LMFDB - Embedded newform 4011.2.a.j.1.19

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			1.19
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)

$f(q)$	$=$	$q+1.34762 q^{2} -1.00000 q^{3} -0.183926 q^{4} -3.65993 q^{5} -1.34762 q^{6} -1.00000 q^{7} -2.94310 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.34762 q^{2} -1.00000 q^{3} -0.183926 q^{4} -3.65993 q^{5} -1.34762 q^{6} -1.00000 q^{7} -2.94310 q^{8} +1.00000 q^{9} -4.93219 q^{10} -4.51891 q^{11} +0.183926 q^{12} +0.810511 q^{13} -1.34762 q^{14} +3.65993 q^{15} -3.59832 q^{16} -5.81414 q^{17} +1.34762 q^{18} -3.44264 q^{19} +0.673156 q^{20} +1.00000 q^{21} -6.08977 q^{22} -4.99239 q^{23} +2.94310 q^{24} +8.39511 q^{25} +1.09226 q^{26} -1.00000 q^{27} +0.183926 q^{28} -0.885289 q^{29} +4.93219 q^{30} -6.11666 q^{31} +1.03703 q^{32} +4.51891 q^{33} -7.83524 q^{34} +3.65993 q^{35} -0.183926 q^{36} -7.76869 q^{37} -4.63937 q^{38} -0.810511 q^{39} +10.7715 q^{40} +1.55405 q^{41} +1.34762 q^{42} +1.52517 q^{43} +0.831144 q^{44} -3.65993 q^{45} -6.72784 q^{46} -8.74857 q^{47} +3.59832 q^{48} +1.00000 q^{49} +11.3134 q^{50} +5.81414 q^{51} -0.149074 q^{52} +3.27677 q^{53} -1.34762 q^{54} +16.5389 q^{55} +2.94310 q^{56} +3.44264 q^{57} -1.19303 q^{58} -7.05932 q^{59} -0.673156 q^{60} +2.23925 q^{61} -8.24292 q^{62} -1.00000 q^{63} +8.59417 q^{64} -2.96642 q^{65} +6.08977 q^{66} +4.75453 q^{67} +1.06937 q^{68} +4.99239 q^{69} +4.93219 q^{70} -2.37424 q^{71} -2.94310 q^{72} -1.89141 q^{73} -10.4692 q^{74} -8.39511 q^{75} +0.633190 q^{76} +4.51891 q^{77} -1.09226 q^{78} +1.39633 q^{79} +13.1696 q^{80} +1.00000 q^{81} +2.09426 q^{82} +10.5464 q^{83} -0.183926 q^{84} +21.2794 q^{85} +2.05534 q^{86} +0.885289 q^{87} +13.2996 q^{88} -7.63510 q^{89} -4.93219 q^{90} -0.810511 q^{91} +0.918229 q^{92} +6.11666 q^{93} -11.7897 q^{94} +12.5998 q^{95} -1.03703 q^{96} -0.647152 q^{97} +1.34762 q^{98} -4.51891 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.34762	0.952910	0.476455	−	0.879199i	$-0.341922\pi$
$2$	1.34762	0.952910	0.476455	+	0.879199i	$0.341922\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.183926	−0.0919628
$5$	−3.65993	−1.63677	−0.818386	−	0.574669i	$-0.805131\pi$
$5$	−3.65993	−1.63677	−0.818386	+	0.574669i	$0.805131\pi$
$6$	−1.34762	−0.550163
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.94310	−1.04054
$9$	1.00000	0.333333
$10$	−4.93219	−1.55970
$11$	−4.51891	−1.36250	−0.681252	−	0.732049i	$-0.738564\pi$
$11$	−4.51891	−1.36250	−0.681252	+	0.732049i	$0.738564\pi$
$12$	0.183926	0.0530948
$13$	0.810511	0.224795	0.112398	−	0.993663i	$-0.464147\pi$
$13$	0.810511	0.224795	0.112398	+	0.993663i	$0.464147\pi$
$14$	−1.34762	−0.360166
$15$	3.65993	0.944991
$16$	−3.59832	−0.899580
$17$	−5.81414	−1.41014	−0.705068	−	0.709139i	$-0.749084\pi$
$17$	−5.81414	−1.41014	−0.705068	+	0.709139i	$0.749084\pi$
$18$	1.34762	0.317637
$19$	−3.44264	−0.789796	−0.394898	−	0.918725i	$-0.629220\pi$
$19$	−3.44264	−0.789796	−0.394898	+	0.918725i	$0.629220\pi$
$20$	0.673156	0.150522
$21$	1.00000	0.218218
$22$	−6.08977	−1.29834
$23$	−4.99239	−1.04099	−0.520493	−	0.853866i	$-0.674252\pi$
$23$	−4.99239	−1.04099	−0.520493	+	0.853866i	$0.674252\pi$
$24$	2.94310	0.600757
$25$	8.39511	1.67902
$26$	1.09226	0.214210
$27$	−1.00000	−0.192450
$28$	0.183926	0.0347587
$29$	−0.885289	−0.164394	−0.0821970	−	0.996616i	$-0.526194\pi$
$29$	−0.885289	−0.164394	−0.0821970	+	0.996616i	$0.526194\pi$
$30$	4.93219	0.900491
$31$	−6.11666	−1.09858	−0.549292	−	0.835630i	$-0.685103\pi$
$31$	−6.11666	−1.09858	−0.549292	+	0.835630i	$0.685103\pi$
$32$	1.03703	0.183323
$33$	4.51891	0.786642
$34$	−7.83524	−1.34373
$35$	3.65993	0.618642
$36$	−0.183926	−0.0306543
$37$	−7.76869	−1.27717	−0.638583	−	0.769553i	$-0.720479\pi$
$37$	−7.76869	−1.27717	−0.638583	+	0.769553i	$0.720479\pi$
$38$	−4.63937	−0.752604
$39$	−0.810511	−0.129786
$40$	10.7715	1.70313
$41$	1.55405	0.242702	0.121351	−	0.992610i	$-0.461277\pi$
$41$	1.55405	0.242702	0.121351	+	0.992610i	$0.461277\pi$
$42$	1.34762	0.207942
$43$	1.52517	0.232586	0.116293	−	0.993215i	$-0.462899\pi$
$43$	1.52517	0.232586	0.116293	+	0.993215i	$0.462899\pi$
$44$	0.831144	0.125300
$45$	−3.65993	−0.545591
$46$	−6.72784	−0.991966
$47$	−8.74857	−1.27611	−0.638055	−	0.769991i	$-0.720261\pi$
