LMFDB - Embedded newform 4011.2.a.j.1.8

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			1.8
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)

$f(q)$	$=$	$q-1.59694 q^{2} -1.00000 q^{3} +0.550208 q^{4} +0.890069 q^{5} +1.59694 q^{6} -1.00000 q^{7} +2.31523 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.59694 q^{2} -1.00000 q^{3} +0.550208 q^{4} +0.890069 q^{5} +1.59694 q^{6} -1.00000 q^{7} +2.31523 q^{8} +1.00000 q^{9} -1.42138 q^{10} +5.65003 q^{11} -0.550208 q^{12} -5.71890 q^{13} +1.59694 q^{14} -0.890069 q^{15} -4.79769 q^{16} -5.71801 q^{17} -1.59694 q^{18} -4.02118 q^{19} +0.489723 q^{20} +1.00000 q^{21} -9.02274 q^{22} +6.76493 q^{23} -2.31523 q^{24} -4.20778 q^{25} +9.13273 q^{26} -1.00000 q^{27} -0.550208 q^{28} -5.32232 q^{29} +1.42138 q^{30} +7.77795 q^{31} +3.03115 q^{32} -5.65003 q^{33} +9.13130 q^{34} -0.890069 q^{35} +0.550208 q^{36} -8.51965 q^{37} +6.42157 q^{38} +5.71890 q^{39} +2.06071 q^{40} +8.78186 q^{41} -1.59694 q^{42} +11.6172 q^{43} +3.10869 q^{44} +0.890069 q^{45} -10.8032 q^{46} +11.5444 q^{47} +4.79769 q^{48} +1.00000 q^{49} +6.71955 q^{50} +5.71801 q^{51} -3.14659 q^{52} -1.23387 q^{53} +1.59694 q^{54} +5.02892 q^{55} -2.31523 q^{56} +4.02118 q^{57} +8.49941 q^{58} -7.61818 q^{59} -0.489723 q^{60} -2.73123 q^{61} -12.4209 q^{62} -1.00000 q^{63} +4.75481 q^{64} -5.09022 q^{65} +9.02274 q^{66} +5.16507 q^{67} -3.14609 q^{68} -6.76493 q^{69} +1.42138 q^{70} -5.29892 q^{71} +2.31523 q^{72} -9.05244 q^{73} +13.6053 q^{74} +4.20778 q^{75} -2.21249 q^{76} -5.65003 q^{77} -9.13273 q^{78} -8.36305 q^{79} -4.27027 q^{80} +1.00000 q^{81} -14.0241 q^{82} +0.406006 q^{83} +0.550208 q^{84} -5.08942 q^{85} -18.5520 q^{86} +5.32232 q^{87} +13.0811 q^{88} +0.301990 q^{89} -1.42138 q^{90} +5.71890 q^{91} +3.72212 q^{92} -7.77795 q^{93} -18.4356 q^{94} -3.57913 q^{95} -3.03115 q^{96} -5.52005 q^{97} -1.59694 q^{98} +5.65003 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.59694	−1.12921	−0.564603	−	0.825363i	$-0.690971\pi$
$2$	−1.59694	−1.12921	−0.564603	+	0.825363i	$0.690971\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.550208	0.275104
$5$	0.890069	0.398051	0.199026	−	0.979994i	$-0.436222\pi$
$5$	0.890069	0.398051	0.199026	+	0.979994i	$0.436222\pi$
$6$	1.59694	0.651947
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.31523	0.818556
$9$	1.00000	0.333333
$10$	−1.42138	−0.449481
$11$	5.65003	1.70355	0.851774	−	0.523910i	$-0.175527\pi$
$11$	5.65003	1.70355	0.851774	+	0.523910i	$0.175527\pi$
$12$	−0.550208	−0.158831
$13$	−5.71890	−1.58614	−0.793069	−	0.609132i	$-0.791518\pi$
$13$	−5.71890	−1.58614	−0.793069	+	0.609132i	$0.791518\pi$
$14$	1.59694	0.426799
$15$	−0.890069	−0.229815
$16$	−4.79769	−1.19942
$17$	−5.71801	−1.38682	−0.693410	−	0.720543i	$-0.743893\pi$
$17$	−5.71801	−1.38682	−0.693410	+	0.720543i	$0.743893\pi$
$18$	−1.59694	−0.376402
$19$	−4.02118	−0.922522	−0.461261	−	0.887265i	$-0.652603\pi$
$19$	−4.02118	−0.922522	−0.461261	+	0.887265i	$0.652603\pi$
$20$	0.489723	0.109505
$21$	1.00000	0.218218
$22$	−9.02274	−1.92365
$23$	6.76493	1.41059	0.705293	−	0.708916i	$-0.250815\pi$
$23$	6.76493	1.41059	0.705293	+	0.708916i	$0.250815\pi$
$24$	−2.31523	−0.472594
$25$	−4.20778	−0.841555
$26$	9.13273	1.79107
$27$	−1.00000	−0.192450
$28$	−0.550208	−0.103980
$29$	−5.32232	−0.988330	−0.494165	−	0.869368i	$-0.664526\pi$
$29$	−5.32232	−0.988330	−0.494165	+	0.869368i	$0.664526\pi$
$30$	1.42138	0.259508
$31$	7.77795	1.39696	0.698480	−	0.715629i	$-0.253860\pi$
$31$	7.77795	1.39696	0.698480	+	0.715629i	$0.253860\pi$
$32$	3.03115	0.535837
$33$	−5.65003	−0.983543
$34$	9.13130	1.56600
$35$	−0.890069	−0.150449
$36$	0.550208	0.0917014
$37$	−8.51965	−1.40062	−0.700311	−	0.713838i	$-0.746955\pi$
$37$	−8.51965	−1.40062	−0.700311	+	0.713838i	$0.746955\pi$
$38$	6.42157	1.04172
$39$	5.71890	0.915757
$40$	2.06071	0.325827
$41$	8.78186	1.37150	0.685748	−	0.727839i	$-0.259475\pi$
$41$	8.78186	1.37150	0.685748	+	0.727839i	$0.259475\pi$
$42$	−1.59694	−0.246413
$43$	11.6172	1.77161	0.885804	−	0.464060i	$-0.153608\pi$
$43$	11.6172	1.77161	0.885804	+	0.464060i	$0.153608\pi$
$44$	3.10869	0.468653
$45$	0.890069	0.132684
$46$	−10.8032	−1.59284
$47$	11.5444	1.68392	0.841960	−	0.539541i	$-0.181402\pi$
$47$	11.5444	1.68392	0.841960	+	0.539541i	$0.181402\pi$
$48$	4.79769	0.692487
$49$	1.00000	0.142857
$50$	6.71955	0.950289
$51$	5.71801	0.800681
$52$	−3.14659	−0.436353
$53$	−1.23387	−0.169485	−0.0847427	−	0.996403i	$-0.527007\pi$
$53$	−1.23387	−0.169485	−0.0847427	+	0.996403i	$0.527007\pi$
$54$	1.59694	0.217316
$55$	5.02892	0.678099
$56$	−2.31523	−0.309385
$57$	4.02118	0.532618
$58$	8.49941	1.11603
$59$	−7.61818	−0.991802	−0.495901	−	0.868379i	$-0.665162\pi$
$59$	−7.61818	−0.991802	−0.495901	+	0.868379i	$0.665162\pi$
$60$	−0.489723	−0.0632230
$61$	−2.73123	−0.349698	−0.174849	−	0.984595i	$-0.555944\pi$
$61$	−2.73123	−0.349698	−0.174849	+	0.984595i	$0.555944\pi$
$62$	−12.4209	−1.57745
$63$	−1.00000	−0.125988
$64$	4.75481	0.594352
$65$	−5.09022	−0.631364
$66$	9.02274	1.11062
$67$	5.16507	0.631014	0.315507	−	0.948923i	$-0.397825\pi$
$67$	5.16507	0.631014	0.315507	+	0.948923i	$0.397825\pi$
$68$	−3.14609	−0.381520
$69$	−6.76493	−0.814402
$70$	1.42138	0.169888
$71$	−5.29892	−0.628866	−0.314433	−	0.949280i	$-0.601814\pi$
$71$	−5.29892	−0.628866	−0.314433	+	0.949280i	$0.601814\pi$
$72$	2.31523	0.272852
$73$	−9.05244	−1.05951	−0.529754	−	0.848151i	$-0.677716\pi$
$73$	−9.05244	−1.05951	−0.529754	+	0.848151i	$0.677716\pi$
$74$	13.6053	1.58159
$75$	4.20778	0.485872
