LMFDB - Embedded newform 8026.2.a.d.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.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:	$64.0879326623$
Analytic rank:	$0$
Dimension:	$96$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.21370 q^{3} +1.00000 q^{4} +0.840207 q^{5} -2.21370 q^{6} -5.05822 q^{7} +1.00000 q^{8} +1.90049 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.21370 q^{3} +1.00000 q^{4} +0.840207 q^{5} -2.21370 q^{6} -5.05822 q^{7} +1.00000 q^{8} +1.90049 q^{9} +0.840207 q^{10} +3.18870 q^{11} -2.21370 q^{12} -6.03830 q^{13} -5.05822 q^{14} -1.85997 q^{15} +1.00000 q^{16} -0.417799 q^{17} +1.90049 q^{18} -1.79978 q^{19} +0.840207 q^{20} +11.1974 q^{21} +3.18870 q^{22} -2.44597 q^{23} -2.21370 q^{24} -4.29405 q^{25} -6.03830 q^{26} +2.43399 q^{27} -5.05822 q^{28} +5.73464 q^{29} -1.85997 q^{30} -8.99262 q^{31} +1.00000 q^{32} -7.05883 q^{33} -0.417799 q^{34} -4.24995 q^{35} +1.90049 q^{36} -7.64209 q^{37} -1.79978 q^{38} +13.3670 q^{39} +0.840207 q^{40} +3.25013 q^{41} +11.1974 q^{42} -9.73316 q^{43} +3.18870 q^{44} +1.59680 q^{45} -2.44597 q^{46} +7.63222 q^{47} -2.21370 q^{48} +18.5856 q^{49} -4.29405 q^{50} +0.924884 q^{51} -6.03830 q^{52} -8.25439 q^{53} +2.43399 q^{54} +2.67917 q^{55} -5.05822 q^{56} +3.98417 q^{57} +5.73464 q^{58} +1.08276 q^{59} -1.85997 q^{60} +9.81827 q^{61} -8.99262 q^{62} -9.61308 q^{63} +1.00000 q^{64} -5.07342 q^{65} -7.05883 q^{66} -11.9714 q^{67} -0.417799 q^{68} +5.41465 q^{69} -4.24995 q^{70} +12.6406 q^{71} +1.90049 q^{72} +8.94335 q^{73} -7.64209 q^{74} +9.50576 q^{75} -1.79978 q^{76} -16.1291 q^{77} +13.3670 q^{78} -13.1129 q^{79} +0.840207 q^{80} -11.0896 q^{81} +3.25013 q^{82} -13.8827 q^{83} +11.1974 q^{84} -0.351038 q^{85} -9.73316 q^{86} -12.6948 q^{87} +3.18870 q^{88} -7.03701 q^{89} +1.59680 q^{90} +30.5430 q^{91} -2.44597 q^{92} +19.9070 q^{93} +7.63222 q^{94} -1.51218 q^{95} -2.21370 q^{96} +2.57536 q^{97} +18.5856 q^{98} +6.06008 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) $ 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19} + 39 q^{20} + 51 q^{21} + 36 q^{22} + 47 q^{23} + 8 q^{24} + 147 q^{25} + 63 q^{26} + 17 q^{27} + 19 q^{28} + 60 q^{29} + 17 q^{30} + 63 q^{31} + 96 q^{32} + 55 q^{33} + 56 q^{34} + 45 q^{35} + 130 q^{36} + 46 q^{37} + 17 q^{38} + 22 q^{39} + 39 q^{40} + 101 q^{41} + 51 q^{42} - 3 q^{43} + 36 q^{44} + 106 q^{45} + 47 q^{46} + 99 q^{47} + 8 q^{48} + 175 q^{49} + 147 q^{50} - q^{51} + 63 q^{52} + 75 q^{53} + 17 q^{54} + 80 q^{55} + 19 q^{56} + 35 q^{57} + 60 q^{58} + 129 q^{59} + 17 q^{60} + 75 q^{61} + 63 q^{62} + 20 q^{63} + 96 q^{64} + 55 q^{65} + 55 q^{66} + 2 q^{67} + 56 q^{68} + 57 q^{69} + 45 q^{70} + 87 q^{71} + 130 q^{72} + 120 q^{73} + 46 q^{74} - 15 q^{75} + 17 q^{76} + 95 q^{77} + 22 q^{78} + 21 q^{79} + 39 q^{80} + 180 q^{81} + 101 q^{82} + 69 q^{83} + 51 q^{84} + 59 q^{85} - 3 q^{86} + 63 q^{87} + 36 q^{88} + 144 q^{89} + 106 q^{90} - 5 q^{91} + 47 q^{92} + 59 q^{93} + 99 q^{94} + 23 q^{95} + 8 q^{96} + 99 q^{97} + 175 q^{98} + 42 q^{99}+O(q^{100}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9 + 39 * q^10 + 36 * q^11 + 8 * q^12 + 63 * q^13 + 19 * q^14 + 17 * q^15 + 96 * q^16 + 56 * q^17 + 130 * q^18 + 17 * q^19 + 39 * q^20 + 51 * q^21 + 36 * q^22 + 47 * q^23 + 8 * q^24 + 147 * q^25 + 63 * q^26 + 17 * q^27 + 19 * q^28 + 60 * q^29 + 17 * q^30 + 63 * q^31 + 96 * q^32 + 55 * q^33 + 56 * q^34 + 45 * q^35 + 130 * q^36 + 46 * q^37 + 17 * q^38 + 22 * q^39 + 39 * q^40 + 101 * q^41 + 51 * q^42 - 3 * q^43 + 36 * q^44 + 106 * q^45 + 47 * q^46 + 99 * q^47 + 8 * q^48 + 175 * q^49 + 147 * q^50 - q^51 + 63 * q^52 + 75 * q^53 + 17 * q^54 + 80 * q^55 + 19 * q^56 + 35 * q^57 + 60 * q^58 + 129 * q^59 + 17 * q^60 + 75 * q^61 + 63 * q^62 + 20 * q^63 + 96 * q^64 + 55 * q^65 + 55 * q^66 + 2 * q^67 + 56 * q^68 + 57 * q^69 + 45 * q^70 + 87 * q^71 + 130 * q^72 + 120 * q^73 + 46 * q^74 - 15 * q^75 + 17 * q^76 + 95 * q^77 + 22 * q^78 + 21 * q^79 + 39 * q^80 + 180 * q^81 + 101 * q^82 + 69 * q^83 + 51 * q^84 + 59 * q^85 - 3 * q^86 + 63 * q^87 + 36 * q^88 + 144 * q^89 + 106 * q^90 - 5 * q^91 + 47 * q^92 + 59 * q^93 + 99 * q^94 + 23 * q^95 + 8 * q^96 + 99 * q^97 + 175 * q^98 + 42 * 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
$3$	−2.21370	−1.27808	−0.639041	−	0.769172i	$-0.720669\pi$
$3$	−2.21370	−1.27808	−0.639041	+	0.769172i	$0.720669\pi$
$4$	1.00000	0.500000
$5$	0.840207	0.375752	0.187876	−	0.982193i	$-0.439840\pi$
$5$	0.840207	0.375752	0.187876	+	0.982193i	$0.439840\pi$
$6$	−2.21370	−0.903741
$7$	−5.05822	−1.91183	−0.955913	−	0.293650i	$-0.905130\pi$
$7$	−5.05822	−1.91183	−0.955913	+	0.293650i	$0.905130\pi$
$8$	1.00000	0.353553
$9$	1.90049	0.633496
$10$	0.840207	0.265697
$11$	3.18870	0.961428	0.480714	−	0.876877i	$-0.340377\pi$
$11$	3.18870	0.961428	0.480714	+	0.876877i	$0.340377\pi$
$12$	−2.21370	−0.639041
$13$	−6.03830	−1.67472	−0.837362	−	0.546649i	$-0.815903\pi$
$13$	−6.03830	−1.67472	−0.837362	+	0.546649i	$0.815903\pi$
$14$	−5.05822	−1.35187
$15$	−1.85997	−0.480242
$16$	1.00000	0.250000
$17$	−0.417799	−0.101331	−0.0506656	−	0.998716i	$-0.516134\pi$
$17$	−0.417799	−0.101331	−0.0506656	+	0.998716i	$0.516134\pi$
$18$	1.90049	0.447949
$19$	−1.79978	−0.412897	−0.206448	−	0.978457i	$-0.566191\pi$
$19$	−1.79978	−0.412897	−0.206448	+	0.978457i	$0.566191\pi$
$20$	0.840207	0.187876
$21$	11.1974	2.44347
$22$	3.18870	0.679833
$23$	−2.44597	−0.510019	−0.255010	−	0.966938i	$-0.582079\pi$
$23$	−2.44597	−0.510019	−0.255010	+	0.966938i	$0.582079\pi$
$24$	−2.21370	−0.451871
$25$	−4.29405	−0.858810
$26$	−6.03830	−1.18421
$27$	2.43399	0.468422
$28$	−5.05822	−0.955913
$29$	5.73464	1.06490	0.532448	−	0.846463i	$-0.321272\pi$
$29$	5.73464	1.06490	0.532448	+	0.846463i	$0.321272\pi$
$30$	−1.85997	−0.339582
$31$	−8.99262	−1.61512	−0.807561	−	0.589784i	$-0.799213\pi$
$31$	−8.99262	−1.61512	−0.807561	+	0.589784i	$0.799213\pi$
$32$	1.00000	0.176777
$33$	−7.05883	−1.22879
$34$	−0.417799	−0.0716520
$35$	−4.24995	−0.718372
$36$	1.90049	0.316748
$37$	−7.64209	−1.25635	−0.628176	−	0.778071i	$-0.716198\pi$
