LMFDB - Embedded newform 8027.2.a.e.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$0$
Dimension:	$169$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.43156 q^{2} +2.09261 q^{3} +3.91247 q^{4} +2.37281 q^{5} -5.08829 q^{6} +3.03145 q^{7} -4.65029 q^{8} +1.37900 q^{9} +O(q^{10})$	\(q-2.43156 q^{2} +2.09261 q^{3} +3.91247 q^{4} +2.37281 q^{5} -5.08829 q^{6} +3.03145 q^{7} -4.65029 q^{8} +1.37900 q^{9} -5.76963 q^{10} +5.71257 q^{11} +8.18727 q^{12} +6.10522 q^{13} -7.37114 q^{14} +4.96536 q^{15} +3.48250 q^{16} +4.91114 q^{17} -3.35313 q^{18} +4.51074 q^{19} +9.28356 q^{20} +6.34363 q^{21} -13.8904 q^{22} -1.00000 q^{23} -9.73123 q^{24} +0.630229 q^{25} -14.8452 q^{26} -3.39211 q^{27} +11.8605 q^{28} -7.65996 q^{29} -12.0736 q^{30} -8.23014 q^{31} +0.832680 q^{32} +11.9542 q^{33} -11.9417 q^{34} +7.19305 q^{35} +5.39531 q^{36} +7.76536 q^{37} -10.9681 q^{38} +12.7758 q^{39} -11.0343 q^{40} -2.14380 q^{41} -15.4249 q^{42} -10.4405 q^{43} +22.3503 q^{44} +3.27211 q^{45} +2.43156 q^{46} -13.0853 q^{47} +7.28750 q^{48} +2.18968 q^{49} -1.53244 q^{50} +10.2771 q^{51} +23.8865 q^{52} +3.62636 q^{53} +8.24811 q^{54} +13.5548 q^{55} -14.0971 q^{56} +9.43921 q^{57} +18.6256 q^{58} +8.71431 q^{59} +19.4268 q^{60} +7.55715 q^{61} +20.0121 q^{62} +4.18038 q^{63} -8.98971 q^{64} +14.4865 q^{65} -29.0672 q^{66} +0.650040 q^{67} +19.2147 q^{68} -2.09261 q^{69} -17.4903 q^{70} -9.91534 q^{71} -6.41276 q^{72} +13.4166 q^{73} -18.8819 q^{74} +1.31882 q^{75} +17.6482 q^{76} +17.3174 q^{77} -31.0652 q^{78} +8.85348 q^{79} +8.26331 q^{80} -11.2354 q^{81} +5.21277 q^{82} +1.73266 q^{83} +24.8193 q^{84} +11.6532 q^{85} +25.3866 q^{86} -16.0293 q^{87} -26.5651 q^{88} +2.30436 q^{89} -7.95633 q^{90} +18.5077 q^{91} -3.91247 q^{92} -17.2224 q^{93} +31.8176 q^{94} +10.7031 q^{95} +1.74247 q^{96} -13.8088 q^{97} -5.32433 q^{98} +7.87765 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) $ 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9 + 28 * q^10 + 17 * q^11 + 10 * q^12 + 91 * q^13 + 20 * q^14 + 29 * q^15 + 200 * q^16 + 16 * q^17 + 31 * q^18 + 30 * q^19 + 45 * q^20 + 49 * q^21 + 76 * q^22 - 169 * q^23 + 3 * q^24 + 241 * q^25 - 15 * q^26 + 14 * q^27 + 118 * q^28 + 23 * q^29 + 52 * q^30 + 45 * q^31 + 42 * q^32 + 62 * q^33 + 65 * q^34 - 16 * q^35 + 199 * q^36 + 226 * q^37 + 49 * q^38 + 17 * q^39 + 95 * q^40 + 19 * q^41 + 32 * q^42 + 71 * q^43 + 46 * q^44 + 127 * q^45 - 6 * q^46 + 27 * q^47 + 5 * q^48 + 239 * q^49 + 24 * q^50 + 39 * q^51 + 154 * q^52 + 111 * q^53 + 22 * q^54 + 47 * q^55 + 39 * q^56 + 122 * q^57 + 146 * q^58 - 73 * q^59 + 109 * q^60 + 125 * q^61 + 14 * q^62 + 109 * q^63 + 260 * q^64 + 73 * q^65 + 26 * q^66 + 152 * q^67 + 40 * q^68 - 2 * q^69 + 76 * q^70 - 79 * q^71 + 126 * q^72 + 106 * q^73 + 23 * q^74 + 12 * q^75 + 122 * q^76 + 63 * q^77 + 101 * q^78 + 82 * q^79 + 134 * q^80 + 225 * q^81 + 125 * q^82 + 28 * q^83 + 73 * q^84 + 197 * q^85 + 97 * q^86 + 18 * q^87 + 183 * q^88 + 54 * q^89 + 52 * q^90 + 106 * q^91 - 186 * q^92 + 194 * q^93 + q^94 + 18 * q^95 - 39 * q^96 + 239 * q^97 + 5 * q^98 + 85 * 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 $

$2$	−2.43156	−1.71937	−0.859685	−	0.510824i	$-0.829340\pi$
$2$	−2.43156	−1.71937	−0.859685	+	0.510824i	$0.829340\pi$
$3$	2.09261	1.20817	0.604084	−	0.796921i	$-0.293539\pi$
$3$	2.09261	1.20817	0.604084	+	0.796921i	$0.293539\pi$
$4$	3.91247	1.95624
$5$	2.37281	1.06115	0.530577	−	0.847637i	$-0.321975\pi$
$5$	2.37281	1.06115	0.530577	+	0.847637i	$0.321975\pi$
$6$	−5.08829	−2.07729
$7$	3.03145	1.14578	0.572890	−	0.819632i	$-0.305822\pi$
$7$	3.03145	1.14578	0.572890	+	0.819632i	$0.305822\pi$
$8$	−4.65029	−1.64413
$9$	1.37900	0.459668
$10$	−5.76963	−1.82452
$11$	5.71257	1.72240	0.861202	−	0.508262i	$-0.169712\pi$
$11$	5.71257	1.72240	0.861202	+	0.508262i	$0.169712\pi$
$12$	8.18727	2.36346
$13$	6.10522	1.69328	0.846642	−	0.532164i	$-0.178621\pi$
$13$	6.10522	1.69328	0.846642	+	0.532164i	$0.178621\pi$
$14$	−7.37114	−1.97002
$15$	4.96536	1.28205
$16$	3.48250	0.870625
$17$	4.91114	1.19113	0.595563	−	0.803309i	$-0.296929\pi$
$17$	4.91114	1.19113	0.595563	+	0.803309i	$0.296929\pi$
$18$	−3.35313	−0.790339
$19$	4.51074	1.03484	0.517418	−	0.855733i	$-0.326893\pi$
$19$	4.51074	1.03484	0.517418	+	0.855733i	$0.326893\pi$
$20$	9.28356	2.07587
$21$	6.34363	1.38429
$22$	−13.8904	−2.96145
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−9.73123	−1.98638
$25$	0.630229	0.126046
$26$	−14.8452	−2.91138
$27$	−3.39211	−0.652812
$28$	11.8605	2.24142
$29$	−7.65996	−1.42242	−0.711210	−	0.702980i	$-0.751852\pi$
$29$	−7.65996	−1.42242	−0.711210	+	0.702980i	$0.751852\pi$
$30$	−12.0736	−2.20432
$31$	−8.23014	−1.47818	−0.739088	−	0.673609i	$-0.764743\pi$
$31$	−8.23014	−1.47818	−0.739088	+	0.673609i	$0.764743\pi$
$32$	0.832680	0.147199
$33$	11.9542	2.08095
$34$	−11.9417	−2.04799
$35$	7.19305	1.21585
$36$	5.39531	0.899219
$37$	7.76536	1.27662	0.638308	−	0.769781i	$-0.279634\pi$
$37$	7.76536	1.27662	0.638308	+	0.769781i	$0.279634\pi$
$38$	−10.9681	−1.77927
$39$	12.7758	2.04577
$40$	−11.0343	−1.74467
$41$	−2.14380	−0.334805	−0.167403	−	0.985889i	$-0.553538\pi$
$41$	−2.14380	−0.334805	−0.167403	+	0.985889i	$0.553538\pi$
$42$	−15.4249	−2.38011
$43$	−10.4405	−1.59215	−0.796077	−	0.605195i	$-0.793095\pi$
$43$	−10.4405	−1.59215	−0.796077	+	0.605195i	$0.793095\pi$
$44$	22.3503	3.36943
$45$	3.27211	0.487778
$46$	2.43156	0.358514
$47$	−13.0853	−1.90868	−0.954341	−	0.298718i	$-0.903441\pi$
$47$	−13.0853	−1.90868	−0.954341	+	0.298718i	$0.903441\pi$
$48$	7.28750	1.05186
$49$	2.18968	0.312811
$50$	−1.53244	−0.216719
$51$	10.2771	1.43908
$52$	23.8865	3.31246
$53$	3.62636	0.498119	0.249059	−	0.968488i	$-0.419879\pi$
$53$	3.62636	0.498119	0.249059	+	0.968488i	$0.419879\pi$
$54$	8.24811	1.12243
