$	−88.7400	−7.84358
$129$	1.15514	0.101704
$130$	−15.2227	−1.33512
$131$	7.27961	0.636023	0.318011	−	0.948087i	$-0.396985\pi$
$131$	7.27961	0.636023	0.318011	+	0.948087i	$0.396985\pi$
$132$	−33.9134	−2.95178
$133$	7.37544	0.639532
$134$	−44.4835	−3.84279
$135$	5.65611	0.486800
$136$	−0.204751	−0.0175573
$137$	−8.75630	−0.748101	−0.374050	−	0.927408i	$-0.622031\pi$
$137$	−8.75630	−0.748101	−0.374050	+	0.927408i	$0.622031\pi$
$138$	−7.75333	−0.660008
$139$	−16.8279	−1.42732	−0.713661	−	0.700491i	$-0.752964\pi$
$139$	−16.8279	−1.42732	−0.713661	+	0.700491i	$0.752964\pi$
$140$	−22.6568	−1.91485
$141$	−0.387561	−0.0326386
$142$	21.9763	1.84421
$143$	21.3841	1.78823
$144$	−19.1029	−1.59191
$145$	−7.74485	−0.643175
$146$	−19.1851	−1.58777
$147$	10.4642	0.863073
$148$	19.6551	1.61564
$149$	−3.54242	−0.290206	−0.145103	−	0.989417i	$-0.546351\pi$
$149$	−3.54242	−0.290206	−0.145103	+	0.989417i	$0.546351\pi$
$150$	−4.03370	−0.329351
$151$	17.4112	1.41690	0.708450	−	0.705761i	$-0.249395\pi$
$151$	17.4112	1.41690	0.708450	+	0.705761i	$0.249395\pi$
$152$	−21.9394	−1.77952
$153$	−0.0174979	−0.00141462
$154$	42.4629	3.42176
$155$	0.113993	0.00915616
$156$	−46.0240	−3.68487
$157$	8.65263	0.690555	0.345278	−	0.938501i	$-0.387785\pi$
$157$	8.65263	0.690555	0.345278	+	0.938501i	$0.387785\pi$
$158$	−15.5004	−1.23315
$159$	−4.36750	−0.346365
$160$	33.5715	2.65406
$161$	7.27641	0.573461
$162$	14.6570	1.15156
$163$	−9.04462	−0.708429	−0.354214	−	0.935164i	$-0.615252\pi$
$163$	−9.04462	−0.708429	−0.354214	+	0.935164i	$0.615252\pi$
$164$	−34.0849	−2.66158
$165$	5.66637	0.441126
$166$	−7.66264	−0.594737
$167$	−4.48661	−0.347184	−0.173592	−	0.984818i	$-0.555537\pi$
$167$	−4.48661	−0.347184	−0.173592	+	0.984818i	$0.555537\pi$
$168$	−60.8510	−4.69475
$169$	16.0205	1.23235
$170$	0.0513802	0.00394068
$171$	−1.87493	−0.143379
$172$	4.84323	0.369293
$173$	−23.8819	−1.81570	−0.907852	−	0.419290i	$-0.862279\pi$
$173$	−23.8819	−1.81570	−0.907852	+	0.419290i	$0.862279\pi$
$174$	−31.2404	−2.36833
$175$	3.78558	0.286163
$176$	−78.7971	−5.93955
$177$	18.5506	1.39435
$178$	−7.64970	−0.573369
$179$	−0.486616	−0.0363714	−0.0181857	−	0.999835i	$-0.505789\pi$
$179$	−0.486616	−0.0363714	−0.0181857	+	0.999835i	$0.505789\pi$
$180$	5.75963	0.429298
$181$	−25.5208	−1.89694	−0.948472	−	0.316861i	$-0.897371\pi$
$181$	−25.5208	−1.89694	−0.948472	+	0.316861i	$0.897371\pi$
$182$	57.6266	4.27157
$183$	−16.6336	−1.22959
$184$	−21.6448	−1.59568
$185$	−3.28405	−0.241448
$186$	0.459815	0.0337153
$187$	−0.0721766	−0.00527808
$188$	−1.62495	−0.118512
$189$	−21.4116	−1.55747
$190$	5.50546	0.399408
$191$	−17.5724	−1.27150	−0.635748	−	0.771897i	$-0.719308\pi$
$191$	−17.5724	−1.27150	−0.635748	+	0.771897i	$0.719308\pi$
$192$	78.7456	5.68297
$193$	−8.99053	−0.647152	−0.323576	−	0.946202i	$-0.604885\pi$
$193$	−8.99053	−0.647152	−0.323576	+	0.946202i	$0.604885\pi$
$194$	−17.7029	−1.27099
$195$	7.68986	0.550682
$196$	43.8739	3.13385
$197$	−20.9582	−1.49321	−0.746604	−	0.665269i	$-0.768317\pi$
$197$	−20.9582	−1.49321	−0.746604	+	0.665269i	$0.768317\pi$
$198$	−10.7946	−0.767138
$199$	5.41372	0.383768	0.191884	−	0.981418i	$-0.438540\pi$
$199$	5.41372	0.383768	0.191884	+	0.981418i	$0.438540\pi$
$200$	−11.2608	−0.796259
$201$	22.4712	1.58500
$202$	−24.7165	−1.73905
$203$	29.3187	2.05777
$204$	0.155342	0.0108761
$205$	5.69503	0.397758
$206$	27.9333	1.94620
$207$	−1.84975	−0.128567
$208$	−106.936	−7.41467
$209$	−7.73383	−0.534960
$210$	15.2699	1.05372
$211$	−3.93641	−0.270994	−0.135497	−	0.990778i	$-0.543263\pi$
$211$	−3.93641	−0.270994	−0.135497	+	0.990778i	$0.543263\pi$
$212$	−18.3119	−1.25767
$213$	−11.1015	−0.760662
$214$	4.87379	0.333166
$215$	−0.809225	−0.0551887
$216$	63.6923	4.33371
$217$	−0.431530	−0.0292942
$218$	−7.30778	−0.494945
$219$	9.69150	0.654891
$220$	23.7577	1.60175
$221$	−0.0979513	−0.00658891
$222$	−13.2469	−0.889072
$223$	−18.3449	−1.22846	−0.614231	−	0.789126i	$-0.710534\pi$
$223$	−18.3449	−1.22846	−0.614231	+	0.789126i	$0.710534\pi$
$224$	−127.087	−8.49139
$225$	−0.962340	−0.0641560
$226$	30.6628	2.03966
$227$	−12.6541	−0.839884	−0.419942	−	0.907551i	$-0.637950\pi$
$227$	−12.6541	−0.839884	−0.419942	+	0.907551i	$0.637950\pi$
$228$	16.6451	1.10235
$229$	24.8900	1.64478	0.822390	−	0.568924i	$-0.192640\pi$
$229$	24.8900	1.64478	0.822390	+	0.568924i	$0.192640\pi$
$230$	5.43154	0.358145
$231$	−21.4505	−1.41134
$232$	−87.2132	−5.72583
$233$	17.5694	1.15101	0.575503	−	0.817799i	$-0.304806\pi$
$233$	17.5694	1.15101	0.575503	+	0.817799i	$0.304806\pi$
$234$	−14.6494	−0.957660
$235$	0.271503	0.0177109
$236$	77.7783	5.06294
$237$	7.83017	0.508624
$238$	−0.194504	−0.0126078
$239$	−14.1707	−0.916627	−0.458313	−	0.888791i	$-0.651546\pi$
$239$	−14.1707	−0.916627	−0.458313	+	0.888791i	$0.651546\pi$
$240$	−28.3359	−1.82907
$241$	−9.13553	−0.588471	−0.294235	−	0.955733i	$-0.595065\pi$