$37$	−7.64209	−1.25635	−0.628176	+	0.778071i	$0.716198\pi$
$38$	−1.79978	−0.291962
$39$	13.3670	2.14044
$40$	0.840207	0.132848
$41$	3.25013	0.507585	0.253792	−	0.967259i	$-0.418322\pi$
$41$	3.25013	0.507585	0.253792	+	0.967259i	$0.418322\pi$
$42$	11.1974	1.72780
$43$	−9.73316	−1.48429	−0.742147	−	0.670238i	$-0.766192\pi$
$43$	−9.73316	−1.48429	−0.742147	+	0.670238i	$0.766192\pi$
$44$	3.18870	0.480714
$45$	1.59680	0.238037
$46$	−2.44597	−0.360638
$47$	7.63222	1.11327	0.556637	−	0.830756i	$-0.312091\pi$
$47$	7.63222	1.11327	0.556637	+	0.830756i	$0.312091\pi$
$48$	−2.21370	−0.319521
$49$	18.5856	2.65508
$50$	−4.29405	−0.607271
$51$	0.924884	0.129510
$52$	−6.03830	−0.837362
$53$	−8.25439	−1.13383	−0.566914	−	0.823777i	$-0.691863\pi$
$53$	−8.25439	−1.13383	−0.566914	+	0.823777i	$0.691863\pi$
$54$	2.43399	0.331225
$55$	2.67917	0.361259
$56$	−5.05822	−0.675933
$57$	3.98417	0.527716
$58$	5.73464	0.752996
$59$	1.08276	0.140963	0.0704816	−	0.997513i	$-0.477546\pi$
$59$	1.08276	0.140963	0.0704816	+	0.997513i	$0.477546\pi$
$60$	−1.85997	−0.240121
$61$	9.81827	1.25710	0.628550	−	0.777769i	$-0.283649\pi$
$61$	9.81827	1.25710	0.628550	+	0.777769i	$0.283649\pi$
$62$	−8.99262	−1.14206
$63$	−9.61308	−1.21113
$64$	1.00000	0.125000
$65$	−5.07342	−0.629281
$66$	−7.05883	−0.868882
$67$	−11.9714	−1.46254	−0.731271	−	0.682087i	$-0.761072\pi$
$67$	−11.9714	−1.46254	−0.731271	+	0.682087i	$0.761072\pi$
$68$	−0.417799	−0.0506656
$69$	5.41465	0.651847
$70$	−4.24995	−0.507966
$71$	12.6406	1.50016	0.750079	−	0.661348i	$-0.230015\pi$
$71$	12.6406	1.50016	0.750079	+	0.661348i	$0.230015\pi$
$72$	1.90049	0.223975
$73$	8.94335	1.04674	0.523370	−	0.852105i	$-0.324674\pi$
$73$	8.94335	1.04674	0.523370	+	0.852105i	$0.324674\pi$
$74$	−7.64209	−0.888375
$75$	9.50576	1.09763
$76$	−1.79978	−0.206448
$77$	−16.1291	−1.83808
$78$	13.3670	1.51352
$79$	−13.1129	−1.47532	−0.737658	−	0.675175i	$-0.764068\pi$
$79$	−13.1129	−1.47532	−0.737658	+	0.675175i	$0.764068\pi$
$80$	0.840207	0.0939380
$81$	−11.0896	−1.23218
$82$	3.25013	0.358917
$83$	−13.8827	−1.52382	−0.761912	−	0.647681i	$-0.775739\pi$
$83$	−13.8827	−1.52382	−0.761912	+	0.647681i	$0.775739\pi$
$84$	11.1974	1.22174
$85$	−0.351038	−0.0380754
$86$	−9.73316	−1.04955
$87$	−12.6948	−1.36103
$88$	3.18870	0.339916
$89$	−7.03701	−0.745922	−0.372961	−	0.927847i	$-0.621657\pi$
$89$	−7.03701	−0.745922	−0.372961	+	0.927847i	$0.621657\pi$
$90$	1.59680	0.168318
$91$	30.5430	3.20178
$92$	−2.44597	−0.255010
$93$	19.9070	2.06426
$94$	7.63222	0.787204
$95$	−1.51218	−0.155147
$96$	−2.21370	−0.225935
$97$	2.57536	0.261488	0.130744	−	0.991416i	$-0.458263\pi$
$97$	2.57536	0.261488	0.130744	+	0.991416i	$0.458263\pi$
$98$	18.5856	1.87742
$99$	6.06008	0.609061
$100$	−4.29405	−0.429405
$101$	1.91390	0.190440	0.0952199	−	0.995456i	$-0.469645\pi$
$101$	1.91390	0.190440	0.0952199	+	0.995456i	$0.469645\pi$
$102$	0.924884	0.0915772
$103$	−1.31144	−0.129220	−0.0646102	−	0.997911i	$-0.520580\pi$
$103$	−1.31144	−0.129220	−0.0646102	+	0.997911i	$0.520580\pi$
$104$	−6.03830	−0.592104
$105$	9.40813	0.918139
$106$	−8.25439	−0.801737
$107$	10.9701	1.06052	0.530258	−	0.847836i	$-0.322095\pi$
$107$	10.9701	1.06052	0.530258	+	0.847836i	$0.322095\pi$
$108$	2.43399	0.234211
$109$	16.6145	1.59138	0.795691	−	0.605703i	$-0.207108\pi$
$109$	16.6145	1.59138	0.795691	+	0.605703i	$0.207108\pi$
$110$	2.67917	0.255448
$111$	16.9173	1.60572
$112$	−5.05822	−0.477957
$113$	−16.7474	−1.57546	−0.787731	−	0.616019i	$-0.788744\pi$
$113$	−16.7474	−1.57546	−0.787731	+	0.616019i	$0.788744\pi$
$114$	3.98417	0.373152
$115$	−2.05512	−0.191641
$116$	5.73464	0.532448
$117$	−11.4757	−1.06093
$118$	1.08276	0.0996761
$119$	2.11332	0.193728
$120$	−1.85997	−0.169791
$121$	−0.832211	−0.0756555
$122$	9.81827	0.888904
$123$	−7.19483	−0.648736
$124$	−8.99262	−0.807561
$125$	−7.80893	−0.698452
$126$	−9.61308	−0.856401
$127$	10.0534	0.892098	0.446049	−	0.895008i	$-0.352831\pi$
$127$	10.0534	0.892098	0.446049	+	0.895008i	$0.352831\pi$
$128$	1.00000	0.0883883
$129$	21.5463	1.89705
$130$	−5.07342	−0.444969
$131$	7.36638	0.643604	0.321802	−	0.946807i	$-0.395711\pi$
$131$	7.36638	0.643604	0.321802	+	0.946807i	$0.395711\pi$
$132$	−7.05883	−0.614393
$133$	9.10366	0.789387
$134$	−11.9714	−1.03417
$135$	2.04506	0.176011
$136$	−0.417799	−0.0358260
$137$	14.0488	1.20027	0.600136	−	0.799898i	$-0.295113\pi$
$137$	14.0488	1.20027	0.600136	+	0.799898i	$0.295113\pi$
$138$	5.41465	0.460926
$139$	2.97182	0.252067	0.126033	−	0.992026i	$-0.459775\pi$
$139$	2.97182	0.252067	0.126033	+	0.992026i	$0.459775\pi$
$140$	−4.24995	−0.359186
$141$	−16.8955	−1.42286
$142$	12.6406	1.06077
$143$	−19.2543	−1.61013
$144$	1.90049	0.158374
$145$	4.81829	0.400137
$146$	8.94335	0.740157
$147$	−41.1429	−3.39341
$148$	−7.64209	−0.628176
$149$	1.85732	0.152157	0.0760787	−	0.997102i	$-0.475760\pi$
$149$	1.85732	0.152157	0.0760787	+	0.997102i	$0.475760\pi$
$150$	9.50576	0.776142
$151$	8.22631	0.669448	0.334724	−	0.942316i	$-0.391357\pi$
$151$	8.22631	0.669448	0.334724	+	0.942316i	$0.391357\pi$
$152$	−1.79978	−0.145981
$153$	−0.794022	−0.0641929
$154$	−16.1291	−1.29972
$155$	−7.55566	−0.606885
$156$	13.3670	1.07022
$157$	13.9202	1.11096	0.555478	−	0.831531i	$-0.312535\pi$
$157$	13.9202	1.11096	0.555478	+	0.831531i	$0.312535\pi$
$158$	−13.1129	−1.04321
$159$	18.2728	1.44913
$160$	0.840207	0.0664242
$161$	12.3722	0.975068
$162$	−11.0896	−0.871282
$163$	−18.9127	−1.48136	−0.740679	−	0.671859i	$-0.765496\pi$
$163$	−18.9127	−1.48136	−0.740679	+	0.671859i	$0.765496\pi$
$164$	3.25013	0.253792
$165$	−5.93088	−0.461718
$166$	−13.8827	−1.07751
$167$	−15.7336	−1.21750	−0.608752	−	0.793361i	$-0.708329\pi$
$167$	−15.7336	−1.21750	−0.608752	+	0.793361i	$0.708329\pi$
$168$	11.1974	0.863898
$169$	23.4611	1.80470
$170$	−0.351038	−0.0269234
$171$	−3.42045	−0.261569
$172$	−9.73316	−0.742147
$173$	9.73165	0.739884	0.369942	−	0.929055i	$-0.379378\pi$
$173$	9.73165	0.739884	0.369942	+	0.929055i	$0.379378\pi$
$174$	−12.6948	−0.962391
$175$	21.7202	1.64190
$176$	3.18870	0.240357
$177$	−2.39691	−0.180163