$76$	−2.21249	−0.253789
$77$	−5.65003	−0.643880
$78$	−9.13273	−1.03408
$79$	−8.36305	−0.940916	−0.470458	−	0.882422i	$-0.655911\pi$
$79$	−8.36305	−0.940916	−0.470458	+	0.882422i	$0.655911\pi$
$80$	−4.27027	−0.477431
$81$	1.00000	0.111111
$82$	−14.0241	−1.54870
$83$	0.406006	0.0445650	0.0222825	−	0.999752i	$-0.492907\pi$
$83$	0.406006	0.0445650	0.0222825	+	0.999752i	$0.492907\pi$
$84$	0.550208	0.0600326
$85$	−5.08942	−0.552025
$86$	−18.5520	−2.00051
$87$	5.32232	0.570613
$88$	13.0811	1.39445
$89$	0.301990	0.0320109	0.0160054	−	0.999872i	$-0.494905\pi$
$89$	0.301990	0.0320109	0.0160054	+	0.999872i	$0.494905\pi$
$90$	−1.42138	−0.149827
$91$	5.71890	0.599504
$92$	3.72212	0.388058
$93$	−7.77795	−0.806535
$94$	−18.4356	−1.90149
$95$	−3.57913	−0.367211
$96$	−3.03115	−0.309366
$97$	−5.52005	−0.560476	−0.280238	−	0.959930i	$-0.590413\pi$
$97$	−5.52005	−0.560476	−0.280238	+	0.959930i	$0.590413\pi$
$98$	−1.59694	−0.161315
$99$	5.65003	0.567849
$100$	−2.31515	−0.231515
$101$	1.14894	0.114324	0.0571619	−	0.998365i	$-0.481795\pi$
$101$	1.14894	0.114324	0.0571619	+	0.998365i	$0.481795\pi$
$102$	−9.13130	−0.904133
$103$	−1.99427	−0.196501	−0.0982505	−	0.995162i	$-0.531325\pi$
$103$	−1.99427	−0.196501	−0.0982505	+	0.995162i	$0.531325\pi$
$104$	−13.2405	−1.29834
$105$	0.890069	0.0868619
$106$	1.97042	0.191384
$107$	0.491768	0.0475411	0.0237705	−	0.999717i	$-0.492433\pi$
$107$	0.491768	0.0475411	0.0237705	+	0.999717i	$0.492433\pi$
$108$	−0.550208	−0.0529438
$109$	13.5576	1.29858	0.649290	−	0.760541i	$-0.275066\pi$
$109$	13.5576	1.29858	0.649290	+	0.760541i	$0.275066\pi$
$110$	−8.03086	−0.765713
$111$	8.51965	0.808649
$112$	4.79769	0.453339
$113$	−11.5216	−1.08386	−0.541931	−	0.840423i	$-0.682307\pi$
$113$	−11.5216	−1.08386	−0.541931	+	0.840423i	$0.682307\pi$
$114$	−6.42157	−0.601435
$115$	6.02126	0.561485
$116$	−2.92838	−0.271894
$117$	−5.71890	−0.528713
$118$	12.1657	1.11995
$119$	5.71801	0.524169
$120$	−2.06071	−0.188116
$121$	20.9228	1.90207
$122$	4.36160	0.394881
$123$	−8.78186	−0.791834
$124$	4.27949	0.384310
$125$	−8.19556	−0.733033
$126$	1.59694	0.142266
$127$	−9.09214	−0.806797	−0.403399	−	0.915024i	$-0.632171\pi$
$127$	−9.09214	−0.806797	−0.403399	+	0.915024i	$0.632171\pi$
$128$	−13.6554	−1.20698
$129$	−11.6172	−1.02284
$130$	8.12876	0.712939
$131$	15.4152	1.34683	0.673414	−	0.739266i	$-0.264827\pi$
$131$	15.4152	1.34683	0.673414	+	0.739266i	$0.264827\pi$
$132$	−3.10869	−0.270577
$133$	4.02118	0.348680
$134$	−8.24830	−0.712545
$135$	−0.890069	−0.0766050
$136$	−13.2385	−1.13519
$137$	−13.3081	−1.13699	−0.568494	−	0.822688i	$-0.692474\pi$
$137$	−13.3081	−1.13699	−0.568494	+	0.822688i	$0.692474\pi$
$138$	10.8032	0.919627
$139$	−5.28682	−0.448422	−0.224211	−	0.974541i	$-0.571981\pi$
$139$	−5.28682	−0.448422	−0.224211	+	0.974541i	$0.571981\pi$
$140$	−0.489723	−0.0413892
$141$	−11.5444	−0.972211
$142$	8.46204	0.710119
$143$	−32.3119	−2.70206
$144$	−4.79769	−0.399807
$145$	−4.73723	−0.393406
$146$	14.4562	1.19640
$147$	−1.00000	−0.0824786
$148$	−4.68758	−0.385317
$149$	12.7411	1.04379	0.521895	−	0.853010i	$-0.325225\pi$
$149$	12.7411	1.04379	0.521895	+	0.853010i	$0.325225\pi$
$150$	−6.71955	−0.548649
$151$	14.2330	1.15827	0.579133	−	0.815233i	$-0.303391\pi$
$151$	14.2330	1.15827	0.579133	+	0.815233i	$0.303391\pi$
$152$	−9.30994	−0.755136
$153$	−5.71801	−0.462273
$154$	9.02274	0.727073
$155$	6.92291	0.556062
$156$	3.14659	0.251929
$157$	1.01460	0.0809741	0.0404871	−	0.999180i	$-0.487109\pi$
$157$	1.01460	0.0809741	0.0404871	+	0.999180i	$0.487109\pi$
$158$	13.3553	1.06249
$159$	1.23387	0.0978524
$160$	2.69794	0.213291
$161$	−6.76493	−0.533151
$162$	−1.59694	−0.125467
$163$	18.5443	1.45250	0.726249	−	0.687431i	$-0.241262\pi$
$163$	18.5443	1.45250	0.726249	+	0.687431i	$0.241262\pi$
$164$	4.83185	0.377304
$165$	−5.02892	−0.391501
$166$	−0.648366	−0.0503230
$167$	−8.88580	−0.687604	−0.343802	−	0.939042i	$-0.611715\pi$
$167$	−8.88580	−0.687604	−0.343802	+	0.939042i	$0.611715\pi$
$168$	2.31523	0.178624
$169$	19.7058	1.51583
$170$	8.12749	0.623350
$171$	−4.02118	−0.307507
$172$	6.39189	0.487377
$173$	7.58537	0.576705	0.288352	−	0.957524i	$-0.406893\pi$
$173$	7.58537	0.576705	0.288352	+	0.957524i	$0.406893\pi$
$174$	−8.49941	−0.644339
$175$	4.20778	0.318078
$176$	−27.1071	−2.04327
$177$	7.61818	0.572617
$178$	−0.482259	−0.0361469
$179$	16.9345	1.26575	0.632873	−	0.774255i	$-0.281875\pi$
$179$	16.9345	1.26575	0.632873	+	0.774255i	$0.281875\pi$
$180$	0.489723	0.0365018
$181$	24.1194	1.79278	0.896391	−	0.443265i	$-0.146180\pi$
$181$	24.1194	1.79278	0.896391	+	0.443265i	$0.146180\pi$
$182$	−9.13273	−0.676963
$183$	2.73123	0.201898
$184$	15.6623	1.15464
$185$	−7.58308	−0.557519
$186$	12.4209	0.910744
$187$	−32.3069	−2.36251
$188$	6.35181	0.463253
$189$	1.00000	0.0727393
$190$	5.71564	0.414656
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	−4.75481	−0.343149
$193$	1.60341	0.115416	0.0577078	−	0.998334i	$-0.481621\pi$
$193$	1.60341	0.115416	0.0577078	+	0.998334i	$0.481621\pi$
$194$	8.81518	0.632893
$195$	5.09022	0.364518
$196$	0.550208	0.0393006
$197$	20.6712	1.47276	0.736381	−	0.676568i	$-0.236533\pi$
$197$	20.6712	1.47276	0.736381	+	0.676568i	$0.236533\pi$
$198$	−9.02274	−0.641218
$199$	−12.0764	−0.856073	−0.428036	−	0.903761i	$-0.640794\pi$
$199$	−12.0764	−0.856073	−0.428036	+	0.903761i	$0.640794\pi$
$200$	−9.74196	−0.688860
$201$	−5.16507	−0.364316
$202$	−1.83479	−0.129095
$203$	5.32232	0.373554
$204$	3.14609	0.220271
$205$	7.81647	0.545926
$206$	3.18472	0.221890