$47$	−8.74857	−1.27611	−0.638055	+	0.769991i	$0.720261\pi$
$48$	3.59832	0.519373
$49$	1.00000	0.142857
$50$	11.3134	1.59996
$51$	5.81414	0.814143
$52$	−0.149074	−0.0206728
$53$	3.27677	0.450099	0.225049	−	0.974347i	$-0.427746\pi$
$53$	3.27677	0.450099	0.225049	+	0.974347i	$0.427746\pi$
$54$	−1.34762	−0.183388
$55$	16.5389	2.23011
$56$	2.94310	0.393288
$57$	3.44264	0.455989
$58$	−1.19303	−0.156653
$59$	−7.05932	−0.919045	−0.459523	−	0.888166i	$-0.651979\pi$
$59$	−7.05932	−0.919045	−0.459523	+	0.888166i	$0.651979\pi$
$60$	−0.673156	−0.0869040
$61$	2.23925	0.286707	0.143353	−	0.989672i	$-0.454211\pi$
$61$	2.23925	0.286707	0.143353	+	0.989672i	$0.454211\pi$
$62$	−8.24292	−1.04685
$63$	−1.00000	−0.125988
$64$	8.59417	1.07427
$65$	−2.96642	−0.367939
$66$	6.08977	0.749599
$67$	4.75453	0.580859	0.290429	−	0.956896i	$-0.406202\pi$
$67$	4.75453	0.580859	0.290429	+	0.956896i	$0.406202\pi$
$68$	1.06937	0.129680
$69$	4.99239	0.601014
$70$	4.93219	0.589510
$71$	−2.37424	−0.281771	−0.140885	−	0.990026i	$-0.544995\pi$
$71$	−2.37424	−0.281771	−0.140885	+	0.990026i	$0.544995\pi$
$72$	−2.94310	−0.346847
$73$	−1.89141	−0.221373	−0.110686	−	0.993855i	$-0.535305\pi$
$73$	−1.89141	−0.221373	−0.110686	+	0.993855i	$0.535305\pi$
$74$	−10.4692	−1.21702
$75$	−8.39511	−0.969384
$76$	0.633190	0.0726319
$77$	4.51891	0.514978
$78$	−1.09226	−0.123674
$79$	1.39633	0.157100	0.0785499	−	0.996910i	$-0.474971\pi$
$79$	1.39633	0.157100	0.0785499	+	0.996910i	$0.474971\pi$
$80$	13.1696	1.47241
$81$	1.00000	0.111111
$82$	2.09426	0.231273
$83$	10.5464	1.15761	0.578807	−	0.815464i	$-0.303518\pi$
$83$	10.5464	1.15761	0.578807	+	0.815464i	$0.303518\pi$
$84$	−0.183926	−0.0200679
$85$	21.2794	2.30807
$86$	2.05534	0.221633
$87$	0.885289	0.0949129
$88$	13.2996	1.41774
$89$	−7.63510	−0.809319	−0.404660	−	0.914467i	$-0.632610\pi$
$89$	−7.63510	−0.809319	−0.404660	+	0.914467i	$0.632610\pi$
$90$	−4.93219	−0.519899
$91$	−0.810511	−0.0849647
$92$	0.918229	0.0957320
$93$	6.11666	0.634268
$94$	−11.7897	−1.21602
$95$	12.5998	1.29272
$96$	−1.03703	−0.105842
$97$	−0.647152	−0.0657084	−0.0328542	−	0.999460i	$-0.510460\pi$
$97$	−0.647152	−0.0657084	−0.0328542	+	0.999460i	$0.510460\pi$
$98$	1.34762	0.136130
$99$	−4.51891	−0.454168
$100$	−1.54408	−0.154408
$101$	7.25952	0.722349	0.361174	−	0.932498i	$-0.382376\pi$
$101$	7.25952	0.722349	0.361174	+	0.932498i	$0.382376\pi$
$102$	7.83524	0.775805
$103$	−1.46833	−0.144679	−0.0723396	−	0.997380i	$-0.523047\pi$
$103$	−1.46833	−0.144679	−0.0723396	+	0.997380i	$0.523047\pi$
$104$	−2.38541	−0.233909
$105$	−3.65993	−0.357173
$106$	4.41583	0.428903
$107$	−14.0456	−1.35784	−0.678922	−	0.734211i	$-0.737553\pi$
$107$	−14.0456	−1.35784	−0.678922	+	0.734211i	$0.737553\pi$
$108$	0.183926	0.0176983
$109$	17.2574	1.65296	0.826480	−	0.562966i	$-0.190340\pi$
$109$	17.2574	1.65296	0.826480	+	0.562966i	$0.190340\pi$
$110$	22.2882	2.12509
$111$	7.76869	0.737372
$112$	3.59832	0.340009
$113$	−7.64379	−0.719067	−0.359534	−	0.933132i	$-0.617064\pi$
$113$	−7.64379	−0.719067	−0.359534	+	0.933132i	$0.617064\pi$
$114$	4.63937	0.434516
$115$	18.2718	1.70386
$116$	0.162827	0.0151181
$117$	0.810511	0.0749318
$118$	−9.51327	−0.875767
$119$	5.81414	0.532982
$120$	−10.7715	−0.983303
$121$	9.42059	0.856417
$122$	3.01766	0.273206
$123$	−1.55405	−0.140124
$124$	1.12501	0.101029
$125$	−12.4259	−1.11140
$126$	−1.34762	−0.120055
$127$	10.9492	0.971586	0.485793	−	0.874074i	$-0.338531\pi$
$127$	10.9492	0.971586	0.485793	+	0.874074i	$0.338531\pi$
$128$	9.50758	0.840360
$129$	−1.52517	−0.134284
$130$	−3.99760	−0.350612
$131$	−15.9463	−1.39323	−0.696615	−	0.717445i	$-0.745311\pi$
$131$	−15.9463	−1.39323	−0.696615	+	0.717445i	$0.745311\pi$
$132$	−0.831144	−0.0723418
$133$	3.44264	0.298515
$134$	6.40730	0.553506
$135$	3.65993	0.314997
$136$	17.1116	1.46731
$137$	17.5454	1.49900	0.749502	−	0.662002i	$-0.230293\pi$
$137$	17.5454	1.49900	0.749502	+	0.662002i	$0.230293\pi$
$138$	6.72784	0.572712
$139$	−12.1234	−1.02830	−0.514148	−	0.857701i	$-0.671892\pi$
$139$	−12.1234	−1.02830	−0.514148	+	0.857701i	$0.671892\pi$
$140$	−0.673156	−0.0568920
$141$	8.74857	0.736762
$142$	−3.19957	−0.268502
$143$	−3.66263	−0.306285
$144$	−3.59832	−0.299860
$145$	3.24010	0.269075