$55$	13.5548	1.82774
$56$	−14.0971	−1.88381
$57$	9.43921	1.25025
$58$	18.6256	2.44567
$59$	8.71431	1.13451	0.567253	−	0.823544i	$-0.308006\pi$
$59$	8.71431	1.13451	0.567253	+	0.823544i	$0.308006\pi$
$60$	19.4268	2.50799
$61$	7.55715	0.967594	0.483797	−	0.875180i	$-0.339257\pi$
$61$	7.55715	0.967594	0.483797	+	0.875180i	$0.339257\pi$
$62$	20.0121	2.54153
$63$	4.18038	0.526678
$64$	−8.98971	−1.12371
$65$	14.4865	1.79683
$66$	−29.0672	−3.57793
$67$	0.650040	0.0794150	0.0397075	−	0.999211i	$-0.487357\pi$
$67$	0.650040	0.0794150	0.0397075	+	0.999211i	$0.487357\pi$
$68$	19.2147	2.33012
$69$	−2.09261	−0.251920
$70$	−17.4903	−2.09049
$71$	−9.91534	−1.17673	−0.588367	−	0.808594i	$-0.700229\pi$
$71$	−9.91534	−1.17673	−0.588367	+	0.808594i	$0.700229\pi$
$72$	−6.41276	−0.755751
$73$	13.4166	1.57029	0.785147	−	0.619309i	$-0.212587\pi$
$73$	13.4166	1.57029	0.785147	+	0.619309i	$0.212587\pi$
$74$	−18.8819	−2.19498
$75$	1.31882	0.152284
$76$	17.6482	2.02438
$77$	17.3174	1.97350
$78$	−31.0652	−3.51744
$79$	8.85348	0.996095	0.498047	−	0.867150i	$-0.334051\pi$
$79$	8.85348	0.996095	0.498047	+	0.867150i	$0.334051\pi$
$80$	8.26331	0.923866
$81$	−11.2354	−1.24837
$82$	5.21277	0.575654
$83$	1.73266	0.190184	0.0950922	−	0.995468i	$-0.469685\pi$
$83$	1.73266	0.190184	0.0950922	+	0.995468i	$0.469685\pi$
$84$	24.8193	2.70801
$85$	11.6532	1.26397
$86$	25.3866	2.73750
$87$	−16.0293	−1.71852
$88$	−26.5651	−2.83185
$89$	2.30436	0.244262	0.122131	−	0.992514i	$-0.461027\pi$
$89$	2.30436	0.244262	0.122131	+	0.992514i	$0.461027\pi$
$90$	−7.95633	−0.838671
$91$	18.5077	1.94013
$92$	−3.91247	−0.407903
$93$	−17.2224	−1.78588
$94$	31.8176	3.28173
$95$	10.7031	1.09812
$96$	1.74247	0.177840
$97$	−13.8088	−1.40207	−0.701034	−	0.713128i	$-0.747278\pi$
$97$	−13.8088	−1.40207	−0.701034	+	0.713128i	$0.747278\pi$
$98$	−5.32433	−0.537839
$99$	7.87765	0.791734
$100$	2.46575	0.246575
$101$	−1.15105	−0.114533	−0.0572667	−	0.998359i	$-0.518239\pi$
$101$	−1.15105	−0.114533	−0.0572667	+	0.998359i	$0.518239\pi$
$102$	−24.9893	−2.47431
$103$	−6.09833	−0.600886	−0.300443	−	0.953800i	$-0.597135\pi$
$103$	−6.09833	−0.600886	−0.300443	+	0.953800i	$0.597135\pi$
$104$	−28.3910	−2.78397
$105$	15.0522	1.46895
$106$	−8.81770	−0.856451
$107$	−7.33109	−0.708723	−0.354362	−	0.935108i	$-0.615302\pi$
$107$	−7.33109	−0.708723	−0.354362	+	0.935108i	$0.615302\pi$
$108$	−13.2715	−1.27705
$109$	1.53752	0.147268	0.0736340	−	0.997285i	$-0.476540\pi$
$109$	1.53752	0.147268	0.0736340	+	0.997285i	$0.476540\pi$
$110$	−32.9594	−3.14255
$111$	16.2498	1.54237
$112$	10.5570	0.997544
$113$	10.9630	1.03131	0.515655	−	0.856796i	$-0.327549\pi$
$113$	10.9630	1.03131	0.515655	+	0.856796i	$0.327549\pi$
$114$	−22.9520	−2.14965
$115$	−2.37281	−0.221266
$116$	−29.9694	−2.78259
$117$	8.41912	0.778348
$118$	−21.1893	−1.95064
$119$	14.8879	1.36477
$120$	−23.0904	−2.10785
$121$	21.6335	1.96668
$122$	−18.3756	−1.66365
$123$	−4.48613	−0.404501
$124$	−32.2002	−2.89166
$125$	−10.3686	−0.927399
$126$	−10.1648	−0.905555
$127$	−5.67989	−0.504008	−0.252004	−	0.967726i	$-0.581090\pi$
$127$	−5.67989	−0.504008	−0.252004	+	0.967726i	$0.581090\pi$
$128$	20.1936	1.78488
$129$	−21.8478	−1.92359
$130$	−35.2248	−3.08942
$131$	4.07182	0.355757	0.177878	−	0.984052i	$-0.443077\pi$
$131$	4.07182	0.355757	0.177878	+	0.984052i	$0.443077\pi$
$132$	46.7703	4.07084
$133$	13.6741	1.18569
$134$	−1.58061	−0.136544
$135$	−8.04883	−0.692733
$136$	−22.8382	−1.95836
$137$	−8.08567	−0.690806	−0.345403	−	0.938454i	$-0.612258\pi$
$137$	−8.08567	−0.690806	−0.345403	+	0.938454i	$0.612258\pi$
$138$	5.08829	0.433144
$139$	0.117660	0.00997980	0.00498990	−	0.999988i	$-0.498412\pi$
$139$	0.117660	0.00997980	0.00498990	+	0.999988i	$0.498412\pi$
$140$	28.1426	2.37849
$141$	−27.3823	−2.30601
$142$	24.1097	2.02324
$143$	34.8765	2.91652
$144$	4.80238	0.400198
$145$	−18.1756	−1.50940
$146$	−32.6232	−2.69992
$147$	4.58214	0.377929
$148$	30.3818	2.49736
$149$	14.2906	1.17073	0.585367	−	0.810768i	$-0.300950\pi$
$149$	14.2906	1.17073	0.585367	+	0.810768i	$0.300950\pi$
$150$	−3.20679	−0.261833
$151$	−1.37141	−0.111604	−0.0558020	−	0.998442i	$-0.517772\pi$
$151$	−1.37141	−0.111604	−0.0558020	+	0.998442i	$0.517772\pi$
$152$	−20.9763	−1.70140
$153$	6.77247	0.547522
$154$	−42.1082	−3.39317
$155$	−19.5286	−1.56857
$156$	49.9851	4.00201
$157$	−0.450536	−0.0359567	−0.0179784	−	0.999838i	$-0.505723\pi$
$157$	−0.450536	−0.0359567	−0.0179784	+	0.999838i	$0.505723\pi$
$158$	−21.5278	−1.71266
$159$	7.58854	0.601811
$160$	1.97579	0.156200
$161$	−3.03145	−0.238912
$162$	27.3194	2.14642
$163$	−18.7471	−1.46838	−0.734192	−	0.678942i	$-0.762439\pi$
$163$	−18.7471	−1.46838	−0.734192	+	0.678942i	$0.762439\pi$
$164$	−8.38756	−0.654958
$165$	28.3650	2.20821
$166$	−4.21307	−0.326998
$167$	−9.70302	−0.750842	−0.375421	−	0.926854i	$-0.622502\pi$
$167$	−9.70302	−0.750842	−0.375421	+	0.926854i	$0.622502\pi$
$168$	−29.4997	−2.27595
$169$	24.2737	1.86721
$170$	−28.3354	−2.17323
$171$	6.22033	0.475681
$172$	−40.8480	−3.11463
$173$	0.306737	0.0233208	0.0116604	−	0.999932i	$-0.496288\pi$
$173$	0.306737	0.0233208	0.0116604	+	0.999932i	$0.496288\pi$
$174$	38.9761	2.95477
$175$	1.91051	0.144421
$176$	19.8940	1.49957
$177$	18.2356	1.37067
$178$	−5.60318	−0.419976
$179$	−10.5512	−0.788637	−0.394319	−	0.918974i	$-0.629019\pi$
$179$	−10.5512	−0.788637	−0.394319	+	0.918974i	$0.629019\pi$
$180$	12.8021	0.954209
$181$	18.7972	1.39718	0.698591	−	0.715521i	$-0.253811\pi$
$181$	18.7972	1.39718	0.698591	+	0.715521i	$0.253811\pi$
$182$	−45.0024	−3.33580
$183$	15.8141	1.16901
$184$	4.65029	0.342824
$185$	18.4257	1.35469
$186$	41.8774	3.07060
$187$	28.0552	2.05160
$188$	−51.1958	−3.73384
$189$	−10.2830	−0.747978
$190$	−26.0253	−1.88807
$191$	−24.3987	−1.76543	−0.882714	−	0.469911i	$-0.844286\pi$