$241$	−9.13553	−0.588471	−0.294235	+	0.955733i	$0.595065\pi$
$242$	−13.4427	−0.864130
$243$	9.56422	0.613545
$244$	−69.7408	−4.46470
$245$	−7.33061	−0.468336
$246$	22.9720	1.46464
$247$	−10.4956	−0.667820
$248$	1.28366	0.0815122
$249$	3.87085	0.245305
$250$	2.82578	0.178718
$251$	−21.4750	−1.35549	−0.677744	−	0.735298i	$-0.737042\pi$
$251$	−21.4750	−1.35549	−0.677744	+	0.735298i	$0.737042\pi$
$252$	−21.8035	−1.37349
$253$	−7.62998	−0.479693
$254$	49.0087	3.07508
$255$	−0.0259551	−0.00162537
$256$	140.430	8.77690
$257$	−20.0462	−1.25045	−0.625224	−	0.780446i	$-0.714992\pi$
$257$	−20.0462	−1.25045	−0.625224	+	0.780446i	$0.714992\pi$
$258$	−3.26417	−0.203218
$259$	12.4320	0.772488
$260$	32.2418	1.99955
$261$	−7.45318	−0.461340
$262$	−20.5706	−1.27085
$263$	14.3949	0.887629	0.443814	−	0.896119i	$-0.353625\pi$
$263$	14.3949	0.887629	0.443814	+	0.896119i	$0.353625\pi$
$264$	63.8079	3.92710
$265$	3.05962	0.187951
$266$	−20.8414	−1.27787
$267$	3.86431	0.236492
$268$	94.2165	5.75519
$269$	29.9939	1.82876	0.914381	−	0.404855i	$-0.132678\pi$
$269$	29.9939	1.82876	0.914381	+	0.404855i	$0.132678\pi$
$270$	−15.9829	−0.972689
$271$	−7.50422	−0.455849	−0.227924	−	0.973679i	$-0.573194\pi$
$271$	−7.50422	−0.455849	−0.227924	+	0.973679i	$0.573194\pi$
$272$	0.360935	0.0218849
$273$	−29.1106	−1.76185
$274$	24.7434	1.49480
$275$	−3.96953	−0.239372
$276$	16.4216	0.988466
$277$	−8.15891	−0.490222	−0.245111	−	0.969495i	$-0.578824\pi$
$277$	−8.15891	−0.490222	−0.245111	+	0.969495i	$0.578824\pi$
$278$	47.5519	2.85197
$279$	0.109700	0.00656758
$280$	42.6287	2.54755
$281$	24.9936	1.49099	0.745496	−	0.666510i	$-0.232213\pi$
$281$	24.9936	1.49099	0.745496	+	0.666510i	$0.232213\pi$
$282$	1.09516	0.0652160
$283$	5.83009	0.346563	0.173281	−	0.984872i	$-0.444563\pi$
$283$	5.83009	0.346563	0.173281	+	0.984872i	$0.444563\pi$
$284$	−46.5460	−2.76199
$285$	−2.78113	−0.164740
$286$	−60.4268	−3.57311
$287$	−21.5590	−1.27259
$288$	32.3072	1.90372
$289$	−16.9997	−0.999981
$290$	21.8852	1.28514
$291$	8.94277	0.524235
$292$	40.6342	2.37793
$293$	−30.0113	−1.75328	−0.876638	−	0.481150i	$-0.840219\pi$
$293$	−30.0113	−1.75328	−0.876638	+	0.481150i	$0.840219\pi$
$294$	−29.5695	−1.72453
$295$	−12.9955	−0.756626
$296$	−36.9810	−2.14948
$297$	22.4521	1.30280
$298$	10.0101	0.579869
$299$	−10.3547	−0.598827
$300$	8.54342	0.493255
$301$	3.06338	0.176570
$302$	−49.2001	−2.83115
$303$	12.4858	0.717289
$304$	38.6747	2.21814
$305$	11.6526	0.667223
$306$	0.0494452	0.00282659
$307$	−17.0818	−0.974911	−0.487456	−	0.873148i	$-0.662075\pi$
$307$	−17.0818	−0.974911	−0.487456	+	0.873148i	$0.662075\pi$
$308$	−89.9368	−5.12463
$309$	−14.1107	−0.802731
$310$	−0.322120	−0.0182952
$311$	−18.7086	−1.06087	−0.530434	−	0.847726i	$-0.677971\pi$
$311$	−18.7086	−1.06087	−0.530434	+	0.847726i	$0.677971\pi$
$312$	86.5940	4.90242
$313$	−4.01254	−0.226802	−0.113401	−	0.993549i	$-0.536174\pi$
$313$	−4.01254	−0.226802	−0.113401	+	0.993549i	$0.536174\pi$
$314$	−24.4504	−1.37982
$315$	3.64302	0.205261
$316$	32.8301	1.84683
$317$	−23.1131	−1.29816	−0.649080	−	0.760720i	$-0.724846\pi$
$317$	−23.1131	−1.29816	−0.649080	+	0.760720i	$0.724846\pi$
$318$	12.3416	0.692082
$319$	−30.7434	−1.72130
$320$	−55.1646	−3.08379
$321$	−2.46204	−0.137418
$322$	−20.5615	−1.14585
$323$	0.0354253	0.00197111
$324$	−31.0436	−1.72465
$325$	−5.38707	−0.298821
$326$	25.5581	1.41553
$327$	3.69159	0.204145
$328$	64.1306	3.54102
$329$	−1.02780	−0.0566642
$330$	−16.0119	−0.881427
$331$	−23.5009	−1.29173	−0.645863	−	0.763453i	$-0.723502\pi$
$331$	−23.5009	−1.29173	−0.645863	+	0.763453i	$0.723502\pi$
$332$	16.2296	0.890712
$333$	−3.16037	−0.173187
$334$	12.6782	0.693718
$335$	−15.7420	−0.860079
$336$	107.268	5.85194
$337$	−24.5335	−1.33643	−0.668213	−	0.743970i	$-0.732941\pi$
$337$	−24.5335	−1.33643	−0.668213	+	0.743970i	$0.732941\pi$
$338$	−45.2704	−2.46239
$339$	−15.4896	−0.841277
$340$	−0.108824	−0.00590179
$341$	0.452500	0.0245042
$342$	5.29813	0.286490
$343$	1.25155	0.0675776
$344$	−9.11252	−0.491314
$345$	−2.74379	−0.147721
$346$	67.4849	3.62801
$347$	−18.7549	−1.00682	−0.503409	−	0.864048i	$-0.667921\pi$
$347$	−18.7549	−1.00682	−0.503409	+	0.864048i	$0.667921\pi$
$348$	66.1675	3.54695
$349$	−29.7201	−1.59088	−0.795440	−	0.606032i	$-0.792760\pi$
$349$	−29.7201	−1.59088	−0.795440	+	0.606032i	$0.792760\pi$
$350$	−10.6972	−0.571790
$351$	30.4698	1.62636
$352$	133.263	7.10294
$353$	−25.9312	−1.38018	−0.690088	−	0.723725i	$-0.742428\pi$
$353$	−25.9312	−1.38018	−0.690088	+	0.723725i	$0.742428\pi$
$354$	−52.4199	−2.78609
$355$	7.77707	0.412764
$356$	16.2021	0.858711
$357$	0.0982552	0.00520022
$358$	1.37507	0.0726747
$359$	28.4773	1.50298	0.751488	−	0.659746i	$-0.229336\pi$
$359$	28.4773	1.50298	0.751488	+	0.659746i	$0.229336\pi$
$360$	−10.8367	−0.571145
$361$	−15.2041	−0.800218
$362$	72.1161	3.79034