$146$	−2.54890	−0.210948
$147$	−1.00000	−0.0824786
$148$	1.42886	0.117452
$149$	1.56132	0.127909	0.0639543	−	0.997953i	$-0.479629\pi$
$149$	1.56132	0.127909	0.0639543	+	0.997953i	$0.479629\pi$
$150$	−11.3134	−0.923736
$151$	−4.44777	−0.361955	−0.180977	−	0.983487i	$-0.557926\pi$
$151$	−4.44777	−0.361955	−0.180977	+	0.983487i	$0.557926\pi$
$152$	10.1320	0.821816
$153$	−5.81414	−0.470046
$154$	6.08977	0.490728
$155$	22.3866	1.79813
$156$	0.149074	0.0119355
$157$	−11.7306	−0.936202	−0.468101	−	0.883675i	$-0.655062\pi$
$157$	−11.7306	−0.936202	−0.468101	+	0.883675i	$0.655062\pi$
$158$	1.88172	0.149702
$159$	−3.27677	−0.259865
$160$	−3.79548	−0.300059
$161$	4.99239	0.393456
$162$	1.34762	0.105879
$163$	−0.356872	−0.0279524	−0.0139762	−	0.999902i	$-0.504449\pi$
$163$	−0.356872	−0.0279524	−0.0139762	+	0.999902i	$0.504449\pi$
$164$	−0.285829	−0.0223195
$165$	−16.5389	−1.28755
$166$	14.2125	1.10310
$167$	−14.6966	−1.13726	−0.568628	−	0.822595i	$-0.692525\pi$
$167$	−14.6966	−1.13726	−0.568628	+	0.822595i	$0.692525\pi$
$168$	−2.94310	−0.227065
$169$	−12.3431	−0.949467
$170$	28.6765	2.19938
$171$	−3.44264	−0.263265
$172$	−0.280517	−0.0213893
$173$	−14.7489	−1.12133	−0.560667	−	0.828041i	$-0.689455\pi$
$173$	−14.7489	−1.12133	−0.560667	+	0.828041i	$0.689455\pi$
$174$	1.19303	0.0904434
$175$	−8.39511	−0.634611
$176$	16.2605	1.22568
$177$	7.05932	0.530611
$178$	−10.2892	−0.771208
$179$	−10.5223	−0.786471	−0.393235	−	0.919438i	$-0.628644\pi$
$179$	−10.5223	−0.786471	−0.393235	+	0.919438i	$0.628644\pi$
$180$	0.673156	0.0501741
$181$	11.7568	0.873874	0.436937	−	0.899492i	$-0.356063\pi$
$181$	11.7568	0.873874	0.436937	+	0.899492i	$0.356063\pi$
$182$	−1.09226	−0.0809637
$183$	−2.23925	−0.165530
$184$	14.6931	1.08319
$185$	28.4329	2.09043
$186$	8.24292	0.604400
$187$	26.2736	1.92132
$188$	1.60909	0.117355
$189$	1.00000	0.0727393
$190$	16.9798	1.23184
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	−8.59417	−0.620231
$193$	−15.4464	−1.11185	−0.555927	−	0.831231i	$-0.687637\pi$
$193$	−15.4464	−1.11185	−0.555927	+	0.831231i	$0.687637\pi$
$194$	−0.872114	−0.0626141
$195$	2.96642	0.212430
$196$	−0.183926	−0.0131375
$197$	2.81678	0.200687	0.100344	−	0.994953i	$-0.468006\pi$
$197$	2.81678	0.200687	0.100344	+	0.994953i	$0.468006\pi$
$198$	−6.08977	−0.432781
$199$	−15.9390	−1.12988	−0.564941	−	0.825131i	$-0.691101\pi$
$199$	−15.9390	−1.12988	−0.564941	+	0.825131i	$0.691101\pi$
$200$	−24.7076	−1.74709
$201$	−4.75453	−0.335359
$202$	9.78305	0.688333
$203$	0.885289	0.0621351
$204$	−1.06937	−0.0748709
$205$	−5.68772	−0.397247
$206$	−1.97875	−0.137866
$207$	−4.99239	−0.346995
$208$	−2.91648	−0.202221
$209$	15.5570	1.07610
$210$	−4.93219	−0.340354
$211$	19.1760	1.32013	0.660064	−	0.751209i	$-0.270529\pi$
$211$	19.1760	1.32013	0.660064	+	0.751209i	$0.270529\pi$
$212$	−0.602681	−0.0413923
$213$	2.37424	0.162680
$214$	−18.9282	−1.29390
$215$	−5.58201	−0.380690
$216$	2.94310	0.200252
$217$	6.11666	0.415226
$218$	23.2564	1.57512
$219$	1.89141	0.127810
$220$	−3.04193	−0.205087
$221$	−4.71243	−0.316992
$222$	10.4692	0.702649
$223$	−1.42957	−0.0957312	−0.0478656	−	0.998854i	$-0.515242\pi$
$223$	−1.42957	−0.0957312	−0.0478656	+	0.998854i	$0.515242\pi$
$224$	−1.03703	−0.0692898
$225$	8.39511	0.559674
$226$	−10.3009	−0.685206
$227$	14.8537	0.985875	0.492938	−	0.870065i	$-0.335923\pi$
$227$	14.8537	0.985875	0.492938	+	0.870065i	$0.335923\pi$
$228$	−0.633190	−0.0419340
$229$	0.674306	0.0445594	0.0222797	−	0.999752i	$-0.492908\pi$
$229$	0.674306	0.0445594	0.0222797	+	0.999752i	$0.492908\pi$
$230$	24.6235	1.62362
$231$	−4.51891	−0.297323
$232$	2.60549	0.171059
$233$	3.95953	0.259398	0.129699	−	0.991553i	$-0.458599\pi$
$233$	3.95953	0.259398	0.129699	+	0.991553i	$0.458599\pi$
$234$	1.09226	0.0714032
$235$	32.0192	2.08870
$236$	1.29839	0.0845180
$237$	−1.39633	−0.0907016
$238$	7.83524	0.507883
$239$	18.7426	1.21236	0.606180	−	0.795327i	$-0.292701\pi$
$239$	18.7426	1.21236	0.606180	+	0.795327i	$0.292701\pi$
$240$	−13.1696	−0.850095
$241$	18.6943	1.20420	0.602102	−	0.798419i	$-0.294330\pi$
$241$	18.6943	1.20420	0.602102	+	0.798419i	$0.294330\pi$
$242$	12.6954	0.816088
$243$	−1.00000	−0.0641500
$244$	−0.411856	−0.0263664
$245$	−3.65993	−0.233825
$246$	−2.09426	−0.133525