$207$	6.76493	0.470195
$208$	27.4375	1.90245
$209$	−22.7198	−1.57156
$210$	−1.42138	−0.0980849
$211$	−5.80115	−0.399367	−0.199684	−	0.979860i	$-0.563991\pi$
$211$	−5.80115	−0.399367	−0.199684	+	0.979860i	$0.563991\pi$
$212$	−0.678887	−0.0466261
$213$	5.29892	0.363076
$214$	−0.785323	−0.0536836
$215$	10.3401	0.705191
$216$	−2.31523	−0.157531
$217$	−7.77795	−0.528001
$218$	−21.6506	−1.46636
$219$	9.05244	0.611707
$220$	2.76695	0.186548
$221$	32.7007	2.19969
$222$	−13.6053	−0.913131
$223$	26.4326	1.77006	0.885030	−	0.465533i	$-0.154138\pi$
$223$	26.4326	1.77006	0.885030	+	0.465533i	$0.154138\pi$
$224$	−3.03115	−0.202527
$225$	−4.20778	−0.280518
$226$	18.3993	1.22390
$227$	−15.1223	−1.00370	−0.501851	−	0.864954i	$-0.667347\pi$
$227$	−15.1223	−1.00370	−0.501851	+	0.864954i	$0.667347\pi$
$228$	2.21249	0.146525
$229$	−6.26288	−0.413863	−0.206931	−	0.978355i	$-0.566348\pi$
$229$	−6.26288	−0.413863	−0.206931	+	0.978355i	$0.566348\pi$
$230$	−9.61557	−0.634032
$231$	5.65003	0.371744
$232$	−12.3224	−0.809004
$233$	20.2945	1.32954	0.664770	−	0.747049i	$-0.268530\pi$
$233$	20.2945	1.32954	0.664770	+	0.747049i	$0.268530\pi$
$234$	9.13273	0.597025
$235$	10.2753	0.670286
$236$	−4.19158	−0.272849
$237$	8.36305	0.543238
$238$	−9.13130	−0.591894
$239$	4.62503	0.299168	0.149584	−	0.988749i	$-0.452207\pi$
$239$	4.62503	0.299168	0.149584	+	0.988749i	$0.452207\pi$
$240$	4.27027	0.275645
$241$	8.77193	0.565050	0.282525	−	0.959260i	$-0.408828\pi$
$241$	8.77193	0.565050	0.282525	+	0.959260i	$0.408828\pi$
$242$	−33.4124	−2.14783
$243$	−1.00000	−0.0641500
$244$	−1.50275	−0.0962034
$245$	0.890069	0.0568644
$246$	14.0241	0.894143
$247$	22.9967	1.46325
$248$	18.0077	1.14349
$249$	−0.406006	−0.0257296
$250$	13.0878	0.827745
$251$	4.61465	0.291274	0.145637	−	0.989338i	$-0.453477\pi$
$251$	4.61465	0.291274	0.145637	+	0.989338i	$0.453477\pi$
$252$	−0.550208	−0.0346599
$253$	38.2220	2.40300
$254$	14.5196	0.911039
$255$	5.08942	0.318712
$256$	12.2973	0.768579
$257$	1.09374	0.0682255	0.0341127	−	0.999418i	$-0.489139\pi$
$257$	1.09374	0.0682255	0.0341127	+	0.999418i	$0.489139\pi$
$258$	18.5520	1.15499
$259$	8.51965	0.529385
$260$	−2.80068	−0.173691
$261$	−5.32232	−0.329443
$262$	−24.6170	−1.52085
$263$	−1.92176	−0.118501	−0.0592505	−	0.998243i	$-0.518871\pi$
$263$	−1.92176	−0.118501	−0.0592505	+	0.998243i	$0.518871\pi$
$264$	−13.0811	−0.805086
$265$	−1.09823	−0.0674638
$266$	−6.42157	−0.393732
$267$	−0.301990	−0.0184815
$268$	2.84187	0.173595
$269$	−31.3671	−1.91248	−0.956242	−	0.292578i	$-0.905487\pi$
$269$	−31.3671	−1.91248	−0.956242	+	0.292578i	$0.905487\pi$
$270$	1.42138	0.0865027
$271$	17.6782	1.07387	0.536937	−	0.843622i	$-0.319581\pi$
$271$	17.6782	1.07387	0.536937	+	0.843622i	$0.319581\pi$
$272$	27.4332	1.66338
$273$	−5.71890	−0.346124
$274$	21.2522	1.28389
$275$	−23.7741	−1.43363
$276$	−3.72212	−0.224045
$277$	−8.90530	−0.535067	−0.267534	−	0.963549i	$-0.586209\pi$
$277$	−8.90530	−0.535067	−0.267534	+	0.963549i	$0.586209\pi$
$278$	8.44272	0.506361
$279$	7.77795	0.465653
$280$	−2.06071	−0.123151
$281$	24.5707	1.46576	0.732882	−	0.680356i	$-0.238175\pi$
$281$	24.5707	1.46576	0.732882	+	0.680356i	$0.238175\pi$
$282$	18.4356	1.09783
$283$	−31.4144	−1.86740	−0.933698	−	0.358063i	$-0.883437\pi$
$283$	−31.4144	−1.86740	−0.933698	+	0.358063i	$0.883437\pi$
$284$	−2.91551	−0.173004
$285$	3.57913	0.212009
$286$	51.6001	3.05118
$287$	−8.78186	−0.518377
$288$	3.03115	0.178612
$289$	15.6956	0.923271
$290$	7.56506	0.444236
$291$	5.52005	0.323591
$292$	−4.98073	−0.291475
$293$	6.78060	0.396127	0.198064	−	0.980189i	$-0.436535\pi$
$293$	6.78060	0.396127	0.198064	+	0.980189i	$0.436535\pi$
$294$	1.59694	0.0931353
$295$	−6.78071	−0.394788
$296$	−19.7249	−1.14649
$297$	−5.65003	−0.327848
$298$	−20.3467	−1.17865
$299$	−38.6880	−2.23738
$300$	2.31515	0.133665
$301$	−11.6172	−0.669605
$302$	−22.7292	−1.30792
$303$	−1.14894	−0.0660049
$304$	19.2924	1.10649
$305$	−2.43098	−0.139198
$306$	9.13130	0.522002
$307$	−2.16242	−0.123416	−0.0617079	−	0.998094i	$-0.519655\pi$
$307$	−2.16242	−0.123416	−0.0617079	+	0.998094i	$0.519655\pi$
$308$	−3.10869	−0.177134
$309$	1.99427	0.113450
$310$	−11.0555	−0.627908
$311$	0.538962	0.0305617	0.0152809	−	0.999883i	$-0.495136\pi$
$311$	0.538962	0.0305617	0.0152809	+	0.999883i	$0.495136\pi$
$312$	13.2405	0.749599
$313$	0.807183	0.0456247	0.0228123	−	0.999740i	$-0.492738\pi$
$313$	0.807183	0.0456247	0.0228123	+	0.999740i	$0.492738\pi$
$314$	−1.62026	−0.0914364
$315$	−0.890069	−0.0501497
$316$	−4.60142	−0.258850
$317$	−10.4968	−0.589558	−0.294779	−	0.955565i	$-0.595246\pi$
$317$	−10.4968	−0.589558	−0.294779	+	0.955565i	$0.595246\pi$
$318$	−1.97042	−0.110495
$319$	−30.0713	−1.68367
$320$	4.23211	0.236582
$321$	−0.491768	−0.0274478
$322$	10.8032	0.602037
$323$	22.9931	1.27937
$324$	0.550208	0.0305671
$325$	24.0639	1.33482
$326$	−29.6140	−1.64017
$327$	−13.5576	−0.749736
$328$	20.3320	1.12265
$329$	−11.5444	−0.636462
$330$	8.03086	0.442084
$331$	22.1977	1.22010	0.610048	−	0.792365i	$-0.291150\pi$
$331$	22.1977	1.22010	0.610048	+	0.792365i	$0.291150\pi$
$332$	0.223388	0.0122600
$333$	−8.51965	−0.466874
$334$	14.1901	0.776446
$335$	4.59727	0.251176
$336$	−4.79769	−0.261735
$337$	−6.55251	−0.356938	−0.178469	−	0.983946i	$-0.557114\pi$
$337$	−6.55251	−0.356938	−0.178469	+	0.983946i	$0.557114\pi$
$338$	−31.4690	−1.71169
$339$	11.5216	0.625768
$340$	−2.80024	−0.151864
$341$	43.9456	2.37979
$342$	6.42157	0.347239
$343$	−1.00000	−0.0539949
$344$	26.8965	1.45016
$345$	−6.02126	−0.324174
$346$	−12.1134	−0.651218