$191$	−24.3987	−1.76543	−0.882714	+	0.469911i	$0.844286\pi$
$192$	−18.8119	−1.35763
$193$	−26.2151	−1.88700	−0.943502	−	0.331366i	$-0.892491\pi$
$193$	−26.2151	−1.88700	−0.943502	+	0.331366i	$0.892491\pi$
$194$	33.5768	2.41068
$195$	30.3146	2.17087
$196$	8.56706	0.611933
$197$	11.0874	0.789942	0.394971	−	0.918694i	$-0.370755\pi$
$197$	11.0874	0.789942	0.394971	+	0.918694i	$0.370755\pi$
$198$	−19.1550	−1.36128
$199$	−2.72219	−0.192971	−0.0964854	−	0.995334i	$-0.530760\pi$
$199$	−2.72219	−0.192971	−0.0964854	+	0.995334i	$0.530760\pi$
$200$	−2.93074	−0.207235
$201$	1.36028	0.0959466
$202$	2.79884	0.196926
$203$	−23.2208	−1.62978
$204$	40.2088	2.81518
$205$	−5.08683	−0.355280
$206$	14.8284	1.03315
$207$	−1.37900	−0.0958474
$208$	21.2614	1.47421
$209$	25.7679	1.78241
$210$	−36.6004	−2.52567
$211$	9.95422	0.685277	0.342638	−	0.939467i	$-0.388679\pi$
$211$	9.95422	0.685277	0.342638	+	0.939467i	$0.388679\pi$
$212$	14.1880	0.974438
$213$	−20.7489	−1.42169
$214$	17.8260	1.21856
$215$	−24.7732	−1.68952
$216$	15.7743	1.07330
$217$	−24.9492	−1.69366
$218$	−3.73858	−0.253208
$219$	28.0757	1.89718
$220$	53.0330	3.57548
$221$	29.9836	2.01691
$222$	−39.5124	−2.65190
$223$	11.6483	0.780025	0.390012	−	0.920810i	$-0.372471\pi$
$223$	11.6483	0.780025	0.390012	+	0.920810i	$0.372471\pi$
$224$	2.52423	0.168657
$225$	0.869087	0.0579392
$226$	−26.6571	−1.77320
$227$	−12.2373	−0.812216	−0.406108	−	0.913825i	$-0.633114\pi$
$227$	−12.2373	−0.812216	−0.406108	+	0.913825i	$0.633114\pi$
$228$	36.9307	2.44579
$229$	−14.6221	−0.966257	−0.483129	−	0.875549i	$-0.660500\pi$
$229$	−14.6221	−0.966257	−0.483129	+	0.875549i	$0.660500\pi$
$230$	5.76963	0.380438
$231$	36.2384	2.38431
$232$	35.6210	2.33864
$233$	−12.8540	−0.842093	−0.421046	−	0.907039i	$-0.638337\pi$
$233$	−12.8540	−0.842093	−0.421046	+	0.907039i	$0.638337\pi$
$234$	−20.4716	−1.33827
$235$	−31.0489	−2.02540
$236$	34.0945	2.21936
$237$	18.5269	1.20345
$238$	−36.2007	−2.34654
$239$	−19.4703	−1.25943	−0.629713	−	0.776828i	$-0.716828\pi$
$239$	−19.4703	−1.25943	−0.629713	+	0.776828i	$0.716828\pi$
$240$	17.2919	1.11618
$241$	24.8836	1.60289	0.801447	−	0.598066i	$-0.204064\pi$
$241$	24.8836	1.60289	0.801447	+	0.598066i	$0.204064\pi$
$242$	−52.6030	−3.38145
$243$	−13.3349	−0.855432
$244$	29.5671	1.89284
$245$	5.19570	0.331941
$246$	10.9083	0.695487
$247$	27.5391	1.75227
$248$	38.2725	2.43031
$249$	3.62578	0.229775
$250$	25.2119	1.59454
$251$	−16.5336	−1.04359	−0.521796	−	0.853070i	$-0.674738\pi$
$251$	−16.5336	−1.04359	−0.521796	+	0.853070i	$0.674738\pi$
$252$	16.3556	1.03031
$253$	−5.71257	−0.359146
$254$	13.8110	0.866577
$255$	24.3855	1.52708
$256$	−31.1226	−1.94516
$257$	21.0777	1.31479	0.657395	−	0.753547i	$-0.271659\pi$
$257$	21.0777	1.31479	0.657395	+	0.753547i	$0.271659\pi$
$258$	53.1241	3.30736
$259$	23.5403	1.46272
$260$	56.6781	3.51503
$261$	−10.5631	−0.653840
$262$	−9.90087	−0.611678
$263$	−21.9375	−1.35272	−0.676361	−	0.736570i	$-0.736444\pi$
$263$	−21.9375	−1.35272	−0.676361	+	0.736570i	$0.736444\pi$
$264$	−55.5903	−3.42135
$265$	8.60466	0.528580
$266$	−33.2493	−2.03865
$267$	4.82212	0.295109
$268$	2.54326	0.155354
$269$	4.95090	0.301862	0.150931	−	0.988544i	$-0.451773\pi$
$269$	4.95090	0.301862	0.150931	+	0.988544i	$0.451773\pi$
$270$	19.5712	1.19106
$271$	10.9831	0.667174	0.333587	−	0.942719i	$-0.391741\pi$
$271$	10.9831	0.667174	0.333587	+	0.942719i	$0.391741\pi$
$272$	17.1030	1.03702
$273$	38.7293	2.34400
$274$	19.6608	1.18775
$275$	3.60023	0.217102
$276$	−8.18727	−0.492816
$277$	21.5612	1.29549	0.647744	−	0.761858i	$-0.275713\pi$
$277$	21.5612	1.29549	0.647744	+	0.761858i	$0.275713\pi$
$278$	−0.286097	−0.0171590
$279$	−11.3494	−0.679470
$280$	−33.4498	−1.99901
$281$	−9.40908	−0.561299	−0.280649	−	0.959810i	$-0.590550\pi$
$281$	−9.40908	−0.561299	−0.280649	+	0.959810i	$0.590550\pi$
$282$	66.5817	3.96488
$283$	−9.80436	−0.582809	−0.291404	−	0.956600i	$-0.594123\pi$
$283$	−9.80436	−0.582809	−0.291404	+	0.956600i	$0.594123\pi$
$284$	−38.7935	−2.30197
$285$	22.3975	1.32671
$286$	−84.8042	−5.01458
$287$	−6.49882	−0.383613
$288$	1.14827	0.0676624
$289$	7.11925	0.418779
$290$	44.1951	2.59523
$291$	−28.8963	−1.69393
$292$	52.4921	3.07187
$293$	12.6649	0.739891	0.369945	−	0.929054i	$-0.379376\pi$
$293$	12.6649	0.739891	0.369945	+	0.929054i	$0.379376\pi$
$294$	−11.1417	−0.649799
$295$	20.6774	1.20388
$296$	−36.1112	−2.09892
$297$	−19.3777	−1.12441
$298$	−34.7485	−2.01293
$299$	−6.10522	−0.353074
$300$	5.15985	0.297904
$301$	−31.6497	−1.82426
$302$	3.33467	0.191889
$303$	−2.40869	−0.138376
$304$	15.7087	0.900953
$305$	17.9317	1.02676
$306$	−16.4677	−0.941393
$307$	0.980000	0.0559315	0.0279658	−	0.999609i	$-0.491097\pi$
$307$	0.980000	0.0559315	0.0279658	+	0.999609i	$0.491097\pi$
$308$	67.7537	3.86063
$309$	−12.7614	−0.725971
$310$	47.4848	2.69696
$311$	13.7731	0.781002	0.390501	−	0.920603i	$-0.372302\pi$
$311$	13.7731	0.781002	0.390501	+	0.920603i	$0.372302\pi$
$312$	−59.4113	−3.36350
$313$	2.34935	0.132793	0.0663965	−	0.997793i	$-0.478850\pi$
$313$	2.34935	0.132793	0.0663965	+	0.997793i	$0.478850\pi$
$314$	1.09550	0.0618229
$315$	9.91924	0.558886
$316$	34.6390	1.94860
$317$	−4.28052	−0.240418	−0.120209	−	0.992749i	$-0.538357\pi$
$317$	−4.28052	−0.240418	−0.120209	+	0.992749i	$0.538357\pi$
$318$	−18.4520	−1.03474
$319$	−43.7581	−2.44998
$320$	−21.3309	−1.19243
$321$	−15.3411	−0.856256
$322$	7.37114	0.410778
$323$	22.1529	1.23262
$324$	−43.9580	−2.44211
$325$	3.84768	0.213431
$326$	45.5846	2.52470
$327$	3.21743	0.177924
$328$	9.96928	0.550462
$329$	−39.6673	−2.18693
$330$	−68.9711	−3.79673
$331$	18.1899	0.999808	0.499904	−	0.866081i	$-0.333369\pi$
$331$	18.1899	0.999808	0.499904	+	0.866081i	$0.333369\pi$
$332$	6.77900	0.372046
$333$	10.7085	0.586820