$363$	6.79070	0.356419
$364$	−122.054	−6.39735
$365$	−6.78930	−0.355368
$366$	47.0029	2.45688
$367$	24.0058	1.25309	0.626547	−	0.779384i	$-0.284468\pi$
$367$	24.0058	1.25309	0.626547	+	0.779384i	$0.284468\pi$
$368$	38.1554	1.98899
$369$	5.48055	0.285306
$370$	9.27999	0.482444
$371$	−11.5824	−0.601329
$372$	−0.973892	−0.0504940
$373$	−24.8939	−1.28896	−0.644479	−	0.764622i	$-0.722926\pi$
$373$	−24.8939	−1.28896	−0.644479	+	0.764622i	$0.722926\pi$
$374$	0.203955	0.0105463
$375$	−1.42747	−0.0737140
$376$	3.05734	0.157670
$377$	−41.7220	−2.14879
$378$	60.5046	3.11202
$379$	7.52199	0.386379	0.193189	−	0.981161i	$-0.438117\pi$
$379$	7.52199	0.386379	0.193189	+	0.981161i	$0.438117\pi$
$380$	−11.6606	−0.598177
$381$	−24.7571	−1.26835
$382$	49.6558	2.54061
$383$	11.2543	0.575066	0.287533	−	0.957771i	$-0.407165\pi$
$383$	11.2543	0.575066	0.287533	+	0.957771i	$0.407165\pi$
$384$	−126.673	−6.46427
$385$	15.0270	0.765845
$386$	25.4052	1.29309
$387$	−0.778749	−0.0395861
$388$	37.4949	1.90352
$389$	−23.7213	−1.20272	−0.601358	−	0.798980i	$-0.705373\pi$
$389$	−23.7213	−1.20272	−0.601358	+	0.798980i	$0.705373\pi$
$390$	−21.7298	−1.10033
$391$	0.0349496	0.00176748
$392$	−82.5486	−4.16933
$393$	10.3914	0.524177
$394$	59.2231	2.98362
$395$	−5.48537	−0.275999
$396$	22.8630	1.14891
$397$	4.89881	0.245864	0.122932	−	0.992415i	$-0.460770\pi$
$397$	4.89881	0.245864	0.122932	+	0.992415i	$0.460770\pi$
$398$	−15.2980	−0.766818
$399$	10.5282	0.527069
$400$	19.8505	0.992524
$401$	15.2308	0.760590	0.380295	−	0.924865i	$-0.375822\pi$
$401$	15.2308	0.760590	0.380295	+	0.924865i	$0.375822\pi$
$402$	−63.4987	−3.16703
$403$	0.614090	0.0305900
$404$	52.3499	2.60450
$405$	5.18688	0.257738
$406$	−82.8483	−4.11169
$407$	−13.0361	−0.646177
$408$	−0.292276	−0.0144698
$409$	−16.8863	−0.834975	−0.417487	−	0.908683i	$-0.637089\pi$
$409$	−16.8863	−0.834975	−0.417487	+	0.908683i	$0.637089\pi$
$410$	−16.0929	−0.794771
$411$	−12.4993	−0.616546
$412$	−59.1629	−2.91475
$413$	49.1954	2.42075
$414$	5.22699	0.256892
$415$	−2.71169	−0.133112
$416$	180.852	8.86699
$417$	−24.0212	−1.17632
$418$	21.8541	1.06892
$419$	10.0719	0.492046	0.246023	−	0.969264i	$-0.420876\pi$
$419$	10.0719	0.492046	0.246023	+	0.969264i	$0.420876\pi$
$420$	−32.3418	−1.57812
$421$	20.0292	0.976162	0.488081	−	0.872798i	$-0.337697\pi$
$421$	20.0292	0.976162	0.488081	+	0.872798i	$0.337697\pi$
$422$	11.1234	0.541480
$423$	0.261278	0.0127038
$424$	34.4537	1.67322
$425$	0.0181827	0.000881989 0
$426$	31.3704	1.51990
$427$	−44.1117	−2.13471
$428$	−10.3227	−0.498968
$429$	30.5251	1.47377
$430$	2.28669	0.110274
$431$	19.8002	0.953740	0.476870	−	0.878974i	$-0.341771\pi$
$431$	19.8002	0.953740	0.476870	+	0.878974i	$0.341771\pi$
$432$	−112.276	−5.40190
$433$	4.59050	0.220605	0.110303	−	0.993898i	$-0.464818\pi$
$433$	4.59050	0.220605	0.110303	+	0.993898i	$0.464818\pi$
$434$	1.21941	0.0585335
$435$	−11.0555	−0.530071
$436$	15.4779	0.741259
$437$	3.74490	0.179143
$438$	−27.3860	−1.30856
$439$	−10.1567	−0.484751	−0.242375	−	0.970183i	$-0.577927\pi$
$439$	−10.1567	−0.484751	−0.242375	+	0.970183i	$0.577927\pi$
$440$	−44.7001	−2.13099
$441$	−7.05454	−0.335931
$442$	0.276789	0.0131655
$443$	−29.8667	−1.41901	−0.709505	−	0.704700i	$-0.751081\pi$
$443$	−29.8667	−1.41901	−0.709505	+	0.704700i	$0.751081\pi$
$444$	28.0570	1.33153
$445$	−2.70711	−0.128329
$446$	51.8385	2.45462
$447$	−5.05669	−0.239173
$448$	208.830	9.86629
$449$	6.34668	0.299519	0.149759	−	0.988722i	$-0.452150\pi$
$449$	6.34668	0.299519	0.149759	+	0.988722i	$0.452150\pi$
$450$	2.71936	0.128192
$451$	22.6066	1.06450
$452$	−64.9440	−3.05471
$453$	24.8538	1.16774
$454$	35.7578	1.67820
$455$	20.3932	0.956047
$456$	−31.3178	−1.46659
$457$	2.33145	0.109060	0.0545302	−	0.998512i	$-0.482634\pi$
$457$	2.33145	0.109060	0.0545302	+	0.998512i	$0.482634\pi$
$458$	−70.3338	−3.28648
$459$	−0.102843	−0.00480030
$460$	−11.5040	−0.536379
$461$	26.2703	1.22353	0.611765	−	0.791040i	$-0.290460\pi$
$461$	26.2703	1.22353	0.611765	+	0.791040i	$0.290460\pi$
$462$	60.6143	2.82003
$463$	−25.7012	−1.19444	−0.597219	−	0.802078i	$-0.703728\pi$
$463$	−25.7012	−1.19444	−0.597219	+	0.802078i	$0.703728\pi$
$464$	153.739	7.13715
$465$	0.162722	0.00754603
$466$	−49.6471	−2.29986
$467$	17.0983	0.791216	0.395608	−	0.918419i	$-0.370534\pi$
$467$	17.0983	0.791216	0.395608	+	0.918419i	$0.370534\pi$
$468$	31.0275	1.43425
$469$	59.5927	2.75174
$470$	−0.767207	−0.0353886
$471$	12.3513	0.569120
$472$	−146.340	−6.73582
$473$	−3.21224	−0.147699
$474$	−22.1263	−1.01630
$475$	1.94830	0.0893941
$476$	0.411961	0.0188822
$477$	2.94439	0.134814
$478$	40.0433	1.83154
$479$	4.04663	0.184895	0.0924476	−	0.995718i	$-0.470531\pi$
$479$	4.04663	0.184895	0.0924476	+	0.995718i	$0.470531\pi$
$480$	47.9221	2.18734
$481$	−17.6914	−0.806658
$482$	25.8150	1.17584
$483$	10.3868	0.472617