$178$	−7.03701	−0.527446
$179$	−6.87921	−0.514176	−0.257088	−	0.966388i	$-0.582763\pi$
$179$	−6.87921	−0.514176	−0.257088	+	0.966388i	$0.582763\pi$
$180$	1.59680	0.119019
$181$	24.8061	1.84382	0.921910	−	0.387403i	$-0.126628\pi$
$181$	24.8061	1.84382	0.921910	+	0.387403i	$0.126628\pi$
$182$	30.5430	2.26400
$183$	−21.7347	−1.60668
$184$	−2.44597	−0.180319
$185$	−6.42094	−0.472077
$186$	19.9070	1.45965
$187$	−1.33224	−0.0974227
$188$	7.63222	0.556637
$189$	−12.3117	−0.895542
$190$	−1.51218	−0.109705
$191$	−5.67122	−0.410355	−0.205177	−	0.978725i	$-0.565777\pi$
$191$	−5.67122	−0.410355	−0.205177	+	0.978725i	$0.565777\pi$
$192$	−2.21370	−0.159760
$193$	−13.5040	−0.972038	−0.486019	−	0.873948i	$-0.661551\pi$
$193$	−13.5040	−0.972038	−0.486019	+	0.873948i	$0.661551\pi$
$194$	2.57536	0.184900
$195$	11.2311	0.804273
$196$	18.5856	1.32754
$197$	−20.5902	−1.46699	−0.733497	−	0.679693i	$-0.762113\pi$
$197$	−20.5902	−1.46699	−0.733497	+	0.679693i	$0.762113\pi$
$198$	6.06008	0.430671
$199$	−4.96621	−0.352045	−0.176023	−	0.984386i	$-0.556323\pi$
$199$	−4.96621	−0.352045	−0.176023	+	0.984386i	$0.556323\pi$
$200$	−4.29405	−0.303635
$201$	26.5012	1.86925
$202$	1.91390	0.134661
$203$	−29.0071	−2.03590
$204$	0.924884	0.0647548
$205$	2.73078	0.190726
$206$	−1.31144	−0.0913726
$207$	−4.64853	−0.323095
$208$	−6.03830	−0.418681
$209$	−5.73894	−0.396971
$210$	9.40813	0.649223
$211$	8.09539	0.557309	0.278655	−	0.960391i	$-0.410112\pi$
$211$	8.09539	0.557309	0.278655	+	0.960391i	$0.410112\pi$
$212$	−8.25439	−0.566914
$213$	−27.9825	−1.91733
$214$	10.9701	0.749898
$215$	−8.17787	−0.557726
$216$	2.43399	0.165612
$217$	45.4866	3.08783
$218$	16.6145	1.12528
$219$	−19.7979	−1.33782
$220$	2.67917	0.180629
$221$	2.52280	0.169702
$222$	16.9173	1.13542
$223$	14.6173	0.978850	0.489425	−	0.872045i	$-0.337207\pi$
$223$	14.6173	0.978850	0.489425	+	0.872045i	$0.337207\pi$
$224$	−5.05822	−0.337966
$225$	−8.16080	−0.544053
$226$	−16.7474	−1.11402
$227$	20.0049	1.32777	0.663886	−	0.747834i	$-0.268906\pi$
$227$	20.0049	1.32777	0.663886	+	0.747834i	$0.268906\pi$
$228$	3.98417	0.263858
$229$	2.99267	0.197761	0.0988807	−	0.995099i	$-0.468474\pi$
$229$	2.99267	0.197761	0.0988807	+	0.995099i	$0.468474\pi$
$230$	−2.05512	−0.135510
$231$	35.7051	2.34922
$232$	5.73464	0.376498
$233$	16.5556	1.08459	0.542297	−	0.840187i	$-0.317555\pi$
$233$	16.5556	1.08459	0.542297	+	0.840187i	$0.317555\pi$
$234$	−11.4757	−0.750191
$235$	6.41265	0.418315
$236$	1.08276	0.0704816
$237$	29.0281	1.88558
$238$	2.11332	0.136986
$239$	21.1994	1.37128	0.685639	−	0.727942i	$-0.259523\pi$
$239$	21.1994	1.37128	0.685639	+	0.727942i	$0.259523\pi$
$240$	−1.85997	−0.120061
$241$	22.0797	1.42228	0.711139	−	0.703051i	$-0.248180\pi$
$241$	22.0797	1.42228	0.711139	+	0.703051i	$0.248180\pi$
$242$	−0.832211	−0.0534965
$243$	17.2471	1.10640
$244$	9.81827	0.628550
$245$	15.6157	0.997651
$246$	−7.19483	−0.458725
$247$	10.8676	0.691488
$248$	−8.99262	−0.571032
$249$	30.7322	1.94757
$250$	−7.80893	−0.493880
$251$	−14.4188	−0.910105	−0.455052	−	0.890465i	$-0.650379\pi$
$251$	−14.4188	−0.910105	−0.455052	+	0.890465i	$0.650379\pi$
$252$	−9.61308	−0.605567
$253$	−7.79945	−0.490347
$254$	10.0534	0.630809
$255$	0.777094	0.0486635
$256$	1.00000	0.0625000
$257$	−19.8288	−1.23689	−0.618444	−	0.785829i	$-0.712237\pi$
$257$	−19.8288	−1.23689	−0.618444	+	0.785829i	$0.712237\pi$
$258$	21.5463	1.34142
$259$	38.6553	2.40193
$260$	−5.07342	−0.314640
$261$	10.8986	0.674608
$262$	7.36638	0.455097
$263$	26.9904	1.66430	0.832148	−	0.554553i	$-0.187111\pi$
$263$	26.9904	1.66430	0.832148	+	0.554553i	$0.187111\pi$
$264$	−7.05883	−0.434441
$265$	−6.93540	−0.426038
$266$	9.10366	0.558181
$267$	15.5779	0.953350
$268$	−11.9714	−0.731271
$269$	13.7466	0.838143	0.419071	−	0.907953i	$-0.362356\pi$
$269$	13.7466	0.838143	0.419071	+	0.907953i	$0.362356\pi$
$270$	2.04506	0.124458
$271$	−27.4424	−1.66701	−0.833504	−	0.552513i	$-0.813669\pi$
$271$	−27.4424	−1.66701	−0.833504	+	0.552513i	$0.813669\pi$
$272$	−0.417799	−0.0253328
$273$	−67.6133	−4.09214
$274$	14.0488	0.848720
$275$	−13.6924	−0.825685
$276$	5.41465	0.325924
$277$	16.5992	0.997348	0.498674	−	0.866790i	$-0.333820\pi$
$277$	16.5992	0.997348	0.498674	+	0.866790i	$0.333820\pi$
$278$	2.97182	0.178238
$279$	−17.0904	−1.02317
$280$	−4.24995	−0.253983
$281$	2.53013	0.150935	0.0754674	−	0.997148i	$-0.475955\pi$
$281$	2.53013	0.150935	0.0754674	+	0.997148i	$0.475955\pi$
$282$	−16.8955	−1.00611
$283$	4.10948	0.244283	0.122142	−	0.992513i	$-0.461024\pi$
$283$	4.10948	0.244283	0.122142	+	0.992513i	$0.461024\pi$
$284$	12.6406	0.750079
$285$	3.34753	0.198290
$286$	−19.2543	−1.13853
$287$	−16.4399	−0.970414
$288$	1.90049	0.111987
$289$	−16.8254	−0.989732
$290$	4.81829	0.282940
$291$	−5.70108	−0.334203
$292$	8.94335	0.523370
$293$	−12.7995	−0.747752	−0.373876	−	0.927479i	$-0.621971\pi$
$293$	−12.7995	−0.747752	−0.373876	+	0.927479i	$0.621971\pi$
$294$	−41.1429	−2.39950
$295$	0.909742	0.0529672
$296$	−7.64209	−0.444187
$297$	7.76127	0.450355
$298$	1.85732	0.107592
$299$	14.7695	0.854142
$300$	9.50576	0.548816
$301$	49.2324	2.83771
$302$	8.22631	0.473371
$303$	−4.23680	−0.243398
$304$	−1.79978	−0.103224
$305$	8.24938	0.472358
$306$	−0.794022	−0.0453912
$307$	29.1685	1.66474	0.832369	−	0.554223i	$-0.186984\pi$
$307$	29.1685	1.66474	0.832369	+	0.554223i	$0.186984\pi$
$308$	−16.1291	−0.919042
$309$	2.90315	0.165154
$310$	−7.55566	−0.429133
$311$	−25.0496	−1.42043	−0.710217	−	0.703983i	$-0.751403\pi$
$311$	−25.0496	−1.42043	−0.710217	+	0.703983i	$0.751403\pi$
$312$	13.3670	0.756758
$313$	24.2080	1.36832	0.684158	−	0.729334i	$-0.260170\pi$
$313$	24.2080	1.36832	0.684158	+	0.729334i	$0.260170\pi$
$314$	13.9202	0.785564
$315$	−8.07698	−0.455086
$316$	−13.1129	−0.737658
$317$	24.1778	1.35796	0.678981	−	0.734156i	$-0.262422\pi$
$317$	24.1778	1.35796	0.678981	+	0.734156i	$0.262422\pi$
$318$	18.2728	1.02469
$319$	18.2860	1.02382
$320$	0.840207	0.0469690
$321$	−24.2845	−1.35543
$322$	12.3722	0.689478
$323$	0.751945	0.0418393
$324$	−11.0896	−0.616089
$325$	25.9288	1.43827