$347$	9.48876	0.509384	0.254692	−	0.967022i	$-0.418026\pi$
$347$	9.48876	0.509384	0.254692	+	0.967022i	$0.418026\pi$
$348$	2.92838	0.156978
$349$	3.69196	0.197626	0.0988130	−	0.995106i	$-0.468495\pi$
$349$	3.69196	0.197626	0.0988130	+	0.995106i	$0.468495\pi$
$350$	−6.71955	−0.359175
$351$	5.71890	0.305252
$352$	17.1261	0.912824
$353$	−25.8875	−1.37785	−0.688927	−	0.724831i	$-0.741918\pi$
$353$	−25.8875	−1.37785	−0.688927	+	0.724831i	$0.741918\pi$
$354$	−12.1657	−0.646602
$355$	−4.71641	−0.250321
$356$	0.166157	0.00880633
$357$	−5.71801	−0.302629
$358$	−27.0434	−1.42929
$359$	30.1058	1.58892	0.794461	−	0.607315i	$-0.207754\pi$
$359$	30.1058	1.58892	0.794461	+	0.607315i	$0.207754\pi$
$360$	2.06071	0.108609
$361$	−2.83013	−0.148954
$362$	−38.5172	−2.02442
$363$	−20.9228	−1.09816
$364$	3.14659	0.164926
$365$	−8.05730	−0.421738
$366$	−4.36160	−0.227985
$367$	−3.22602	−0.168397	−0.0841985	−	0.996449i	$-0.526833\pi$
$367$	−3.22602	−0.168397	−0.0841985	+	0.996449i	$0.526833\pi$
$368$	−32.4560	−1.69189
$369$	8.78186	0.457165
$370$	12.1097	0.629553
$371$	1.23387	0.0640595
$372$	−4.27949	−0.221881
$373$	−2.58448	−0.133819	−0.0669097	−	0.997759i	$-0.521314\pi$
$373$	−2.58448	−0.133819	−0.0669097	+	0.997759i	$0.521314\pi$
$374$	51.5921	2.66776
$375$	8.19556	0.423217
$376$	26.7278	1.37838
$377$	30.4378	1.56763
$378$	−1.59694	−0.0821376
$379$	−7.36565	−0.378348	−0.189174	−	0.981944i	$-0.560581\pi$
$379$	−7.36565	−0.378348	−0.189174	+	0.981944i	$0.560581\pi$
$380$	−1.96927	−0.101021
$381$	9.09214	0.465804
$382$	−1.59694	−0.0817064
$383$	−10.0109	−0.511534	−0.255767	−	0.966738i	$-0.582328\pi$
$383$	−10.0109	−0.511534	−0.255767	+	0.966738i	$0.582328\pi$
$384$	13.6554	0.696852
$385$	−5.02892	−0.256297
$386$	−2.56054	−0.130328
$387$	11.6172	0.590536
$388$	−3.03718	−0.154189
$389$	24.1828	1.22612	0.613058	−	0.790038i	$-0.289939\pi$
$389$	24.1828	1.22612	0.613058	+	0.790038i	$0.289939\pi$
$390$	−8.12876	−0.411616
$391$	−38.6819	−1.95623
$392$	2.31523	0.116937
$393$	−15.4152	−0.777592
$394$	−33.0106	−1.66305
$395$	−7.44369	−0.374533
$396$	3.10869	0.156218
$397$	25.8751	1.29863	0.649316	−	0.760518i	$-0.275055\pi$
$397$	25.8751	1.29863	0.649316	+	0.760518i	$0.275055\pi$
$398$	19.2852	0.966682
$399$	−4.02118	−0.201311
$400$	20.1876	1.00938
$401$	−6.22590	−0.310907	−0.155453	−	0.987843i	$-0.549684\pi$
$401$	−6.22590	−0.310907	−0.155453	+	0.987843i	$0.549684\pi$
$402$	8.24830	0.411388
$403$	−44.4813	−2.21577
$404$	0.632156	0.0314510
$405$	0.890069	0.0442279
$406$	−8.49941	−0.421819
$407$	−48.1362	−2.38602
$408$	13.2385	0.655402
$409$	−8.48483	−0.419548	−0.209774	−	0.977750i	$-0.567273\pi$
$409$	−8.48483	−0.419548	−0.209774	+	0.977750i	$0.567273\pi$
$410$	−12.4824	−0.616462
$411$	13.3081	0.656440
$412$	−1.09726	−0.0540582
$413$	7.61818	0.374866
$414$	−10.8032	−0.530947
$415$	0.361374	0.0177391
$416$	−17.3349	−0.849912
$417$	5.28682	0.258897
$418$	36.2820	1.77461
$419$	36.7414	1.79494	0.897468	−	0.441079i	$-0.145404\pi$
$419$	36.7414	1.79494	0.897468	+	0.441079i	$0.145404\pi$
$420$	0.489723	0.0238961
$421$	1.54123	0.0751150	0.0375575	−	0.999294i	$-0.488042\pi$
$421$	1.54123	0.0751150	0.0375575	+	0.999294i	$0.488042\pi$
$422$	9.26407	0.450968
$423$	11.5444	0.561306
$424$	−2.85669	−0.138733
$425$	24.0601	1.16709
$426$	−8.46204	−0.409987
$427$	2.73123	0.132173
$428$	0.270575	0.0130787
$429$	32.3119	1.56004
$430$	−16.5125	−0.796305
$431$	−18.4225	−0.887382	−0.443691	−	0.896180i	$-0.646331\pi$
$431$	−18.4225	−0.887382	−0.443691	+	0.896180i	$0.646331\pi$
$432$	4.79769	0.230829
$433$	−4.68507	−0.225150	−0.112575	−	0.993643i	$-0.535910\pi$
$433$	−4.68507	−0.225150	−0.112575	+	0.993643i	$0.535910\pi$
$434$	12.4209	0.596222
$435$	4.73723	0.227133
$436$	7.45949	0.357245
$437$	−27.2030	−1.30130
$438$	−14.4562	−0.690743
$439$	31.2319	1.49062	0.745308	−	0.666720i	$-0.232302\pi$
$439$	31.2319	1.49062	0.745308	+	0.666720i	$0.232302\pi$
$440$	11.6431	0.555062
$441$	1.00000	0.0476190
$442$	−52.2210	−2.48390
$443$	24.4987	1.16397	0.581985	−	0.813199i	$-0.302276\pi$
$443$	24.4987	1.16397	0.581985	+	0.813199i	$0.302276\pi$
$444$	4.68758	0.222463
$445$	0.268792	0.0127420
$446$	−42.2113	−1.99876
$447$	−12.7411	−0.602632
$448$	−4.75481	−0.224644
$449$	38.0204	1.79430	0.897148	−	0.441731i	$-0.145635\pi$
$449$	38.0204	1.79430	0.897148	+	0.441731i	$0.145635\pi$
$450$	6.71955	0.316763
$451$	49.6178	2.33641
$452$	−6.33929	−0.298175
$453$	−14.2330	−0.668725
$454$	24.1493	1.13339
$455$	5.09022	0.238633
$456$	9.30994	0.435978
$457$	2.84953	0.133295	0.0666476	−	0.997777i	$-0.478770\pi$
$457$	2.84953	0.133295	0.0666476	+	0.997777i	$0.478770\pi$
$458$	10.0014	0.467336
$459$	5.71801	0.266894
$460$	3.31295	0.154467
$461$	8.85328	0.412338	0.206169	−	0.978516i	$-0.433900\pi$
$461$	8.85328	0.412338	0.206169	+	0.978516i	$0.433900\pi$
$462$	−9.02274	−0.419776
$463$	−1.77704	−0.0825861	−0.0412931	−	0.999147i	$-0.513148\pi$
$463$	−1.77704	−0.0825861	−0.0412931	+	0.999147i	$0.513148\pi$
$464$	25.5348	1.18542
$465$	−6.92291	−0.321042
$466$	−32.4091	−1.50132
$467$	42.4308	1.96346	0.981731	−	0.190272i	$-0.0609369\pi$
$467$	42.4308	1.96346	0.981731	+	0.190272i	$0.0609369\pi$
$468$	−3.14659	−0.145451
$469$	−5.16507	−0.238501
$470$	−16.4090	−0.756890
$471$	−1.01460	−0.0467504
$472$	−17.6378	−0.811846
$473$	65.6376	3.01802
$474$	−13.3553	−0.613427
$475$	16.9202	0.776353
$476$	3.14609	0.144201
$477$	−1.23387	−0.0564951
$478$	−7.38588	−0.337822
$479$	−24.1592	−1.10386	−0.551930	−	0.833890i	$-0.686109\pi$