$247$	−2.79030	−0.177542
$248$	18.0019	1.14312
$249$	−10.5464	−0.668349
$250$	−16.7453	−1.05907
$251$	−16.8651	−1.06452	−0.532258	−	0.846582i	$-0.678656\pi$
$251$	−16.8651	−1.06452	−0.532258	+	0.846582i	$0.678656\pi$
$252$	0.183926	0.0115862
$253$	22.5602	1.41835
$254$	14.7554	0.925834
$255$	−21.2794	−1.33257
$256$	−4.37574	−0.273484
$257$	−15.1204	−0.943182	−0.471591	−	0.881817i	$-0.656320\pi$
$257$	−15.1204	−0.943182	−0.471591	+	0.881817i	$0.656320\pi$
$258$	−2.05534	−0.127960
$259$	7.76869	0.482723
$260$	0.545600	0.0338367
$261$	−0.885289	−0.0547980
$262$	−21.4895	−1.32762
$263$	−28.6223	−1.76493	−0.882464	−	0.470381i	$-0.844117\pi$
$263$	−28.6223	−1.76493	−0.882464	+	0.470381i	$0.844117\pi$
$264$	−13.2996	−0.818534
$265$	−11.9927	−0.736709
$266$	4.63937	0.284458
$267$	7.63510	0.467261
$268$	−0.874481	−0.0534174
$269$	−7.71000	−0.470087	−0.235043	−	0.971985i	$-0.575523\pi$
$269$	−7.71000	−0.470087	−0.235043	+	0.971985i	$0.575523\pi$
$270$	4.93219	0.300164
$271$	−16.5694	−1.00652	−0.503261	−	0.864134i	$-0.667867\pi$
$271$	−16.5694	−1.00652	−0.503261	+	0.864134i	$0.667867\pi$
$272$	20.9211	1.26853
$273$	0.810511	0.0490544
$274$	23.6445	1.42842
$275$	−37.9368	−2.28767
$276$	−0.918229	−0.0552709
$277$	−12.1366	−0.729217	−0.364608	−	0.931161i	$-0.618797\pi$
$277$	−12.1366	−0.729217	−0.364608	+	0.931161i	$0.618797\pi$
$278$	−16.3378	−0.979873
$279$	−6.11666	−0.366195
$280$	−10.7715	−0.643723
$281$	−22.2539	−1.32755	−0.663777	−	0.747930i	$-0.731048\pi$
$281$	−22.2539	−1.32755	−0.663777	+	0.747930i	$0.731048\pi$
$282$	11.7897	0.702068
$283$	11.7920	0.700960	0.350480	−	0.936570i	$-0.386019\pi$
$283$	11.7920	0.700960	0.350480	+	0.936570i	$0.386019\pi$
$284$	0.436684	0.0259124
$285$	−12.5998	−0.746350
$286$	−4.93583	−0.291862
$287$	−1.55405	−0.0917326
$288$	1.03703	0.0611078
$289$	16.8043	0.988485
$290$	4.36641	0.256405
$291$	0.647152	0.0379367
$292$	0.347879	0.0203581
$293$	−15.2212	−0.889231	−0.444616	−	0.895722i	$-0.646660\pi$
$293$	−15.2212	−0.889231	−0.444616	+	0.895722i	$0.646660\pi$
$294$	−1.34762	−0.0785947
$295$	25.8366	1.50427
$296$	22.8640	1.32894
$297$	4.51891	0.262214
$298$	2.10407	0.121885
$299$	−4.04639	−0.234009
$300$	1.54408	0.0891473
$301$	−1.52517	−0.0879092
$302$	−5.99390	−0.344910
$303$	−7.25952	−0.417048
$304$	12.3877	0.710485
$305$	−8.19551	−0.469274
$306$	−7.83524	−0.447911
$307$	−27.1315	−1.54848	−0.774239	−	0.632893i	$-0.781867\pi$
$307$	−27.1315	−1.54848	−0.774239	+	0.632893i	$0.781867\pi$
$308$	−0.831144	−0.0473588
$309$	1.46833	0.0835306
$310$	30.1685	1.71346
$311$	−28.6466	−1.62440	−0.812199	−	0.583380i	$-0.801730\pi$
$311$	−28.6466	−1.62440	−0.812199	+	0.583380i	$0.801730\pi$
$312$	2.38541	0.135047
$313$	−0.270231	−0.0152743	−0.00763717	−	0.999971i	$-0.502431\pi$
$313$	−0.270231	−0.0152743	−0.00763717	+	0.999971i	$0.502431\pi$
$314$	−15.8083	−0.892116
$315$	3.65993	0.206214
$316$	−0.256821	−0.0144473
$317$	14.7483	0.828348	0.414174	−	0.910198i	$-0.364070\pi$
$317$	14.7483	0.828348	0.414174	+	0.910198i	$0.364070\pi$
$318$	−4.41583	−0.247627
$319$	4.00054	0.223987
$320$	−31.4541	−1.75834
$321$	14.0456	0.783951
$322$	6.72784	0.374928
$323$	20.0160	1.11372
$324$	−0.183926	−0.0102181
$325$	6.80433	0.377436
$326$	−0.480927	−0.0266361
$327$	−17.2574	−0.954337
$328$	−4.57372	−0.252541
$329$	8.74857	0.482324
$330$	−22.2882	−1.22692
$331$	−11.5274	−0.633601	−0.316800	−	0.948492i	$-0.602609\pi$
$331$	−11.5274	−0.633601	−0.316800	+	0.948492i	$0.602609\pi$
$332$	−1.93975	−0.106458
$333$	−7.76869	−0.425722
$334$	−19.8054	−1.08370
$335$	−17.4013	−0.950733
$336$	−3.59832	−0.196304
$337$	−14.9433	−0.814011	−0.407006	−	0.913426i	$-0.633427\pi$
$337$	−14.9433	−0.814011	−0.407006	+	0.913426i	$0.633427\pi$
$338$	−16.6337	−0.904757
$339$	7.64379	0.415154
$340$	−3.91382	−0.212257
$341$	27.6407	1.49683
$342$	−4.63937	−0.250868
$343$	−1.00000	−0.0539949
$344$	−4.48872	−0.242015
$345$	−18.2718	−0.983722
$346$	−19.8758	−1.06853
$347$	18.1155	0.972493	0.486247	−	0.873822i	$-0.338366\pi$
$347$	18.1155	0.972493	0.486247	+	0.873822i	$0.338366\pi$
$348$	−0.162827	−0.00872846
$349$	20.8833	1.11786	0.558928	−	0.829216i	$-0.311213\pi$
$349$	20.8833	1.11786	0.558928	+	0.829216i	$0.311213\pi$
$350$	−11.3134	−0.604727
$351$	−0.810511	−0.0432619