$334$	23.5935	1.29098
$335$	1.54242	0.0842714
$336$	22.0917	1.20520
$337$	−26.1791	−1.42607	−0.713034	−	0.701129i	$-0.752680\pi$
$337$	−26.1791	−1.42607	−0.713034	+	0.701129i	$0.752680\pi$
$338$	−59.0229	−3.21042
$339$	22.9412	1.24599
$340$	45.5928	2.47262
$341$	−47.0152	−2.54602
$342$	−15.1251	−0.817871
$343$	−14.5822	−0.787367
$344$	48.5511	2.61770
$345$	−4.96536	−0.267326
$346$	−0.745848	−0.0400971
$347$	−11.5828	−0.621797	−0.310899	−	0.950443i	$-0.600630\pi$
$347$	−11.5828	−0.621797	−0.310899	+	0.950443i	$0.600630\pi$
$348$	−62.7142	−3.36183
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	−4.64550	−0.248313
$351$	−20.7096	−1.10539
$352$	4.75675	0.253535
$353$	−23.8985	−1.27199	−0.635994	−	0.771694i	$-0.719410\pi$
$353$	−23.8985	−1.27199	−0.635994	+	0.771694i	$0.719410\pi$
$354$	−44.3410	−2.35670
$355$	−23.5272	−1.24869
$356$	9.01574	0.477833
$357$	31.1544	1.64887
$358$	25.6560	1.35596
$359$	−17.4449	−0.920705	−0.460352	−	0.887736i	$-0.652277\pi$
$359$	−17.4449	−0.920705	−0.460352	+	0.887736i	$0.652277\pi$
$360$	−15.2163	−0.801968
$361$	1.34680	0.0708844
$362$	−45.7064	−2.40227
$363$	45.2703	2.37608
$364$	72.4107	3.79535
$365$	31.8350	1.66632
$366$	−38.4530	−2.00997
$367$	14.6704	0.765790	0.382895	−	0.923792i	$-0.374927\pi$
$367$	14.6704	0.765790	0.382895	+	0.923792i	$0.374927\pi$
$368$	−3.48250	−0.181538
$369$	−2.95631	−0.153899
$370$	−44.8032	−2.32921
$371$	10.9931	0.570734
$372$	−67.3823	−3.49361
$373$	20.7048	1.07206	0.536028	−	0.844200i	$-0.319924\pi$
$373$	20.7048	1.07206	0.536028	+	0.844200i	$0.319924\pi$
$374$	−68.2179	−3.52746
$375$	−21.6975	−1.12045
$376$	60.8503	3.13811
$377$	−46.7658	−2.40856
$378$	25.0037	1.28605
$379$	−31.3955	−1.61268	−0.806339	−	0.591453i	$-0.798554\pi$
$379$	−31.3955	−1.61268	−0.806339	+	0.591453i	$0.798554\pi$
$380$	41.8757	2.14818
$381$	−11.8858	−0.608926
$382$	59.3268	3.03543
$383$	−2.24841	−0.114888	−0.0574442	−	0.998349i	$-0.518295\pi$
$383$	−2.24841	−0.114888	−0.0574442	+	0.998349i	$0.518295\pi$
$384$	42.2573	2.15644
$385$	41.0908	2.09418
$386$	63.7435	3.24446
$387$	−14.3974	−0.731862
$388$	−54.0265	−2.74278
$389$	18.4876	0.937359	0.468680	−	0.883368i	$-0.344730\pi$
$389$	18.4876	0.937359	0.468680	+	0.883368i	$0.344730\pi$
$390$	−73.7117	−3.73254
$391$	−4.91114	−0.248367
$392$	−10.1826	−0.514301
$393$	8.52073	0.429814
$394$	−26.9596	−1.35820
$395$	21.0076	1.05701
$396$	30.8211	1.54882
$397$	24.8599	1.24768	0.623841	−	0.781552i	$-0.285571\pi$
$397$	24.8599	1.24768	0.623841	+	0.781552i	$0.285571\pi$
$398$	6.61916	0.331788
$399$	28.6145	1.43252
$400$	2.19477	0.109738
$401$	−19.9990	−0.998700	−0.499350	−	0.866400i	$-0.666428\pi$
$401$	−19.9990	−0.998700	−0.499350	+	0.866400i	$0.666428\pi$
$402$	−3.30759	−0.164968
$403$	−50.2468	−2.50297
$404$	−4.50344	−0.224055
$405$	−26.6594	−1.32472
$406$	56.4627	2.80220
$407$	44.3602	2.19885
$408$	−47.7914	−2.36602
$409$	−31.4440	−1.55480	−0.777402	−	0.629004i	$-0.783463\pi$
$409$	−31.4440	−1.55480	−0.777402	+	0.629004i	$0.783463\pi$
$410$	12.3689	0.610857
$411$	−16.9201	−0.834609
$412$	−23.8595	−1.17547
$413$	26.4170	1.29989
$414$	3.35313	0.164797
$415$	4.11128	0.201815
$416$	5.08370	0.249249
$417$	0.246216	0.0120573
$418$	−62.6562	−3.06462
$419$	31.7145	1.54936	0.774678	−	0.632356i	$-0.217912\pi$
$419$	31.7145	1.54936	0.774678	+	0.632356i	$0.217912\pi$
$420$	58.8914	2.87361
$421$	−18.9961	−0.925813	−0.462907	−	0.886407i	$-0.653193\pi$
$421$	−18.9961	−0.925813	−0.462907	+	0.886407i	$0.653193\pi$
$422$	−24.2043	−1.17825
$423$	−18.0446	−0.877360
$424$	−16.8636	−0.818969
$425$	3.09514	0.150136
$426$	50.4521	2.44441
$427$	22.9091	1.10865
$428$	−28.6827	−1.38643
$429$	72.9828	3.52364
$430$	60.2375	2.90491
$431$	1.01474	0.0488784	0.0244392	−	0.999701i	$-0.492220\pi$
$431$	1.01474	0.0488784	0.0244392	+	0.999701i	$0.492220\pi$
$432$	−11.8130	−0.568354
$433$	10.4218	0.500838	0.250419	−	0.968138i	$-0.419432\pi$
$433$	10.4218	0.500838	0.250419	+	0.968138i	$0.419432\pi$
$434$	60.6655	2.91204
$435$	−38.0345	−1.82361
$436$	6.01552	0.288091
$437$	−4.51074	−0.215778
$438$	−68.2676	−3.26195
$439$	10.6482	0.508209	0.254104	−	0.967177i	$-0.418219\pi$
$439$	10.6482	0.508209	0.254104	+	0.967177i	$0.418219\pi$
$440$	−63.0339	−3.00503
$441$	3.01958	0.143789
$442$	−72.9067	−3.46782
$443$	−19.4676	−0.924935	−0.462468	−	0.886636i	$-0.653036\pi$
$443$	−19.4676	−0.924935	−0.462468	+	0.886636i	$0.653036\pi$
$444$	63.5771	3.01723
$445$	5.46781	0.259199
$446$	−28.3234	−1.34115
$447$	29.9047	1.41444
$448$	−27.2518	−1.28753
$449$	36.0011	1.69900	0.849499	−	0.527591i	$-0.176905\pi$
$449$	36.0011	1.69900	0.849499	+	0.527591i	$0.176905\pi$
$450$	−2.11324	−0.0996189
$451$	−12.2466	−0.576670
$452$	42.8923	2.01749
$453$	−2.86983	−0.134836
$454$	29.7556	1.39650
$455$	43.9152	2.05877
$456$	−43.8951	−2.05557
$457$	9.38515	0.439019	0.219509	−	0.975610i	$-0.429554\pi$
$457$	9.38515	0.439019	0.219509	+	0.975610i	$0.429554\pi$
$458$	35.5546	1.66136
$459$	−16.6591	−0.777580
$460$	−9.28356	−0.432848
$461$	−29.2306	−1.36141	−0.680703	−	0.732560i	$-0.738326\pi$
$461$	−29.2306	−1.36141	−0.680703	+	0.732560i	$0.738326\pi$
$462$	−88.1158	−4.09952
$463$	37.2825	1.73266	0.866331	−	0.499470i	$-0.166472\pi$
$463$	37.2825	1.73266	0.866331	+	0.499470i	$0.166472\pi$
$464$	−26.6758	−1.23839
$465$	−40.8656	−1.89510
$466$	31.2552	1.44787
$467$	−13.0628	−0.604473	−0.302236	−	0.953233i	$-0.597733\pi$
$467$	−13.0628	−0.604473	−0.302236	+	0.953233i	$0.597733\pi$
$468$	32.9396	1.52263
$469$	1.97056	0.0909921
$470$	75.4971	3.48242
$471$	−0.942795	−0.0434417
$472$	−40.5240	−1.86527
$473$	−59.6418	−2.74233
$474$	−45.0491	−2.06917
$475$	2.84280	0.130437
$476$	58.2483	2.66981
$477$	5.00076	0.228969
$478$	47.3430	2.16542
$479$	6.27899	0.286895	0.143447	−	0.989658i	$-0.454181\pi$