$479$	−24.1592	−1.10386	−0.551930	+	0.833890i	$0.686109\pi$
$480$	−2.69794	−0.123143
$481$	48.7230	2.22158
$482$	−14.0082	−0.638057
$483$	6.76493	0.307815
$484$	11.5119	0.523268
$485$	−4.91323	−0.223098
$486$	1.59694	0.0724385
$487$	9.86300	0.446935	0.223468	−	0.974711i	$-0.428262\pi$
$487$	9.86300	0.446935	0.223468	+	0.974711i	$0.428262\pi$
$488$	−6.32342	−0.286248
$489$	−18.5443	−0.838601
$490$	−1.42138	−0.0642116
$491$	19.9368	0.899737	0.449869	−	0.893095i	$-0.351471\pi$
$491$	19.9368	0.899737	0.449869	+	0.893095i	$0.351471\pi$
$492$	−4.83185	−0.217837
$493$	30.4331	1.37064
$494$	−36.7243	−1.65231
$495$	5.02892	0.226033
$496$	−37.3162	−1.67554
$497$	5.29892	0.237689
$498$	0.648366	0.0290540
$499$	20.8314	0.932543	0.466272	−	0.884642i	$-0.345597\pi$
$499$	20.8314	0.932543	0.466272	+	0.884642i	$0.345597\pi$
$500$	−4.50926	−0.201660
$501$	8.88580	0.396988
$502$	−7.36930	−0.328908
$503$	−43.5901	−1.94358	−0.971792	−	0.235839i	$-0.924216\pi$
$503$	−43.5901	−1.94358	−0.971792	+	0.235839i	$0.924216\pi$
$504$	−2.31523	−0.103128
$505$	1.02264	0.0455067
$506$	−61.0382	−2.71348
$507$	−19.7058	−0.875167
$508$	−5.00257	−0.221953
$509$	25.5574	1.13281	0.566407	−	0.824126i	$-0.308333\pi$
$509$	25.5574	1.13281	0.566407	+	0.824126i	$0.308333\pi$
$510$	−8.12749	−0.359891
$511$	9.05244	0.400456
$512$	7.67294	0.339099
$513$	4.02118	0.177539
$514$	−1.74663	−0.0770405
$515$	−1.77504	−0.0782174
$516$	−6.39189	−0.281387
$517$	65.2260	2.86864
$518$	−13.6053	−0.597784
$519$	−7.58537	−0.332961
$520$	−11.7850	−0.516807
$521$	−35.6099	−1.56010	−0.780049	−	0.625718i	$-0.784806\pi$
$521$	−35.6099	−1.56010	−0.780049	+	0.625718i	$0.784806\pi$
$522$	8.49941	0.372009
$523$	28.9432	1.26560	0.632798	−	0.774317i	$-0.281906\pi$
$523$	28.9432	1.26560	0.632798	+	0.774317i	$0.281906\pi$
$524$	8.48154	0.370518
$525$	−4.20778	−0.183642
$526$	3.06893	0.133812
$527$	−44.4743	−1.93733
$528$	27.1071	1.17968
$529$	22.7643	0.989752
$530$	1.75381	0.0761805
$531$	−7.61818	−0.330601
$532$	2.21249	0.0959234
$533$	−50.2226	−2.17538
$534$	0.482259	0.0208694
$535$	0.437708	0.0189238
$536$	11.9583	0.516521
$537$	−16.9345	−0.730779
$538$	50.0912	2.15959
$539$	5.65003	0.243364
$540$	−0.489723	−0.0210743
$541$	20.1217	0.865101	0.432550	−	0.901610i	$-0.357614\pi$
$541$	20.1217	0.865101	0.432550	+	0.901610i	$0.357614\pi$
$542$	−28.2310	−1.21262
$543$	−24.1194	−1.03506
$544$	−17.3322	−0.743110
$545$	12.0672	0.516901
$546$	9.13273	0.390845
$547$	10.6764	0.456488	0.228244	−	0.973604i	$-0.426702\pi$
$547$	10.6764	0.456488	0.228244	+	0.973604i	$0.426702\pi$
$548$	−7.32222	−0.312790
$549$	−2.73123	−0.116566
$550$	37.9657	1.61886
$551$	21.4020	0.911756
$552$	−15.6623	−0.666634
$553$	8.36305	0.355633
$554$	14.2212	0.604201
$555$	7.58308	0.321884
$556$	−2.90885	−0.123363
$557$	−0.832548	−0.0352762	−0.0176381	−	0.999844i	$-0.505615\pi$
$557$	−0.832548	−0.0352762	−0.0176381	+	0.999844i	$0.505615\pi$
$558$	−12.4209	−0.525818
$559$	−66.4377	−2.81001
$560$	4.27027	0.180452
$561$	32.3069	1.36400
$562$	−39.2378	−1.65515
$563$	28.2927	1.19240	0.596198	−	0.802838i	$-0.296677\pi$
$563$	28.2927	1.19240	0.596198	+	0.802838i	$0.296677\pi$
$564$	−6.35181	−0.267459
$565$	−10.2550	−0.431433
$566$	50.1669	2.10867
$567$	−1.00000	−0.0419961
$568$	−12.2682	−0.514762
$569$	38.7929	1.62628	0.813141	−	0.582066i	$-0.197756\pi$
$569$	38.7929	1.62628	0.813141	+	0.582066i	$0.197756\pi$
$570$	−5.71564	−0.239402
$571$	5.24646	0.219558	0.109779	−	0.993956i	$-0.464986\pi$
$571$	5.24646	0.219558	0.109779	+	0.993956i	$0.464986\pi$
$572$	−17.7783	−0.743348
$573$	−1.00000	−0.0417756
$574$	14.0241	0.585354
$575$	−28.4653	−1.18709
$576$	4.75481	0.198117
$577$	32.7203	1.36216	0.681081	−	0.732208i	$-0.261510\pi$
$577$	32.7203	1.36216	0.681081	+	0.732208i	$0.261510\pi$
$578$	−25.0649	−1.04256
$579$	−1.60341	−0.0666352
$580$	−2.60647	−0.108228
$581$	−0.406006	−0.0168440
$582$	−8.81518	−0.365401
$583$	−6.97141	−0.288726
$584$	−20.9584	−0.867266
$585$	−5.09022	−0.210455
$586$	−10.8282	−0.447309
$587$	−16.4525	−0.679069	−0.339534	−	0.940594i	$-0.610269\pi$
$587$	−16.4525	−0.679069	−0.339534	+	0.940594i	$0.610269\pi$
$588$	−0.550208	−0.0226902
$589$	−31.2765	−1.28873
$590$	10.8284	0.445797
$591$	−20.6712	−0.850299
$592$	40.8746	1.67994
$593$	−16.5807	−0.680886	−0.340443	−	0.940265i	$-0.610577\pi$
$593$	−16.5807	−0.680886	−0.340443	+	0.940265i	$0.610577\pi$
$594$	9.02274	0.370207
$595$	5.08942	0.208646
$596$	7.01024	0.287151
$597$	12.0764	0.494254
$598$	61.7823	2.52646
$599$	−9.94548	−0.406361	−0.203181	−	0.979141i	$-0.565128\pi$
$599$	−9.94548	−0.406361	−0.203181	+	0.979141i	$0.565128\pi$
$600$	9.74196	0.397714
$601$	−38.5482	−1.57241	−0.786207	−	0.617963i	$-0.787958\pi$
$601$	−38.5482	−1.57241	−0.786207	+	0.617963i	$0.787958\pi$
$602$	18.5520	0.756121
$603$	5.16507	0.210338
$604$	7.83112	0.318644
$605$	18.6227	0.757122
$606$	1.83479	0.0745331
$607$	16.6766	0.676882	0.338441	−	0.940988i	$-0.390100\pi$
$607$	16.6766	0.676882	0.338441	+	0.940988i	$0.390100\pi$
$608$	−12.1888	−0.494321
$609$	−5.32232	−0.215671
$610$	3.88213	0.157183
$611$	−66.0211	−2.67093
$612$	−3.14609	−0.127173
$613$	−4.98180	−0.201213	−0.100606	−	0.994926i	$-0.532078\pi$
$613$	−4.98180	−0.201213	−0.100606	+	0.994926i	$0.532078\pi$
$614$	3.45325	0.139362
$615$	−7.81647	−0.315190
$616$	−13.0811	−0.527052
$617$	8.68947	0.349825	0.174912	−	0.984584i	$-0.444036\pi$
$617$	8.68947	0.349825	0.174912	+	0.984584i	$0.444036\pi$
$618$	−3.18472	−0.128108
$619$	−3.41941	−0.137438	−0.0687188	−	0.997636i	$-0.521891\pi$