$326$	−18.9127	−1.04748
$327$	−36.7796	−2.03392
$328$	3.25013	0.179458
$329$	−38.6054	−2.12839
$330$	−5.93088	−0.326484
$331$	−32.5223	−1.78759	−0.893795	−	0.448476i	$-0.851967\pi$
$331$	−32.5223	−1.78759	−0.893795	+	0.448476i	$0.851967\pi$
$332$	−13.8827	−0.761912
$333$	−14.5237	−0.795894
$334$	−15.7336	−0.860905
$335$	−10.0585	−0.549553
$336$	11.1974	0.610868
$337$	−6.09859	−0.332211	−0.166106	−	0.986108i	$-0.553119\pi$
$337$	−6.09859	−0.332211	−0.166106	+	0.986108i	$0.553119\pi$
$338$	23.4611	1.27612
$339$	37.0738	2.01357
$340$	−0.351038	−0.0190377
$341$	−28.6747	−1.55282
$342$	−3.42045	−0.184957
$343$	−58.6022	−3.16422
$344$	−9.73316	−0.524777
$345$	4.54943	0.244933
$346$	9.73165	0.523177
$347$	4.24918	0.228108	0.114054	−	0.993475i	$-0.463616\pi$
$347$	4.24918	0.228108	0.114054	+	0.993475i	$0.463616\pi$
$348$	−12.6948	−0.680513
$349$	20.3187	1.08764	0.543818	−	0.839203i	$-0.316978\pi$
$349$	20.3187	1.08764	0.543818	+	0.839203i	$0.316978\pi$
$350$	21.7202	1.16100
$351$	−14.6972	−0.784478
$352$	3.18870	0.169958
$353$	23.3656	1.24363	0.621813	−	0.783166i	$-0.286396\pi$
$353$	23.3656	1.24363	0.621813	+	0.783166i	$0.286396\pi$
$354$	−2.39691	−0.127394
$355$	10.6207	0.563687
$356$	−7.03701	−0.372961
$357$	−4.67826	−0.247600
$358$	−6.87921	−0.363578
$359$	14.6502	0.773209	0.386604	−	0.922246i	$-0.373648\pi$
$359$	14.6502	0.773209	0.386604	+	0.922246i	$0.373648\pi$
$360$	1.59680	0.0841589
$361$	−15.7608	−0.829516
$362$	24.8061	1.30378
$363$	1.84227	0.0966940
$364$	30.5430	1.60089
$365$	7.51427	0.393315
$366$	−21.7347	−1.13609
$367$	14.9315	0.779417	0.389709	−	0.920938i	$-0.372576\pi$
$367$	14.9315	0.779417	0.389709	+	0.920938i	$0.372576\pi$
$368$	−2.44597	−0.127505
$369$	6.17683	0.321553
$370$	−6.42094	−0.333809
$371$	41.7525	2.16768
$372$	19.9070	1.03213
$373$	25.1456	1.30199	0.650995	−	0.759082i	$-0.274352\pi$
$373$	25.1456	1.30199	0.650995	+	0.759082i	$0.274352\pi$
$374$	−1.33224	−0.0688882
$375$	17.2867	0.892679
$376$	7.63222	0.393602
$377$	−34.6275	−1.78341
$378$	−12.3117	−0.633244
$379$	−16.3426	−0.839461	−0.419730	−	0.907649i	$-0.637875\pi$
$379$	−16.3426	−0.839461	−0.419730	+	0.907649i	$0.637875\pi$
$380$	−1.51218	−0.0775734
$381$	−22.2553	−1.14018
$382$	−5.67122	−0.290165
$383$	2.64820	0.135317	0.0676583	−	0.997709i	$-0.478447\pi$
$383$	2.64820	0.135317	0.0676583	+	0.997709i	$0.478447\pi$
$384$	−2.21370	−0.112968
$385$	−13.5518	−0.690664
$386$	−13.5040	−0.687335
$387$	−18.4978	−0.940294
$388$	2.57536	0.130744
$389$	−11.3715	−0.576556	−0.288278	−	0.957547i	$-0.593083\pi$
$389$	−11.3715	−0.576556	−0.288278	+	0.957547i	$0.593083\pi$
$390$	11.2311	0.568707
$391$	1.02192	0.0516809
$392$	18.5856	0.938712
$393$	−16.3070	−0.822579
$394$	−20.5902	−1.03732
$395$	−11.0175	−0.554353
$396$	6.06008	0.304531
$397$	−5.89784	−0.296004	−0.148002	−	0.988987i	$-0.547284\pi$
$397$	−5.89784	−0.296004	−0.148002	+	0.988987i	$0.547284\pi$
$398$	−4.96621	−0.248934
$399$	−20.1528	−1.00890
$400$	−4.29405	−0.214703
$401$	31.6792	1.58198	0.790992	−	0.611827i	$-0.209565\pi$
$401$	31.6792	1.58198	0.790992	+	0.611827i	$0.209565\pi$
$402$	26.5012	1.32176
$403$	54.3002	2.70488
$404$	1.91390	0.0952199
$405$	−9.31757	−0.462994
$406$	−29.0071	−1.43960
$407$	−24.3683	−1.20789
$408$	0.924884	0.0457886
$409$	−20.0573	−0.991768	−0.495884	−	0.868389i	$-0.665156\pi$
$409$	−20.0573	−0.991768	−0.495884	+	0.868389i	$0.665156\pi$
$410$	2.73078	0.134864
$411$	−31.0999	−1.53405
$412$	−1.31144	−0.0646102
$413$	−5.47683	−0.269497
$414$	−4.64853	−0.228463
$415$	−11.6643	−0.572580
$416$	−6.03830	−0.296052
$417$	−6.57873	−0.322162
$418$	−5.73894	−0.280701
$419$	38.8888	1.89984	0.949922	−	0.312488i	$-0.101162\pi$
$419$	38.8888	1.89984	0.949922	+	0.312488i	$0.101162\pi$
$420$	9.40813	0.459070
$421$	−30.9708	−1.50942	−0.754711	−	0.656057i	$-0.772223\pi$
$421$	−30.9708	−1.50942	−0.754711	+	0.656057i	$0.772223\pi$
$422$	8.09539	0.394077
$423$	14.5050	0.705255
$424$	−8.25439	−0.400869
$425$	1.79405	0.0870243
$426$	−27.9825	−1.35575
$427$	−49.6629	−2.40336
$428$	10.9701	0.530258
$429$	42.6234	2.05788
$430$	−8.17787	−0.394372
$431$	9.69971	0.467219	0.233609	−	0.972331i	$-0.424946\pi$
$431$	9.69971	0.467219	0.233609	+	0.972331i	$0.424946\pi$
$432$	2.43399	0.117106
$433$	−31.7846	−1.52747	−0.763736	−	0.645529i	$-0.776637\pi$
$433$	−31.7846	−1.52747	−0.763736	+	0.645529i	$0.776637\pi$
$434$	45.4866	2.18343
$435$	−10.6663	−0.511408
$436$	16.6145	0.795691
$437$	4.40219	0.210585
$438$	−19.7979	−0.945982
$439$	−8.26023	−0.394239	−0.197120	−	0.980379i	$-0.563159\pi$
$439$	−8.26023	−0.394239	−0.197120	+	0.980379i	$0.563159\pi$
$440$	2.67917	0.127724
$441$	35.3216	1.68198
$442$	2.52280	0.119997
$443$	4.47083	0.212416	0.106208	−	0.994344i	$-0.466129\pi$
$443$	4.47083	0.212416	0.106208	+	0.994344i	$0.466129\pi$
$444$	16.9173	0.802861
$445$	−5.91254	−0.280282
$446$	14.6173	0.692151
$447$	−4.11156	−0.194470
$448$	−5.05822	−0.238978
$449$	−11.7219	−0.553191	−0.276595	−	0.960986i	$-0.589206\pi$
$449$	−11.7219	−0.553191	−0.276595	+	0.960986i	$0.589206\pi$
$450$	−8.16080	−0.384704
$451$	10.3637	0.488006
$452$	−16.7474	−0.787731
$453$	−18.2106	−0.855610
$454$	20.0049	0.938877
$455$	25.6625	1.20308
$456$	3.98417	0.186576
$457$	−8.61410	−0.402951	−0.201475	−	0.979494i	$-0.564574\pi$
$457$	−8.61410	−0.402951	−0.201475	+	0.979494i	$0.564574\pi$
$458$	2.99267	0.139838
$459$	−1.01692	−0.0474658
$460$	−2.05512	−0.0958204
$461$	2.92669	0.136309	0.0681547	−	0.997675i	$-0.478289\pi$
$461$	2.92669	0.136309	0.0681547	+	0.997675i	$0.478289\pi$
$462$	35.7051	1.66115
$463$	25.4159	1.18118	0.590588	−	0.806974i	$-0.298896\pi$
$463$	25.4159	1.18118	0.590588	+	0.806974i	$0.298896\pi$
$464$	5.73464	0.266224
$465$	16.7260	0.775650
$466$	16.5556	0.766924
$467$	1.64266	0.0760134	0.0380067	−	0.999277i	$-0.487899\pi$
$467$	1.64266	0.0760134	0.0380067	+	0.999277i	$0.487899\pi$
$468$	−11.4757	−0.530465
$469$	60.5540	2.79612
$470$	6.41265	0.295793
$471$	−30.8153	−1.41989
$472$	1.08276	0.0498380
$473$	−31.0361	−1.42704
$474$	29.0281	1.33330
$475$	7.72833	0.354600
$476$	2.11332	0.0968638