$352$	−4.68627	−0.249779
$353$	−10.6518	−0.566940	−0.283470	−	0.958981i	$-0.591486\pi$
$353$	−10.6518	−0.566940	−0.283470	+	0.958981i	$0.591486\pi$
$354$	9.51327	0.505624
$355$	8.68956	0.461194
$356$	1.40429	0.0744273
$357$	−5.81414	−0.307717
$358$	−14.1800	−0.749436
$359$	27.7902	1.46671	0.733355	−	0.679846i	$-0.237953\pi$
$359$	27.7902	1.46671	0.733355	+	0.679846i	$0.237953\pi$
$360$	10.7715	0.567710
$361$	−7.14822	−0.376222
$362$	15.8436	0.832723
$363$	−9.42059	−0.494453
$364$	0.149074	0.00781359
$365$	6.92243	0.362337
$366$	−3.01766	−0.157735
$367$	0.799078	0.0417115	0.0208558	−	0.999782i	$-0.493361\pi$
$367$	0.799078	0.0417115	0.0208558	+	0.999782i	$0.493361\pi$
$368$	17.9642	0.936450
$369$	1.55405	0.0809006
$370$	38.3167	1.99199
$371$	−3.27677	−0.170121
$372$	−1.12501	−0.0583291
$373$	−19.1764	−0.992915	−0.496458	−	0.868061i	$-0.665366\pi$
$373$	−19.1764	−0.992915	−0.496458	+	0.868061i	$0.665366\pi$
$374$	35.4068	1.83084
$375$	12.4259	0.641670
$376$	25.7479	1.32785
$377$	−0.717536	−0.0369550
$378$	1.34762	0.0693140
$379$	−18.3416	−0.942147	−0.471073	−	0.882094i	$-0.656133\pi$
$379$	−18.3416	−0.942147	−0.471073	+	0.882094i	$0.656133\pi$
$380$	−2.31743	−0.118882
$381$	−10.9492	−0.560945
$382$	1.34762	0.0689501
$383$	25.9009	1.32347	0.661736	−	0.749737i	$-0.269820\pi$
$383$	25.9009	1.32347	0.661736	+	0.749737i	$0.269820\pi$
$384$	−9.50758	−0.485182
$385$	−16.5389	−0.842902
$386$	−20.8158	−1.05950
$387$	1.52517	0.0775286
$388$	0.119028	0.00604273
$389$	14.2314	0.721562	0.360781	−	0.932651i	$-0.382510\pi$
$389$	14.2314	0.721562	0.360781	+	0.932651i	$0.382510\pi$
$390$	3.99760	0.202426
$391$	29.0265	1.46793
$392$	−2.94310	−0.148649
$393$	15.9463	0.804382
$394$	3.79595	0.191237
$395$	−5.11049	−0.257136
$396$	0.831144	0.0417666
$397$	−26.2912	−1.31952	−0.659759	−	0.751477i	$-0.729342\pi$
$397$	−26.2912	−1.31952	−0.659759	+	0.751477i	$0.729342\pi$
$398$	−21.4796	−1.07668
$399$	−3.44264	−0.172348
$400$	−30.2083	−1.51041
$401$	13.6343	0.680862	0.340431	−	0.940269i	$-0.389427\pi$
$401$	13.6343	0.680862	0.340431	+	0.940269i	$0.389427\pi$
$402$	−6.40730	−0.319567
$403$	−4.95762	−0.246957
$404$	−1.33521	−0.0664292
$405$	−3.65993	−0.181864
$406$	1.19303	0.0592091
$407$	35.1061	1.74014
$408$	−17.1116	−0.847150
$409$	30.5073	1.50849	0.754244	−	0.656594i	$-0.228003\pi$
$409$	30.5073	1.50849	0.754244	+	0.656594i	$0.228003\pi$
$410$	−7.66487	−0.378541
$411$	−17.5454	−0.865450
$412$	0.270064	0.0133051
$413$	7.05932	0.347366
$414$	−6.72784	−0.330655
$415$	−38.5990	−1.89475
$416$	0.840528	0.0412103
$417$	12.1234	0.593687
$418$	20.9649	1.02543
$419$	−6.55596	−0.320280	−0.160140	−	0.987094i	$-0.551195\pi$
$419$	−6.55596	−0.320280	−0.160140	+	0.987094i	$0.551195\pi$
$420$	0.673156	0.0328466
$421$	2.29837	0.112016	0.0560079	−	0.998430i	$-0.482163\pi$
$421$	2.29837	0.112016	0.0560079	+	0.998430i	$0.482163\pi$
$422$	25.8419	1.25796
$423$	−8.74857	−0.425370
$424$	−9.64385	−0.468347
$425$	−48.8104	−2.36765
$426$	3.19957	0.155020
$427$	−2.23925	−0.108365
$428$	2.58335	0.124871
$429$	3.66263	0.176833
$430$	−7.52242	−0.362763
$431$	−4.20649	−0.202620	−0.101310	−	0.994855i	$-0.532303\pi$
$431$	−4.20649	−0.202620	−0.101310	+	0.994855i	$0.532303\pi$
$432$	3.59832	0.173124
$433$	−32.3666	−1.55544	−0.777719	−	0.628612i	$-0.783623\pi$
$433$	−32.3666	−1.55544	−0.777719	+	0.628612i	$0.783623\pi$
$434$	8.24292	0.395673
$435$	−3.24010	−0.155351
$436$	−3.17408	−0.152011
$437$	17.1870	0.822167
$438$	2.54890	0.121791
$439$	−18.3868	−0.877554	−0.438777	−	0.898596i	$-0.644588\pi$
$439$	−18.3868	−0.877554	−0.438777	+	0.898596i	$0.644588\pi$
$440$	−48.6757	−2.32052
$441$	1.00000	0.0476190
$442$	−6.35055	−0.302065
$443$	−18.1632	−0.862958	−0.431479	−	0.902123i	$-0.642008\pi$
$443$	−18.1632	−0.862958	−0.431479	+	0.902123i	$0.642008\pi$
$444$	−1.42886	−0.0678108
$445$	27.9440	1.32467
$446$	−1.92652	−0.0912232
$447$	−1.56132	−0.0738480
$448$	−8.59417	−0.406036
$449$	−11.7074	−0.552507	−0.276253	−	0.961085i	$-0.589093\pi$
$449$	−11.7074	−0.552507	−0.276253	+	0.961085i	$0.589093\pi$
$450$	11.3134	0.533319
$451$	−7.02262	−0.330682
$452$	1.40589	0.0661274
$453$	4.44777	0.208975
$454$	20.0171	0.939450
$455$	2.96642	0.139068
$456$	−10.1320	−0.474476