$619$	−3.41941	−0.137438	−0.0687188	+	0.997636i	$0.521891\pi$
$620$	3.80904	0.152975
$621$	−6.76493	−0.271467
$622$	−0.860688	−0.0345104
$623$	−0.301990	−0.0120990
$624$	−27.4375	−1.09838
$625$	13.7443	0.549771
$626$	−1.28902	−0.0515196
$627$	22.7198	0.907340
$628$	0.558243	0.0222763
$629$	48.7154	1.94241
$630$	1.42138	0.0566293
$631$	−6.90980	−0.275075	−0.137537	−	0.990497i	$-0.543919\pi$
$631$	−6.90980	−0.275075	−0.137537	+	0.990497i	$0.543919\pi$
$632$	−19.3623	−0.770193
$633$	5.80115	0.230575
$634$	16.7627	0.665732
$635$	−8.09264	−0.321146
$636$	0.678887	0.0269196
$637$	−5.71890	−0.226591
$638$	48.0219	1.90121
$639$	−5.29892	−0.209622
$640$	−12.1543	−0.480441
$641$	29.5606	1.16758	0.583788	−	0.811906i	$-0.301570\pi$
$641$	29.5606	1.16758	0.583788	+	0.811906i	$0.301570\pi$
$642$	0.785323	0.0309942
$643$	30.0311	1.18431	0.592156	−	0.805823i	$-0.298277\pi$
$643$	30.0311	1.18431	0.592156	+	0.805823i	$0.298277\pi$
$644$	−3.72212	−0.146672
$645$	−10.3401	−0.407142
$646$	−36.7186	−1.44467
$647$	32.9504	1.29541	0.647707	−	0.761890i	$-0.275728\pi$
$647$	32.9504	1.29541	0.647707	+	0.761890i	$0.275728\pi$
$648$	2.31523	0.0909507
$649$	−43.0429	−1.68958
$650$	−38.4285	−1.50729
$651$	7.77795	0.304842
$652$	10.2032	0.399588
$653$	23.2636	0.910377	0.455188	−	0.890395i	$-0.349572\pi$
$653$	23.2636	0.910377	0.455188	+	0.890395i	$0.349572\pi$
$654$	21.6506	0.846605
$655$	13.7206	0.536106
$656$	−42.1326	−1.64500
$657$	−9.05244	−0.353169
$658$	18.4356	0.718696
$659$	−14.5081	−0.565157	−0.282578	−	0.959244i	$-0.591190\pi$
$659$	−14.5081	−0.565157	−0.282578	+	0.959244i	$0.591190\pi$
$660$	−2.76695	−0.107703
$661$	−7.53515	−0.293083	−0.146542	−	0.989204i	$-0.546814\pi$
$661$	−7.53515	−0.293083	−0.146542	+	0.989204i	$0.546814\pi$
$662$	−35.4483	−1.37774
$663$	−32.7007	−1.26999
$664$	0.939996	0.0364789
$665$	3.57913	0.138793
$666$	13.6053	0.527196
$667$	−36.0051	−1.39412
$668$	−4.88904	−0.189163
$669$	−26.4326	−1.02194
$670$	−7.34156	−0.283629
$671$	−15.4315	−0.595727
$672$	3.03115	0.116929
$673$	−39.1066	−1.50745	−0.753724	−	0.657192i	$-0.771744\pi$
$673$	−39.1066	−1.50745	−0.753724	+	0.657192i	$0.771744\pi$
$674$	10.4639	0.403056
$675$	4.20778	0.161957
$676$	10.8423	0.417012
$677$	−25.8174	−0.992244	−0.496122	−	0.868253i	$-0.665243\pi$
$677$	−25.8174	−0.992244	−0.496122	+	0.868253i	$0.665243\pi$
$678$	−18.3993	−0.706621
$679$	5.52005	0.211840
$680$	−11.7832	−0.451864
$681$	15.1223	0.579487
$682$	−70.1784	−2.68727
$683$	−36.6982	−1.40422	−0.702109	−	0.712070i	$-0.747758\pi$
$683$	−36.6982	−1.40422	−0.702109	+	0.712070i	$0.747758\pi$
$684$	−2.21249	−0.0845965
$685$	−11.8451	−0.452579
$686$	1.59694	0.0609713
$687$	6.26288	0.238944
$688$	−55.7357	−2.12491
$689$	7.05639	0.268827
$690$	9.61557	0.366059
$691$	37.2419	1.41675	0.708374	−	0.705837i	$-0.249429\pi$
$691$	37.2419	1.41675	0.708374	+	0.705837i	$0.249429\pi$
$692$	4.17353	0.158654
$693$	−5.65003	−0.214627
$694$	−15.1530	−0.575199
$695$	−4.70564	−0.178495
$696$	12.3224	0.467078
$697$	−50.2147	−1.90202
$698$	−5.89583	−0.223160
$699$	−20.2945	−0.767610
$700$	2.31515	0.0875046
$701$	39.0243	1.47393	0.736965	−	0.675931i	$-0.236258\pi$
$701$	39.0243	1.47393	0.736965	+	0.675931i	$0.236258\pi$
$702$	−9.13273	−0.344693
$703$	34.2590	1.29210
$704$	26.8648	1.01251
$705$	−10.2753	−0.386990
$706$	41.3407	1.55588
$707$	−1.14894	−0.0432103
$708$	4.19158	0.157529
$709$	−31.3971	−1.17914	−0.589572	−	0.807716i	$-0.700704\pi$
$709$	−31.3971	−1.17914	−0.589572	+	0.807716i	$0.700704\pi$
$710$	7.53180	0.282664
$711$	−8.36305	−0.313639
$712$	0.699175	0.0262027
$713$	52.6173	1.97053
$714$	9.13130	0.341730
$715$	−28.7599	−1.07556
$716$	9.31752	0.348212
$717$	−4.62503	−0.172725
$718$	−48.0770	−1.79422
$719$	34.1732	1.27444	0.637222	−	0.770680i	$-0.280083\pi$
$719$	34.1732	1.27444	0.637222	+	0.770680i	$0.280083\pi$
$720$	−4.27027	−0.159144
$721$	1.99427	0.0742704
$722$	4.51954	0.168200
$723$	−8.77193	−0.326232
$724$	13.2707	0.493202
$725$	22.3951	0.831734
$726$	33.4124	1.24005
$727$	41.9463	1.55570	0.777850	−	0.628449i	$-0.216310\pi$
$727$	41.9463	1.55570	0.777850	+	0.628449i	$0.216310\pi$
$728$	13.2405	0.490727
$729$	1.00000	0.0370370
$730$	12.8670	0.476229
$731$	−66.4273	−2.45690
$732$	1.50275	0.0555431
$733$	−28.4250	−1.04990	−0.524951	−	0.851133i	$-0.675916\pi$
$733$	−28.4250	−1.04990	−0.524951	+	0.851133i	$0.675916\pi$
$734$	5.15175	0.190155
$735$	−0.890069	−0.0328307
$736$	20.5055	0.755844
$737$	29.1828	1.07496
$738$	−14.0241	−0.516234
$739$	−51.7995	−1.90547	−0.952737	−	0.303796i	$-0.901746\pi$
$739$	−51.7995	−1.90547	−0.952737	+	0.303796i	$0.901746\pi$
$740$	−4.17227	−0.153376
$741$	−22.9967	−0.844806
$742$	−1.97042	−0.0723363
$743$	−9.04418	−0.331799	−0.165899	−	0.986143i	$-0.553053\pi$
$743$	−9.04418	−0.331799	−0.165899	+	0.986143i	$0.553053\pi$
$744$	−18.0077	−0.660195
$745$	11.3404	0.415482
$746$	4.12726	0.151110
$747$	0.406006	0.0148550
$748$	−17.7755	−0.649937
$749$	−0.491768	−0.0179688
$750$	−13.0878	−0.477899
$751$	45.1076	1.64600	0.823001	−	0.568040i	$-0.192298\pi$
$751$	45.1076	1.64600	0.823001	+	0.568040i	$0.192298\pi$
$752$	−55.3863	−2.01973
$753$	−4.61465	−0.168167
$754$	−48.6073	−1.77017
$755$	12.6684	0.461049
$756$	0.550208	0.0200109
$757$	52.2706	1.89981	0.949904	−	0.312543i	$-0.101181\pi$
$757$	52.2706	1.89981	0.949904	+	0.312543i	$0.101181\pi$
$758$	11.7625	0.427232
$759$	−38.2220	−1.38737
$760$	−8.28649	−0.300583
$761$	−39.4896	−1.43150	−0.715748	−	0.698359i	$-0.753914\pi$
$761$	−39.4896	−1.43150	−0.715748	+	0.698359i	$0.753914\pi$