$477$	−15.6874	−0.718275
$478$	21.1994	0.969639
$479$	−10.1994	−0.466020	−0.233010	−	0.972474i	$-0.574858\pi$
$479$	−10.1994	−0.466020	−0.233010	+	0.972474i	$0.574858\pi$
$480$	−1.85997	−0.0848956
$481$	46.1453	2.10404
$482$	22.0797	1.00570
$483$	−27.3885	−1.24622
$484$	−0.832211	−0.0378278
$485$	2.16383	0.0982546
$486$	17.2471	0.782346
$487$	7.81285	0.354034	0.177017	−	0.984208i	$-0.443355\pi$
$487$	7.81285	0.354034	0.177017	+	0.984208i	$0.443355\pi$
$488$	9.81827	0.444452
$489$	41.8672	1.89330
$490$	15.6157	0.705446
$491$	14.6615	0.661666	0.330833	−	0.943689i	$-0.392670\pi$
$491$	14.6615	0.661666	0.330833	+	0.943689i	$0.392670\pi$
$492$	−7.19483	−0.324368
$493$	−2.39593	−0.107907
$494$	10.8676	0.488956
$495$	5.09172	0.228856
$496$	−8.99262	−0.403781
$497$	−63.9387	−2.86804
$498$	30.7322	1.37714
$499$	−32.4523	−1.45276	−0.726381	−	0.687292i	$-0.758799\pi$
$499$	−32.4523	−1.45276	−0.726381	+	0.687292i	$0.758799\pi$
$500$	−7.80893	−0.349226
$501$	34.8296	1.55607
$502$	−14.4188	−0.643541
$503$	−14.5406	−0.648335	−0.324167	−	0.946000i	$-0.605084\pi$
$503$	−14.5406	−0.648335	−0.324167	+	0.946000i	$0.605084\pi$
$504$	−9.61308	−0.428201
$505$	1.60807	0.0715581
$506$	−7.79945	−0.346728
$507$	−51.9359	−2.30656
$508$	10.0534	0.446049
$509$	31.9801	1.41749	0.708746	−	0.705464i	$-0.249261\pi$
$509$	31.9801	1.41749	0.708746	+	0.705464i	$0.249261\pi$
$510$	0.777094	0.0344103
$511$	−45.2374	−2.00119
$512$	1.00000	0.0441942
$513$	−4.38064	−0.193410
$514$	−19.8288	−0.874612
$515$	−1.10188	−0.0485548
$516$	21.5463	0.948525
$517$	24.3369	1.07033
$518$	38.6553	1.69842
$519$	−21.5430	−0.945633
$520$	−5.07342	−0.222484
$521$	−0.697126	−0.0305416	−0.0152708	−	0.999883i	$-0.504861\pi$
$521$	−0.697126	−0.0305416	−0.0152708	+	0.999883i	$0.504861\pi$
$522$	10.8986	0.477020
$523$	−2.98629	−0.130581	−0.0652907	−	0.997866i	$-0.520797\pi$
$523$	−2.98629	−0.130581	−0.0652907	+	0.997866i	$0.520797\pi$
$524$	7.36638	0.321802
$525$	−48.0822	−2.09848
$526$	26.9904	1.17684
$527$	3.75711	0.163662
$528$	−7.05883	−0.307196
$529$	−17.0172	−0.739880
$530$	−6.93540	−0.301254
$531$	2.05777	0.0892997
$532$	9.10366	0.394694
$533$	−19.6253	−0.850064
$534$	15.5779	0.674120
$535$	9.21712	0.398491
$536$	−11.9714	−0.517086
$537$	15.2285	0.657160
$538$	13.7466	0.592656
$539$	59.2637	2.55267
$540$	2.04506	0.0880053
$541$	−10.9724	−0.471740	−0.235870	−	0.971785i	$-0.575794\pi$
$541$	−10.9724	−0.471740	−0.235870	+	0.971785i	$0.575794\pi$
$542$	−27.4424	−1.17875
$543$	−54.9133	−2.35656
$544$	−0.417799	−0.0179130
$545$	13.9596	0.597964
$546$	−67.6133	−2.89358
$547$	−9.26455	−0.396124	−0.198062	−	0.980190i	$-0.563465\pi$
$547$	−9.26455	−0.396124	−0.198062	+	0.980190i	$0.563465\pi$
$548$	14.0488	0.600136
$549$	18.6595	0.796368
$550$	−13.6924	−0.583847
$551$	−10.3211	−0.439692
$552$	5.41465	0.230463
$553$	66.3278	2.82055
$554$	16.5992	0.705232
$555$	14.2141	0.603353
$556$	2.97182	0.126033
$557$	36.4889	1.54609	0.773043	−	0.634354i	$-0.218734\pi$
$557$	36.4889	1.54609	0.773043	+	0.634354i	$0.218734\pi$
$558$	−17.0904	−0.723493
$559$	58.7718	2.48578
$560$	−4.24995	−0.179593
$561$	2.94918	0.124514
$562$	2.53013	0.106727
$563$	−22.4983	−0.948189	−0.474095	−	0.880474i	$-0.657225\pi$
$563$	−22.4983	−0.948189	−0.474095	+	0.880474i	$0.657225\pi$
$564$	−16.8955	−0.711428
$565$	−14.0713	−0.591983
$566$	4.10948	0.172734
$567$	56.0936	2.35571
$568$	12.6406	0.530386
$569$	8.29956	0.347936	0.173968	−	0.984751i	$-0.444341\pi$
$569$	8.29956	0.347936	0.173968	+	0.984751i	$0.444341\pi$
$570$	3.34753	0.140213
$571$	−8.80245	−0.368371	−0.184186	−	0.982891i	$-0.558965\pi$
$571$	−8.80245	−0.368371	−0.184186	+	0.982891i	$0.558965\pi$
$572$	−19.2543	−0.805063
$573$	12.5544	0.524467
$574$	−16.4399	−0.686186
$575$	10.5031	0.438010
$576$	1.90049	0.0791870
$577$	26.9088	1.12023	0.560114	−	0.828415i	$-0.310757\pi$
$577$	26.9088	1.12023	0.560114	+	0.828415i	$0.310757\pi$
$578$	−16.8254	−0.699846
$579$	29.8938	1.24235
$580$	4.81829	0.200068
$581$	70.2217	2.91329
$582$	−5.70108	−0.236317
$583$	−26.3208	−1.09009
$584$	8.94335	0.370079
$585$	−9.64198	−0.398647
$586$	−12.7995	−0.528740
$587$	26.9493	1.11232	0.556159	−	0.831076i	$-0.312274\pi$
$587$	26.9493	1.11232	0.556159	+	0.831076i	$0.312274\pi$
$588$	−41.1429	−1.69671
$589$	16.1847	0.666879
$590$	0.909742	0.0374535
$591$	45.5807	1.87494
$592$	−7.64209	−0.314088
$593$	44.7845	1.83908	0.919539	−	0.392999i	$-0.128562\pi$
$593$	44.7845	1.83908	0.919539	+	0.392999i	$0.128562\pi$
$594$	7.76127	0.318449
$595$	1.77562	0.0727935
$596$	1.85732	0.0760787
$597$	10.9937	0.449943
$598$	14.7695	0.603969
$599$	−47.8584	−1.95544	−0.977722	−	0.209906i	$-0.932684\pi$
$599$	−47.8584	−1.95544	−0.977722	+	0.209906i	$0.932684\pi$
$600$	9.50576	0.388071
$601$	39.1322	1.59624	0.798118	−	0.602501i	$-0.205829\pi$
$601$	39.1322	1.59624	0.798118	+	0.602501i	$0.205829\pi$
$602$	49.2324	2.00656
$603$	−22.7515	−0.926514
$604$	8.22631	0.334724
$605$	−0.699229	−0.0284277
$606$	−4.23680	−0.172108
$607$	34.8009	1.41253	0.706263	−	0.707949i	$-0.250379\pi$
$607$	34.8009	1.41253	0.706263	+	0.707949i	$0.250379\pi$
$608$	−1.79978	−0.0729905
$609$	64.2131	2.60205
$610$	8.24938	0.334007
$611$	−46.0857	−1.86443
$612$	−0.794022	−0.0320965
$613$	13.8781	0.560530	0.280265	−	0.959923i	$-0.409578\pi$
$613$	13.8781	0.560530	0.280265	+	0.959923i	$0.409578\pi$
$614$	29.1685	1.17715
$615$	−6.04514	−0.243764
$616$	−16.1291	−0.649861
$617$	−33.0247	−1.32952	−0.664762	−	0.747055i	$-0.731467\pi$
$617$	−33.0247	−1.32952	−0.664762	+	0.747055i	$0.731467\pi$
$618$	2.90315	0.116782
$619$	3.22376	0.129574	0.0647869	−	0.997899i	$-0.479363\pi$
$619$	3.22376	0.129574	0.0647869	+	0.997899i	$0.479363\pi$
$620$	−7.55566	−0.303443
$621$	−5.95347	−0.238905
$622$	−25.0496	−1.00440
$623$	35.5947	1.42607
$624$	13.3670	0.535109
$625$	14.9091	0.596366
$626$	24.2080	0.967546
$627$	12.7043	0.507362
$628$	13.9202	0.555478
$629$	3.19286	0.127308
$630$	−8.07698	−0.321794
$631$	−41.0400	−1.63378	−0.816888	−	0.576796i	$-0.804303\pi$
$631$	−41.0400	−1.63378	−0.816888	+	0.576796i	$0.804303\pi$
$632$	−13.1129	−0.521603