$479$	6.27899	0.286895	0.143447	+	0.989658i	$0.454181\pi$
$480$	4.13456	0.188716
$481$	47.4092	2.16167
$482$	−60.5059	−2.75597
$483$	−6.34363	−0.288645
$484$	84.6404	3.84729
$485$	−32.7656	−1.48781
$486$	32.4245	1.47080
$487$	−18.8347	−0.853484	−0.426742	−	0.904374i	$-0.640339\pi$
$487$	−18.8347	−0.853484	−0.426742	+	0.904374i	$0.640339\pi$
$488$	−35.1429	−1.59085
$489$	−39.2302	−1.77405
$490$	−12.6336	−0.570729
$491$	−35.4890	−1.60160	−0.800799	−	0.598934i	$-0.795591\pi$
$491$	−35.4890	−1.60160	−0.800799	+	0.598934i	$0.795591\pi$
$492$	−17.5519	−0.791299
$493$	−37.6191	−1.69428
$494$	−66.9628	−3.01280
$495$	18.6922	0.840151
$496$	−28.6614	−1.28694
$497$	−30.0578	−1.34828
$498$	−8.81630	−0.395068
$499$	16.1085	0.721113	0.360557	−	0.932737i	$-0.382587\pi$
$499$	16.1085	0.721113	0.360557	+	0.932737i	$0.382587\pi$
$500$	−40.5670	−1.81421
$501$	−20.3046	−0.907143
$502$	40.2024	1.79432
$503$	6.15889	0.274611	0.137306	−	0.990529i	$-0.456156\pi$
$503$	6.15889	0.274611	0.137306	+	0.990529i	$0.456156\pi$
$504$	−19.4400	−0.865925
$505$	−2.73122	−0.121538
$506$	13.8904	0.617506
$507$	50.7953	2.25590
$508$	−22.2224	−0.985960
$509$	−32.8474	−1.45594	−0.727969	−	0.685611i	$-0.759535\pi$
$509$	−32.8474	−1.45594	−0.727969	+	0.685611i	$0.759535\pi$
$510$	−59.2949	−2.62562
$511$	40.6717	1.79921
$512$	35.2891	1.55957
$513$	−15.3009	−0.675553
$514$	−51.2516	−2.26061
$515$	−14.4702	−0.637632
$516$	−85.4788	−3.76299
$517$	−74.7505	−3.28752
$518$	−57.2396	−2.51496
$519$	0.641880	0.0281754
$520$	−67.3665	−2.95422
$521$	−8.75284	−0.383469	−0.191734	−	0.981447i	$-0.561411\pi$
$521$	−8.75284	−0.383469	−0.191734	+	0.981447i	$0.561411\pi$
$522$	25.6848	1.12419
$523$	4.80840	0.210257	0.105128	−	0.994459i	$-0.466475\pi$
$523$	4.80840	0.210257	0.105128	+	0.994459i	$0.466475\pi$
$524$	15.9309	0.695945
$525$	3.99794	0.174484
$526$	53.3422	2.32583
$527$	−40.4193	−1.76069
$528$	41.6304	1.81173
$529$	1.00000	0.0434783
$530$	−20.9227	−0.908825
$531$	12.0171	0.521496
$532$	53.4995	2.31950
$533$	−13.0884	−0.566920
$534$	−11.7253	−0.507401
$535$	−17.3953	−0.752064
$536$	−3.02287	−0.130568
$537$	−22.0796	−0.952806
$538$	−12.0384	−0.519012
$539$	12.5087	0.538788
$540$	−31.4908	−1.35515
$541$	36.6547	1.57591	0.787954	−	0.615735i	$-0.211141\pi$
$541$	36.6547	1.57591	0.787954	+	0.615735i	$0.211141\pi$
$542$	−26.7059	−1.14712
$543$	39.3351	1.68803
$544$	4.08941	0.175332
$545$	3.64825	0.156274
$546$	−94.1724	−4.03021
$547$	24.6837	1.05540	0.527700	−	0.849431i	$-0.323055\pi$
$547$	24.6837	1.05540	0.527700	+	0.849431i	$0.323055\pi$
$548$	−31.6350	−1.35138
$549$	10.4213	0.444772
$550$	−8.75416	−0.373278
$551$	−34.5521	−1.47197
$552$	9.73123	0.414188
$553$	26.8389	1.14131
$554$	−52.4273	−2.22742
$555$	38.5578	1.63669
$556$	0.460342	0.0195228
$557$	−43.9176	−1.86085	−0.930424	−	0.366486i	$-0.880561\pi$
$557$	−43.9176	−1.86085	−0.930424	+	0.366486i	$0.880561\pi$
$558$	27.5967	1.16826
$559$	−63.7412	−2.69597
$560$	25.0498	1.05855
$561$	58.7085	2.47868
$562$	22.8787	0.965081
$563$	45.3566	1.91155	0.955776	−	0.294095i	$-0.0950183\pi$
$563$	45.3566	1.91155	0.955776	+	0.294095i	$0.0950183\pi$
$564$	−107.133	−4.51110
$565$	26.0131	1.09438
$566$	23.8399	1.00206
$567$	−34.0594	−1.43036
$568$	46.1092	1.93470
$569$	28.8118	1.20785	0.603926	−	0.797040i	$-0.293602\pi$
$569$	28.8118	1.20785	0.603926	+	0.797040i	$0.293602\pi$
$570$	−54.4607	−2.28111
$571$	−21.0608	−0.881366	−0.440683	−	0.897663i	$-0.645264\pi$
$571$	−21.0608	−0.881366	−0.440683	+	0.897663i	$0.645264\pi$
$572$	136.453	5.70540
$573$	−51.0569	−2.13293
$574$	15.8022	0.659573
$575$	−0.630229	−0.0262823
$576$	−12.3968	−0.516535
$577$	−13.5488	−0.564045	−0.282022	−	0.959408i	$-0.591005\pi$
$577$	−13.5488	−0.564045	−0.282022	+	0.959408i	$0.591005\pi$
$578$	−17.3109	−0.720037
$579$	−54.8579	−2.27982
$580$	−71.1117	−2.95275
$581$	5.25248	0.217910
$582$	70.2631	2.91250
$583$	20.7158	0.857962
$584$	−62.3911	−2.58176
$585$	19.9770	0.825946
$586$	−30.7954	−1.27215
$587$	−43.8012	−1.80787	−0.903935	−	0.427670i	$-0.859335\pi$
$587$	−43.8012	−1.80787	−0.903935	+	0.427670i	$0.859335\pi$
$588$	17.9275	0.739318
$589$	−37.1240	−1.52967
$590$	−50.2783	−2.06992
$591$	23.2015	0.954382
$592$	27.0428	1.11145
$593$	−8.17977	−0.335903	−0.167952	−	0.985795i	$-0.553715\pi$
$593$	−8.17977	−0.335903	−0.167952	+	0.985795i	$0.553715\pi$
$594$	47.1179	1.93327
$595$	35.3261	1.44823
$596$	55.9117	2.29023
$597$	−5.69647	−0.233141
$598$	14.8452	0.607065
$599$	−18.1136	−0.740101	−0.370051	−	0.929012i	$-0.620660\pi$
$599$	−18.1136	−0.740101	−0.370051	+	0.929012i	$0.620660\pi$
$600$	−6.13290	−0.250374
$601$	13.8617	0.565431	0.282715	−	0.959204i	$-0.408765\pi$
$601$	13.8617	0.565431	0.282715	+	0.959204i	$0.408765\pi$
$602$	76.9580	3.13658
$603$	0.896407	0.0365045
$604$	−5.36561	−0.218324
$605$	51.3321	2.08695
$606$	5.85687	0.237919
$607$	29.4531	1.19546	0.597732	−	0.801696i	$-0.296069\pi$
$607$	29.4531	1.19546	0.597732	+	0.801696i	$0.296069\pi$
$608$	3.75601	0.152326
$609$	−48.5920	−1.96905
$610$	−43.6019	−1.76539
$611$	−79.8884	−3.23194
$612$	26.4971	1.07108
$613$	−6.11777	−0.247094	−0.123547	−	0.992339i	$-0.539427\pi$
$613$	−6.11777	−0.247094	−0.123547	+	0.992339i	$0.539427\pi$
$614$	−2.38293	−0.0961671
$615$	−10.6447	−0.429237
$616$	−80.5307	−3.24468
$617$	25.4943	1.02636	0.513180	−	0.858281i	$-0.328467\pi$
$617$	25.4943	1.02636	0.513180	+	0.858281i	$0.328467\pi$
$618$	31.0301	1.24821
$619$	2.97006	0.119377	0.0596883	−	0.998217i	$-0.480989\pi$
$619$	2.97006	0.119377	0.0596883	+	0.998217i	$0.480989\pi$
$620$	−76.4049	−3.06850
$621$	3.39211	0.136121
$622$	−33.4901	−1.34283
$623$	6.98554	0.279870
$624$	44.4918	1.78110
$625$	−27.7540	−1.11016
$626$	−5.71257	−0.228320
$627$	53.9222	2.15344
$628$	−1.76271	−0.0703398
$629$	38.1367	1.52061
$630$	−24.1192	−0.960932