$457$	−13.8502	−0.647887	−0.323943	−	0.946076i	$-0.605009\pi$
$457$	−13.8502	−0.647887	−0.323943	+	0.946076i	$0.605009\pi$
$458$	0.908707	0.0424611
$459$	5.81414	0.271381
$460$	−3.36066	−0.156692
$461$	3.43295	0.159888	0.0799441	−	0.996799i	$-0.474526\pi$
$461$	3.43295	0.159888	0.0799441	+	0.996799i	$0.474526\pi$
$462$	−6.08977	−0.283322
$463$	41.2545	1.91726	0.958630	−	0.284656i	$-0.0918795\pi$
$463$	41.2545	1.91726	0.958630	+	0.284656i	$0.0918795\pi$
$464$	3.18555	0.147886
$465$	−22.3866	−1.03815
$466$	5.33594	0.247183
$467$	−0.625110	−0.0289266	−0.0144633	−	0.999895i	$-0.504604\pi$
$467$	−0.625110	−0.0289266	−0.0144633	+	0.999895i	$0.504604\pi$
$468$	−0.149074	−0.00689094
$469$	−4.75453	−0.219544
$470$	43.1496	1.99034
$471$	11.7306	0.540516
$472$	20.7763	0.956305
$473$	−6.89210	−0.316899
$474$	−1.88172	−0.0864304
$475$	−28.9014	−1.32609
$476$	−1.06937	−0.0490145
$477$	3.27677	0.150033
$478$	25.2579	1.15527
$479$	−38.8979	−1.77729	−0.888646	−	0.458594i	$-0.848353\pi$
$479$	−38.8979	−1.77729	−0.888646	+	0.458594i	$0.848353\pi$
$480$	3.79548	0.173239
$481$	−6.29661	−0.287101
$482$	25.1927	1.14750
$483$	−4.99239	−0.227162
$484$	−1.73269	−0.0787585
$485$	2.36853	0.107550
$486$	−1.34762	−0.0611292
$487$	28.5352	1.29305	0.646526	−	0.762892i	$-0.276221\pi$
$487$	28.5352	1.29305	0.646526	+	0.762892i	$0.276221\pi$
$488$	−6.59034	−0.298330
$489$	0.356872	0.0161383
$490$	−4.93219	−0.222814
$491$	26.2616	1.18517	0.592585	−	0.805508i	$-0.298108\pi$
$491$	26.2616	1.18517	0.592585	+	0.805508i	$0.298108\pi$
$492$	0.285829	0.0128862
$493$	5.14719	0.231818
$494$	−3.76026	−0.169182
$495$	16.5389	0.743369
$496$	22.0097	0.988265
$497$	2.37424	0.106499
$498$	−14.2125	−0.636876
$499$	−3.95169	−0.176902	−0.0884510	−	0.996081i	$-0.528192\pi$
$499$	−3.95169	−0.176902	−0.0884510	+	0.996081i	$0.528192\pi$
$500$	2.28544	0.102208
$501$	14.6966	0.656595
$502$	−22.7277	−1.01439
$503$	−36.8780	−1.64431	−0.822153	−	0.569266i	$-0.807227\pi$
$503$	−36.8780	−1.64431	−0.822153	+	0.569266i	$0.807227\pi$
$504$	2.94310	0.131096
$505$	−26.5693	−1.18232
$506$	30.4025	1.35156
$507$	12.3431	0.548175
$508$	−2.01384	−0.0893498
$509$	−19.6279	−0.869990	−0.434995	−	0.900433i	$-0.643250\pi$
$509$	−19.6279	−0.869990	−0.434995	+	0.900433i	$0.643250\pi$
$510$	−28.6765	−1.26982
$511$	1.89141	0.0836711
$512$	−24.9120	−1.10097
$513$	3.44264	0.151996
$514$	−20.3765	−0.898768
$515$	5.37400	0.236807
$516$	0.280517	0.0123491
$517$	39.5340	1.73871
$518$	10.4692	0.459992
$519$	14.7489	0.647403
$520$	8.73045	0.382856
$521$	12.1504	0.532319	0.266159	−	0.963929i	$-0.414245\pi$
$521$	12.1504	0.532319	0.266159	+	0.963929i	$0.414245\pi$
$522$	−1.19303	−0.0522175
$523$	2.93459	0.128321	0.0641603	−	0.997940i	$-0.479563\pi$
$523$	2.93459	0.128321	0.0641603	+	0.997940i	$0.479563\pi$
$524$	2.93292	0.128125
$525$	8.39511	0.366393
$526$	−38.5719	−1.68182
$527$	35.5631	1.54915
$528$	−16.2605	−0.707647
$529$	1.92401	0.0836525
$530$	−16.1616	−0.702017
$531$	−7.05932	−0.306348
$532$	−0.633190	−0.0274523
$533$	1.25957	0.0545582
$534$	10.2892	0.445257
$535$	51.4061	2.22248
$536$	−13.9931	−0.604408
$537$	10.5223	0.454069
$538$	−10.3901	−0.447950
$539$	−4.51891	−0.194643
$540$	−0.673156	−0.0289680
$541$	−41.7313	−1.79417	−0.897084	−	0.441860i	$-0.854319\pi$
$541$	−41.7313	−1.79417	−0.897084	+	0.441860i	$0.854319\pi$
$542$	−22.3293	−0.959125
$543$	−11.7568	−0.504531
$544$	−6.02946	−0.258511
$545$	−63.1610	−2.70552
$546$	1.09226	0.0467444
$547$	−0.755609	−0.0323075	−0.0161537	−	0.999870i	$-0.505142\pi$
$547$	−0.755609	−0.0323075	−0.0161537	+	0.999870i	$0.505142\pi$
$548$	−3.22705	−0.137853
$549$	2.23925	0.0955689
$550$	−51.1243	−2.17995
$551$	3.04773	0.129838
$552$	−14.6931	−0.625380
$553$	−1.39633	−0.0593781
$554$	−16.3555	−0.694878
$555$	−28.4329	−1.20691
$556$	2.22981	0.0945650
$557$	11.7007	0.495775	0.247887	−	0.968789i	$-0.420264\pi$
$557$	11.7007	0.495775	0.247887	+	0.968789i	$0.420264\pi$
$558$	−8.24292	−0.348951
$559$	1.23617	0.0522842
$560$	−13.1696	−0.556518
$561$	−26.2736	−1.10927
$562$	−29.9897	−1.26504
$563$	14.4861	0.610518	0.305259	−	0.952269i	$-0.401257\pi$
$563$	14.4861	0.610518	0.305259	+	0.952269i	$0.401257\pi$
$564$	−1.60909	−0.0677548
$565$	27.9758	1.17695
$566$	15.8911	0.667951
$567$	−1.00000	−0.0419961
