LMFDB - Embedded newform 4011.2.a.j.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.506999 q^{2} -1.00000 q^{3} -1.74295 q^{4} +3.81191 q^{5} -0.506999 q^{6} -1.00000 q^{7} -1.89767 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.506999 q^{2} -1.00000 q^{3} -1.74295 q^{4} +3.81191 q^{5} -0.506999 q^{6} -1.00000 q^{7} -1.89767 q^{8} +1.00000 q^{9} +1.93264 q^{10} +1.15333 q^{11} +1.74295 q^{12} -3.12285 q^{13} -0.506999 q^{14} -3.81191 q^{15} +2.52378 q^{16} -7.80145 q^{17} +0.506999 q^{18} +2.41797 q^{19} -6.64398 q^{20} +1.00000 q^{21} +0.584739 q^{22} -1.70514 q^{23} +1.89767 q^{24} +9.53066 q^{25} -1.58328 q^{26} -1.00000 q^{27} +1.74295 q^{28} -1.90087 q^{29} -1.93264 q^{30} +3.23564 q^{31} +5.07490 q^{32} -1.15333 q^{33} -3.95533 q^{34} -3.81191 q^{35} -1.74295 q^{36} +8.94998 q^{37} +1.22591 q^{38} +3.12285 q^{39} -7.23376 q^{40} +6.74818 q^{41} +0.506999 q^{42} +10.7435 q^{43} -2.01020 q^{44} +3.81191 q^{45} -0.864507 q^{46} -13.0336 q^{47} -2.52378 q^{48} +1.00000 q^{49} +4.83204 q^{50} +7.80145 q^{51} +5.44298 q^{52} +9.24653 q^{53} -0.506999 q^{54} +4.39640 q^{55} +1.89767 q^{56} -2.41797 q^{57} -0.963739 q^{58} +13.7634 q^{59} +6.64398 q^{60} -10.5466 q^{61} +1.64047 q^{62} -1.00000 q^{63} -2.47459 q^{64} -11.9040 q^{65} -0.584739 q^{66} -8.41170 q^{67} +13.5976 q^{68} +1.70514 q^{69} -1.93264 q^{70} +7.90427 q^{71} -1.89767 q^{72} -5.14832 q^{73} +4.53764 q^{74} -9.53066 q^{75} -4.21441 q^{76} -1.15333 q^{77} +1.58328 q^{78} -2.73477 q^{79} +9.62044 q^{80} +1.00000 q^{81} +3.42132 q^{82} +2.65632 q^{83} -1.74295 q^{84} -29.7384 q^{85} +5.44693 q^{86} +1.90087 q^{87} -2.18865 q^{88} +5.80825 q^{89} +1.93264 q^{90} +3.12285 q^{91} +2.97198 q^{92} -3.23564 q^{93} -6.60802 q^{94} +9.21710 q^{95} -5.07490 q^{96} +18.7736 q^{97} +0.506999 q^{98} +1.15333 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9}+O(q^{10}) $ 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9	$ 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9} - q^{10} + 13 q^{11} - 34 q^{12} - q^{13} - 2 q^{15} + 54 q^{16} + q^{19} - 22 q^{20} + 26 q^{21} + 17 q^{22} - 3 q^{23} + 48 q^{25} + 6 q^{26} - 26 q^{27} - 34 q^{28} + 23 q^{29} + q^{30} + 18 q^{31} + 10 q^{32} - 13 q^{33} - 19 q^{34} - 2 q^{35} + 34 q^{36} + 23 q^{37} - 15 q^{38} + q^{39} + 14 q^{40} - 4 q^{41} + 5 q^{43} + 60 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{47} - 54 q^{48} + 26 q^{49} + 26 q^{50} + 19 q^{52} + 31 q^{53} + 41 q^{55} - q^{57} + 19 q^{58} - 2 q^{59} + 22 q^{60} - 2 q^{61} - 35 q^{62} - 26 q^{63} + 132 q^{64} + 40 q^{65} - 17 q^{66} + 47 q^{67} - 60 q^{68} + 3 q^{69} + q^{70} + 16 q^{71} - 23 q^{73} + 34 q^{74} - 48 q^{75} + 72 q^{76} - 13 q^{77} - 6 q^{78} + 14 q^{79} - 21 q^{80} + 26 q^{81} + 60 q^{82} - 4 q^{83} + 34 q^{84} + 36 q^{85} + 21 q^{86} - 23 q^{87} + 67 q^{88} + 14 q^{89} - q^{90} + q^{91} + 20 q^{92} - 18 q^{93} + 58 q^{94} - 4 q^{95} - 10 q^{96} + 48 q^{97} + 13 q^{99}+O(q^{100}) $ 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9 - q^10 + 13 * q^11 - 34 * q^12 - q^13 - 2 * q^15 + 54 * q^16 + q^19 - 22 * q^20 + 26 * q^21 + 17 * q^22 - 3 * q^23 + 48 * q^25 + 6 * q^26 - 26 * q^27 - 34 * q^28 + 23 * q^29 + q^30 + 18 * q^31 + 10 * q^32 - 13 * q^33 - 19 * q^34 - 2 * q^35 + 34 * q^36 + 23 * q^37 - 15 * q^38 + q^39 + 14 * q^40 - 4 * q^41 + 5 * q^43 + 60 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^47 - 54 * q^48 + 26 * q^49 + 26 * q^50 + 19 * q^52 + 31 * q^53 + 41 * q^55 - q^57 + 19 * q^58 - 2 * q^59 + 22 * q^60 - 2 * q^61 - 35 * q^62 - 26 * q^63 + 132 * q^64 + 40 * q^65 - 17 * q^66 + 47 * q^67 - 60 * q^68 + 3 * q^69 + q^70 + 16 * q^71 - 23 * q^73 + 34 * q^74 - 48 * q^75 + 72 * q^76 - 13 * q^77 - 6 * q^78 + 14 * q^79 - 21 * q^80 + 26 * q^81 + 60 * q^82 - 4 * q^83 + 34 * q^84 + 36 * q^85 + 21 * q^86 - 23 * q^87 + 67 * q^88 + 14 * q^89 - q^90 + q^91 + 20 * q^92 - 18 * q^93 + 58 * q^94 - 4 * q^95 - 10 * q^96 + 48 * q^97 + 13 * 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 $

$2$	0.506999	0.358503	0.179251	−	0.983803i	$-0.442632\pi$
$2$	0.506999	0.358503	0.179251	+	0.983803i	$0.442632\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.74295	−0.871476
$5$	3.81191	1.70474	0.852369	−	0.522941i	$-0.175165\pi$
$5$	3.81191	1.70474	0.852369	+	0.522941i	$0.175165\pi$
$6$	−0.506999	−0.206982
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.89767	−0.670929
$9$	1.00000	0.333333
$10$	1.93264	0.611153
$11$	1.15333	0.347743	0.173871	−	0.984768i	$-0.444372\pi$
$11$	1.15333	0.347743	0.173871	+	0.984768i	$0.444372\pi$
$12$	1.74295	0.503147
$13$	−3.12285	−0.866123	−0.433061	−	0.901364i	$-0.642567\pi$
$13$	−3.12285	−0.866123	−0.433061	+	0.901364i	$0.642567\pi$
$14$	−0.506999	−0.135501
$15$	−3.81191	−0.984231
$16$	2.52378	0.630946
$17$	−7.80145	−1.89213	−0.946065	−	0.323976i	$-0.894980\pi$
$17$	−7.80145	−1.89213	−0.946065	+	0.323976i	$0.894980\pi$
$18$	0.506999	0.119501
$19$	2.41797	0.554721	0.277361	−	0.960766i	$-0.410540\pi$
$19$	2.41797	0.554721	0.277361	+	0.960766i	$0.410540\pi$
$20$	−6.64398	−1.48564
$21$	1.00000	0.218218
$22$	0.584739	0.124667
$23$	−1.70514	−0.355547	−0.177774	−	0.984071i	$-0.556889\pi$
$23$	−1.70514	−0.355547	−0.177774	+	0.984071i	$0.556889\pi$
$24$	1.89767	0.387361
$25$	9.53066	1.90613
$26$	−1.58328	−0.310507
$27$	−1.00000	−0.192450
$28$	1.74295	0.329387
$29$	−1.90087	−0.352982	−0.176491	−	0.984302i	$-0.556475\pi$
$29$	−1.90087	−0.352982	−0.176491	+	0.984302i	$0.556475\pi$
$30$	−1.93264	−0.352850
$31$	3.23564	0.581137	0.290569	−	0.956854i	$-0.406156\pi$
$31$	3.23564	0.581137	0.290569	+	0.956854i	$0.406156\pi$
$32$	5.07490	0.897125
$33$	−1.15333	−0.200769
$34$	−3.95533	−0.678334
$35$	−3.81191	−0.644331
$36$	−1.74295	−0.290492
$37$	8.94998	1.47137	0.735684	−	0.677325i	$-0.236861\pi$
$37$	8.94998	1.47137	0.735684	+	0.677325i	$0.236861\pi$
$38$	1.22591	0.198869
$39$	3.12285	0.500056
$40$	−7.23376	−1.14376
$41$	6.74818	1.05389	0.526945	−	0.849900i	$-0.323338\pi$
$41$	6.74818	1.05389	0.526945	+	0.849900i	$0.323338\pi$