$631$	−8.26568	−0.329051	−0.164526	−	0.986373i	$-0.552609\pi$
$631$	−8.26568	−0.329051	−0.164526	+	0.986373i	$0.552609\pi$
$632$	−41.1712	−1.63770
$633$	20.8303	0.827929
$634$	10.4083	0.413368
$635$	−13.4773	−0.534830
$636$	29.6900	1.17728
$637$	13.3685	0.529678
$638$	106.400	4.21243
$639$	−13.6733	−0.540907
$640$	47.9157	1.89403
$641$	29.4577	1.16351	0.581755	−	0.813364i	$-0.302366\pi$
$641$	29.4577	1.16351	0.581755	+	0.813364i	$0.302366\pi$
$642$	37.3028	1.47222
$643$	17.7057	0.698246	0.349123	−	0.937077i	$-0.386480\pi$
$643$	17.7057	0.698246	0.349123	+	0.937077i	$0.386480\pi$
$644$	−11.8605	−0.467368
$645$	−51.8406	−2.04122
$646$	−53.8660	−2.11933
$647$	−28.8695	−1.13498	−0.567488	−	0.823382i	$-0.692085\pi$
$647$	−28.8695	−1.13498	−0.567488	+	0.823382i	$0.692085\pi$
$648$	52.2477	2.05248
$649$	49.7811	1.95408
$650$	−9.35586	−0.366967
$651$	−52.2089	−2.04623
$652$	−73.3474	−2.87250
$653$	28.1984	1.10349	0.551745	−	0.834013i	$-0.313962\pi$
$653$	28.1984	1.10349	0.551745	+	0.834013i	$0.313962\pi$
$654$	−7.82337	−0.305918
$655$	9.66166	0.377512
$656$	−7.46578	−0.291490
$657$	18.5015	0.721814
$658$	96.4534	3.76014
$659$	6.81531	0.265487	0.132743	−	0.991150i	$-0.457621\pi$
$659$	6.81531	0.265487	0.132743	+	0.991150i	$0.457621\pi$
$660$	110.977	4.31978
$661$	33.6876	1.31029	0.655147	−	0.755501i	$-0.272606\pi$
$661$	33.6876	1.31029	0.655147	+	0.755501i	$0.272606\pi$
$662$	−44.2298	−1.71904
$663$	62.7438	2.43677
$664$	−8.05738	−0.312687
$665$	32.4460	1.25820
$666$	−26.0382	−1.00896
$667$	7.65996	0.296595
$668$	−37.9628	−1.46882
$669$	24.3752	0.942400
$670$	−3.75048	−0.144894
$671$	43.1707	1.66659
$672$	5.28222	0.203766
$673$	−22.4845	−0.866713	−0.433356	−	0.901223i	$-0.642671\pi$
$673$	−22.4845	−0.866713	−0.433356	+	0.901223i	$0.642671\pi$
$674$	63.6561	2.45194
$675$	−2.13780	−0.0822841
$676$	94.9702	3.65270
$677$	−19.4675	−0.748197	−0.374099	−	0.927389i	$-0.622048\pi$
$677$	−19.4675	−0.748197	−0.374099	+	0.927389i	$0.622048\pi$
$678$	−55.7828	−2.14233
$679$	−41.8606	−1.60646
$680$	−54.1907	−2.07812
$681$	−25.6078	−0.981292
$682$	114.320	4.37755
$683$	26.7841	1.02487	0.512433	−	0.858727i	$-0.328744\pi$
$683$	26.7841	1.02487	0.512433	+	0.858727i	$0.328744\pi$
$684$	24.3369	0.930544
$685$	−19.1858	−0.733051
$686$	35.4576	1.35378
$687$	−30.5984	−1.16740
$688$	−36.3589	−1.38617
$689$	22.1397	0.843456
$690$	12.0736	0.459632
$691$	−4.65053	−0.176914	−0.0884572	−	0.996080i	$-0.528194\pi$
$691$	−4.65053	−0.176914	−0.0884572	+	0.996080i	$0.528194\pi$
$692$	1.20010	0.0456209
$693$	23.8807	0.907153
$694$	28.1642	1.06910
$695$	0.279185	0.0105901
$696$	74.5408	2.82546
$697$	−10.5285	−0.398795
$698$	−2.43156	−0.0920358
$699$	−26.8983	−1.01739
$700$	7.47480	0.282521
$701$	−39.9442	−1.50867	−0.754336	−	0.656489i	$-0.772041\pi$
$701$	−39.9442	−1.50867	−0.754336	+	0.656489i	$0.772041\pi$
$702$	50.3565	1.90058
$703$	35.0275	1.32109
$704$	−51.3543	−1.93549
$705$	−64.9731	−2.44703
$706$	58.1105	2.18702
$707$	−3.48934	−0.131230
$708$	71.3464	2.68136
$709$	9.17450	0.344556	0.172278	−	0.985048i	$-0.444887\pi$
$709$	9.17450	0.344556	0.172278	+	0.985048i	$0.444887\pi$
$710$	57.2078	2.14697
$711$	12.2090	0.457873
$712$	−10.7159	−0.401596
$713$	8.23014	0.308221
$714$	−75.7538	−2.83501
$715$	82.7553	3.09487
$716$	−41.2815	−1.54276
$717$	−40.7436	−1.52160
$718$	42.4182	1.58303
$719$	42.3193	1.57824	0.789122	−	0.614236i	$-0.210536\pi$
$719$	42.3193	1.57824	0.789122	+	0.614236i	$0.210536\pi$
$720$	11.3951	0.424671
$721$	−18.4868	−0.688483
$722$	−3.27483	−0.121877
$723$	52.0716	1.93656
$724$	73.5434	2.73322
$725$	−4.82753	−0.179290
$726$	−110.077	−4.08536
$727$	34.7987	1.29061	0.645306	−	0.763925i	$-0.276730\pi$
$727$	34.7987	1.29061	0.645306	+	0.763925i	$0.276730\pi$
$728$	−86.0659	−3.18982
$729$	5.80145	0.214868
$730$	−77.4088	−2.86503
$731$	−51.2745	−1.89645
$732$	61.8724	2.28687
$733$	19.9555	0.737072	0.368536	−	0.929613i	$-0.379859\pi$
$733$	19.9555	0.737072	0.368536	+	0.929613i	$0.379859\pi$
$734$	−35.6720	−1.31668
$735$	10.8725	0.401040
$736$	−0.832680	−0.0306930
$737$	3.71340	0.136785
$738$	7.18843	0.264610
$739$	−16.7934	−0.617756	−0.308878	−	0.951102i	$-0.599953\pi$
$739$	−16.7934	−0.617756	−0.308878	+	0.951102i	$0.599953\pi$
$740$	72.0901	2.65009
$741$	57.6285	2.11703
$742$	−26.7304	−0.981304
$743$	24.1314	0.885296	0.442648	−	0.896695i	$-0.354039\pi$
$743$	24.1314	0.885296	0.442648	+	0.896695i	$0.354039\pi$
$744$	80.0893	2.93622
$745$	33.9090	1.24233
$746$	−50.3450	−1.84326
$747$	2.38935	0.0874217
$748$	109.765	4.01341
$749$	−22.2238	−0.812041
$750$	52.7587	1.92647
$751$	−48.1066	−1.75543	−0.877717	−	0.479179i	$-0.840935\pi$
$751$	−48.1066	−1.75543	−0.877717	+	0.479179i	$0.840935\pi$
$752$	−45.5694	−1.66175
$753$	−34.5984	−1.26083
$754$	113.714	4.14121
$755$	−3.25410	−0.118429
$756$	−40.2320	−1.46322
$757$	22.4126	0.814601	0.407300	−	0.913294i	$-0.366470\pi$
$757$	22.4126	0.814601	0.407300	+	0.913294i	$0.366470\pi$
$758$	76.3400	2.77279
$759$	−11.9542	−0.433909
$760$	−49.7727	−1.80544
$761$	14.3844	0.521434	0.260717	−	0.965415i	$-0.416041\pi$
$761$	14.3844	0.521434	0.260717	+	0.965415i	$0.416041\pi$
$762$	28.9009	1.04697
$763$	4.66092	0.168737
$764$	−95.4592	−3.45359
$765$	16.0698	0.581005
$766$	5.46714	0.197536
$767$	53.2028	1.92104
$768$	−65.1273	−2.35008
$769$	−18.5201	−0.667851	−0.333926	−	0.942599i	$-0.608373\pi$
$769$	−18.5201	−0.667851	−0.333926	+	0.942599i	$0.608373\pi$
$770$	−99.9147	−3.60068
$771$	44.1073	1.58848
$772$	−102.566	−3.69143
$773$	−35.5989	−1.28040	−0.640201	−	0.768208i	$-0.721149\pi$
$773$	−35.5989	−1.28040	−0.640201	+	0.768208i	$0.721149\pi$
$774$	35.0082	1.25834
$775$	−5.18687	−0.186318
$776$	64.2148	2.30518
$777$	49.2606	1.76721
$778$	−44.9537	−1.61167
$779$	−9.67013	−0.346468