$633$	−17.9208	−0.712288
$634$	24.1778	0.960225
$635$	8.44697	0.335208
$636$	18.2728	0.724563
$637$	−112.225	−4.44652
$638$	18.2860	0.723951
$639$	24.0232	0.950344
$640$	0.840207	0.0332121
$641$	4.97886	0.196653	0.0983266	−	0.995154i	$-0.468651\pi$
$641$	4.97886	0.196653	0.0983266	+	0.995154i	$0.468651\pi$
$642$	−24.2845	−0.958432
$643$	25.0375	0.987382	0.493691	−	0.869637i	$-0.335647\pi$
$643$	25.0375	0.987382	0.493691	+	0.869637i	$0.335647\pi$
$644$	12.3722	0.487534
$645$	18.1034	0.712820
$646$	0.751945	0.0295849
$647$	−16.3486	−0.642729	−0.321364	−	0.946956i	$-0.604141\pi$
$647$	−16.3486	−0.642729	−0.321364	+	0.946956i	$0.604141\pi$
$648$	−11.0896	−0.435641
$649$	3.45259	0.135526
$650$	25.9288	1.01701
$651$	−100.694	−3.94651
$652$	−18.9127	−0.740679
$653$	26.9175	1.05336	0.526681	−	0.850063i	$-0.323436\pi$
$653$	26.9175	1.05336	0.526681	+	0.850063i	$0.323436\pi$
$654$	−36.7796	−1.43820
$655$	6.18929	0.241835
$656$	3.25013	0.126896
$657$	16.9967	0.663106
$658$	−38.6054	−1.50500
$659$	−43.0814	−1.67821	−0.839106	−	0.543967i	$-0.816921\pi$
$659$	−43.0814	−1.67821	−0.839106	+	0.543967i	$0.816921\pi$
$660$	−5.93088	−0.230859
$661$	14.8722	0.578460	0.289230	−	0.957260i	$-0.406601\pi$
$661$	14.8722	0.578460	0.289230	+	0.957260i	$0.406601\pi$
$662$	−32.5223	−1.26402
$663$	−5.58473	−0.216893
$664$	−13.8827	−0.538753
$665$	7.64895	0.296614
$666$	−14.5237	−0.562782
$667$	−14.0267	−0.543118
$668$	−15.7336	−0.608752
$669$	−32.3585	−1.25105
$670$	−10.0585	−0.388592
$671$	31.3075	1.20861
$672$	11.1974	0.431949
$673$	22.6263	0.872181	0.436091	−	0.899903i	$-0.356363\pi$
$673$	22.6263	0.872181	0.436091	+	0.899903i	$0.356363\pi$
$674$	−6.09859	−0.234909
$675$	−10.4517	−0.402286
$676$	23.4611	0.902350
$677$	33.1072	1.27241	0.636207	−	0.771519i	$-0.280502\pi$
$677$	33.1072	1.27241	0.636207	+	0.771519i	$0.280502\pi$
$678$	37.0738	1.42381
$679$	−13.0267	−0.499920
$680$	−0.351038	−0.0134617
$681$	−44.2849	−1.69700
$682$	−28.6747	−1.09801
$683$	−11.3648	−0.434863	−0.217431	−	0.976076i	$-0.569768\pi$
$683$	−11.3648	−0.434863	−0.217431	+	0.976076i	$0.569768\pi$
$684$	−3.42045	−0.130784
$685$	11.8039	0.451005
$686$	−58.6022	−2.23744
$687$	−6.62489	−0.252755
$688$	−9.73316	−0.371073
$689$	49.8425	1.89885
$690$	4.54943	0.173194
$691$	43.4735	1.65381	0.826904	−	0.562343i	$-0.190100\pi$
$691$	43.4735	1.65381	0.826904	+	0.562343i	$0.190100\pi$
$692$	9.73165	0.369942
$693$	−30.6532	−1.16442
$694$	4.24918	0.161297
$695$	2.49694	0.0947145
$696$	−12.6948	−0.481195
$697$	−1.35790	−0.0514342
$698$	20.3187	0.769075
$699$	−36.6492	−1.38620
$700$	21.7202	0.820948
$701$	−16.7220	−0.631579	−0.315790	−	0.948829i	$-0.602269\pi$
$701$	−16.7220	−0.631579	−0.315790	+	0.948829i	$0.602269\pi$
$702$	−14.6972	−0.554710
$703$	13.7540	0.518744
$704$	3.18870	0.120179
$705$	−14.1957	−0.534641
$706$	23.3656	0.879377
$707$	−9.68090	−0.364088
$708$	−2.39691	−0.0900814
$709$	−8.69804	−0.326662	−0.163331	−	0.986571i	$-0.552224\pi$
$709$	−8.69804	−0.326662	−0.163331	+	0.986571i	$0.552224\pi$
$710$	10.6207	0.398587
$711$	−24.9209	−0.934607
$712$	−7.03701	−0.263723
$713$	21.9957	0.823744
$714$	−4.67826	−0.175080
$715$	−16.1776	−0.605008
$716$	−6.87921	−0.257088
$717$	−46.9293	−1.75261
$718$	14.6502	0.546741
$719$	−24.5273	−0.914714	−0.457357	−	0.889283i	$-0.651204\pi$
$719$	−24.5273	−0.914714	−0.457357	+	0.889283i	$0.651204\pi$
$720$	1.59680	0.0595093
$721$	6.63357	0.247047
$722$	−15.7608	−0.586557
$723$	−48.8779	−1.81779
$724$	24.8061	0.921910
$725$	−24.6249	−0.914544
$726$	1.84227	0.0683730
$727$	−27.0137	−1.00188	−0.500941	−	0.865482i	$-0.667013\pi$
$727$	−27.0137	−1.00188	−0.500941	+	0.865482i	$0.667013\pi$
$728$	30.5430	1.13200
$729$	−4.91124	−0.181898
$730$	7.51427	0.278116
$731$	4.06651	0.150405
$732$	−21.7347	−0.803339
$733$	30.3918	1.12255	0.561274	−	0.827630i	$-0.310311\pi$
$733$	30.3918	1.12255	0.561274	+	0.827630i	$0.310311\pi$
$734$	14.9315	0.551131
$735$	−34.5686	−1.27508
$736$	−2.44597	−0.0901595
$737$	−38.1732	−1.40613
$738$	6.17683	0.227372
$739$	5.02021	0.184671	0.0923356	−	0.995728i	$-0.470567\pi$
$739$	5.02021	0.184671	0.0923356	+	0.995728i	$0.470567\pi$
$740$	−6.42094	−0.236038
$741$	−24.0576	−0.883779
$742$	41.7525	1.53278
$743$	−4.03794	−0.148138	−0.0740689	−	0.997253i	$-0.523598\pi$
$743$	−4.03794	−0.148138	−0.0740689	+	0.997253i	$0.523598\pi$
$744$	19.9070	0.729826
$745$	1.56053	0.0571735
$746$	25.1456	0.920646
$747$	−26.3839	−0.965336
$748$	−1.33224	−0.0487113
$749$	−55.4889	−2.02752
$750$	17.2867	0.631219
$751$	−9.49319	−0.346412	−0.173206	−	0.984886i	$-0.555413\pi$
$751$	−9.49319	−0.346412	−0.173206	+	0.984886i	$0.555413\pi$
$752$	7.63222	0.278319
$753$	31.9189	1.16319
$754$	−34.6275	−1.26106
$755$	6.91180	0.251546
$756$	−12.3117	−0.447771
$757$	40.3655	1.46711	0.733554	−	0.679631i	$-0.237860\pi$
$757$	40.3655	1.46711	0.733554	+	0.679631i	$0.237860\pi$
$758$	−16.3426	−0.593589
$759$	17.2657	0.626704
$760$	−1.51218	−0.0548527
$761$	1.48411	0.0537989	0.0268994	−	0.999638i	$-0.491437\pi$
$761$	1.48411	0.0537989	0.0268994	+	0.999638i	$0.491437\pi$
$762$	−22.2553	−0.806226
$763$	−84.0398	−3.04244
$764$	−5.67122	−0.205177
$765$	−0.667143	−0.0241206
$766$	2.64820	0.0956832
$767$	−6.53803	−0.236074
$768$	−2.21370	−0.0798802
$769$	−41.5256	−1.49745	−0.748726	−	0.662880i	$-0.769334\pi$
$769$	−41.5256	−1.49745	−0.748726	+	0.662880i	$0.769334\pi$
$770$	−13.5518	−0.488373
$771$	43.8952	1.58085
$772$	−13.5040	−0.486019
$773$	−46.0877	−1.65766	−0.828830	−	0.559500i	$-0.810993\pi$
$773$	−46.0877	−1.65766	−0.828830	+	0.559500i	$0.810993\pi$
$774$	−18.4978	−0.664888
$775$	38.6148	1.38708
$776$	2.57536	0.0924500
$777$	−85.5715	−3.06986
$778$	−11.3715	−0.407687
$779$	−5.84950	−0.209580
$780$	11.2311	0.402136
$781$	40.3069	1.44229
$782$	1.02192	0.0365439
$783$	13.9581	0.498821
$784$	18.5856	0.663770
$785$	11.6959	0.417444
$786$	−16.3070	−0.581651
$787$	−0.125634	−0.00447838	−0.00223919	−	0.999997i	$-0.500713\pi$
$787$	−0.125634	−0.00447838	−0.00223919	+	0.999997i	$0.500713\pi$
$788$	−20.5902	−0.733497
$789$	−59.7487	−2.12711