$42$	0.506999	0.0782317
$43$	10.7435	1.63836	0.819182	−	0.573534i	$-0.194428\pi$
$43$	10.7435	1.63836	0.819182	+	0.573534i	$0.194428\pi$
$44$	−2.01020	−0.303049
$45$	3.81191	0.568246
$46$	−0.864507	−0.127465
$47$	−13.0336	−1.90114	−0.950572	−	0.310503i	$-0.899502\pi$
$47$	−13.0336	−1.90114	−0.950572	+	0.310503i	$0.899502\pi$
$48$	−2.52378	−0.364277
$49$	1.00000	0.142857
$50$	4.83204	0.683354
$51$	7.80145	1.09242
$52$	5.44298	0.754805
$53$	9.24653	1.27011	0.635054	−	0.772468i	$-0.280978\pi$
$53$	9.24653	1.27011	0.635054	+	0.772468i	$0.280978\pi$
$54$	−0.506999	−0.0689939
$55$	4.39640	0.592810
$56$	1.89767	0.253587
$57$	−2.41797	−0.320269
$58$	−0.963739	−0.126545
$59$	13.7634	1.79184	0.895920	−	0.444215i	$-0.146517\pi$
$59$	13.7634	1.79184	0.895920	+	0.444215i	$0.146517\pi$
$60$	6.64398	0.857734
$61$	−10.5466	−1.35036	−0.675180	−	0.737653i	$-0.735934\pi$
$61$	−10.5466	−1.35036	−0.675180	+	0.737653i	$0.735934\pi$
$62$	1.64047	0.208339
$63$	−1.00000	−0.125988
$64$	−2.47459	−0.309324
$65$	−11.9040	−1.47651
$66$	−0.584739	−0.0719764
$67$	−8.41170	−1.02765	−0.513826	−	0.857894i	$-0.671772\pi$
$67$	−8.41170	−1.02765	−0.513826	+	0.857894i	$0.671772\pi$
$68$	13.5976	1.64895
$69$	1.70514	0.205275
$70$	−1.93264	−0.230994
$71$	7.90427	0.938065	0.469032	−	0.883181i	$-0.344603\pi$
$71$	7.90427	0.938065	0.469032	+	0.883181i	$0.344603\pi$
$72$	−1.89767	−0.223643
$73$	−5.14832	−0.602566	−0.301283	−	0.953535i	$-0.597415\pi$
$73$	−5.14832	−0.602566	−0.301283	+	0.953535i	$0.597415\pi$
$74$	4.53764	0.527489
$75$	−9.53066	−1.10051
$76$	−4.21441	−0.483426
$77$	−1.15333	−0.131434
$78$	1.58328	0.179271
$79$	−2.73477	−0.307686	−0.153843	−	0.988095i	$-0.549165\pi$
$79$	−2.73477	−0.307686	−0.153843	+	0.988095i	$0.549165\pi$
$80$	9.62044	1.07560
$81$	1.00000	0.111111
$82$	3.42132	0.377822
$83$	2.65632	0.291569	0.145785	−	0.989316i	$-0.453429\pi$
$83$	2.65632	0.291569	0.145785	+	0.989316i	$0.453429\pi$
$84$	−1.74295	−0.190172
$85$	−29.7384	−3.22559
$86$	5.44693	0.587358
$87$	1.90087	0.203794
$88$	−2.18865	−0.233311
$89$	5.80825	0.615674	0.307837	−	0.951439i	$-0.400395\pi$
$89$	5.80825	0.615674	0.307837	+	0.951439i	$0.400395\pi$
$90$	1.93264	0.203718
$91$	3.12285	0.327364
$92$	2.97198	0.309851
$93$	−3.23564	−0.335520
$94$	−6.60802	−0.681565
$95$	9.21710	0.945655
$96$	−5.07490	−0.517955
$97$	18.7736	1.90617	0.953086	−	0.302700i	$-0.0978882\pi$
$97$	18.7736	1.90617	0.953086	+	0.302700i	$0.0978882\pi$
$98$	0.506999	0.0512147
$99$	1.15333	0.115914
$100$	−16.6115	−1.66115
$101$	−10.1174	−1.00672	−0.503359	−	0.864077i	$-0.667903\pi$
$101$	−10.1174	−1.00672	−0.503359	+	0.864077i	$0.667903\pi$
$102$	3.95533	0.391636
$103$	−3.57052	−0.351814	−0.175907	−	0.984407i	$-0.556286\pi$
$103$	−3.57052	−0.351814	−0.175907	+	0.984407i	$0.556286\pi$
$104$	5.92615	0.581107
$105$	3.81191	0.372004
$106$	4.68798	0.455337
$107$	4.15931	0.402096	0.201048	−	0.979581i	$-0.435565\pi$
$107$	4.15931	0.402096	0.201048	+	0.979581i	$0.435565\pi$
$108$	1.74295	0.167716
$109$	19.8020	1.89669	0.948344	−	0.317244i	$-0.102757\pi$
$109$	19.8020	1.89669	0.948344	+	0.317244i	$0.102757\pi$
$110$	2.22897	0.212524
$111$	−8.94998	−0.849495
$112$	−2.52378	−0.238475
$113$	6.55447	0.616593	0.308296	−	0.951290i	$-0.400241\pi$
$113$	6.55447	0.616593	0.308296	+	0.951290i	$0.400241\pi$
$114$	−1.22591	−0.114817
$115$	−6.49986	−0.606115
$116$	3.31312	0.307616
$117$	−3.12285	−0.288708
$118$	6.97803	0.642380
$119$	7.80145	0.715158
$120$	7.23376	0.660349
$121$	−9.66982	−0.879075
$122$	−5.34714	−0.484107
$123$	−6.74818	−0.608463
$124$	−5.63956	−0.506447
$125$	17.2705	1.54472
$126$	−0.506999	−0.0451671
$127$	−10.5349	−0.934826	−0.467413	−	0.884039i	$-0.654814\pi$
$127$	−10.5349	−0.934826	−0.467413	+	0.884039i	$0.654814\pi$
$128$	−11.4044	−1.00802
$129$	−10.7435	−0.945910
$130$	−6.03533	−0.529334
$131$	−12.8556	−1.12320	−0.561600	−	0.827409i	$-0.689814\pi$
$131$	−12.8556	−1.12320	−0.561600	+	0.827409i	$0.689814\pi$
$132$	2.01020	0.174966
$133$	−2.41797	−0.209665
$134$	−4.26472	−0.368416
$135$	−3.81191	−0.328077
$136$	14.8046	1.26949
$137$	17.8192	1.52239	0.761197	−	0.648520i	$-0.224612\pi$
$137$	17.8192	1.52239	0.761197	+	0.648520i	$0.224612\pi$
$138$	0.864507	0.0735917
$139$	5.49020	0.465672	0.232836	−	0.972516i	$-0.425199\pi$
$139$	5.49020	0.465672	0.232836	+	0.972516i	$0.425199\pi$
$140$	6.64398	0.561518
$141$	13.0336	1.09763
$142$	4.00746	0.336299
$143$	−3.60168	−0.301188
$144$	2.52378	0.210315
$145$	−7.24594	−0.601743
$146$	−2.61020	−0.216021
$147$	−1.00000	−0.0824786
$148$	−15.5994	−1.28226
$149$	6.99762	0.573267	0.286634	−	0.958040i	$-0.407464\pi$
$149$	6.99762	0.573267	0.286634	+	0.958040i	$0.407464\pi$
$150$	−4.83204	−0.394534
$151$	15.2605	1.24188	0.620941	−	0.783857i	$-0.286750\pi$
$151$	15.2605	1.24188	0.620941	+	0.783857i	$0.286750\pi$
$152$	−4.58853	−0.372179
$153$	−7.80145	−0.630710
$154$	−0.584739	−0.0471196
$155$	12.3340	0.990687
$156$	−5.44298	−0.435787
$157$	17.7161	1.41390	0.706948	−	0.707265i	$-0.250071\pi$
$157$	17.7161	1.41390	0.706948	+	0.707265i	$0.250071\pi$
$158$	−1.38653	−0.110306
$159$	−9.24653	−0.733297
$160$	19.3451	1.52936
$161$	1.70514	0.134384
$162$	0.506999	0.0398336
$163$	−19.4808	−1.52585	−0.762927	−	0.646485i	$-0.776238\pi$
$163$	−19.4808	−1.52585	−0.762927	+	0.646485i	$0.776238\pi$
$164$	−11.7618	−0.918439
$165$	−4.39640	−0.342259
$166$	1.34675	0.104528
$167$	−2.63695	−0.204053	−0.102027	−	0.994782i	$-0.532533\pi$
$167$	−2.63695	−0.204053	−0.102027	+	0.994782i	$0.532533\pi$
$168$	−1.89767	−0.146409
$169$	−3.24781	−0.249832
$170$	−15.0774	−1.15638
$171$	2.41797	0.184907
$172$	−18.7253	−1.42779
$173$	10.1726	0.773410	0.386705	−	0.922204i	$-0.373613\pi$
$173$	10.1726	0.773410	0.386705	+	0.922204i	$0.373613\pi$
$174$	0.963739	0.0730609
$175$	−9.53066	−0.720450
$176$	2.91076	0.219407
$177$	−13.7634	−1.03452
$178$	2.94478	0.220721
$179$	−10.5630	−0.789512	−0.394756	−	0.918786i	$-0.629171\pi$
$179$	−10.5630	−0.789512	−0.394756	+	0.918786i	$0.629171\pi$
$180$	−6.64398	−0.495213