$762$	−14.5196	−0.525989
$763$	−13.5576	−0.490817
$764$	0.550208	0.0199058
$765$	−5.08942	−0.184008
$766$	15.9868	0.577627
$767$	43.5676	1.57313
$768$	−12.2973	−0.443739
$769$	0.459510	0.0165703	0.00828517	−	0.999966i	$-0.497363\pi$
$769$	0.459510	0.0165703	0.00828517	+	0.999966i	$0.497363\pi$
$770$	8.03086	0.289412
$771$	−1.09374	−0.0393900
$772$	0.882207	0.0317513
$773$	−22.2279	−0.799483	−0.399742	−	0.916628i	$-0.630900\pi$
$773$	−22.2279	−0.799483	−0.399742	+	0.916628i	$0.630900\pi$
$774$	−18.5520	−0.666836
$775$	−32.7279	−1.17562
$776$	−12.7802	−0.458781
$777$	−8.51965	−0.305641
$778$	−38.6184	−1.38454
$779$	−35.3134	−1.26523
$780$	2.80068	0.100280
$781$	−29.9390	−1.07130
$782$	61.7726	2.20898
$783$	5.32232	0.190204
$784$	−4.79769	−0.171346
$785$	0.903067	0.0322318
$786$	24.6170	0.878060
$787$	3.92335	0.139852	0.0699262	−	0.997552i	$-0.477724\pi$
$787$	3.92335	0.139852	0.0699262	+	0.997552i	$0.477724\pi$
$788$	11.3735	0.405163
$789$	1.92176	0.0684166
$790$	11.8871	0.422924
$791$	11.5216	0.409662
$792$	13.0811	0.464816
$793$	15.6196	0.554669
$794$	−41.3209	−1.46642
$795$	1.09823	0.0389503
$796$	−6.64453	−0.235509
$797$	13.4523	0.476506	0.238253	−	0.971203i	$-0.423425\pi$
$797$	13.4523	0.476506	0.238253	+	0.971203i	$0.423425\pi$
$798$	6.42157	0.227321
$799$	−66.0108	−2.33529
$800$	−12.7544	−0.450937
$801$	0.301990	0.0106703
$802$	9.94237	0.351077
$803$	−51.1465	−1.80492
$804$	−2.84187	−0.100225
$805$	−6.02126	−0.212221
$806$	71.0338	2.50206
$807$	31.3671	1.10417
$808$	2.66006	0.0935805
$809$	11.9765	0.421071	0.210535	−	0.977586i	$-0.432479\pi$
$809$	11.9765	0.421071	0.210535	+	0.977586i	$0.432479\pi$
$810$	−1.42138	−0.0499424
$811$	−35.2953	−1.23939	−0.619693	−	0.784844i	$-0.712743\pi$
$811$	−35.2953	−1.23939	−0.619693	+	0.784844i	$0.712743\pi$
$812$	2.92838	0.102766
$813$	−17.6782	−0.620002
$814$	76.8705	2.69431
$815$	16.5057	0.578169
$816$	−27.4332	−0.960354
$817$	−46.7149	−1.63435
$818$	13.5497	0.473756
$819$	5.71890	0.199835
$820$	4.30068	0.150186
$821$	−8.95709	−0.312605	−0.156302	−	0.987709i	$-0.549957\pi$
$821$	−8.95709	−0.312605	−0.156302	+	0.987709i	$0.549957\pi$
$822$	−21.2522	−0.741255
$823$	19.8210	0.690917	0.345459	−	0.938434i	$-0.387723\pi$
$823$	19.8210	0.690917	0.345459	+	0.938434i	$0.387723\pi$
$824$	−4.61718	−0.160847
$825$	23.7741	0.827706
$826$	−12.1657	−0.423301
$827$	46.0915	1.60276	0.801379	−	0.598156i	$-0.204100\pi$
$827$	46.0915	1.60276	0.801379	+	0.598156i	$0.204100\pi$
$828$	3.72212	0.129353
$829$	33.0588	1.14818	0.574090	−	0.818792i	$-0.305356\pi$
$829$	33.0588	1.14818	0.574090	+	0.818792i	$0.305356\pi$
$830$	−0.577091	−0.0200311
$831$	8.90530	0.308921
$832$	−27.1923	−0.942724
$833$	−5.71801	−0.198117
$834$	−8.44272	−0.292348
$835$	−7.90898	−0.273701
$836$	−12.5006	−0.432342
$837$	−7.77795	−0.268845
$838$	−58.6738	−2.02685
$839$	52.3281	1.80657	0.903284	−	0.429043i	$-0.141149\pi$
$839$	52.3281	1.80657	0.903284	+	0.429043i	$0.141149\pi$
$840$	2.06071	0.0711013
$841$	−0.672908	−0.0232037
$842$	−2.46125	−0.0848202
$843$	−24.5707	−0.846259
$844$	−3.19184	−0.109868
$845$	17.5396	0.603379
$846$	−18.4356	−0.633830
$847$	−20.9228	−0.718916
$848$	5.91973	0.203284
$849$	31.4144	1.07814
$850$	−38.4225	−1.31788
$851$	−57.6348	−1.97570
$852$	2.91551	0.0998837
$853$	−26.0967	−0.893533	−0.446766	−	0.894651i	$-0.647425\pi$
$853$	−26.0967	−0.893533	−0.446766	+	0.894651i	$0.647425\pi$
$854$	−4.36160	−0.149251
$855$	−3.57913	−0.122404
$856$	1.13856	0.0389150
$857$	52.8573	1.80557	0.902786	−	0.430090i	$-0.141518\pi$
$857$	52.8573	1.80557	0.902786	+	0.430090i	$0.141518\pi$
$858$	−51.6001	−1.76160
$859$	−8.02510	−0.273813	−0.136906	−	0.990584i	$-0.543716\pi$
$859$	−8.02510	−0.273813	−0.136906	+	0.990584i	$0.543716\pi$
$860$	5.68922	0.194001
$861$	8.78186	0.299285
$862$	29.4196	1.00204
$863$	23.0442	0.784432	0.392216	−	0.919873i	$-0.371709\pi$
$863$	23.0442	0.784432	0.392216	+	0.919873i	$0.371709\pi$
$864$	−3.03115	−0.103122
$865$	6.75150	0.229558
$866$	7.48177	0.254241
$867$	−15.6956	−0.533051
$868$	−4.27949	−0.145255
$869$	−47.2514	−1.60290
$870$	−7.56506	−0.256480
$871$	−29.5385	−1.00088
$872$	31.3889	1.06296
$873$	−5.52005	−0.186825
$874$	43.4415	1.46943
$875$	8.19556	0.277060
$876$	4.98073	0.168283
$877$	−41.4376	−1.39925	−0.699623	−	0.714512i	$-0.746649\pi$
$877$	−41.4376	−1.39925	−0.699623	+	0.714512i	$0.746649\pi$
$878$	−49.8754	−1.68321
$879$	−6.78060	−0.228704
$880$	−24.1272	−0.813327
$881$	−25.2716	−0.851422	−0.425711	−	0.904859i	$-0.639976\pi$
$881$	−25.2716	−0.851422	−0.425711	+	0.904859i	$0.639976\pi$
$882$	−1.59694	−0.0537717
$883$	3.50049	0.117801	0.0589004	−	0.998264i	$-0.481241\pi$
$883$	3.50049	0.117801	0.0589004	+	0.998264i	$0.481241\pi$
$884$	17.9922	0.605143
$885$	6.78071	0.227931
$886$	−39.1230	−1.31436
$887$	−44.8411	−1.50562	−0.752809	−	0.658239i	$-0.771302\pi$
$887$	−44.8411	−1.50562	−0.752809	+	0.658239i	$0.771302\pi$
$888$	19.7249	0.661925
$889$	9.09214	0.304941
$890$	−0.429244	−0.0143883
$891$	5.65003	0.189283
$892$	14.5435	0.486951
$893$	−46.4220	−1.55345
$894$	20.3467	0.680495
$895$	15.0729	0.503832
$896$	13.6554	0.456196
$897$	38.6880	1.29175
$898$	−60.7162	−2.02613
$899$	−41.3967	−1.38066
$900$	−2.31515	−0.0771718
$901$	7.05529	0.235046
$902$	−79.2364	−2.63828
$903$	11.6172	0.386597
$904$	−26.6752	−0.887203
$905$	21.4679	0.713619
$906$	22.7292	0.755128
$907$	54.8853	1.82244	0.911219	−	0.411923i	$-0.135143\pi$
$907$	54.8853	1.82244	0.911219	+	0.411923i	$0.135143\pi$
$908$	−8.32041	−0.276122
$909$	1.14894	0.0381079