$568$	6.98762	0.293194
$569$	29.2929	1.22802	0.614011	−	0.789297i	$-0.289555\pi$
$569$	29.2929	1.22802	0.614011	+	0.789297i	$0.289555\pi$
$570$	−16.9798	−0.711204
$571$	27.5223	1.15177	0.575886	−	0.817530i	$-0.304657\pi$
$571$	27.5223	1.15177	0.575886	+	0.817530i	$0.304657\pi$
$572$	0.673652	0.0281668
$573$	−1.00000	−0.0417756
$574$	−2.09426	−0.0874129
$575$	−41.9117	−1.74784
$576$	8.59417	0.358090
$577$	−29.8730	−1.24363	−0.621816	−	0.783164i	$-0.713605\pi$
$577$	−29.8730	−1.24363	−0.621816	+	0.783164i	$0.713605\pi$
$578$	22.6457	0.941937
$579$	15.4464	0.641929
$580$	−0.595937	−0.0247449
$581$	−10.5464	−0.437537
$582$	0.872114	0.0361503
$583$	−14.8074	−0.613261
$584$	5.56660	0.230348
$585$	−2.96642	−0.122646
$586$	−20.5123	−0.847357
$587$	−8.66100	−0.357478	−0.178739	−	0.983897i	$-0.557202\pi$
$587$	−8.66100	−0.357478	−0.178739	+	0.983897i	$0.557202\pi$
$588$	0.183926	0.00758497
$589$	21.0575	0.867658
$590$	34.8179	1.43343
$591$	−2.81678	−0.115867
$592$	27.9542	1.14891
$593$	−3.01744	−0.123911	−0.0619557	−	0.998079i	$-0.519734\pi$
$593$	−3.01744	−0.123911	−0.0619557	+	0.998079i	$0.519734\pi$
$594$	6.08977	0.249866
$595$	−21.2794	−0.872369
$596$	−0.287167	−0.0117628
$597$	15.9390	0.652338
$598$	−5.45299	−0.222989
$599$	−45.5278	−1.86022	−0.930108	−	0.367286i	$-0.880287\pi$
$599$	−45.5278	−1.86022	−0.930108	+	0.367286i	$0.880287\pi$
$600$	24.7076	1.00868
$601$	−26.9303	−1.09851	−0.549254	−	0.835655i	$-0.685088\pi$
$601$	−26.9303	−1.09851	−0.549254	+	0.835655i	$0.685088\pi$
$602$	−2.05534	−0.0837695
$603$	4.75453	0.193620
$604$	0.818060	0.0332864
$605$	−34.4787	−1.40176
$606$	−9.78305	−0.397409
$607$	−8.45964	−0.343366	−0.171683	−	0.985152i	$-0.554920\pi$
$607$	−8.45964	−0.343366	−0.171683	+	0.985152i	$0.554920\pi$
$608$	−3.57014	−0.144788
$609$	−0.885289	−0.0358737
$610$	−11.0444	−0.447175
$611$	−7.09081	−0.286864
$612$	1.06937	0.0432267
$613$	−1.77751	−0.0717930	−0.0358965	−	0.999356i	$-0.511429\pi$
$613$	−1.77751	−0.0717930	−0.0358965	+	0.999356i	$0.511429\pi$
$614$	−36.5629	−1.47556
$615$	5.68772	0.229351
$616$	−13.2996	−0.535856
$617$	1.65039	0.0664422	0.0332211	−	0.999448i	$-0.489423\pi$
$617$	1.65039	0.0664422	0.0332211	+	0.999448i	$0.489423\pi$
$618$	1.97875	0.0795971
$619$	−16.6892	−0.670795	−0.335397	−	0.942077i	$-0.608871\pi$
$619$	−16.6892	−0.670795	−0.335397	+	0.942077i	$0.608871\pi$
$620$	−4.11746	−0.165361
$621$	4.99239	0.200338
$622$	−38.6047	−1.54791
$623$	7.63510	0.305894
$624$	2.91648	0.116753
$625$	3.50234	0.140094
$626$	−0.364168	−0.0145551
$627$	−15.5570	−0.621287
$628$	2.15755	0.0860957
$629$	45.1683	1.80098
$630$	4.93219	0.196503
$631$	−8.29485	−0.330213	−0.165106	−	0.986276i	$-0.552797\pi$
$631$	−8.29485	−0.330213	−0.165106	+	0.986276i	$0.552797\pi$
$632$	−4.10954	−0.163469
$633$	−19.1760	−0.762177
$634$	19.8751	0.789341
$635$	−40.0734	−1.59026
$636$	0.602681	0.0238979
$637$	0.810511	0.0321136
$638$	5.39120	0.213440
$639$	−2.37424	−0.0939235
$640$	−34.7971	−1.37548
$641$	−43.4283	−1.71531	−0.857657	−	0.514222i	$-0.828081\pi$
$641$	−43.4283	−1.71531	−0.857657	+	0.514222i	$0.828081\pi$
$642$	18.9282	0.747035
$643$	23.6141	0.931249	0.465625	−	0.884982i	$-0.345830\pi$
$643$	23.6141	0.931249	0.465625	+	0.884982i	$0.345830\pi$
$644$	−0.918229	−0.0361833
$645$	5.58201	0.219791
$646$	26.9739	1.06128
$647$	48.4096	1.90318	0.951590	−	0.307371i	$-0.0994493\pi$
$647$	48.4096	1.90318	0.951590	+	0.307371i	$0.0994493\pi$
$648$	−2.94310	−0.115616
$649$	31.9005	1.25220
$650$	9.16964	0.359663
$651$	−6.11666	−0.239731
$652$	0.0656379	0.00257058
$653$	38.6248	1.51150	0.755752	−	0.654858i	$-0.227272\pi$
$653$	38.6248	1.51150	0.755752	+	0.654858i	$0.227272\pi$
$654$	−23.2564	−0.909397
$655$	58.3622	2.28040
$656$	−5.59197	−0.218330
$657$	−1.89141	−0.0737909
$658$	11.7897	0.459612
$659$	33.1090	1.28974	0.644872	−	0.764290i	$-0.276911\pi$
$659$	33.1090	1.28974	0.644872	+	0.764290i	$0.276911\pi$
$660$	3.04193	0.118407
$661$	9.48082	0.368761	0.184381	−	0.982855i	$-0.440972\pi$
$661$	9.48082	0.368761	0.184381	+	0.982855i	$0.440972\pi$
$662$	−15.5345	−0.603765
$663$	4.71243	0.183016
$664$	−31.0390	−1.20455
$665$	−12.5998	−0.488601
$666$	−10.4692	−0.405674
$667$	4.41971	0.171132
$668$	2.70308	0.104585
$669$	1.42957	0.0552704