$181$	24.0553	1.78802	0.894010	−	0.448048i	$-0.147881\pi$
$181$	24.0553	1.78802	0.894010	+	0.448048i	$0.147881\pi$
$182$	1.58328	0.117361
$183$	10.5466	0.779630
$184$	3.23581	0.238547
$185$	34.1165	2.50830
$186$	−1.64047	−0.120285
$187$	−8.99767	−0.657975
$188$	22.7169	1.65680
$189$	1.00000	0.0727393
$190$	4.67307	0.339020
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	2.47459	0.178588
$193$	18.2018	1.31019	0.655097	−	0.755545i	$-0.272628\pi$
$193$	18.2018	1.31019	0.655097	+	0.755545i	$0.272628\pi$
$194$	9.51821	0.683368
$195$	11.9040	0.852465
$196$	−1.74295	−0.124497
$197$	−18.4474	−1.31433	−0.657163	−	0.753748i	$-0.728244\pi$
$197$	−18.4474	−1.31433	−0.657163	+	0.753748i	$0.728244\pi$
$198$	0.584739	0.0415556
$199$	25.3729	1.79864	0.899319	−	0.437292i	$-0.144063\pi$
$199$	25.3729	1.79864	0.899319	+	0.437292i	$0.144063\pi$
$200$	−18.0861	−1.27888
$201$	8.41170	0.593315
$202$	−5.12951	−0.360911
$203$	1.90087	0.133415
$204$	−13.5976	−0.952019
$205$	25.7235	1.79661
$206$	−1.81025	−0.126126
$207$	−1.70514	−0.118516
$208$	−7.88140	−0.546477
$209$	2.78873	0.192900
$210$	1.93264	0.133365
$211$	3.22635	0.222111	0.111056	−	0.993814i	$-0.464577\pi$
$211$	3.22635	0.222111	0.111056	+	0.993814i	$0.464577\pi$
$212$	−16.1162	−1.10687
$213$	−7.90427	−0.541592
$214$	2.10877	0.144153
$215$	40.9531	2.79298
$216$	1.89767	0.129120
$217$	−3.23564	−0.219649
$218$	10.0396	0.679968
$219$	5.14832	0.347891
$220$	−7.66271	−0.516620
$221$	24.3628	1.63882
$222$	−4.53764	−0.304546
$223$	19.8111	1.32665	0.663324	−	0.748333i	$-0.269145\pi$
$223$	19.8111	1.32665	0.663324	+	0.748333i	$0.269145\pi$
$224$	−5.07490	−0.339081
$225$	9.53066	0.635378
$226$	3.32311	0.221050
$227$	16.8161	1.11612	0.558062	−	0.829799i	$-0.311545\pi$
$227$	16.8161	1.11612	0.558062	+	0.829799i	$0.311545\pi$
$228$	4.21441	0.279106
$229$	5.01220	0.331216	0.165608	−	0.986192i	$-0.447041\pi$
$229$	5.01220	0.331216	0.165608	+	0.986192i	$0.447041\pi$
$230$	−3.29542	−0.217294
$231$	1.15333	0.0758837
$232$	3.60723	0.236826
$233$	17.7921	1.16560	0.582799	−	0.812616i	$-0.301957\pi$
$233$	17.7921	1.16560	0.582799	+	0.812616i	$0.301957\pi$
$234$	−1.58328	−0.103502
$235$	−49.6829	−3.24095
$236$	−23.9889	−1.56155
$237$	2.73477	0.177643
$238$	3.95533	0.256386
$239$	−11.8709	−0.767867	−0.383934	−	0.923361i	$-0.625431\pi$
$239$	−11.8709	−0.767867	−0.383934	+	0.923361i	$0.625431\pi$
$240$	−9.62044	−0.620997
$241$	12.9171	0.832065	0.416033	−	0.909350i	$-0.363420\pi$
$241$	12.9171	0.832065	0.416033	+	0.909350i	$0.363420\pi$
$242$	−4.90260	−0.315151
$243$	−1.00000	−0.0641500
$244$	18.3823	1.17681
$245$	3.81191	0.243534
$246$	−3.42132	−0.218136
$247$	−7.55097	−0.480457
$248$	−6.14018	−0.389902
$249$	−2.65632	−0.168337
$250$	8.75613	0.553786
$251$	−12.1681	−0.768045	−0.384022	−	0.923324i	$-0.625461\pi$
$251$	−12.1681	−0.768045	−0.384022	+	0.923324i	$0.625461\pi$
$252$	1.74295	0.109796
$253$	−1.96660	−0.123639
$254$	−5.34121	−0.335137
$255$	29.7384	1.86229
$256$	−0.832850	−0.0520531
$257$	−8.17806	−0.510133	−0.255067	−	0.966923i	$-0.582097\pi$
$257$	−8.17806	−0.510133	−0.255067	+	0.966923i	$0.582097\pi$
$258$	−5.44693	−0.339111
$259$	−8.94998	−0.556125
$260$	20.7481	1.28674
$261$	−1.90087	−0.117661
$262$	−6.51779	−0.402671
$263$	22.1941	1.36855	0.684273	−	0.729226i	$-0.260120\pi$
$263$	22.1941	1.36855	0.684273	+	0.729226i	$0.260120\pi$
$264$	2.18865	0.134702
$265$	35.2469	2.16520
$266$	−1.22591	−0.0751655
$267$	−5.80825	−0.355459
$268$	14.6612	0.895574
$269$	14.9096	0.909053	0.454526	−	0.890733i	$-0.349809\pi$
$269$	14.9096	0.909053	0.454526	+	0.890733i	$0.349809\pi$
$270$	−1.93264	−0.117617
$271$	−9.13252	−0.554761	−0.277381	−	0.960760i	$-0.589466\pi$
$271$	−9.13252	−0.554761	−0.277381	+	0.960760i	$0.589466\pi$
$272$	−19.6892	−1.19383
$273$	−3.12285	−0.189003
$274$	9.03431	0.545783
$275$	10.9920	0.662844
$276$	−2.97198	−0.178892
$277$	−17.0757	−1.02598	−0.512990	−	0.858395i	$-0.671462\pi$
$277$	−17.0757	−1.02598	−0.512990	+	0.858395i	$0.671462\pi$
$278$	2.78353	0.166945
$279$	3.23564	0.193712
$280$	7.23376	0.432300
$281$	6.66486	0.397592	0.198796	−	0.980041i	$-0.436297\pi$
$281$	6.66486	0.397592	0.198796	+	0.980041i	$0.436297\pi$
$282$	6.60802	0.393502
$283$	−27.0944	−1.61060	−0.805298	−	0.592870i	$-0.797995\pi$
$283$	−27.0944	−1.61060	−0.805298	+	0.592870i	$0.797995\pi$
$284$	−13.7768	−0.817501
$285$	−9.21710	−0.545974
$286$	−1.82605	−0.107977
$287$	−6.74818	−0.398333
$288$	5.07490	0.299042
$289$	43.8627	2.58016
$290$	−3.67369	−0.215726
$291$	−18.7736	−1.10053
$292$	8.97328	0.525121
$293$	−14.3994	−0.841224	−0.420612	−	0.907241i	$-0.638185\pi$
$293$	−14.3994	−0.841224	−0.420612	+	0.907241i	$0.638185\pi$
$294$	−0.506999	−0.0295688
$295$	52.4648	3.05462
$296$	−16.9841	−0.987184
$297$	−1.15333	−0.0669231
$298$	3.54779	0.205518
$299$	5.32491	0.307947
$300$	16.6115	0.959065
$301$	−10.7435	−0.619243
$302$	7.73707	0.445218
$303$	10.1174	0.581229
$304$	6.10244	0.349999
$305$	−40.2029	−2.30201
$306$	−3.95533	−0.226111
$307$	−24.3210	−1.38807	−0.694036	−	0.719940i	$-0.744169\pi$
$307$	−24.3210	−1.38807	−0.694036	+	0.719940i	$0.744169\pi$
$308$	2.01020	0.114542
$309$	3.57052	0.203120
$310$	6.25331	0.355164
$311$	7.84611	0.444912	0.222456	−	0.974943i	$-0.428593\pi$
$311$	7.84611	0.444912	0.222456	+	0.974943i	$0.428593\pi$
$312$	−5.92615	−0.335502
$313$	−26.6741	−1.50771	−0.753856	−	0.657040i	$-0.771808\pi$
$313$	−26.6741	−1.50771	−0.753856	+	0.657040i	$0.771808\pi$
$314$	8.98204	0.506886
$315$	−3.81191	−0.214777
$316$	4.76658	0.268141
$317$	23.9848	1.34712	0.673560	−	0.739133i	$-0.264764\pi$
$317$	23.9848	1.34712	0.673560	+	0.739133i	$0.264764\pi$
$318$	−4.68798	−0.262889
$319$	−2.19233	−0.122747
$320$	−9.43293	−0.527317
$321$	−4.15931	−0.232150
$322$	0.864507	0.0481771
$323$	−18.8637	−1.04961
$324$	−1.74295	−0.0968306
$325$	−29.7628	−1.65094
$326$	−9.87675	−0.547023
$327$	−19.8020	−1.09505
$328$	−12.8059	−0.707085
$329$	13.0336	0.718565
$330$	−2.22897	−0.122701
$331$	10.5492	0.579836	0.289918	−	0.957051i	$-0.406372\pi$
$331$	10.5492	0.579836	0.289918	+	0.957051i	$0.406372\pi$