$780$	118.605	4.24674
$781$	−56.6421	−2.02681
$782$	11.9417	0.427035
$783$	25.9834	0.928572
$784$	7.62556	0.272341
$785$	−1.06904	−0.0381556
$786$	−20.7186	−0.739009
$787$	−6.84666	−0.244057	−0.122029	−	0.992527i	$-0.538940\pi$
$787$	−6.84666	−0.244057	−0.122029	+	0.992527i	$0.538940\pi$
$788$	43.3790	1.54531
$789$	−45.9065	−1.63431
$790$	−51.0813	−1.81739
$791$	33.2337	1.18165
$792$	−36.6334	−1.30171
$793$	46.1380	1.63841
$794$	−60.4482	−2.14523
$795$	18.0062	0.638613
$796$	−10.6505	−0.377496
$797$	−27.2376	−0.964806	−0.482403	−	0.875949i	$-0.660236\pi$
$797$	−27.2376	−0.964806	−0.482403	+	0.875949i	$0.660236\pi$
$798$	−69.5778	−2.46303
$799$	−64.2635	−2.27348
$800$	0.524779	0.0185537
$801$	3.17772	0.112279
$802$	48.6286	1.71714
$803$	76.6433	2.70468
$804$	5.32205	0.187694
$805$	−7.19305	−0.253522
$806$	122.178	4.30354
$807$	10.3603	0.364699
$808$	5.35270	0.188307
$809$	−32.0095	−1.12539	−0.562696	−	0.826664i	$-0.690236\pi$
$809$	−32.0095	−1.12539	−0.562696	+	0.826664i	$0.690236\pi$
$810$	64.8238	2.27768
$811$	45.5079	1.59800	0.798999	−	0.601333i	$-0.205363\pi$
$811$	45.5079	1.59800	0.798999	+	0.601333i	$0.205363\pi$
$812$	−90.8507	−3.18823
$813$	22.9832	0.806057
$814$	−107.864	−3.78064
$815$	−44.4832	−1.55818
$816$	35.7899	1.25290
$817$	−47.0942	−1.64762
$818$	76.4578	2.67329
$819$	25.5221	0.891815
$820$	−19.9021	−0.695011
$821$	−4.74403	−0.165568	−0.0827838	−	0.996568i	$-0.526381\pi$
$821$	−4.74403	−0.165568	−0.0827838	+	0.996568i	$0.526381\pi$
$822$	41.1423	1.43500
$823$	51.8726	1.80817	0.904083	−	0.427356i	$-0.140555\pi$
$823$	51.8726	1.80817	0.904083	+	0.427356i	$0.140555\pi$
$824$	28.3590	0.987932
$825$	7.53386	0.262295
$826$	−64.2344	−2.23500
$827$	20.9187	0.727413	0.363707	−	0.931514i	$-0.381511\pi$
$827$	20.9187	0.727413	0.363707	+	0.931514i	$0.381511\pi$
$828$	−5.39531	−0.187500
$829$	38.4964	1.33703	0.668517	−	0.743697i	$-0.266929\pi$
$829$	38.4964	1.33703	0.668517	+	0.743697i	$0.266929\pi$
$830$	−9.99682	−0.346995
$831$	45.1191	1.56517
$832$	−54.8841	−1.90277
$833$	10.7538	0.372598
$834$	−0.598689	−0.0207309
$835$	−23.0234	−0.796758
$836$	100.816	3.48681
$837$	27.9175	0.964971
$838$	−77.1157	−2.66392
$839$	−36.5196	−1.26080	−0.630398	−	0.776272i	$-0.717108\pi$
$839$	−36.5196	−1.26080	−0.630398	+	0.776272i	$0.717108\pi$
$840$	−69.9972	−2.41513
$841$	29.6750	1.02328
$842$	46.1901	1.59182
$843$	−19.6895	−0.678143
$844$	38.9456	1.34056
$845$	57.5969	1.98139
$846$	43.8766	1.50851
$847$	65.5807	2.25338
$848$	12.6288	0.433674
$849$	−20.5167	−0.704130
$850$	−7.52601	−0.258140
$851$	−7.76536	−0.266193
$852$	−81.1795	−2.78116
$853$	−8.45002	−0.289323	−0.144662	−	0.989481i	$-0.546209\pi$
$853$	−8.45002	−0.289323	−0.144662	+	0.989481i	$0.546209\pi$
$854$	−55.7048	−1.90618
$855$	14.7597	0.504770
$856$	34.0917	1.16523
$857$	−6.45462	−0.220486	−0.110243	−	0.993905i	$-0.535163\pi$
$857$	−6.45462	−0.220486	−0.110243	+	0.993905i	$0.535163\pi$
$858$	−177.462	−6.05845
$859$	−5.51204	−0.188068	−0.0940342	−	0.995569i	$-0.529976\pi$
$859$	−5.51204	−0.188068	−0.0940342	+	0.995569i	$0.529976\pi$
$860$	−96.9245	−3.30510
$861$	−13.5995	−0.463469
$862$	−2.46740	−0.0840401
$863$	−27.4514	−0.934458	−0.467229	−	0.884136i	$-0.654748\pi$
$863$	−27.4514	−0.934458	−0.467229	+	0.884136i	$0.654748\pi$
$864$	−2.82454	−0.0960929
$865$	0.727828	0.0247469
$866$	−25.3411	−0.861126
$867$	14.8978	0.505955
$868$	−97.6132	−3.31321
$869$	50.5761	1.71568
$870$	92.4830	3.13547
$871$	3.96863	0.134472
$872$	−7.14992	−0.242127
$873$	−19.0423	−0.644486
$874$	10.9681	0.371003
$875$	−31.4320	−1.06260
$876$	109.845	3.71133
$877$	12.8715	0.434638	0.217319	−	0.976101i	$-0.430269\pi$
$877$	12.8715	0.434638	0.217319	+	0.976101i	$0.430269\pi$
$878$	−25.8916	−0.873799
$879$	26.5026	0.893911
$880$	47.2047	1.59127
$881$	−40.3752	−1.36027	−0.680137	−	0.733085i	$-0.738080\pi$
$881$	−40.3752	−1.36027	−0.680137	+	0.733085i	$0.738080\pi$
$882$	−7.34227	−0.247227
$883$	−33.5161	−1.12791	−0.563954	−	0.825807i	$-0.690720\pi$
$883$	−33.5161	−1.12791	−0.563954	+	0.825807i	$0.690720\pi$
$884$	117.310	3.94556
$885$	43.2697	1.45449
$886$	47.3367	1.59031
$887$	21.2783	0.714455	0.357227	−	0.934017i	$-0.383722\pi$
$887$	21.2783	0.714455	0.357227	+	0.934017i	$0.383722\pi$
$888$	−75.5664	−2.53584
$889$	−17.2183	−0.577483
$890$	−13.2953	−0.445659
$891$	−64.1828	−2.15020
$892$	45.5735	1.52591
$893$	−59.0243	−1.97517
$894$	−72.7149	−2.43195
$895$	−25.0361	−0.836865
$896$	61.2160	2.04508
$897$	−12.7758	−0.426572
$898$	−87.5388	−2.92121
$899$	63.0425	2.10259
$900$	3.40028	0.113343
$901$	17.8095	0.593322
$902$	29.7783	0.991510
$903$	−66.2304	−2.20401
$904$	−50.9810	−1.69560
$905$	44.6021	1.48262
$906$	6.97815	0.231833
$907$	−32.9623	−1.09450	−0.547248	−	0.836971i	$-0.684325\pi$
$907$	−32.9623	−1.09450	−0.547248	+	0.836971i	$0.684325\pi$
$908$	−47.8780	−1.58889
$909$	−1.58730	−0.0526473
$910$	−106.782	−3.53980
$911$	−20.4706	−0.678223	−0.339111	−	0.940746i	$-0.610126\pi$
$911$	−20.4706	−0.678223	−0.339111	+	0.940746i	$0.610126\pi$
$912$	32.8720	1.08850
$913$	9.89796	0.327575
$914$	−22.8205	−0.754836
$915$	37.5240	1.24050
$916$	−57.2087	−1.89023
$917$	12.3435	0.407619
$918$	40.5076	1.33695
$919$	15.6386	0.515870	0.257935	−	0.966162i	$-0.416958\pi$
$919$	15.6386	0.515870	0.257935	+	0.966162i	$0.416958\pi$
$920$	11.0343	0.363789
$921$	2.05075	0.0675747
$922$	71.0759	2.34076
$923$	−60.5353	−1.99254
$924$	141.782	4.66428
$925$	4.89395	0.160912
$926$	−90.6545	−2.97909
$927$	−8.40961	−0.276208
$928$	−6.37830	−0.209378
$929$	−2.02036	−0.0662857	−0.0331429	−	0.999451i	$-0.510552\pi$
$929$	−2.02036	−0.0662857	−0.0331429	+	0.999451i	$0.510552\pi$
$930$	99.3670	3.25837
$931$	9.87709	0.323708
$932$	−50.2909	−1.64733
$933$	28.8217	0.943580
$934$	31.7629	1.03931
$935$	66.5697	2.17706