$484$	28.4718	1.29417
$485$	−6.26479	−0.284469
$486$	−27.0264	−1.22594
$487$	28.0366	1.27046	0.635230	−	0.772323i	$-0.280905\pi$
$487$	28.0366	1.27046	0.635230	+	0.772323i	$0.280905\pi$
$488$	131.217	5.93992
$489$	−12.9109	−0.583850
$490$	20.7147	0.935794
$491$	5.07885	0.229205	0.114603	−	0.993411i	$-0.463441\pi$
$491$	5.07885	0.229205	0.114603	+	0.993411i	$0.463441\pi$
$492$	−48.6550	−2.19354
$493$	0.140822	0.00634230
$494$	29.6583	1.33439
$495$	−3.82004	−0.171698
$496$	−2.26282	−0.101604
$497$	−29.4407	−1.32060
$498$	−10.9382	−0.490151
$499$	−12.1608	−0.544392	−0.272196	−	0.962242i	$-0.587750\pi$
$499$	−12.1608	−0.544392	−0.272196	+	0.962242i	$0.587750\pi$
$500$	−5.98503	−0.267658
$501$	−6.40448	−0.286131
$502$	60.6835	2.70844
$503$	−6.17382	−0.275277	−0.137638	−	0.990483i	$-0.543951\pi$
$503$	−6.17382	−0.275277	−0.137638	+	0.990483i	$0.543951\pi$
$504$	41.0233	1.82732
$505$	−8.74681	−0.389228
$506$	21.5606	0.958488
$507$	22.8687	1.01564
$508$	−103.801	−4.60542
$509$	−7.68882	−0.340801	−0.170401	−	0.985375i	$-0.554506\pi$
$509$	−7.68882	−0.340801	−0.170401	+	0.985375i	$0.554506\pi$
$510$	0.0733435	0.00324770
$511$	25.7014	1.13697
$512$	−219.345	−9.69378
$513$	−11.0198	−0.486535
$514$	56.6461	2.49855
$515$	9.88516	0.435592
$516$	6.91355	0.304352
$517$	1.07774	0.0473989
$518$	−35.1301	−1.54353
$519$	−34.0906	−1.49641
$520$	−60.6627	−2.66024
$521$	37.7377	1.65332	0.826659	−	0.562703i	$-0.190238\pi$
$521$	37.7377	1.65332	0.826659	+	0.562703i	$0.190238\pi$
$522$	21.0610	0.921817
$523$	−35.1398	−1.53656	−0.768278	−	0.640116i	$-0.778886\pi$
$523$	−35.1398	−1.53656	−0.768278	+	0.640116i	$0.778886\pi$
$524$	43.5687	1.90331
$525$	5.40379	0.235841
$526$	−40.6769	−1.77360
$527$	−0.00207270	−9.02883e−5 0
$528$	−112.480	−4.89507
$529$	−19.3054	−0.839365
$530$	−8.64580	−0.375549
$531$	−12.5061	−0.542717
$532$	44.1422	1.91381
$533$	30.6795	1.32888
$534$	−10.9197	−0.472541
$535$	1.72476	0.0745679
$536$	−177.268	−7.65681
$537$	−0.694628	−0.0299754
$538$	−84.7562	−3.65410
$539$	−29.0991	−1.25339
$540$	33.8519	1.45676
$541$	14.9764	0.643888	0.321944	−	0.946759i	$-0.395664\pi$
$541$	14.9764	0.643888	0.321944	+	0.946759i	$0.395664\pi$
$542$	21.2053	0.910844
$543$	−36.4300	−1.56336
$544$	−0.610419	−0.0261715
$545$	−2.58611	−0.110777
$546$	82.2600	3.52040
$547$	8.37214	0.357967	0.178984	−	0.983852i	$-0.442719\pi$
$547$	8.37214	0.357967	0.178984	+	0.983852i	$0.442719\pi$
$548$	−52.4067	−2.23870
$549$	11.2137	0.478590
$550$	11.2170	0.478295
$551$	15.0893	0.642825
$552$	−30.8972	−1.31507
$553$	20.7653	0.883030
$554$	23.0553	0.979525
$555$	−4.68787	−0.198989
$556$	−100.715	−4.27128
$557$	30.2899	1.28342	0.641711	−	0.766946i	$-0.278225\pi$
$557$	30.2899	1.28342	0.641711	+	0.766946i	$0.278225\pi$
$558$	−0.309989	−0.0131229
$559$	−4.35935	−0.184381
$560$	−75.1456	−3.17548
$561$	−0.103030	−0.00434992
$562$	−70.6263	−2.97919
$563$	−39.4778	−1.66379	−0.831896	−	0.554931i	$-0.812745\pi$
$563$	−39.4778	−1.66379	−0.831896	+	0.554931i	$0.812745\pi$
$564$	−2.31956	−0.0976713
$565$	10.8511	0.456509
$566$	−16.4745	−0.692477
$567$	−19.6353	−0.824607
$568$	87.5760	3.67461
$569$	−19.3496	−0.811177	−0.405588	−	0.914056i	$-0.632933\pi$
$569$	−19.3496	−0.811177	−0.405588	+	0.914056i	$0.632933\pi$
$570$	7.85886	0.329171
$571$	8.16285	0.341605	0.170802	−	0.985305i	$-0.445364\pi$
$571$	8.16285	0.341605	0.170802	+	0.985305i	$0.445364\pi$
$572$	127.985	5.35130
$573$	−25.0840	−1.04790
$574$	60.9209	2.54279
$575$	1.92214	0.0801587
$576$	−53.0871	−2.21196
$577$	27.3439	1.13834	0.569170	−	0.822220i	$-0.307265\pi$
$577$	27.3439	1.13834	0.569170	+	0.822220i	$0.307265\pi$
$578$	48.0373	1.99809
$579$	−12.8337	−0.533349
$580$	−46.3531	−1.92471
$581$	10.2653	0.425878
$582$	−25.2703	−1.04749
$583$	12.1452	0.503004
$584$	−76.4530	−3.16365
$585$	−5.18419	−0.214340
$586$	84.8052	3.50327
$587$	32.9839	1.36139	0.680697	−	0.732565i	$-0.261677\pi$
$587$	32.9839	1.36139	0.680697	+	0.732565i	$0.261677\pi$
$588$	62.6285	2.58276
$589$	−0.222093	−0.00915118
$590$	36.7224	1.51184
$591$	−29.9171	−1.23062
$592$	65.1899	2.67929
$593$	17.7767	0.730003	0.365002	−	0.931007i	$-0.381068\pi$
$593$	17.7767	0.730003	0.365002	+	0.931007i	$0.381068\pi$
$594$	−63.4446	−2.60316
$595$	−0.0688319	−0.00282183
$596$	−21.2015	−0.868446
$597$	7.72790	0.316282
$598$	29.2601	1.19653
$599$	21.9123	0.895313	0.447657	−	0.894206i	$-0.352259\pi$
$599$	21.9123	0.895313	0.447657	+	0.894206i	$0.352259\pi$
$600$	−16.0744	−0.656235
$601$	20.3776	0.831221	0.415611	−	0.909543i	$-0.363568\pi$
$601$	20.3776	0.831221	0.415611	+	0.909543i	$0.363568\pi$
$602$	−8.65644	−0.352810
$603$	−15.1492	−0.616923
$604$	104.206	4.24009
$605$	−4.75717	−0.193406
$606$	−35.2820	−1.43323
$607$	−25.0658	−1.01739	−0.508694	−	0.860947i	$-0.669872\pi$
$607$	−25.0658	−1.01739	−0.508694	+	0.860947i	$0.669872\pi$
$608$	−65.4072	−2.65261