$332$	−4.62984	−0.254095
$333$	8.94998	0.490456
$334$	−1.33693	−0.0731536
$335$	−32.0646	−1.75188
$336$	2.52378	0.137684
$337$	12.5895	0.685795	0.342898	−	0.939373i	$-0.388592\pi$
$337$	12.5895	0.685795	0.342898	+	0.939373i	$0.388592\pi$
$338$	−1.64664	−0.0895653
$339$	−6.55447	−0.355990
$340$	51.8327	2.81102
$341$	3.73176	0.202086
$342$	1.22591	0.0662897
$343$	−1.00000	−0.0539949
$344$	−20.3876	−1.09923
$345$	6.49986	0.349940
$346$	5.15751	0.277269
$347$	−15.8156	−0.849026	−0.424513	−	0.905422i	$-0.639555\pi$
$347$	−15.8156	−0.849026	−0.424513	+	0.905422i	$0.639555\pi$
$348$	−3.31312	−0.177602
$349$	16.2238	0.868441	0.434220	−	0.900807i	$-0.357024\pi$
$349$	16.2238	0.868441	0.434220	+	0.900807i	$0.357024\pi$
$350$	−4.83204	−0.258283
$351$	3.12285	0.166685
$352$	5.85305	0.311969
$353$	−9.37322	−0.498886	−0.249443	−	0.968389i	$-0.580248\pi$
$353$	−9.37322	−0.498886	−0.249443	+	0.968389i	$0.580248\pi$
$354$	−6.97803	−0.370878
$355$	30.1304	1.59915
$356$	−10.1235	−0.536545
$357$	−7.80145	−0.412897
$358$	−5.35541	−0.283042
$359$	−19.9915	−1.05511	−0.527556	−	0.849520i	$-0.676891\pi$
$359$	−19.9915	−1.05511	−0.527556	+	0.849520i	$0.676891\pi$
$360$	−7.23376	−0.381253
$361$	−13.1534	−0.692284
$362$	12.1960	0.641010
$363$	9.66982	0.507534
$364$	−5.44298	−0.285289
$365$	−19.6249	−1.02722
$366$	5.34714	0.279500
$367$	−4.73510	−0.247170	−0.123585	−	0.992334i	$-0.539439\pi$
$367$	−4.73510	−0.247170	−0.123585	+	0.992334i	$0.539439\pi$
$368$	−4.30341	−0.224331
$369$	6.74818	0.351296
$370$	17.2971	0.899231
$371$	−9.24653	−0.480056
$372$	5.63956	0.292397
$373$	−13.0318	−0.674763	−0.337381	−	0.941368i	$-0.609541\pi$
$373$	−13.0318	−0.674763	−0.337381	+	0.941368i	$0.609541\pi$
$374$	−4.56181	−0.235886
$375$	−17.2705	−0.891844
$376$	24.7335	1.27553
$377$	5.93613	0.305726
$378$	0.506999	0.0260772
$379$	19.1134	0.981790	0.490895	−	0.871219i	$-0.336670\pi$
$379$	19.1134	0.981790	0.490895	+	0.871219i	$0.336670\pi$
$380$	−16.0650	−0.824115
$381$	10.5349	0.539722
$382$	0.506999	0.0259403
$383$	9.77339	0.499397	0.249698	−	0.968324i	$-0.419669\pi$
$383$	9.77339	0.499397	0.249698	+	0.968324i	$0.419669\pi$
$384$	11.4044	0.581980
$385$	−4.39640	−0.224061
$386$	9.22830	0.469708
$387$	10.7435	0.546121
$388$	−32.7215	−1.66118
$389$	29.8364	1.51277	0.756383	−	0.654129i	$-0.226965\pi$
$389$	29.8364	1.51277	0.756383	+	0.654129i	$0.226965\pi$
$390$	6.03533	0.305611
$391$	13.3026	0.672741
$392$	−1.89767	−0.0958470
$393$	12.8556	0.648480
$394$	−9.35284	−0.471189
$395$	−10.4247	−0.524524
$396$	−2.01020	−0.101016
$397$	−6.39694	−0.321053	−0.160527	−	0.987032i	$-0.551319\pi$
$397$	−6.39694	−0.321053	−0.160527	+	0.987032i	$0.551319\pi$
$398$	12.8641	0.644817
$399$	2.41797	0.121050
$400$	24.0533	1.20267
$401$	−6.07689	−0.303466	−0.151733	−	0.988422i	$-0.548485\pi$
$401$	−6.07689	−0.303466	−0.151733	+	0.988422i	$0.548485\pi$
$402$	4.26472	0.212705
$403$	−10.1044	−0.503336
$404$	17.6341	0.877331
$405$	3.81191	0.189415
$406$	0.963739	0.0478296
$407$	10.3223	0.511658
$408$	−14.8046	−0.732938
$409$	24.3782	1.20543	0.602713	−	0.797958i	$-0.294086\pi$
$409$	24.3782	1.20543	0.602713	+	0.797958i	$0.294086\pi$
$410$	13.0418	0.644088
$411$	−17.8192	−0.878955
$412$	6.22324	0.306597
$413$	−13.7634	−0.677252
$414$	−0.864507	−0.0424882
$415$	10.1257	0.497049
$416$	−15.8482	−0.777020
$417$	−5.49020	−0.268856
$418$	1.41388	0.0691553
$419$	7.39814	0.361423	0.180711	−	0.983536i	$-0.442160\pi$
$419$	7.39814	0.361423	0.180711	+	0.983536i	$0.442160\pi$
$420$	−6.64398	−0.324193
$421$	−38.3437	−1.86876	−0.934380	−	0.356279i	$-0.884045\pi$
$421$	−38.3437	−1.86876	−0.934380	+	0.356279i	$0.884045\pi$
$422$	1.63576	0.0796275
$423$	−13.0336	−0.633715
$424$	−17.5469	−0.852152
$425$	−74.3530	−3.60665
$426$	−4.00746	−0.194162
$427$	10.5466	0.510388
$428$	−7.24948	−0.350417
$429$	3.60168	0.173891
$430$	20.7632	1.00129
$431$	−8.07052	−0.388743	−0.194372	−	0.980928i	$-0.562267\pi$
$431$	−8.07052	−0.388743	−0.194372	+	0.980928i	$0.562267\pi$
$432$	−2.52378	−0.121426
$433$	−21.1084	−1.01440	−0.507202	−	0.861827i	$-0.669320\pi$
$433$	−21.1084	−1.01440	−0.507202	+	0.861827i	$0.669320\pi$
$434$	−1.64047	−0.0787448
$435$	7.24594	0.347416
$436$	−34.5139	−1.65292
$437$	−4.12299	−0.197230
$438$	2.61020	0.124720
$439$	−17.2203	−0.821882	−0.410941	−	0.911662i	$-0.634800\pi$
$439$	−17.2203	−0.821882	−0.410941	+	0.911662i	$0.634800\pi$
$440$	−8.34293	−0.397734
$441$	1.00000	0.0476190
$442$	12.3519	0.587520
$443$	18.3428	0.871491	0.435746	−	0.900070i	$-0.356485\pi$
$443$	18.3428	0.871491	0.435746	+	0.900070i	$0.356485\pi$
$444$	15.5994	0.740314
$445$	22.1405	1.04956
$446$	10.0442	0.475607
$447$	−6.99762	−0.330976
$448$	2.47459	0.116914
$449$	16.4398	0.775843	0.387922	−	0.921692i	$-0.373193\pi$
$449$	16.4398	0.775843	0.387922	+	0.921692i	$0.373193\pi$
$450$	4.83204	0.227785
$451$	7.78290	0.366482
$452$	−11.4241	−0.537346
$453$	−15.2605	−0.717001
$454$	8.52576	0.400134
$455$	11.9040	0.558069
$456$	4.58853	0.214877
$457$	3.37336	0.157799	0.0788996	−	0.996883i	$-0.474859\pi$
$457$	3.37336	0.157799	0.0788996	+	0.996883i	$0.474859\pi$
$458$	2.54118	0.118742
$459$	7.80145	0.364141
$460$	11.3289	0.528214
$461$	−36.4900	−1.69951	−0.849754	−	0.527180i	$-0.823249\pi$
$461$	−36.4900	−1.69951	−0.849754	+	0.527180i	$0.823249\pi$
$462$	0.584739	0.0272045
$463$	16.4535	0.764660	0.382330	−	0.924026i	$-0.375122\pi$
$463$	16.4535	0.764660	0.382330	+	0.924026i	$0.375122\pi$
$464$	−4.79738	−0.222713
$465$	−12.3340	−0.571973
$466$	9.02058	0.417870
$467$	18.0914	0.837170	0.418585	−	0.908178i	$-0.362526\pi$
$467$	18.0914	0.837170	0.418585	+	0.908178i	$0.362526\pi$
$468$	5.44298	0.251602
$469$	8.41170	0.388416
$470$	−25.1892	−1.16189
$471$	−17.7161	−0.816314
$472$	−26.1184	−1.20220
$473$	12.3908	0.569729
$474$	1.38653	0.0636854
$475$	23.0449	1.05737
$476$	−13.5976	−0.623243
$477$	9.24653	0.423369
$478$	−6.01856	−0.275282
$479$	24.2136	1.10635	0.553174	−	0.833066i	$-0.313417\pi$
$479$	24.2136	1.10635	0.553174	+	0.833066i	$0.313417\pi$