$910$	−8.12876	−0.269466
$911$	−42.0913	−1.39455	−0.697274	−	0.716805i	$-0.745604\pi$
$911$	−42.0913	−1.39455	−0.697274	+	0.716805i	$0.745604\pi$
$912$	−19.2924	−0.638834
$913$	2.29395	0.0759185
$914$	−4.55051	−0.150518
$915$	2.43098	0.0803659
$916$	−3.44589	−0.113855
$917$	−15.4152	−0.509053
$918$	−9.13130	−0.301378
$919$	41.6453	1.37375	0.686876	−	0.726774i	$-0.258981\pi$
$919$	41.6453	1.37375	0.686876	+	0.726774i	$0.258981\pi$
$920$	13.9406	0.459607
$921$	2.16242	0.0712541
$922$	−14.1381	−0.465615
$923$	30.3040	0.997468
$924$	3.10869	0.102268
$925$	35.8488	1.17870
$926$	2.83782	0.0932567
$927$	−1.99427	−0.0655003
$928$	−16.1328	−0.529584
$929$	−46.7082	−1.53245	−0.766223	−	0.642574i	$-0.777866\pi$
$929$	−46.7082	−1.53245	−0.766223	+	0.642574i	$0.777866\pi$
$930$	11.0555	0.362523
$931$	−4.02118	−0.131789
$932$	11.1662	0.365762
$933$	−0.538962	−0.0176448
$934$	−67.7593	−2.21715
$935$	−28.7554	−0.940401
$936$	−13.2405	−0.432781
$937$	15.6592	0.511563	0.255781	−	0.966735i	$-0.417667\pi$
$937$	15.6592	0.511563	0.255781	+	0.966735i	$0.417667\pi$
$938$	8.24830	0.269317
$939$	−0.807183	−0.0263414
$940$	5.65355	0.184398
$941$	8.01824	0.261387	0.130694	−	0.991423i	$-0.458280\pi$
$941$	8.01824	0.261387	0.130694	+	0.991423i	$0.458280\pi$
$942$	1.62026	0.0527908
$943$	59.4087	1.93461
$944$	36.5496	1.18959
$945$	0.890069	0.0289540
$946$	−104.819	−3.40796
$947$	−29.2617	−0.950879	−0.475439	−	0.879748i	$-0.657711\pi$
$947$	−29.2617	−0.950879	−0.475439	+	0.879748i	$0.657711\pi$
$948$	4.60142	0.149447
$949$	51.7700	1.68052
$950$	−27.0205	−0.876662
$951$	10.4968	0.340382
$952$	13.2385	0.429062
$953$	−28.0996	−0.910234	−0.455117	−	0.890432i	$-0.650403\pi$
$953$	−28.0996	−0.910234	−0.455117	+	0.890432i	$0.650403\pi$
$954$	1.97042	0.0637946
$955$	0.890069	0.0288020
$956$	2.54473	0.0823024
$957$	30.0713	0.972066
$958$	38.5807	1.24648
$959$	13.3081	0.429741
$960$	−4.23211	−0.136591
$961$	29.4964	0.951498
$962$	−77.8076	−2.50862
$963$	0.491768	0.0158470
$964$	4.82639	0.155447
$965$	1.42714	0.0459413
$966$	−10.8032	−0.347586
$967$	−25.5427	−0.821397	−0.410699	−	0.911771i	$-0.634715\pi$
$967$	−25.5427	−0.821397	−0.410699	+	0.911771i	$0.634715\pi$
$968$	48.4410	1.55695
$969$	−22.9931	−0.738646
$970$	7.84612	0.251924
$971$	19.1678	0.615124	0.307562	−	0.951528i	$-0.400487\pi$
$971$	19.1678	0.615124	0.307562	+	0.951528i	$0.400487\pi$
$972$	−0.550208	−0.0176479
$973$	5.28682	0.169488
$974$	−15.7506	−0.504682
$975$	−24.0639	−0.770660
$976$	13.1036	0.419436
$977$	5.29141	0.169287	0.0846436	−	0.996411i	$-0.473025\pi$
$977$	5.29141	0.169287	0.0846436	+	0.996411i	$0.473025\pi$
$978$	29.6140	0.946952
$979$	1.70625	0.0545321
$980$	0.489723	0.0156436
$981$	13.5576	0.432860
$982$	−31.8379	−1.01599
$983$	8.17589	0.260770	0.130385	−	0.991463i	$-0.458379\pi$
$983$	8.17589	0.260770	0.130385	+	0.991463i	$0.458379\pi$
$984$	−20.3320	−0.648160
$985$	18.3988	0.586234
$986$	−48.5997	−1.54773
$987$	11.5444	0.367461
$988$	12.6530	0.402545
$989$	78.5896	2.49901
$990$	−8.03086	−0.255238
$991$	53.5201	1.70012	0.850062	−	0.526683i	$-0.176565\pi$
$991$	53.5201	1.70012	0.850062	+	0.526683i	$0.176565\pi$
$992$	23.5761	0.748543
$993$	−22.1977	−0.704422
$994$	−8.46204	−0.268400
$995$	−10.7488	−0.340761
$996$	−0.223388	−0.00707832
$997$	10.7287	0.339782	0.169891	−	0.985463i	$-0.445659\pi$
$997$	10.7287	0.339782	0.169891	+	0.985463i	$0.445659\pi$
$998$	−33.2665	−1.05303
$999$	8.51965	0.269550

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.j.1.8	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.j.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-1.59694 q^{2} -1.00000 q^{3} +0.550208 q^{4} +0.890069 q^{5} +1.59694 q^{6} -1.00000 q^{7} +2.31523 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.59694 q^{2} -1.00000 q^{3} +0.550208 q^{4} +0.890069 q^{5} +1.59694 q^{6} -1.00000 q^{7} +2.31523 q^{8} +1.00000 q^{9} -1.42138 q^{10} +5.65003 q^{11} -0.550208 q^{12} -5.71890 q^{13} +1.59694 q^{14} -0.890069 q^{15} -4.79769 q^{16} -5.71801 q^{17} -1.59694 q^{18} -4.02118 q^{19} +0.489723 q^{20} +1.00000 q^{21} -9.02274 q^{22} +6.76493 q^{23} -2.31523 q^{24} -4.20778 q^{25} +9.13273 q^{26} -1.00000 q^{27} -0.550208 q^{28} -5.32232 q^{29} +1.42138 q^{30} +7.77795 q^{31} +3.03115 q^{32} -5.65003 q^{33} +9.13130 q^{34} -0.890069 q^{35} +0.550208 q^{36} -8.51965 q^{37} +6.42157 q^{38} +5.71890 q^{39} +2.06071 q^{40} +8.78186 q^{41} -1.59694 q^{42} +11.6172 q^{43} +3.10869 q^{44} +0.890069 q^{45} -10.8032 q^{46} +11.5444 q^{47} +4.79769 q^{48} +1.00000 q^{49} +6.71955 q^{50} +5.71801 q^{51} -3.14659 q^{52} -1.23387 q^{53} +1.59694 q^{54} +5.02892 q^{55} -2.31523 q^{56} +4.02118 q^{57} +8.49941 q^{58} -7.61818 q^{59} -0.489723 q^{60} -2.73123 q^{61} -12.4209 q^{62} -1.00000 q^{63} +4.75481 q^{64} -5.09022 q^{65} +9.02274 q^{66} +5.16507 q^{67} -3.14609 q^{68} -6.76493 q^{69} +1.42138 q^{70} -5.29892 q^{71} +2.31523 q^{72} -9.05244 q^{73} +13.6053 q^{74} +4.20778 q^{75} -2.21249 q^{76} -5.65003 q^{77} -9.13273 q^{78} -8.36305 q^{79} -4.27027 q^{80} +1.00000 q^{81} -14.0241 q^{82} +0.406006 q^{83} +0.550208 q^{84} -5.08942 q^{85} -18.5520 q^{86} +5.32232 q^{87} +13.0811 q^{88} +0.301990 q^{89} -1.42138 q^{90} +5.71890 q^{91} +3.72212 q^{92} -7.77795 q^{93} -18.4356 q^{94} -3.57913 q^{95} -3.03115 q^{96} -5.52005 q^{97} -1.59694 q^{98} +5.65003 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9}+O(q^{10}) \) 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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