$790$	−11.0175	−0.391987
$791$	84.7119	3.01201
$792$	6.06008	0.215336
$793$	−59.2857	−2.10530
$794$	−5.89784	−0.209307
$795$	15.3529	0.544512
$796$	−4.96621	−0.176023
$797$	−16.3316	−0.578496	−0.289248	−	0.957254i	$-0.593405\pi$
$797$	−16.3316	−0.578496	−0.289248	+	0.957254i	$0.593405\pi$
$798$	−20.1528	−0.713402
$799$	−3.18874	−0.112809
$800$	−4.29405	−0.151818
$801$	−13.3738	−0.472538
$802$	31.6792	1.11863
$803$	28.5176	1.00637
$804$	26.5012	0.934625
$805$	10.3952	0.366384
$806$	54.3002	1.91264
$807$	−30.4308	−1.07122
$808$	1.91390	0.0673306
$809$	−21.8812	−0.769302	−0.384651	−	0.923062i	$-0.625678\pi$
$809$	−21.8812	−0.769302	−0.384651	+	0.923062i	$0.625678\pi$
$810$	−9.31757	−0.327386
$811$	−35.6147	−1.25060	−0.625301	−	0.780384i	$-0.715024\pi$
$811$	−35.6147	−1.25060	−0.625301	+	0.780384i	$0.715024\pi$
$812$	−29.0071	−1.01795
$813$	60.7494	2.13057
$814$	−24.3683	−0.854109
$815$	−15.8906	−0.556623
$816$	0.924884	0.0323774
$817$	17.5175	0.612860
$818$	−20.0573	−0.701286
$819$	58.0467	2.02832
$820$	2.73078	0.0953630
$821$	−49.5127	−1.72801	−0.864003	−	0.503486i	$-0.832051\pi$
$821$	−49.5127	−1.72801	−0.864003	+	0.503486i	$0.832051\pi$
$822$	−31.0999	−1.08474
$823$	−14.1793	−0.494258	−0.247129	−	0.968983i	$-0.579487\pi$
$823$	−14.1793	−0.494258	−0.247129	+	0.968983i	$0.579487\pi$
$824$	−1.31144	−0.0456863
$825$	30.3110	1.05529
$826$	−5.47683	−0.190563
$827$	6.71445	0.233484	0.116742	−	0.993162i	$-0.462755\pi$
$827$	6.71445	0.233484	0.116742	+	0.993162i	$0.462755\pi$
$828$	−4.64853	−0.161548
$829$	15.8383	0.550086	0.275043	−	0.961432i	$-0.411308\pi$
$829$	15.8383	0.550086	0.275043	+	0.961432i	$0.411308\pi$
$830$	−11.6643	−0.404875
$831$	−36.7457	−1.27469
$832$	−6.03830	−0.209340
$833$	−7.76503	−0.269042
$834$	−6.57873	−0.227803
$835$	−13.2195	−0.457479
$836$	−5.73894	−0.198485
$837$	−21.8880	−0.756559
$838$	38.8888	1.34339
$839$	11.9524	0.412642	0.206321	−	0.978484i	$-0.433851\pi$
$839$	11.9524	0.412642	0.206321	+	0.978484i	$0.433851\pi$
$840$	9.40813	0.324611
$841$	3.88613	0.134005
$842$	−30.9708	−1.06732
$843$	−5.60096	−0.192907
$844$	8.09539	0.278655
$845$	19.7122	0.678119
$846$	14.5050	0.498691
$847$	4.20950	0.144640
$848$	−8.25439	−0.283457
$849$	−9.09717	−0.312214
$850$	1.79405	0.0615355
$851$	18.6923	0.640764
$852$	−27.9825	−0.958663
$853$	16.1453	0.552804	0.276402	−	0.961042i	$-0.410858\pi$
$853$	16.1453	0.552804	0.276402	+	0.961042i	$0.410858\pi$
$854$	−49.6629	−1.69943
$855$	−2.87389	−0.0982849
$856$	10.9701	0.374949
$857$	3.75657	0.128322	0.0641610	−	0.997940i	$-0.479563\pi$
$857$	3.75657	0.128322	0.0641610	+	0.997940i	$0.479563\pi$
$858$	42.6234	1.45514
$859$	5.77210	0.196941	0.0984707	−	0.995140i	$-0.468605\pi$
$859$	5.77210	0.196941	0.0984707	+	0.995140i	$0.468605\pi$
$860$	−8.17787	−0.278863
$861$	36.3930	1.24027
$862$	9.69971	0.330374
$863$	−2.08180	−0.0708653	−0.0354327	−	0.999372i	$-0.511281\pi$
$863$	−2.08180	−0.0708653	−0.0354327	+	0.999372i	$0.511281\pi$
$864$	2.43399	0.0828062
$865$	8.17660	0.278013
$866$	−31.7846	−1.08009
$867$	37.2466	1.26496
$868$	45.4866	1.54392
$869$	−41.8130	−1.41841
$870$	−10.6663	−0.361620
$871$	72.2870	2.44935
$872$	16.6145	0.562638
$873$	4.89444	0.165652
$874$	4.40219	0.148906
$875$	39.4992	1.33532
$876$	−19.7979	−0.668911
$877$	45.6599	1.54183	0.770913	−	0.636941i	$-0.219800\pi$
$877$	45.6599	1.54183	0.770913	+	0.636941i	$0.219800\pi$
$878$	−8.26023	−0.278769
$879$	28.3342	0.955689
$880$	2.67917	0.0903146
$881$	−36.8067	−1.24005	−0.620025	−	0.784582i	$-0.712878\pi$
$881$	−36.8067	−1.24005	−0.620025	+	0.784582i	$0.712878\pi$
$882$	35.3216	1.18934
$883$	41.1050	1.38329	0.691647	−	0.722236i	$-0.256885\pi$
$883$	41.1050	1.38329	0.691647	+	0.722236i	$0.256885\pi$
$884$	2.52280	0.0848509
$885$	−2.01390	−0.0676965
$886$	4.47083	0.150201
$887$	23.2505	0.780674	0.390337	−	0.920672i	$-0.372359\pi$
$887$	23.2505	0.780674	0.390337	+	0.920672i	$0.372359\pi$
$888$	16.9173	0.567708
$889$	−50.8525	−1.70554
$890$	−5.91254	−0.198189
$891$	−35.3614	−1.18465
$892$	14.6173	0.489425
$893$	−13.7363	−0.459667
$894$	−4.11156	−0.137511
$895$	−5.77996	−0.193203
$896$	−5.05822	−0.168983
$897$	−32.6953	−1.09166
$898$	−11.7219	−0.391165
$899$	−51.5695	−1.71994
$900$	−8.16080	−0.272027
$901$	3.44868	0.114892
$902$	10.3637	0.345073
$903$	−108.986	−3.62683
$904$	−16.7474	−0.557010
$905$	20.8422	0.692819
$906$	−18.2106	−0.605007
$907$	−28.9835	−0.962383	−0.481191	−	0.876616i	$-0.659796\pi$
$907$	−28.9835	−0.962383	−0.481191	+	0.876616i	$0.659796\pi$
$908$	20.0049	0.663886
$909$	3.63734	0.120643
$910$	25.6625	0.850703
$911$	6.28903	0.208365	0.104182	−	0.994558i	$-0.466777\pi$
$911$	6.28903	0.208365	0.104182	+	0.994558i	$0.466777\pi$
$912$	3.98417	0.131929
$913$	−44.2677	−1.46505
$914$	−8.61410	−0.284929
$915$	−18.2617	−0.603713
$916$	2.99267	0.0988807
$917$	−37.2608	−1.23046
$918$	−1.01692	−0.0335634
$919$	−2.93893	−0.0969463	−0.0484732	−	0.998824i	$-0.515436\pi$
$919$	−2.93893	−0.0969463	−0.0484732	+	0.998824i	$0.515436\pi$
$920$	−2.05512	−0.0677552
$921$	−64.5706	−2.12767
$922$	2.92669	0.0963854
$923$	−76.3275	−2.51235
$924$	35.7051	1.17461
$925$	32.8155	1.07897
$926$	25.4159	0.835217
$927$	−2.49238	−0.0818606
$928$	5.73464	0.188249
$929$	29.3009	0.961331	0.480666	−	0.876904i	$-0.340395\pi$
$929$	29.3009	0.961331	0.480666	+	0.876904i	$0.340395\pi$
$930$	16.7260	0.548467
$931$	−33.4498	−1.09627
$932$	16.5556	0.542297
$933$	55.4525	1.81543
$934$	1.64266	0.0537496
$935$	−1.11935	−0.0366068
$936$	−11.4757	−0.375096
$937$	40.2840	1.31602	0.658011	−	0.753008i	$-0.271398\pi$
$937$	40.2840	1.31602	0.658011	+	0.753008i	$0.271398\pi$
$938$	60.5540	1.97716
$939$	−53.5893	−1.74882
$940$	6.41265	0.209157
$941$	−60.8422	−1.98340	−0.991700	−	0.128572i	$-0.958961\pi$
$941$	−60.8422	−1.98340	−0.991700	+	0.128572i	$0.958961\pi$
$942$	−30.8153	−1.00402
$943$	−7.94971	−0.258878
$944$	1.08276	0.0352408
$945$	−10.3444	−0.336502
$946$	−31.0361	−1.00907
$947$	−19.5833	−0.636373	−0.318186	−	0.948028i	$-0.603074\pi$
$947$	−19.5833	−0.636373	−0.318186	+	0.948028i	$0.603074\pi$
$948$	29.0281	0.942788