$480$	−19.3451	−0.882978
$481$	−27.9494	−1.27439
$482$	6.54898	0.298298
$483$	−1.70514	−0.0775867
$484$	16.8540	0.766093
$485$	71.5633	3.24952
$486$	−0.506999	−0.0229980
$487$	−7.34354	−0.332768	−0.166384	−	0.986061i	$-0.553209\pi$
$487$	−7.34354	−0.332768	−0.166384	+	0.986061i	$0.553209\pi$
$488$	20.0141	0.905995
$489$	19.4808	0.880952
$490$	1.93264	0.0873076
$491$	−13.9250	−0.628425	−0.314212	−	0.949353i	$-0.601740\pi$
$491$	−13.9250	−0.628425	−0.314212	+	0.949353i	$0.601740\pi$
$492$	11.7618	0.530261
$493$	14.8295	0.667889
$494$	−3.82834	−0.172245
$495$	4.39640	0.197603
$496$	8.16604	0.366666
$497$	−7.90427	−0.354555
$498$	−1.34675	−0.0603494
$499$	38.9243	1.74249	0.871246	−	0.490847i	$-0.163313\pi$
$499$	38.9243	1.74249	0.871246	+	0.490847i	$0.163313\pi$
$500$	−30.1016	−1.34619
$501$	2.63695	0.117810
$502$	−6.16923	−0.275346
$503$	−12.7100	−0.566712	−0.283356	−	0.959015i	$-0.591448\pi$
$503$	−12.7100	−0.566712	−0.283356	+	0.959015i	$0.591448\pi$
$504$	1.89767	0.0845291
$505$	−38.5666	−1.71619
$506$	−0.997064	−0.0443249
$507$	3.24781	0.144240
$508$	18.3619	0.814678
$509$	36.0376	1.59734	0.798669	−	0.601770i	$-0.205538\pi$
$509$	36.0376	1.59734	0.798669	+	0.601770i	$0.205538\pi$
$510$	15.0774	0.667637
$511$	5.14832	0.227748
$512$	22.3866	0.989357
$513$	−2.41797	−0.106756
$514$	−4.14627	−0.182884
$515$	−13.6105	−0.599750
$516$	18.7253	0.824337
$517$	−15.0321	−0.661109
$518$	−4.53764	−0.199372
$519$	−10.1726	−0.446528
$520$	22.5900	0.990635
$521$	−2.42813	−0.106378	−0.0531891	−	0.998584i	$-0.516939\pi$
$521$	−2.42813	−0.106378	−0.0531891	+	0.998584i	$0.516939\pi$
$522$	−0.963739	−0.0421817
$523$	−26.8718	−1.17502	−0.587511	−	0.809216i	$-0.699892\pi$
$523$	−26.8718	−1.17502	−0.587511	+	0.809216i	$0.699892\pi$
$524$	22.4067	0.978842
$525$	9.53066	0.415952
$526$	11.2524	0.490627
$527$	−25.2427	−1.09959
$528$	−2.91076	−0.126675
$529$	−20.0925	−0.873586
$530$	17.8702	0.776231
$531$	13.7634	0.597280
$532$	4.21441	0.182718
$533$	−21.0736	−0.912797
$534$	−2.94478	−0.127433
$535$	15.8549	0.685469
$536$	15.9627	0.689482
$537$	10.5630	0.455825
$538$	7.55915	0.325898
$539$	1.15333	0.0496775
$540$	6.64398	0.285911
$541$	−18.9801	−0.816017	−0.408008	−	0.912978i	$-0.633777\pi$
$541$	−18.9801	−0.816017	−0.408008	+	0.912978i	$0.633777\pi$
$542$	−4.63018	−0.198883
$543$	−24.0553	−1.03231
$544$	−39.5916	−1.69748
$545$	75.4835	3.23336
$546$	−1.58328	−0.0677582
$547$	4.98616	0.213193	0.106596	−	0.994302i	$-0.466005\pi$
$547$	4.98616	0.213193	0.106596	+	0.994302i	$0.466005\pi$
$548$	−31.0580	−1.32673
$549$	−10.5466	−0.450120
$550$	5.57295	0.237631
$551$	−4.59625	−0.195807
$552$	−3.23581	−0.137725
$553$	2.73477	0.116294
$554$	−8.65737	−0.367816
$555$	−34.1165	−1.44817
$556$	−9.56915	−0.405822
$557$	−0.227993	−0.00966036	−0.00483018	−	0.999988i	$-0.501538\pi$
$557$	−0.227993	−0.00966036	−0.00483018	+	0.999988i	$0.501538\pi$
$558$	1.64047	0.0694464
$559$	−33.5502	−1.41902
$560$	−9.62044	−0.406538
$561$	8.99767	0.379882
$562$	3.37908	0.142538
$563$	−37.5873	−1.58411	−0.792057	−	0.610447i	$-0.790990\pi$
$563$	−37.5873	−1.58411	−0.792057	+	0.610447i	$0.790990\pi$
$564$	−22.7169	−0.956555
$565$	24.9851	1.05113
$566$	−13.7369	−0.577403
$567$	−1.00000	−0.0419961
$568$	−14.9997	−0.629375
$569$	−0.751008	−0.0314839	−0.0157420	−	0.999876i	$-0.505011\pi$
$569$	−0.751008	−0.0314839	−0.0157420	+	0.999876i	$0.505011\pi$
$570$	−4.67307	−0.195733
$571$	24.7416	1.03541	0.517703	−	0.855561i	$-0.326787\pi$
$571$	24.7416	1.03541	0.517703	+	0.855561i	$0.326787\pi$
$572$	6.27756	0.262478
$573$	−1.00000	−0.0417756
$574$	−3.42132	−0.142803
$575$	−16.2512	−0.677720
$576$	−2.47459	−0.103108
$577$	45.1506	1.87965	0.939823	−	0.341662i	$-0.110990\pi$
$577$	45.1506	1.87965	0.939823	+	0.341662i	$0.110990\pi$
$578$	22.2383	0.924993
$579$	−18.2018	−0.756441
$580$	12.6293	0.524404
$581$	−2.65632	−0.110203
$582$	−9.51821	−0.394542
$583$	10.6643	0.441671
$584$	9.76984	0.404279
$585$	−11.9040	−0.492171
$586$	−7.30050	−0.301581
$587$	−4.05704	−0.167452	−0.0837259	−	0.996489i	$-0.526682\pi$
$587$	−4.05704	−0.167452	−0.0837259	+	0.996489i	$0.526682\pi$
$588$	1.74295	0.0718781
$589$	7.82368	0.322369
$590$	26.5996	1.09509
$591$	18.4474	0.758827
$592$	22.5878	0.928354
$593$	−33.4274	−1.37270	−0.686348	−	0.727273i	$-0.740788\pi$
$593$	−33.4274	−1.37270	−0.686348	+	0.727273i	$0.740788\pi$
$594$	−0.584739	−0.0239921
$595$	29.7384	1.21916
$596$	−12.1965	−0.499588
$597$	−25.3729	−1.03844
$598$	2.69972	0.110400
$599$	28.2020	1.15230	0.576151	−	0.817343i	$-0.304554\pi$
$599$	28.2020	1.15230	0.576151	+	0.817343i	$0.304554\pi$
$600$	18.0861	0.738362
$601$	23.4739	0.957521	0.478760	−	0.877946i	$-0.341086\pi$
$601$	23.4739	0.957521	0.478760	+	0.877946i	$0.341086\pi$
$602$	−5.44693	−0.222000
$603$	−8.41170	−0.342551
$604$	−26.5983	−1.08227
$605$	−36.8605	−1.49859
$606$	5.12951	0.208372
$607$	−32.2143	−1.30754	−0.653770	−	0.756693i	$-0.726814\pi$
$607$	−32.2143	−1.30754	−0.653770	+	0.756693i	$0.726814\pi$
$608$	12.2710	0.497654
$609$	−1.90087	−0.0770271
$610$	−20.3828	−0.825276
$611$	40.7019	1.64662
$612$	13.5976	0.549649
$613$	47.6295	1.92374	0.961869	−	0.273511i	$-0.0881850\pi$
$613$	47.6295	1.92374	0.961869	+	0.273511i	$0.0881850\pi$
$614$	−12.3307	−0.497628
$615$	−25.7235	−1.03727
$616$	2.18865	0.0881832
$617$	5.47388	0.220370	0.110185	−	0.993911i	$-0.464856\pi$
$617$	5.47388	0.220370	0.110185	+	0.993911i	$0.464856\pi$
$618$	1.81025	0.0728189
$619$	−19.8521	−0.797924	−0.398962	−	0.916968i	$-0.630629\pi$
$619$	−19.8521	−0.797924	−0.398962	+	0.916968i	$0.630629\pi$
$620$	−21.4975	−0.863360
$621$	1.70514	0.0684251
$622$	3.97797	0.159502
$623$	−5.80825	−0.232703
$624$	7.88140	0.315508
$625$	18.1802	0.727209
$626$	−13.5238	−0.540519
$627$	−2.78873	−0.111371
$628$	−30.8783	−1.23218
$629$	−69.8229	−2.78402
$630$	−1.93264	−0.0769981
$631$	−5.41254	−0.215470	−0.107735	−	0.994180i	$-0.534360\pi$
$631$	−5.41254	−0.215470	−0.107735	+	0.994180i	$0.534360\pi$
$632$	5.18971	0.206436
$633$	−3.22635	−0.128236
$634$	12.1603	0.482946