$609$	41.8515	1.69591
$610$	−32.9275	−1.33320
$611$	1.46261	0.0591707
$612$	−0.104725	−0.00423327
$613$	38.8907	1.57078	0.785390	−	0.619001i	$-0.212462\pi$
$613$	38.8907	1.57078	0.785390	+	0.619001i	$0.212462\pi$
$614$	48.2694	1.94800
$615$	8.12946	0.327811
$616$	169.216	6.81790
$617$	−9.91885	−0.399318	−0.199659	−	0.979865i	$-0.563983\pi$
$617$	−9.91885	−0.399318	−0.199659	+	0.979865i	$0.563983\pi$
$618$	39.8738	1.60396
$619$	−2.92232	−0.117458	−0.0587290	−	0.998274i	$-0.518705\pi$
$619$	−2.92232	−0.117458	−0.0587290	+	0.998274i	$0.518705\pi$
$620$	0.682253	0.0273999
$621$	−10.8718	−0.436271
$622$	52.8664	2.11975
$623$	10.2480	0.410577
$624$	−152.647	−6.11079
$625$	1.00000	0.0400000
$626$	11.3385	0.453179
$627$	−11.0398	−0.440886
$628$	51.7862	2.06649
$629$	0.0597127	0.00238090
$630$	−10.2944	−0.410137
$631$	32.8763	1.30878	0.654392	−	0.756156i	$-0.272925\pi$
$631$	32.8763	1.30878	0.654392	+	0.756156i	$0.272925\pi$
$632$	−61.7696	−2.45706
$633$	−5.61910	−0.223339
$634$	65.3124	2.59389
$635$	17.3434	0.688252
$636$	−26.1396	−1.03650
$637$	−39.4905	−1.56467
$638$	86.8741	3.43938
$639$	7.48419	0.296070
$640$	88.7400	3.50776
$641$	2.61146	0.103146	0.0515732	−	0.998669i	$-0.483576\pi$
$641$	2.61146	0.103146	0.0515732	+	0.998669i	$0.483576\pi$
$642$	6.95717	0.274578
$643$	8.45407	0.333396	0.166698	−	0.986008i	$-0.446689\pi$
$643$	8.45407	0.333396	0.166698	+	0.986008i	$0.446689\pi$
$644$	43.5495	1.71609
$645$	−1.15514	−0.0454836
$646$	−0.100104	−0.00393854
$647$	−19.6011	−0.770600	−0.385300	−	0.922791i	$-0.625902\pi$
$647$	−19.6011	−0.770600	−0.385300	+	0.922791i	$0.625902\pi$
$648$	58.4084	2.29450
$649$	−51.5860	−2.02493
$650$	15.2227	0.597082
$651$	−0.615995	−0.0241428
$652$	−54.1323	−2.11998
$653$	−5.37392	−0.210298	−0.105149	−	0.994456i	$-0.533532\pi$
$653$	−5.37392	−0.210298	−0.105149	+	0.994456i	$0.533532\pi$
$654$	−10.4316	−0.407908
$655$	−7.27961	−0.284438
$656$	−113.049	−4.41382
$657$	−6.53362	−0.254901
$658$	2.90432	0.113222
$659$	−4.13533	−0.161090	−0.0805448	−	0.996751i	$-0.525666\pi$
$659$	−4.13533	−0.161090	−0.0805448	+	0.996751i	$0.525666\pi$
$660$	33.9134	1.32008
$661$	44.4225	1.72784	0.863918	−	0.503633i	$-0.168004\pi$
$661$	44.4225	1.72784	0.863918	+	0.503633i	$0.168004\pi$
$662$	66.4083	2.58103
$663$	−0.139822	−0.00543024
$664$	−30.5358	−1.18502
$665$	−7.37544	−0.286007
$666$	8.93051	0.346050
$667$	14.8867	0.576414
$668$	−26.8525	−1.03895
$669$	−26.1867	−1.01243
$670$	44.4835	1.71855
$671$	46.2552	1.78566
$672$	−181.413	−6.99816
$673$	18.4444	0.710978	0.355489	−	0.934680i	$-0.384314\pi$
$673$	18.4444	0.710978	0.355489	+	0.934680i	$0.384314\pi$
$674$	69.3263	2.67035
$675$	−5.65611	−0.217704
$676$	95.8832	3.68782
$677$	9.35109	0.359391	0.179696	−	0.983722i	$-0.442489\pi$
$677$	9.35109	0.359391	0.179696	+	0.983722i	$0.442489\pi$
$678$	43.7701	1.68098
$679$	23.7159	0.910131
$680$	0.204751	0.00785186
$681$	−18.0634	−0.692189
$682$	−1.27866	−0.0489626
$683$	−45.1231	−1.72659	−0.863294	−	0.504701i	$-0.831603\pi$
$683$	−45.1231	−1.72659	−0.863294	+	0.504701i	$0.831603\pi$
$684$	−11.2215	−0.429064
$685$	8.75630	0.334561
$686$	−3.53662	−0.135029
$687$	35.5297	1.35554
$688$	16.0635	0.612415
$689$	16.4824	0.627928
$690$	7.75333	0.295164
$691$	38.4817	1.46391	0.731956	−	0.681352i	$-0.238607\pi$
$691$	38.4817	1.46391	0.731956	+	0.681352i	$0.238607\pi$
$692$	−142.934	−5.43352
$693$	14.4611	0.549330
$694$	52.9973	2.01175
$695$	16.8279	0.638318
$696$	−124.494	−4.71893
$697$	−0.103551	−0.00392226
$698$	83.9824	3.17878
$699$	25.0797	0.948600
$700$	22.6568	0.856346
$701$	−34.2206	−1.29250	−0.646248	−	0.763127i	$-0.723663\pi$
$701$	−34.2206	−1.29250	−0.646248	+	0.763127i	$0.723663\pi$
$702$	−86.1010	−3.24967
$703$	6.39830	0.241317
$704$	−218.977	−8.25302
$705$	0.387561	0.0145964
$706$	73.2757	2.75777
$707$	33.1117	1.24530
$708$	111.026	4.17261
$709$	22.1185	0.830677	0.415339	−	0.909667i	$-0.363663\pi$
$709$	22.1185	0.830677	0.415339	+	0.909667i	$0.363663\pi$
$710$	−21.9763	−0.824755
$711$	−5.27879	−0.197970
$712$	−30.4842	−1.14245
$713$	−0.219111	−0.00820576
$714$	−0.277648	−0.0103907
$715$	−21.3841	−0.799721
$716$	−2.91241	−0.108842
$717$	−20.2282	−0.755436
$718$	−80.4707	−3.00314
$719$	14.2562	0.531666	0.265833	−	0.964019i	$-0.414353\pi$
$719$	14.2562	0.531666	0.265833	+	0.964019i	$0.414353\pi$
$720$	19.1029	0.711924
$721$	−37.4210	−1.39363
$722$	42.9635	1.59894
$723$	−13.0407	−0.484987
$724$	−152.742	−5.67663
$725$	7.74485	0.287636
$726$	−19.1890	−0.712171
$727$	−27.1914	−1.00847	−0.504237	−	0.863565i	$-0.668226\pi$
$727$	−27.1914	−1.00847	−0.504237	+	0.863565i	$0.668226\pi$
$728$	229.644	8.51116
$729$	29.2132	1.08197
$730$	19.1851	0.710071
$731$	0.0147139	0.000544212 0
$732$	−99.5527	−3.67957
$733$	−14.6326	−0.540469	−0.270234	−	0.962795i	$-0.587101\pi$
$733$	−14.6326	−0.540469	−0.270234	+	0.962795i	$0.587101\pi$