$936$	−39.1513	−1.27970
$937$	−54.8893	−1.79315	−0.896577	−	0.442888i	$-0.853954\pi$
$937$	−54.8893	−1.79315	−0.896577	+	0.442888i	$0.853954\pi$
$938$	−4.79153	−0.156449
$939$	4.91626	0.160436
$940$	−121.478	−3.96217
$941$	−0.0251856	−0.000821027 0	−0.000410513	−	1.00000i	$-0.500131\pi$
$941$	−0.0251856	−0.000821027 0	−0.000410513		1.00000i	$0.500131\pi$
$942$	2.29246	0.0746924
$943$	2.14380	0.0698117
$944$	30.3476	0.987729
$945$	−24.3996	−0.793719
$946$	145.023	4.71509
$947$	20.0287	0.650846	0.325423	−	0.945569i	$-0.394493\pi$
$947$	20.0287	0.650846	0.325423	+	0.945569i	$0.394493\pi$
$948$	72.4858	2.35423
$949$	81.9113	2.65895
$950$	−6.91243	−0.224269
$951$	−8.95746	−0.290465
$952$	−69.2328	−2.24385
$953$	37.0256	1.19938	0.599688	−	0.800234i	$-0.295291\pi$
$953$	37.0256	1.19938	0.599688	+	0.800234i	$0.295291\pi$
$954$	−12.1596	−0.393683
$955$	−57.8935	−1.87339
$956$	−76.1768	−2.46374
$957$	−91.5685	−2.95999
$958$	−15.2677	−0.493278
$959$	−24.5113	−0.791511
$960$	−44.6371	−1.44066
$961$	36.7351	1.18500
$962$	−115.278	−3.71672
$963$	−10.1096	−0.325777
$964$	97.3564	3.13564
$965$	−62.2035	−2.00240
$966$	15.4249	0.496288
$967$	31.5563	1.01478	0.507391	−	0.861716i	$-0.330610\pi$
$967$	31.5563	1.01478	0.507391	+	0.861716i	$0.330610\pi$
$968$	−100.602	−3.23347
$969$	46.3572	1.48921
$970$	79.6714	2.55810
$971$	21.7614	0.698355	0.349178	−	0.937057i	$-0.386461\pi$
$971$	21.7614	0.698355	0.349178	+	0.937057i	$0.386461\pi$
$972$	−52.1723	−1.67343
$973$	0.356680	0.0114347
$974$	45.7978	1.46745
$975$	8.05169	0.257860
$976$	26.3178	0.842411
$977$	40.0926	1.28268	0.641338	−	0.767259i	$-0.278380\pi$
$977$	40.0926	1.28268	0.641338	+	0.767259i	$0.278380\pi$
$978$	95.3906	3.05025
$979$	13.1638	0.420717
$980$	20.3280	0.649355
$981$	2.12025	0.0676943
$982$	86.2936	2.75374
$983$	−49.2865	−1.57200	−0.785998	−	0.618230i	$-0.787850\pi$
$983$	−49.2865	−1.57200	−0.785998	+	0.618230i	$0.787850\pi$
$984$	20.8618	0.665050
$985$	26.3082	0.838249
$986$	91.4731	2.91310
$987$	−83.0081	−2.64218
$988$	107.746	3.42785
$989$	10.4405	0.331987
$990$	−45.4511	−1.44453
$991$	25.2446	0.801922	0.400961	−	0.916095i	$-0.368676\pi$
$991$	25.2446	0.801922	0.400961	+	0.916095i	$0.368676\pi$
$992$	−6.85307	−0.217585
$993$	38.0643	1.20793
$994$	73.0873	2.31819
$995$	−6.45923	−0.204771
$996$	14.1858	0.449494
$997$	−32.9080	−1.04221	−0.521103	−	0.853494i	$-0.674479\pi$
$997$	−32.9080	−1.04221	−0.521103	+	0.853494i	$0.674479\pi$
$998$	−39.1686	−1.23986
$999$	−26.3409	−0.833390

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.e.1.16	✓	169

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.e.1.16	✓	169	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.43156 q^{2} +2.09261 q^{3} +3.91247 q^{4} +2.37281 q^{5} -5.08829 q^{6} +3.03145 q^{7} -4.65029 q^{8} +1.37900 q^{9} +O(q^{10})\)	\(q-2.43156 q^{2} +2.09261 q^{3} +3.91247 q^{4} +2.37281 q^{5} -5.08829 q^{6} +3.03145 q^{7} -4.65029 q^{8} +1.37900 q^{9} -5.76963 q^{10} +5.71257 q^{11} +8.18727 q^{12} +6.10522 q^{13} -7.37114 q^{14} +4.96536 q^{15} +3.48250 q^{16} +4.91114 q^{17} -3.35313 q^{18} +4.51074 q^{19} +9.28356 q^{20} +6.34363 q^{21} -13.8904 q^{22} -1.00000 q^{23} -9.73123 q^{24} +0.630229 q^{25} -14.8452 q^{26} -3.39211 q^{27} +11.8605 q^{28} -7.65996 q^{29} -12.0736 q^{30} -8.23014 q^{31} +0.832680 q^{32} +11.9542 q^{33} -11.9417 q^{34} +7.19305 q^{35} +5.39531 q^{36} +7.76536 q^{37} -10.9681 q^{38} +12.7758 q^{39} -11.0343 q^{40} -2.14380 q^{41} -15.4249 q^{42} -10.4405 q^{43} +22.3503 q^{44} +3.27211 q^{45} +2.43156 q^{46} -13.0853 q^{47} +7.28750 q^{48} +2.18968 q^{49} -1.53244 q^{50} +10.2771 q^{51} +23.8865 q^{52} +3.62636 q^{53} +8.24811 q^{54} +13.5548 q^{55} -14.0971 q^{56} +9.43921 q^{57} +18.6256 q^{58} +8.71431 q^{59} +19.4268 q^{60} +7.55715 q^{61} +20.0121 q^{62} +4.18038 q^{63} -8.98971 q^{64} +14.4865 q^{65} -29.0672 q^{66} +0.650040 q^{67} +19.2147 q^{68} -2.09261 q^{69} -17.4903 q^{70} -9.91534 q^{71} -6.41276 q^{72} +13.4166 q^{73} -18.8819 q^{74} +1.31882 q^{75} +17.6482 q^{76} +17.3174 q^{77} -31.0652 q^{78} +8.85348 q^{79} +8.26331 q^{80} -11.2354 q^{81} +5.21277 q^{82} +1.73266 q^{83} +24.8193 q^{84} +11.6532 q^{85} +25.3866 q^{86} -16.0293 q^{87} -26.5651 q^{88} +2.30436 q^{89} -7.95633 q^{90} +18.5077 q^{91} -3.91247 q^{92} -17.2224 q^{93} +31.8176 q^{94} +10.7031 q^{95} +1.74247 q^{96} -13.8088 q^{97} -5.32433 q^{98} +7.87765 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9	\( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 169 * q + 6 * q^2 + 2 * q^3 + 186 * q^4 + 28 * q^5 + 5 * q^6 + 38 * q^7 + 18 * q^8 + 185 * q^9 + 28 * q^10 + 17 * q^11 + 10 * q^12 + 91 * q^13 + 20 * q^14 + 29 * q^15 + 200 * q^16 + 16 * q^17 + 31 * q^18 + 30 * q^19 + 45 * q^20 + 49 * q^21 + 76 * q^22 - 169 * q^23 + 3 * q^24 + 241 * q^25 - 15 * q^26 + 14 * q^27 + 118 * q^28 + 23 * q^29 + 52 * q^30 + 45 * q^31 + 42 * q^32 + 62 * q^33 + 65 * q^34 - 16 * q^35 + 199 * q^36 + 226 * q^37 + 49 * q^38 + 17 * q^39 + 95 * q^40 + 19 * q^41 + 32 * q^42 + 71 * q^43 + 46 * q^44 + 127 * q^45 - 6 * q^46 + 27 * q^47 + 5 * q^48 + 239 * q^49 + 24 * q^50 + 39 * q^51 + 154 * q^52 + 111 * q^53 + 22 * q^54 + 47 * q^55 + 39 * q^56 + 122 * q^57 + 146 * q^58 - 73 * q^59 + 109 * q^60 + 125 * q^61 + 14 * q^62 + 109 * q^63 + 260 * q^64 + 73 * q^65 + 26 * q^66 + 152 * q^67 + 40 * q^68 - 2 * q^69 + 76 * q^70 - 79 * q^71 + 126 * q^72 + 106 * q^73 + 23 * q^74 + 12 * q^75 + 122 * q^76 + 63 * q^77 + 101 * q^78 + 82 * q^79 + 134 * q^80 + 225 * q^81 + 125 * q^82 + 28 * q^83 + 73 * q^84 + 197 * q^85 + 97 * q^86 + 18 * q^87 + 183 * q^88 + 54 * q^89 + 52 * q^90 + 106 * q^91 - 186 * q^92 + 194 * q^93 + q^94 + 18 * q^95 - 39 * q^96 + 239 * q^97 + 5 * q^98 + 85 * q^99

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