$635$	−40.1583	−1.59363
$636$	16.1162	0.639051
$637$	−3.12285	−0.123732
$638$	−1.11151	−0.0440052
$639$	7.90427	0.312688
$640$	−43.4727	−1.71841
$641$	−9.08769	−0.358942	−0.179471	−	0.983763i	$-0.557439\pi$
$641$	−9.08769	−0.358942	−0.179471	+	0.983763i	$0.557439\pi$
$642$	−2.10877	−0.0832265
$643$	−35.9382	−1.41727	−0.708633	−	0.705577i	$-0.750688\pi$
$643$	−35.9382	−1.41727	−0.708633	+	0.705577i	$0.750688\pi$
$644$	−2.97198	−0.117113
$645$	−40.9531	−1.61253
$646$	−9.56389	−0.376286
$647$	−32.2591	−1.26823	−0.634117	−	0.773237i	$-0.718636\pi$
$647$	−32.2591	−1.26823	−0.634117	+	0.773237i	$0.718636\pi$
$648$	−1.89767	−0.0745477
$649$	15.8738	0.623100
$650$	−15.0897	−0.591868
$651$	3.23564	0.126815
$652$	33.9541	1.32974
$653$	−38.6149	−1.51112	−0.755559	−	0.655081i	$-0.772634\pi$
$653$	−38.6149	−1.51112	−0.755559	+	0.655081i	$0.772634\pi$
$654$	−10.0396	−0.392580
$655$	−49.0045	−1.91476
$656$	17.0310	0.664947
$657$	−5.14832	−0.200855
$658$	6.60802	0.257608
$659$	−26.3867	−1.02788	−0.513939	−	0.857827i	$-0.671814\pi$
$659$	−26.3867	−1.02788	−0.513939	+	0.857827i	$0.671814\pi$
$660$	7.66271	0.298271
$661$	5.74713	0.223537	0.111769	−	0.993734i	$-0.464348\pi$
$661$	5.74713	0.223537	0.111769	+	0.993734i	$0.464348\pi$
$662$	5.34843	0.207873
$663$	−24.3628	−0.946171
$664$	−5.04083	−0.195622
$665$	−9.21710	−0.357424
$666$	4.53764	0.175830
$667$	3.24125	0.125502
$668$	4.59607	0.177827
$669$	−19.8111	−0.765940
$670$	−16.2567	−0.628053
$671$	−12.1638	−0.469578
$672$	5.07490	0.195769
$673$	−14.9580	−0.576590	−0.288295	−	0.957542i	$-0.593088\pi$
$673$	−14.9580	−0.576590	−0.288295	+	0.957542i	$0.593088\pi$
$674$	6.38288	0.245859
$675$	−9.53066	−0.366835
$676$	5.66078	0.217722
$677$	11.7060	0.449900	0.224950	−	0.974370i	$-0.427778\pi$
$677$	11.7060	0.449900	0.224950	+	0.974370i	$0.427778\pi$
$678$	−3.32311	−0.127623
$679$	−18.7736	−0.720465
$680$	56.4339	2.16414
$681$	−16.8161	−0.644395
$682$	1.89200	0.0724485
$683$	22.4390	0.858605	0.429303	−	0.903161i	$-0.358759\pi$
$683$	22.4390	0.858605	0.429303	+	0.903161i	$0.358759\pi$
$684$	−4.21441	−0.161142
$685$	67.9251	2.59528
$686$	−0.506999	−0.0193573
$687$	−5.01220	−0.191227
$688$	27.1142	1.03372
$689$	−28.8755	−1.10007
$690$	3.29542	0.125455
$691$	−48.7960	−1.85629	−0.928143	−	0.372223i	$-0.878596\pi$
$691$	−48.7960	−1.85629	−0.928143	+	0.372223i	$0.878596\pi$
$692$	−17.7304	−0.674008
$693$	−1.15333	−0.0438115
$694$	−8.01850	−0.304378
$695$	20.9281	0.793850
$696$	−3.60723	−0.136732
$697$	−52.6456	−1.99410
$698$	8.22546	0.311338
$699$	−17.7921	−0.672959
$700$	16.6115	0.627855
$701$	34.8293	1.31549	0.657743	−	0.753243i	$-0.271511\pi$
$701$	34.8293	1.31549	0.657743	+	0.753243i	$0.271511\pi$
$702$	1.58328	0.0597572
$703$	21.6408	0.816199
$704$	−2.85403	−0.107565
$705$	49.6829	1.87117
$706$	−4.75222	−0.178852
$707$	10.1174	0.380504
$708$	23.9889	0.901559
$709$	13.5131	0.507494	0.253747	−	0.967271i	$-0.418337\pi$
$709$	13.5131	0.507494	0.253747	+	0.967271i	$0.418337\pi$
$710$	15.2761	0.573301
$711$	−2.73477	−0.102562
$712$	−11.0222	−0.413073
$713$	−5.51722	−0.206622
$714$	−3.95533	−0.148025
$715$	−13.7293	−0.513446
$716$	18.4107	0.688041
$717$	11.8709	0.443328
$718$	−10.1357	−0.378260
$719$	−30.6638	−1.14357	−0.571783	−	0.820405i	$-0.693748\pi$
$719$	−30.6638	−1.14357	−0.571783	+	0.820405i	$0.693748\pi$
$720$	9.62044	0.358533
$721$	3.57052	0.132973
$722$	−6.66877	−0.248186
$723$	−12.9171	−0.480393
$724$	−41.9273	−1.55822
$725$	−18.1165	−0.672831
$726$	4.90260	0.181952
$727$	11.7320	0.435117	0.217558	−	0.976047i	$-0.430191\pi$
$727$	11.7320	0.435117	0.217558	+	0.976047i	$0.430191\pi$
$728$	−5.92615	−0.219638
$729$	1.00000	0.0370370
$730$	−9.94984	−0.368260
$731$	−83.8147	−3.10000
$732$	−18.3823	−0.679429
$733$	27.8401	1.02830	0.514148	−	0.857701i	$-0.328108\pi$
$733$	27.8401	1.02830	0.514148	+	0.857701i	$0.328108\pi$
$734$	−2.40069	−0.0886111
$735$	−3.81191	−0.140604
$736$	−8.65344	−0.318970
$737$	−9.70148	−0.357359
$738$	3.42132	0.125941
$739$	25.2869	0.930194	0.465097	−	0.885260i	$-0.346020\pi$
$739$	25.2869	0.930194	0.465097	+	0.885260i	$0.346020\pi$
$740$	−59.4635	−2.18592
$741$	7.55097	0.277392
$742$	−4.68798	−0.172101
$743$	−53.1130	−1.94853	−0.974264	−	0.225410i	$-0.927628\pi$
$743$	−53.1130	−1.94853	−0.974264	+	0.225410i	$0.927628\pi$
$744$	6.14018	0.225110
$745$	26.6743	0.977270
$746$	−6.60713	−0.241904
$747$	2.65632	0.0971897
$748$	15.6825	0.573409
$749$	−4.15931	−0.151978
$750$	−8.75613	−0.319729
$751$	34.4616	1.25752	0.628762	−	0.777598i	$-0.283562\pi$
$751$	34.4616	1.25752	0.628762	+	0.777598i	$0.283562\pi$
$752$	−32.8940	−1.19952
$753$	12.1681	0.443431
$754$	3.00961	0.109604
$755$	58.1717	2.11709
$756$	−1.74295	−0.0633905
$757$	−29.4107	−1.06895	−0.534475	−	0.845184i	$-0.679491\pi$
$757$	−29.4107	−1.06895	−0.534475	+	0.845184i	$0.679491\pi$
$758$	9.69049	0.351974
$759$	1.96660	0.0713830
$760$	−17.4911	−0.634467
$761$	0.820356	0.0297379	0.0148689	−	0.999889i	$-0.495267\pi$
$761$	0.820356	0.0297379	0.0148689	+	0.999889i	$0.495267\pi$
$762$	5.34121	0.193492
$763$	−19.8020	−0.716881
$764$	−1.74295	−0.0630578
$765$	−29.7384	−1.07520
$766$	4.95510	0.179035
$767$	−42.9810	−1.55195
$768$	0.832850	0.0300529
$769$	39.0653	1.40873	0.704365	−	0.709838i	$-0.251232\pi$
$769$	39.0653	1.40873	0.704365	+	0.709838i	$0.251232\pi$
$770$	−2.22897	−0.0803266
$771$	8.17806	0.294526
$772$	−31.7248	−1.14180
$773$	−4.05253	−0.145759	−0.0728797	−	0.997341i	$-0.523219\pi$
$773$	−4.05253	−0.145759	−0.0728797	+	0.997341i	$0.523219\pi$
$774$	5.44693	0.195786
$775$	30.8378	1.10772
$776$	−35.6262	−1.27891
$777$	8.94998	0.321079
$778$	15.1270	0.542331
$779$	16.3169	0.584615
$780$	−20.7481	−0.742902
$781$	9.11625	0.326205
$782$	6.74441	0.241180
$783$	1.90087	0.0679315
$784$	2.52378	0.0901351
$785$	67.5321	2.41032
$786$	6.51779	0.232482
$787$	−27.4592	−0.978814	−0.489407	−	0.872056i	$-0.662787\pi$
$787$	−27.4592	−0.978814	−0.489407	+	0.872056i	$0.662787\pi$
$788$	32.1530	1.14540
$789$	−22.1941	−0.790130
$790$	−5.28532	−0.188043