$734$	−67.8352	−2.50384
$735$	−10.4642	−0.385978
$736$	−64.5290	−2.37857
$737$	−62.4885	−2.30179
$738$	−15.4868	−0.570078
$739$	−18.3640	−0.675532	−0.337766	−	0.941230i	$-0.609671\pi$
$739$	−18.3640	−0.675532	−0.337766	+	0.941230i	$0.609671\pi$
$740$	−19.6551	−0.722536
$741$	−14.9821	−0.550383
$742$	32.7294	1.20153
$743$	32.4515	1.19053	0.595266	−	0.803529i	$-0.297047\pi$
$743$	32.4515	1.19053	0.595266	+	0.803529i	$0.297047\pi$
$744$	1.83237	0.0671781
$745$	3.54242	0.129784
$746$	70.3447	2.57550
$747$	−2.60957	−0.0954792
$748$	−0.431979	−0.0157947
$749$	−6.52922	−0.238572
$750$	4.03370	0.147290
$751$	−9.19656	−0.335587	−0.167794	−	0.985822i	$-0.553664\pi$
$751$	−9.19656	−0.335587	−0.167794	+	0.985822i	$0.553664\pi$
$752$	−5.38947	−0.196534
$753$	−30.6548	−1.11712
$754$	117.897	4.29356
$755$	−17.4112	−0.633657
$756$	−128.149	−4.66074
$757$	−47.6265	−1.73101	−0.865507	−	0.500896i	$-0.833004\pi$
$757$	−47.6265	−1.73101	−0.865507	+	0.500896i	$0.833004\pi$
$758$	−21.2555	−0.772034
$759$	−10.8915	−0.395338
$760$	21.9394	0.795826
$761$	−13.4156	−0.486317	−0.243158	−	0.969987i	$-0.578183\pi$
$761$	−13.4156	−0.486317	−0.243158	+	0.969987i	$0.578183\pi$
$762$	69.9582	2.53432
$763$	9.78993	0.354419
$764$	−105.171	−3.80497
$765$	0.0174979	0.000632638 0
$766$	−31.8021	−1.14906
$767$	−70.0076	−2.52783
$768$	200.460	7.23346
$769$	0.518259	0.0186889	0.00934445	−	0.999956i	$-0.497026\pi$
$769$	0.518259	0.0186889	0.00934445	+	0.999956i	$0.497026\pi$
$770$	−42.4629	−1.53026
$771$	−28.6153	−1.03055
$772$	−53.8085	−1.93661
$773$	3.68649	0.132594	0.0662970	−	0.997800i	$-0.478882\pi$
$773$	3.68649	0.132594	0.0662970	+	0.997800i	$0.478882\pi$
$774$	2.20057	0.0790980
$775$	−0.113993	−0.00409476
$776$	−70.5465	−2.53247
$777$	17.7463	0.636644
$778$	67.0310	2.40318
$779$	−11.0956	−0.397542
$780$	46.0240	1.64792
$781$	30.8713	1.10466
$782$	−0.0987598	−0.00353164
$783$	−43.8057	−1.56549
$784$	145.516	5.19701
$785$	−8.65263	−0.308826
$786$	−29.3638	−1.04737
$787$	−52.3059	−1.86450	−0.932252	−	0.361808i	$-0.882159\pi$
$787$	−52.3059	−1.86450	−0.932252	+	0.361808i	$0.882159\pi$
$788$	−125.435	−4.46844
$789$	20.5483	0.731538
$790$	15.5004	0.551481
$791$	−41.0776	−1.46055
$792$	−43.0167	−1.52853
$793$	62.7731	2.22914
$794$	−13.8430	−0.491268
$795$	4.36750	0.154899
$796$	32.4013	1.14843
$797$	18.5406	0.656742	0.328371	−	0.944549i	$-0.393500\pi$
$797$	18.5406	0.656742	0.328371	+	0.944549i	$0.393500\pi$
$798$	−29.7503	−1.05315
$799$	−0.00493665	−0.000174646 0
$800$	−33.5715	−1.18693
$801$	−2.60516	−0.0920489
$802$	−43.0389	−1.51976
$803$	−26.9503	−0.951057
$804$	134.491	4.74313
$805$	−7.27641	−0.256460
$806$	−1.73528	−0.0611227
$807$	42.8153	1.50717
$808$	−98.4961	−3.46508
$809$	−6.85358	−0.240959	−0.120480	−	0.992716i	$-0.538443\pi$
$809$	−6.85358	−0.240959	−0.120480	+	0.992716i	$0.538443\pi$
$810$	−14.6570	−0.514994
$811$	−56.0053	−1.96661	−0.983305	−	0.181964i	$-0.941755\pi$
$811$	−56.0053	−1.96661	−0.983305	+	0.181964i	$0.941755\pi$
$812$	175.473	6.15791
$813$	−10.7120	−0.375687
$814$	36.8372	1.29114
$815$	9.04462	0.316819
$816$	0.515222	0.0180364
$817$	1.57661	0.0551586
$818$	47.7170	1.66839
$819$	19.6252	0.685759
$820$	34.0849	1.19030
$821$	26.6600	0.930442	0.465221	−	0.885195i	$-0.345975\pi$
$821$	26.6600	0.930442	0.465221	+	0.885195i	$0.345975\pi$
$822$	35.3203	1.23194
$823$	24.6366	0.858780	0.429390	−	0.903119i	$-0.358729\pi$
$823$	24.6366	0.858780	0.429390	+	0.903119i	$0.358729\pi$
$824$	111.315	3.87783
$825$	−5.66637	−0.197278
$826$	−139.015	−4.83696
$827$	15.3482	0.533710	0.266855	−	0.963737i	$-0.414016\pi$
$827$	15.3482	0.533710	0.266855	+	0.963737i	$0.414016\pi$
$828$	−11.0708	−0.384737
$829$	20.6740	0.718037	0.359018	−	0.933330i	$-0.383112\pi$
$829$	20.6740	0.718037	0.359018	+	0.933330i	$0.383112\pi$
$830$	7.66264	0.265974
$831$	−11.6466	−0.404015
$832$	−297.175	−10.3027
$833$	0.133290	0.00461823
$834$	67.8787	2.35045
$835$	4.48661	0.155266
$836$	−46.2872	−1.60088
$837$	0.644758	0.0222861
$838$	−28.4610	−0.983171
$839$	−20.4562	−0.706227	−0.353114	−	0.935580i	$-0.614877\pi$
$839$	−20.4562	−0.706227	−0.353114	+	0.935580i	$0.614877\pi$
$840$	60.8510	2.09956
$841$	30.9827	1.06837
$842$	−56.5980	−1.95050
$843$	35.6775	1.22880
$844$	−23.5595	−0.810953
$845$	−16.0205	−0.551123
$846$	−0.738315	−0.0253838
$847$	18.0086	0.618784
$848$	−60.7349	−2.08564
$849$	8.32226	0.285619
$850$	−0.0513802	−0.00176233
$851$	6.31239	0.216386
$852$	−66.4428	−2.27629
$853$	−33.0922	−1.13306	−0.566528	−	0.824042i	$-0.691714\pi$
$853$	−33.0922	−1.13306	−0.566528	+	0.824042i	$0.691714\pi$
$854$	124.650	4.26543
$855$	1.87493	0.0641211
$856$	19.4222	0.663837
$857$	−25.7807	−0.880653	−0.440327	−	0.897838i	$-0.645137\pi$
$857$	−25.7807	−0.880653	−0.440327	+	0.897838i	$0.645137\pi$
$858$	−86.2573	−2.94477
$859$	−36.4879	−1.24495	−0.622476	−	0.782639i	$-0.713873\pi$