$949$	−54.0027	−1.75300
$950$	7.72833	0.250740
$951$	−53.5226	−1.73559
$952$	2.11332	0.0684931
$953$	5.70817	0.184906	0.0924528	−	0.995717i	$-0.470529\pi$
$953$	5.70817	0.184906	0.0924528	+	0.995717i	$0.470529\pi$
$954$	−15.6874	−0.507897
$955$	−4.76499	−0.154192
$956$	21.1994	0.685639
$957$	−40.4799	−1.30853
$958$	−10.1994	−0.329526
$959$	−71.0620	−2.29471
$960$	−1.85997	−0.0600303
$961$	49.8672	1.60862
$962$	46.1453	1.48778
$963$	20.8485	0.671833
$964$	22.0797	0.711139
$965$	−11.3461	−0.365245
$966$	−27.3885	−0.881209
$967$	12.9213	0.415520	0.207760	−	0.978180i	$-0.433383\pi$
$967$	12.9213	0.415520	0.207760	+	0.978180i	$0.433383\pi$
$968$	−0.832211	−0.0267483
$969$	−1.66458	−0.0534741
$970$	2.16383	0.0694765
$971$	−43.7070	−1.40262	−0.701312	−	0.712855i	$-0.747402\pi$
$971$	−43.7070	−1.40262	−0.701312	+	0.712855i	$0.747402\pi$
$972$	17.2471	0.553202
$973$	−15.0321	−0.481907
$974$	7.81285	0.250340
$975$	−57.3987	−1.83823
$976$	9.81827	0.314275
$977$	38.0070	1.21595	0.607976	−	0.793955i	$-0.291982\pi$
$977$	38.0070	1.21595	0.607976	+	0.793955i	$0.291982\pi$
$978$	41.8672	1.33876
$979$	−22.4389	−0.717150
$980$	15.6157	0.498826
$981$	31.5757	1.00813
$982$	14.6615	0.467868
$983$	0.416162	0.0132735	0.00663676	−	0.999978i	$-0.497887\pi$
$983$	0.416162	0.0132735	0.00663676	+	0.999978i	$0.497887\pi$
$984$	−7.19483	−0.229363
$985$	−17.3001	−0.551226
$986$	−2.39593	−0.0763019
$987$	85.4611	2.72026
$988$	10.8676	0.345744
$989$	23.8070	0.757018
$990$	5.09172	0.161826
$991$	15.2850	0.485545	0.242773	−	0.970083i	$-0.421943\pi$
$991$	15.2850	0.485545	0.242773	+	0.970083i	$0.421943\pi$
$992$	−8.99262	−0.285516
$993$	71.9948	2.28469
$994$	−63.9387	−2.02801
$995$	−4.17265	−0.132282
$996$	30.7322	0.973786
$997$	−24.9688	−0.790769	−0.395384	−	0.918516i	$-0.629389\pi$
$997$	−24.9688	−0.790769	−0.395384	+	0.918516i	$0.629389\pi$
$998$	−32.4523	−1.02726
$999$	−18.6008	−0.588503

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.d.1.20	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.d.1.20	✓	96	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.21370 q^{3} +1.00000 q^{4} +0.840207 q^{5} -2.21370 q^{6} -5.05822 q^{7} +1.00000 q^{8} +1.90049 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.21370 q^{3} +1.00000 q^{4} +0.840207 q^{5} -2.21370 q^{6} -5.05822 q^{7} +1.00000 q^{8} +1.90049 q^{9} +0.840207 q^{10} +3.18870 q^{11} -2.21370 q^{12} -6.03830 q^{13} -5.05822 q^{14} -1.85997 q^{15} +1.00000 q^{16} -0.417799 q^{17} +1.90049 q^{18} -1.79978 q^{19} +0.840207 q^{20} +11.1974 q^{21} +3.18870 q^{22} -2.44597 q^{23} -2.21370 q^{24} -4.29405 q^{25} -6.03830 q^{26} +2.43399 q^{27} -5.05822 q^{28} +5.73464 q^{29} -1.85997 q^{30} -8.99262 q^{31} +1.00000 q^{32} -7.05883 q^{33} -0.417799 q^{34} -4.24995 q^{35} +1.90049 q^{36} -7.64209 q^{37} -1.79978 q^{38} +13.3670 q^{39} +0.840207 q^{40} +3.25013 q^{41} +11.1974 q^{42} -9.73316 q^{43} +3.18870 q^{44} +1.59680 q^{45} -2.44597 q^{46} +7.63222 q^{47} -2.21370 q^{48} +18.5856 q^{49} -4.29405 q^{50} +0.924884 q^{51} -6.03830 q^{52} -8.25439 q^{53} +2.43399 q^{54} +2.67917 q^{55} -5.05822 q^{56} +3.98417 q^{57} +5.73464 q^{58} +1.08276 q^{59} -1.85997 q^{60} +9.81827 q^{61} -8.99262 q^{62} -9.61308 q^{63} +1.00000 q^{64} -5.07342 q^{65} -7.05883 q^{66} -11.9714 q^{67} -0.417799 q^{68} +5.41465 q^{69} -4.24995 q^{70} +12.6406 q^{71} +1.90049 q^{72} +8.94335 q^{73} -7.64209 q^{74} +9.50576 q^{75} -1.79978 q^{76} -16.1291 q^{77} +13.3670 q^{78} -13.1129 q^{79} +0.840207 q^{80} -11.0896 q^{81} +3.25013 q^{82} -13.8827 q^{83} +11.1974 q^{84} -0.351038 q^{85} -9.73316 q^{86} -12.6948 q^{87} +3.18870 q^{88} -7.03701 q^{89} +1.59680 q^{90} +30.5430 q^{91} -2.44597 q^{92} +19.9070 q^{93} +7.63222 q^{94} -1.51218 q^{95} -2.21370 q^{96} +2.57536 q^{97} +18.5856 q^{98} +6.06008 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19} + 39 q^{20} + 51 q^{21} + 36 q^{22} + 47 q^{23} + 8 q^{24} + 147 q^{25} + 63 q^{26} + 17 q^{27} + 19 q^{28} + 60 q^{29} + 17 q^{30} + 63 q^{31} + 96 q^{32} + 55 q^{33} + 56 q^{34} + 45 q^{35} + 130 q^{36} + 46 q^{37} + 17 q^{38} + 22 q^{39} + 39 q^{40} + 101 q^{41} + 51 q^{42} - 3 q^{43} + 36 q^{44} + 106 q^{45} + 47 q^{46} + 99 q^{47} + 8 q^{48} + 175 q^{49} + 147 q^{50} - q^{51} + 63 q^{52} + 75 q^{53} + 17 q^{54} + 80 q^{55} + 19 q^{56} + 35 q^{57} + 60 q^{58} + 129 q^{59} + 17 q^{60} + 75 q^{61} + 63 q^{62} + 20 q^{63} + 96 q^{64} + 55 q^{65} + 55 q^{66} + 2 q^{67} + 56 q^{68} + 57 q^{69} + 45 q^{70} + 87 q^{71} + 130 q^{72} + 120 q^{73} + 46 q^{74} - 15 q^{75} + 17 q^{76} + 95 q^{77} + 22 q^{78} + 21 q^{79} + 39 q^{80} + 180 q^{81} + 101 q^{82} + 69 q^{83} + 51 q^{84} + 59 q^{85} - 3 q^{86} + 63 q^{87} + 36 q^{88} + 144 q^{89} + 106 q^{90} - 5 q^{91} + 47 q^{92} + 59 q^{93} + 99 q^{94} + 23 q^{95} + 8 q^{96} + 99 q^{97} + 175 q^{98} + 42 q^{99}+O(q^{100}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9 + 39 * q^10 + 36 * q^11 + 8 * q^12 + 63 * q^13 + 19 * q^14 + 17 * q^15 + 96 * q^16 + 56 * q^17 + 130 * q^18 + 17 * q^19 + 39 * q^20 + 51 * q^21 + 36 * q^22 + 47 * q^23 + 8 * q^24 + 147 * q^25 + 63 * q^26 + 17 * q^27 + 19 * q^28 + 60 * q^29 + 17 * q^30 + 63 * q^31 + 96 * q^32 + 55 * q^33 + 56 * q^34 + 45 * q^35 + 130 * q^36 + 46 * q^37 + 17 * q^38 + 22 * q^39 + 39 * q^40 + 101 * q^41 + 51 * q^42 - 3 * q^43 + 36 * q^44 + 106 * q^45 + 47 * q^46 + 99 * q^47 + 8 * q^48 + 175 * q^49 + 147 * q^50 - q^51 + 63 * q^52 + 75 * q^53 + 17 * q^54 + 80 * q^55 + 19 * q^56 + 35 * q^57 + 60 * q^58 + 129 * q^59 + 17 * q^60 + 75 * q^61 + 63 * q^62 + 20 * q^63 + 96 * q^64 + 55 * q^65 + 55 * q^66 + 2 * q^67 + 56 * q^68 + 57 * q^69 + 45 * q^70 + 87 * q^71 + 130 * q^72 + 120 * q^73 + 46 * q^74 - 15 * q^75 + 17 * q^76 + 95 * q^77 + 22 * q^78 + 21 * q^79 + 39 * q^80 + 180 * q^81 + 101 * q^82 + 69 * q^83 + 51 * q^84 + 59 * q^85 - 3 * q^86 + 63 * q^87 + 36 * q^88 + 144 * q^89 + 106 * q^90 - 5 * q^91 + 47 * q^92 + 59 * q^93 + 99 * q^94 + 23 * q^95 + 8 * q^96 + 99 * q^97 + 175 * q^98 + 42 * q^99

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