$791$	−6.55447	−0.233050
$792$	−2.18865	−0.0777702
$793$	32.9356	1.16958
$794$	−3.24325	−0.115098
$795$	−35.2469	−1.25008
$796$	−44.2238	−1.56747
$797$	−24.5164	−0.868414	−0.434207	−	0.900813i	$-0.642971\pi$
$797$	−24.5164	−0.868414	−0.434207	+	0.900813i	$0.642971\pi$
$798$	1.22591	0.0433968
$799$	101.681	3.59721
$800$	48.3672	1.71004
$801$	5.80825	0.205225
$802$	−3.08098	−0.108793
$803$	−5.93773	−0.209538
$804$	−14.6612	−0.517060
$805$	6.49986	0.229090
$806$	−5.12293	−0.180447
$807$	−14.9096	−0.524842
$808$	19.1995	0.675437
$809$	17.8439	0.627358	0.313679	−	0.949529i	$-0.398438\pi$
$809$	17.8439	0.627358	0.313679	+	0.949529i	$0.398438\pi$
$810$	1.93264	0.0679059
$811$	19.9645	0.701048	0.350524	−	0.936554i	$-0.386003\pi$
$811$	19.9645	0.701048	0.350524	+	0.936554i	$0.386003\pi$
$812$	−3.31312	−0.116268
$813$	9.13252	0.320291
$814$	5.23340	0.183431
$815$	−74.2591	−2.60118
$816$	19.6892	0.689259
$817$	25.9774	0.908835
$818$	12.3597	0.432148
$819$	3.12285	0.109121
$820$	−44.8348	−1.56570
$821$	−22.6761	−0.791400	−0.395700	−	0.918380i	$-0.629498\pi$
$821$	−22.6761	−0.791400	−0.395700	+	0.918380i	$0.629498\pi$
$822$	−9.03431	−0.315108
$823$	−11.9789	−0.417557	−0.208779	−	0.977963i	$-0.566949\pi$
$823$	−11.9789	−0.417557	−0.208779	+	0.977963i	$0.566949\pi$
$824$	6.77568	0.236042
$825$	−10.9920	−0.382693
$826$	−6.97803	−0.242797
$827$	−31.5074	−1.09562	−0.547810	−	0.836603i	$-0.684538\pi$
$827$	−31.5074	−1.09562	−0.547810	+	0.836603i	$0.684538\pi$
$828$	2.97198	0.103284
$829$	34.2123	1.18824	0.594121	−	0.804376i	$-0.297500\pi$
$829$	34.2123	1.18824	0.594121	+	0.804376i	$0.297500\pi$
$830$	5.13370	0.178193
$831$	17.0757	0.592349
$832$	7.72778	0.267913
$833$	−7.80145	−0.270304
$834$	−2.78353	−0.0963856
$835$	−10.0518	−0.347857
$836$	−4.86062	−0.168108
$837$	−3.23564	−0.111840
$838$	3.75085	0.129571
$839$	−22.6308	−0.781300	−0.390650	−	0.920539i	$-0.627750\pi$
$839$	−22.6308	−0.781300	−0.390650	+	0.920539i	$0.627750\pi$
$840$	−7.23376	−0.249589
$841$	−25.3867	−0.875403
$842$	−19.4402	−0.669955
$843$	−6.66486	−0.229550
$844$	−5.62338	−0.193565
$845$	−12.3804	−0.425898
$846$	−6.60802	−0.227188
$847$	9.66982	0.332259
$848$	23.3362	0.801369
$849$	27.0944	0.929878
$850$	−37.6969	−1.29299
$851$	−15.2610	−0.523141
$852$	13.7768	0.471984
$853$	7.22254	0.247295	0.123648	−	0.992326i	$-0.460541\pi$
$853$	7.22254	0.247295	0.123648	+	0.992326i	$0.460541\pi$
$854$	5.34714	0.182975
$855$	9.21710	0.315218
$856$	−7.89302	−0.269778
$857$	31.7298	1.08387	0.541934	−	0.840421i	$-0.317692\pi$
$857$	31.7298	1.08387	0.541934	+	0.840421i	$0.317692\pi$
$858$	1.82605	0.0623403
$859$	−47.5838	−1.62354	−0.811769	−	0.583978i	$-0.801495\pi$
$859$	−47.5838	−1.62354	−0.811769	+	0.583978i	$0.801495\pi$
$860$	−71.3793	−2.43402
$861$	6.74818	0.229977
$862$	−4.09175	−0.139366
$863$	−33.8979	−1.15390	−0.576949	−	0.816780i	$-0.695757\pi$
$863$	−33.8979	−1.15390	−0.576949	+	0.816780i	$0.695757\pi$
$864$	−5.07490	−0.172652
$865$	38.7771	1.31846
$866$	−10.7019	−0.363667
$867$	−43.8627	−1.48965
$868$	5.63956	0.191419
$869$	−3.15410	−0.106996
$870$	3.67369	0.124550
$871$	26.2685	0.890073
$872$	−37.5777	−1.27254
$873$	18.7736	0.635390
$874$	−2.09036	−0.0707073
$875$	−17.2705	−0.583849
$876$	−8.97328	−0.303179
$877$	6.06253	0.204717	0.102359	−	0.994748i	$-0.467361\pi$
$877$	6.06253	0.204717	0.102359	+	0.994748i	$0.467361\pi$
$878$	−8.73070	−0.294647
$879$	14.3994	0.485681
$880$	11.0956	0.374031
$881$	−44.9522	−1.51448	−0.757239	−	0.653138i	$-0.773452\pi$
$881$	−44.9522	−1.51448	−0.757239	+	0.653138i	$0.773452\pi$
$882$	0.506999	0.0170716
$883$	−49.1719	−1.65476	−0.827382	−	0.561639i	$-0.810171\pi$
$883$	−49.1719	−1.65476	−0.827382	+	0.561639i	$0.810171\pi$
$884$	−42.4631	−1.42819
$885$	−52.4648	−1.76359
$886$	9.29977	0.312432
$887$	−14.1709	−0.475813	−0.237907	−	0.971288i	$-0.576461\pi$
$887$	−14.1709	−0.475813	−0.237907	+	0.971288i	$0.576461\pi$
$888$	16.9841	0.569951
$889$	10.5349	0.353331
$890$	11.2252	0.376271
$891$	1.15333	0.0386381
$892$	−34.5297	−1.15614
$893$	−31.5149	−1.05461
$894$	−3.54779	−0.118656
$895$	−40.2650	−1.34591
$896$	11.4044	0.380995
$897$	−5.32491	−0.177793
$898$	8.33498	0.278142
$899$	−6.15052	−0.205131
$900$	−16.6115	−0.553716
$901$	−72.1363	−2.40321
$902$	3.94592	0.131385
$903$	10.7435	0.357520
$904$	−12.4383	−0.413690
$905$	91.6968	3.04810
$906$	−7.73707	−0.257047
$907$	−19.1608	−0.636224	−0.318112	−	0.948053i	$-0.603049\pi$
$907$	−19.1608	−0.636224	−0.318112	+	0.948053i	$0.603049\pi$
$908$	−29.3097	−0.972675
$909$	−10.1174	−0.335573
$910$	6.03533	0.200069
$911$	20.6663	0.684705	0.342352	−	0.939572i	$-0.388776\pi$
$911$	20.6663	0.684705	0.342352	+	0.939572i	$0.388776\pi$
$912$	−6.10244	−0.202072
$913$	3.06362	0.101391
$914$	1.71029	0.0565714
$915$	40.2029	1.32907
$916$	−8.73602	−0.288646
$917$	12.8556	0.424530
$918$	3.95533	0.130545
$919$	−10.1596	−0.335135	−0.167567	−	0.985861i	$-0.553591\pi$
$919$	−10.1596	−0.335135	−0.167567	+	0.985861i	$0.553591\pi$
$920$	12.3346	0.406660
$921$	24.3210	0.801404
$922$	−18.5004	−0.609278
$923$	−24.6839	−0.812479
$924$	−2.01020	−0.0661308
$925$	85.2993	2.80462
$926$	8.34193	0.274133
$927$	−3.57052	−0.117271
$928$	−9.64673	−0.316669
$929$	−1.44696	−0.0474731	−0.0237366	−	0.999718i	$-0.507556\pi$
$929$	−1.44696	−0.0474731	−0.0237366	+	0.999718i	$0.507556\pi$
$930$	−6.25331	−0.205054
$931$	2.41797	0.0792459
$932$	−31.0108	−1.01579
$933$	−7.84611	−0.256870
$934$	9.17233	0.300128
$935$	−34.2983	−1.12167
$936$	5.92615	0.193702
$937$	17.0282	0.556286	0.278143	−	0.960540i	$-0.410281\pi$
$937$	17.0282	0.556286	0.278143	+	0.960540i	$0.410281\pi$
$938$	4.26472	0.139248
$939$	26.6741	0.870478
$940$	86.5949	2.82441
$941$	15.4801	0.504637	0.252319	−	0.967644i	$-0.418807\pi$
$941$	15.4801	0.504637	0.252319	+	0.967644i	$0.418807\pi$
$942$	−8.98204	−0.292651
$943$	−11.5066	−0.374707
$944$	34.7358	1.13055
$945$	3.81191	0.124001
$946$	6.28212	0.204249
$947$	−33.7721	−1.09745	−0.548723	−	0.836004i	$-0.684886\pi$
$947$	−33.7721	−1.09745	−0.548723	+	0.836004i	$0.684886\pi$