$859$	−36.4879	−1.24495	−0.622476	+	0.782639i	$0.713873\pi$
$860$	−4.84323	−0.165153
$861$	−30.7747	−1.04880
$862$	−55.9508	−1.90569
$863$	48.1836	1.64019	0.820094	−	0.572229i	$-0.193921\pi$
$863$	48.1836	1.64019	0.820094	+	0.572229i	$0.193921\pi$
$864$	189.884	6.45998
$865$	23.8819	0.812008
$866$	−12.9717	−0.440798
$867$	−24.2665	−0.824132
$868$	−2.58272	−0.0876633
$869$	−21.7743	−0.738643
$870$	31.2404	1.05915
$871$	−84.8034	−2.87345
$872$	−29.1217	−0.986185
$873$	−6.02886	−0.204046
$874$	−10.5823	−0.357950
$875$	−3.78558	−0.127976
$876$	58.0039	1.95977
$877$	3.60675	0.121791	0.0608957	−	0.998144i	$-0.480604\pi$
$877$	3.60675	0.121791	0.0608957	+	0.998144i	$0.480604\pi$
$878$	28.7005	0.968594
$879$	−42.8401	−1.44496
$880$	78.7971	2.65625
$881$	34.2543	1.15406	0.577028	−	0.816725i	$-0.304212\pi$
$881$	34.2543	1.15406	0.577028	+	0.816725i	$0.304212\pi$
$882$	19.9346	0.671232
$883$	4.37427	0.147206	0.0736030	−	0.997288i	$-0.476550\pi$
$883$	4.37427	0.147206	0.0736030	+	0.997288i	$0.476550\pi$
$884$	−0.586241	−0.0197174
$885$	−18.5506	−0.623572
$886$	84.3967	2.83536
$887$	−45.5761	−1.53029	−0.765147	−	0.643855i	$-0.777334\pi$
$887$	−45.5761	−1.53029	−0.765147	+	0.643855i	$0.777334\pi$
$888$	−52.7891	−1.77149
$889$	−65.6549	−2.20199
$890$	7.64970	0.256418
$891$	20.5895	0.689773
$892$	−109.794	−3.67619
$893$	−0.528969	−0.0177013
$894$	14.2891	0.477898
$895$	0.486616	0.0162658
$896$	−335.932	−11.2227
$897$	−14.7810	−0.493522
$898$	−17.9343	−0.598476
$899$	−0.882860	−0.0294450
$900$	−5.75963	−0.191988
$901$	−0.0556320	−0.00185337
$902$	−63.8812	−2.12701
$903$	4.37288	0.145520
$904$	122.192	4.06404
$905$	25.5208	0.848339
$906$	−70.2314	−2.33328
$907$	−25.6979	−0.853286	−0.426643	−	0.904420i	$-0.640304\pi$
$907$	−25.6979	−0.853286	−0.426643	+	0.904420i	$0.640304\pi$
$908$	−75.7353	−2.51337
$909$	−8.41741	−0.279188
$910$	−57.6266	−1.91030
$911$	−7.78422	−0.257903	−0.128951	−	0.991651i	$-0.541161\pi$
$911$	−7.78422	−0.257903	−0.128951	+	0.991651i	$0.541161\pi$
$912$	55.2068	1.82808
$913$	−10.7641	−0.356241
$914$	−6.58815	−0.217917
$915$	16.6336	0.549891
$916$	148.968	4.92203
$917$	27.5576	0.910031
$918$	0.290612	0.00959162
$919$	−31.6413	−1.04375	−0.521876	−	0.853022i	$-0.674768\pi$
$919$	−31.6413	−1.04375	−0.521876	+	0.853022i	$0.674768\pi$
$920$	21.6448	0.713608
$921$	−24.3837	−0.803471
$922$	−74.2340	−2.44477
$923$	41.8956	1.37901
$924$	−128.382	−4.22345
$925$	3.28405	0.107979
$926$	72.6260	2.38664
$927$	9.51288	0.312444
$928$	−260.006	−8.53511
$929$	26.9328	0.883635	0.441818	−	0.897105i	$-0.354334\pi$
$929$	26.9328	0.883635	0.441818	+	0.897105i	$0.354334\pi$
$930$	−0.459815	−0.0150779
$931$	14.2822	0.468081
$932$	105.153	3.44440
$933$	−26.7059	−0.874312
$934$	−48.3161	−1.58095
$935$	0.0721766	0.00236043
$936$	−58.3782	−1.90815
$937$	51.1624	1.67140	0.835701	−	0.549185i	$-0.185062\pi$
$937$	51.1624	1.67140	0.835701	+	0.549185i	$0.185062\pi$
$938$	−168.396	−5.49832
$939$	−5.72776	−0.186918
$940$	1.62495	0.0530001
$941$	48.2520	1.57297	0.786484	−	0.617610i	$-0.211899\pi$
$941$	48.2520	1.57297	0.786484	+	0.617610i	$0.211899\pi$
$942$	−34.9021	−1.13717
$943$	−10.9466	−0.356471
$944$	257.967	8.39610
$945$	21.4116	0.696521
$946$	9.07708	0.295121
$947$	13.5335	0.439780	0.219890	−	0.975525i	$-0.429430\pi$
$947$	13.5335	0.439780	0.219890	+	0.975525i	$0.429430\pi$
$948$	46.8638	1.52207
$949$	−36.5744	−1.18726
$950$	−5.50546	−0.178621
$951$	−32.9931	−1.06988
$952$	−0.775102	−0.0251212
$953$	0.0343867	0.00111389	0.000556947	−	1.00000i	$-0.499823\pi$
$953$	0.0343867	0.00111389	0.000556947		1.00000i	$0.499823\pi$
$954$	−8.32020	−0.269376
$955$	17.5724	0.568630
$956$	−84.8120	−2.74302
$957$	−43.8852	−1.41861
$958$	−11.4349	−0.369444
$959$	−33.1477	−1.07039
$960$	−78.7456	−2.54150
$961$	−30.9870	−0.999581
$962$	49.9919	1.61181
$963$	1.65981	0.0534865
$964$	−54.6764	−1.76101
$965$	8.99053	0.289415
$966$	−29.3509	−0.944349
$967$	−49.0683	−1.57793	−0.788965	−	0.614438i	$-0.789383\pi$
$967$	−49.0683	−1.57793	−0.788965	+	0.614438i	$0.789383\pi$
$968$	−53.5695	−1.72179
$969$	0.0505683	0.00162449
$970$	17.7029	0.568406
$971$	−18.6704	−0.599163	−0.299581	−	0.954071i	$-0.596847\pi$
$971$	−18.6704	−0.599163	−0.299581	+	0.954071i	$0.596847\pi$
$972$	57.2421	1.83604
$973$	−63.7033	−2.04223
$974$	−79.2253	−2.53854
$975$	−7.68986	−0.246273
$976$	−231.309	−7.40401
$977$	3.85033	0.123183	0.0615914	−	0.998101i	$-0.480382\pi$
$977$	3.85033	0.123183	0.0615914	+	0.998101i	$0.480382\pi$
$978$	36.4833	1.16661
$979$	−10.7460	−0.343442
$980$	−43.8739	−1.40150
$981$	−2.48872	−0.0794587
$982$	−14.3517	−0.457981
$983$	5.54408	0.176829	0.0884144	−	0.996084i	$-0.471820\pi$
$983$	5.54408	0.176829	0.0884144	+	0.996084i	$0.471820\pi$
$984$	91.5442	2.91832
$985$	20.9582	0.667783
$986$	−0.397932	−0.0126727
$987$	−1.46714	−0.0466997