$948$	−4.76658	−0.154811
$949$	16.0774	0.521896
$950$	11.6838	0.379071
$951$	−23.9848	−0.777760
$952$	−14.8046	−0.479820
$953$	31.2540	1.01242	0.506209	−	0.862411i	$-0.331047\pi$
$953$	31.2540	1.01242	0.506209	+	0.862411i	$0.331047\pi$
$954$	4.68798	0.151779
$955$	3.81191	0.123351
$956$	20.6905	0.669178
$957$	2.19233	0.0708680
$958$	12.2763	0.396629
$959$	−17.8192	−0.575411
$960$	9.43293	0.304447
$961$	−20.5307	−0.662279
$962$	−14.1704	−0.456870
$963$	4.15931	0.134032
$964$	−22.5139	−0.725125
$965$	69.3836	2.23354
$966$	−0.864507	−0.0278151
$967$	50.6013	1.62723	0.813613	−	0.581406i	$-0.197497\pi$
$967$	50.6013	1.62723	0.813613	+	0.581406i	$0.197497\pi$
$968$	18.3502	0.589797
$969$	18.8637	0.605990
$970$	36.2826	1.16496
$971$	15.9574	0.512099	0.256049	−	0.966664i	$-0.417579\pi$
$971$	15.9574	0.512099	0.256049	+	0.966664i	$0.417579\pi$
$972$	1.74295	0.0559052
$973$	−5.49020	−0.176008
$974$	−3.72317	−0.119298
$975$	29.7628	0.953173
$976$	−26.6174	−0.852004
$977$	−48.2540	−1.54378	−0.771892	−	0.635754i	$-0.780689\pi$
$977$	−48.2540	−1.54378	−0.771892	+	0.635754i	$0.780689\pi$
$978$	9.87675	0.315824
$979$	6.69884	0.214096
$980$	−6.64398	−0.212234
$981$	19.8020	0.632229
$982$	−7.05995	−0.225292
$983$	−51.5678	−1.64476	−0.822379	−	0.568940i	$-0.807354\pi$
$983$	−51.5678	−1.64476	−0.822379	+	0.568940i	$0.807354\pi$
$984$	12.8059	0.408236
$985$	−70.3200	−2.24058
$986$	7.51856	0.239440
$987$	−13.0336	−0.414864
$988$	13.1610	0.418706
$989$	−18.3192	−0.582515
$990$	2.22897	0.0708414
$991$	9.14713	0.290568	0.145284	−	0.989390i	$-0.453590\pi$
$991$	9.14713	0.290568	0.145284	+	0.989390i	$0.453590\pi$
$992$	16.4205	0.521353
$993$	−10.5492	−0.334768
$994$	−4.00746	−0.127109
$995$	96.7193	3.06621
$996$	4.62984	0.146702
$997$	34.4428	1.09081	0.545407	−	0.838171i	$-0.316375\pi$
$997$	34.4428	1.09081	0.545407	+	0.838171i	$0.316375\pi$
$998$	19.7346	0.624688
$999$	−8.94998	−0.283165

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.j.1.15	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.j.1.15	✓	26	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q+0.506999 q^{2} -1.00000 q^{3} -1.74295 q^{4} +3.81191 q^{5} -0.506999 q^{6} -1.00000 q^{7} -1.89767 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.506999 q^{2} -1.00000 q^{3} -1.74295 q^{4} +3.81191 q^{5} -0.506999 q^{6} -1.00000 q^{7} -1.89767 q^{8} +1.00000 q^{9} +1.93264 q^{10} +1.15333 q^{11} +1.74295 q^{12} -3.12285 q^{13} -0.506999 q^{14} -3.81191 q^{15} +2.52378 q^{16} -7.80145 q^{17} +0.506999 q^{18} +2.41797 q^{19} -6.64398 q^{20} +1.00000 q^{21} +0.584739 q^{22} -1.70514 q^{23} +1.89767 q^{24} +9.53066 q^{25} -1.58328 q^{26} -1.00000 q^{27} +1.74295 q^{28} -1.90087 q^{29} -1.93264 q^{30} +3.23564 q^{31} +5.07490 q^{32} -1.15333 q^{33} -3.95533 q^{34} -3.81191 q^{35} -1.74295 q^{36} +8.94998 q^{37} +1.22591 q^{38} +3.12285 q^{39} -7.23376 q^{40} +6.74818 q^{41} +0.506999 q^{42} +10.7435 q^{43} -2.01020 q^{44} +3.81191 q^{45} -0.864507 q^{46} -13.0336 q^{47} -2.52378 q^{48} +1.00000 q^{49} +4.83204 q^{50} +7.80145 q^{51} +5.44298 q^{52} +9.24653 q^{53} -0.506999 q^{54} +4.39640 q^{55} +1.89767 q^{56} -2.41797 q^{57} -0.963739 q^{58} +13.7634 q^{59} +6.64398 q^{60} -10.5466 q^{61} +1.64047 q^{62} -1.00000 q^{63} -2.47459 q^{64} -11.9040 q^{65} -0.584739 q^{66} -8.41170 q^{67} +13.5976 q^{68} +1.70514 q^{69} -1.93264 q^{70} +7.90427 q^{71} -1.89767 q^{72} -5.14832 q^{73} +4.53764 q^{74} -9.53066 q^{75} -4.21441 q^{76} -1.15333 q^{77} +1.58328 q^{78} -2.73477 q^{79} +9.62044 q^{80} +1.00000 q^{81} +3.42132 q^{82} +2.65632 q^{83} -1.74295 q^{84} -29.7384 q^{85} +5.44693 q^{86} +1.90087 q^{87} -2.18865 q^{88} +5.80825 q^{89} +1.93264 q^{90} +3.12285 q^{91} +2.97198 q^{92} -3.23564 q^{93} -6.60802 q^{94} +9.21710 q^{95} -5.07490 q^{96} +18.7736 q^{97} +0.506999 q^{98} +1.15333 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9}+O(q^{10}) \) 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9	\( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9} - q^{10} + 13 q^{11} - 34 q^{12} - q^{13} - 2 q^{15} + 54 q^{16} + q^{19} - 22 q^{20} + 26 q^{21} + 17 q^{22} - 3 q^{23} + 48 q^{25} + 6 q^{26} - 26 q^{27} - 34 q^{28} + 23 q^{29} + q^{30} + 18 q^{31} + 10 q^{32} - 13 q^{33} - 19 q^{34} - 2 q^{35} + 34 q^{36} + 23 q^{37} - 15 q^{38} + q^{39} + 14 q^{40} - 4 q^{41} + 5 q^{43} + 60 q^{44} + 2 q^{45} + 8 q^{46} - 20 q^{47} - 54 q^{48} + 26 q^{49} + 26 q^{50} + 19 q^{52} + 31 q^{53} + 41 q^{55} - q^{57} + 19 q^{58} - 2 q^{59} + 22 q^{60} - 2 q^{61} - 35 q^{62} - 26 q^{63} + 132 q^{64} + 40 q^{65} - 17 q^{66} + 47 q^{67} - 60 q^{68} + 3 q^{69} + q^{70} + 16 q^{71} - 23 q^{73} + 34 q^{74} - 48 q^{75} + 72 q^{76} - 13 q^{77} - 6 q^{78} + 14 q^{79} - 21 q^{80} + 26 q^{81} + 60 q^{82} - 4 q^{83} + 34 q^{84} + 36 q^{85} + 21 q^{86} - 23 q^{87} + 67 q^{88} + 14 q^{89} - q^{90} + q^{91} + 20 q^{92} - 18 q^{93} + 58 q^{94} - 4 q^{95} - 10 q^{96} + 48 q^{97} + 13 q^{99}+O(q^{100}) \) 26 * q - 26 * q^3 + 34 * q^4 + 2 * q^5 - 26 * q^7 + 26 * q^9 - q^10 + 13 * q^11 - 34 * q^12 - q^13 - 2 * q^15 + 54 * q^16 + q^19 - 22 * q^20 + 26 * q^21 + 17 * q^22 - 3 * q^23 + 48 * q^25 + 6 * q^26 - 26 * q^27 - 34 * q^28 + 23 * q^29 + q^30 + 18 * q^31 + 10 * q^32 - 13 * q^33 - 19 * q^34 - 2 * q^35 + 34 * q^36 + 23 * q^37 - 15 * q^38 + q^39 + 14 * q^40 - 4 * q^41 + 5 * q^43 + 60 * q^44 + 2 * q^45 + 8 * q^46 - 20 * q^47 - 54 * q^48 + 26 * q^49 + 26 * q^50 + 19 * q^52 + 31 * q^53 + 41 * q^55 - q^57 + 19 * q^58 - 2 * q^59 + 22 * q^60 - 2 * q^61 - 35 * q^62 - 26 * q^63 + 132 * q^64 + 40 * q^65 - 17 * q^66 + 47 * q^67 - 60 * q^68 + 3 * q^69 + q^70 + 16 * q^71 - 23 * q^73 + 34 * q^74 - 48 * q^75 + 72 * q^76 - 13 * q^77 - 6 * q^78 + 14 * q^79 - 21 * q^80 + 26 * q^81 + 60 * q^82 - 4 * q^83 + 34 * q^84 + 36 * q^85 + 21 * q^86 - 23 * q^87 + 67 * q^88 + 14 * q^89 - q^90 + q^91 + 20 * q^92 - 18 * q^93 + 58 * q^94 - 4 * q^95 - 10 * q^96 + 48 * q^97 + 13 * q^99

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