$988$	−62.8166	−1.99846
$989$	1.55544	0.0494601
$990$	10.7946	0.343074
$991$	−12.1489	−0.385921	−0.192961	−	0.981206i	$-0.561809\pi$
$991$	−12.1489	−0.385921	−0.192961	+	0.981206i	$0.561809\pi$
$992$	3.82692	0.121505
$993$	−33.5467	−1.06457
$994$	83.1929	2.63872
$995$	−5.41372	−0.171626
$996$	23.1671	0.734079
$997$	21.3495	0.676147	0.338073	−	0.941120i	$-0.390225\pi$
$997$	21.3495	0.676147	0.338073	+	0.941120i	$0.390225\pi$
$998$	34.3637	1.08777
$999$	−18.5749	−0.587684

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.d.1.1	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.d.1.1	✓	140	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.82578 q^{2} +1.42747 q^{3} +5.98503 q^{4} -1.00000 q^{5} -4.03370 q^{6} +3.78558 q^{7} -11.2608 q^{8} -0.962340 q^{9} +O(q^{10})\)	\(q-2.82578 q^{2} +1.42747 q^{3} +5.98503 q^{4} -1.00000 q^{5} -4.03370 q^{6} +3.78558 q^{7} -11.2608 q^{8} -0.962340 q^{9} +2.82578 q^{10} -3.96953 q^{11} +8.54342 q^{12} -5.38707 q^{13} -10.6972 q^{14} -1.42747 q^{15} +19.8505 q^{16} +0.0181827 q^{17} +2.71936 q^{18} +1.94830 q^{19} -5.98503 q^{20} +5.40379 q^{21} +11.2170 q^{22} +1.92214 q^{23} -16.0744 q^{24} +1.00000 q^{25} +15.2227 q^{26} -5.65611 q^{27} +22.6568 q^{28} +7.74485 q^{29} +4.03370 q^{30} -0.113993 q^{31} -33.5715 q^{32} -5.66637 q^{33} -0.0513802 q^{34} -3.78558 q^{35} -5.75963 q^{36} +3.28405 q^{37} -5.50546 q^{38} -7.68986 q^{39} +11.2608 q^{40} -5.69503 q^{41} -15.2699 q^{42} +0.809225 q^{43} -23.7577 q^{44} +0.962340 q^{45} -5.43154 q^{46} -0.271503 q^{47} +28.3359 q^{48} +7.33061 q^{49} -2.82578 q^{50} +0.0259551 q^{51} -32.2418 q^{52} -3.05962 q^{53} +15.9829 q^{54} +3.96953 q^{55} -42.6287 q^{56} +2.78113 q^{57} -21.8852 q^{58} +12.9955 q^{59} -8.54342 q^{60} -11.6526 q^{61} +0.322120 q^{62} -3.64302 q^{63} +55.1646 q^{64} +5.38707 q^{65} +16.0119 q^{66} +15.7420 q^{67} +0.108824 q^{68} +2.74379 q^{69} +10.6972 q^{70} -7.77707 q^{71} +10.8367 q^{72} +6.78930 q^{73} -9.27999 q^{74} +1.42747 q^{75} +11.6606 q^{76} -15.0270 q^{77} +21.7298 q^{78} +5.48537 q^{79} -19.8505 q^{80} -5.18688 q^{81} +16.0929 q^{82} +2.71169 q^{83} +32.3418 q^{84} -0.0181827 q^{85} -2.28669 q^{86} +11.0555 q^{87} +44.7001 q^{88} +2.70711 q^{89} -2.71936 q^{90} -20.3932 q^{91} +11.5040 q^{92} -0.162722 q^{93} +0.767207 q^{94} -1.94830 q^{95} -47.9221 q^{96} +6.26479 q^{97} -20.7147 q^{98} +3.82004 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9}+O(q^{10}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9} + 20 q^{10} - 26 q^{11} - 31 q^{12} - 32 q^{13} - 37 q^{14} + 12 q^{15} + 152 q^{16} - 69 q^{17} - 64 q^{18} + 37 q^{19} - 144 q^{20} - 43 q^{21} - 25 q^{22} - 63 q^{23} - 5 q^{24} + 140 q^{25} - 16 q^{26} - 48 q^{27} - 52 q^{28} - 136 q^{29} + 25 q^{31} - 151 q^{32} - 48 q^{33} + 29 q^{34} + 15 q^{35} + 120 q^{36} - 82 q^{37} - 69 q^{38} - 26 q^{39} + 63 q^{40} - 11 q^{41} - 35 q^{42} - 54 q^{43} - 83 q^{44} - 134 q^{45} + 25 q^{46} - 39 q^{47} - 83 q^{48} + 215 q^{49} - 20 q^{50} - 75 q^{51} - 56 q^{52} - 196 q^{53} - 29 q^{54} + 26 q^{55} - 132 q^{56} - 110 q^{57} - 29 q^{58} - 31 q^{59} + 31 q^{60} - 18 q^{61} - 107 q^{62} - 67 q^{63} + 165 q^{64} + 32 q^{65} - 16 q^{66} - 50 q^{67} - 201 q^{68} - 46 q^{69} + 37 q^{70} - 84 q^{71} - 200 q^{72} - 70 q^{73} - 101 q^{74} - 12 q^{75} + 118 q^{76} - 166 q^{77} - 106 q^{78} - 35 q^{79} - 152 q^{80} + 116 q^{81} - 72 q^{82} - 66 q^{83} - 60 q^{84} + 69 q^{85} - 66 q^{86} - 75 q^{87} - 101 q^{88} + 8 q^{89} + 64 q^{90} + 2 q^{91} - 197 q^{92} - 134 q^{93} + 65 q^{94} - 37 q^{95} + 6 q^{96} - 73 q^{97} - 151 q^{98} - 51 q^{99}+O(q^{100}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9 + 20 * q^10 - 26 * q^11 - 31 * q^12 - 32 * q^13 - 37 * q^14 + 12 * q^15 + 152 * q^16 - 69 * q^17 - 64 * q^18 + 37 * q^19 - 144 * q^20 - 43 * q^21 - 25 * q^22 - 63 * q^23 - 5 * q^24 + 140 * q^25 - 16 * q^26 - 48 * q^27 - 52 * q^28 - 136 * q^29 + 25 * q^31 - 151 * q^32 - 48 * q^33 + 29 * q^34 + 15 * q^35 + 120 * q^36 - 82 * q^37 - 69 * q^38 - 26 * q^39 + 63 * q^40 - 11 * q^41 - 35 * q^42 - 54 * q^43 - 83 * q^44 - 134 * q^45 + 25 * q^46 - 39 * q^47 - 83 * q^48 + 215 * q^49 - 20 * q^50 - 75 * q^51 - 56 * q^52 - 196 * q^53 - 29 * q^54 + 26 * q^55 - 132 * q^56 - 110 * q^57 - 29 * q^58 - 31 * q^59 + 31 * q^60 - 18 * q^61 - 107 * q^62 - 67 * q^63 + 165 * q^64 + 32 * q^65 - 16 * q^66 - 50 * q^67 - 201 * q^68 - 46 * q^69 + 37 * q^70 - 84 * q^71 - 200 * q^72 - 70 * q^73 - 101 * q^74 - 12 * q^75 + 118 * q^76 - 166 * q^77 - 106 * q^78 - 35 * q^79 - 152 * q^80 + 116 * q^81 - 72 * q^82 - 66 * q^83 - 60 * q^84 + 69 * q^85 - 66 * q^86 - 75 * q^87 - 101 * q^88 + 8 * q^89 + 64 * q^90 + 2 * q^91 - 197 * q^92 - 134 * q^93 + 65 * q^94 - 37 * q^95 + 6 * q^96 - 73 * q^97 - 151 * q^98 - 51 * q^99

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