$670$	−23.4503	−0.905963
$671$	−10.1190	−0.390639
$672$	1.03703	0.0400045
$673$	−5.83454	−0.224905	−0.112452	−	0.993657i	$-0.535871\pi$
$673$	−5.83454	−0.224905	−0.112452	+	0.993657i	$0.535871\pi$
$674$	−20.1378	−0.775679
$675$	−8.39511	−0.323128
$676$	2.27021	0.0873157
$677$	19.6070	0.753558	0.376779	−	0.926303i	$-0.377032\pi$
$677$	19.6070	0.753558	0.376779	+	0.926303i	$0.377032\pi$
$678$	10.3009	0.395604
$679$	0.647152	0.0248354
$680$	−62.6273	−2.40165
$681$	−14.8537	−0.569195
$682$	37.2491	1.42634
$683$	−46.4530	−1.77748	−0.888738	−	0.458416i	$-0.848417\pi$
$683$	−46.4530	−1.77748	−0.888738	+	0.458416i	$0.848417\pi$
$684$	0.633190	0.0242106
$685$	−64.2149	−2.45353
$686$	−1.34762	−0.0514523
$687$	−0.674306	−0.0257264
$688$	−5.48804	−0.209230
$689$	2.65586	0.101180
$690$	−24.6235	−0.937399
$691$	0.0757973	0.00288347	0.00144173	−	0.999999i	$-0.499541\pi$
$691$	0.0757973	0.00288347	0.00144173	+	0.999999i	$0.499541\pi$
$692$	2.71269	0.103121
$693$	4.51891	0.171659
$694$	24.4128	0.926698
$695$	44.3709	1.68309
$696$	−2.60549	−0.0987609
$697$	−9.03546	−0.342243
$698$	28.1427	1.06522
$699$	−3.95953	−0.149763
$700$	1.54408	0.0583606
$701$	27.5496	1.04053	0.520266	−	0.854004i	$-0.325833\pi$
$701$	27.5496	1.04053	0.520266	+	0.854004i	$0.325833\pi$
$702$	−1.09226	−0.0412247
$703$	26.7448	1.00870
$704$	−38.8363	−1.46370
$705$	−32.0192	−1.20591
$706$	−14.3546	−0.540243
$707$	−7.25952	−0.273022
$708$	−1.29839	−0.0487965
$709$	25.8522	0.970901	0.485450	−	0.874264i	$-0.338656\pi$
$709$	25.8522	0.970901	0.485450	+	0.874264i	$0.338656\pi$
$710$	11.7102	0.439476
$711$	1.39633	0.0523666
$712$	22.4709	0.842131
$713$	30.5368	1.14361
$714$	−7.83524	−0.293227
$715$	13.4050	0.501318
$716$	1.93531	0.0723261
$717$	−18.7426	−0.699956
$718$	37.4506	1.39764
$719$	24.8467	0.926625	0.463312	−	0.886195i	$-0.346661\pi$
$719$	24.8467	0.926625	0.463312	+	0.886195i	$0.346661\pi$
$720$	13.1696	0.490802
$721$	1.46833	0.0546836
$722$	−9.63307	−0.358506
$723$	−18.6943	−0.695247
$724$	−2.16237	−0.0803639
$725$	−7.43210	−0.276021
$726$	−12.6954	−0.471169
$727$	22.7812	0.844909	0.422455	−	0.906384i	$-0.361169\pi$
$727$	22.7812	0.844909	0.422455	+	0.906384i	$0.361169\pi$
$728$	2.38541	0.0884093
$729$	1.00000	0.0370370
$730$	9.32880	0.345274
$731$	−8.86754	−0.327978
$732$	0.411856	0.0152226
$733$	−22.6421	−0.836305	−0.418152	−	0.908377i	$-0.637322\pi$
$733$	−22.6421	−0.836305	−0.418152	+	0.908377i	$0.637322\pi$
$734$	1.07685	0.0397473
$735$	3.65993	0.134999
$736$	−5.17728	−0.190837
$737$	−21.4853	−0.791422
$738$	2.09426	0.0770910
$739$	49.0168	1.80311	0.901556	−	0.432662i	$-0.142426\pi$
$739$	49.0168	1.80311	0.901556	+	0.432662i	$0.142426\pi$
$740$	−5.22954	−0.192242
$741$	2.79030	0.102504
$742$	−4.41583	−0.162110
$743$	−42.9852	−1.57697	−0.788486	−	0.615052i	$-0.789135\pi$
$743$	−42.9852	−1.57697	−0.788486	+	0.615052i	$0.789135\pi$
$744$	−18.0019	−0.659983
$745$	−5.71434	−0.209357
$746$	−25.8424	−0.946159
$747$	10.5464	0.385872
$748$	−4.83239	−0.176690
$749$	14.0456	0.513217
$750$	16.7453	0.611453
$751$	−44.7326	−1.63232	−0.816158	−	0.577829i	$-0.803900\pi$
$751$	−44.7326	−1.63232	−0.816158	+	0.577829i	$0.803900\pi$
$752$	31.4802	1.14796
$753$	16.8651	0.614598
$754$	−0.966965	−0.0352148
$755$	16.2786	0.592437
$756$	−0.183926	−0.00668931
$757$	16.1607	0.587371	0.293685	−	0.955902i	$-0.405118\pi$
$757$	16.1607	0.587371	0.293685	+	0.955902i	$0.405118\pi$
$758$	−24.7175	−0.897781
$759$	−22.5602	−0.818884
$760$	−37.0825	−1.34513
$761$	30.0214	1.08828	0.544138	−	0.838996i	$-0.316857\pi$
$761$	30.0214	1.08828	0.544138	+	0.838996i	$0.316857\pi$
$762$	−14.7554	−0.534530
$763$	−17.2574	−0.624760
$764$	−0.183926	−0.00665420
$765$	21.2794	0.769357
$766$	34.9045	1.26115
$767$	−5.72166	−0.206597
$768$	4.37574	0.157896
$769$	24.1661	0.871452	0.435726	−	0.900079i	$-0.356492\pi$
$769$	24.1661	0.871452	0.435726	+	0.900079i	$0.356492\pi$
$770$	−22.2882	−0.803209
$771$	15.1204	0.544547
$772$	2.84098	0.102249
$773$	−7.04095	−0.253245	−0.126623	−	0.991951i	$-0.540414\pi$
$773$	−7.04095	−0.253245	−0.126623	+	0.991951i	$0.540414\pi$
$774$	2.05534	0.0738778
$775$	−51.3501	−1.84455
$776$	1.90463	0.0683723
$777$	−7.76869	−0.278700
$778$	19.1785	0.687584
$779$	−5.35003	−0.191685
$780$	−0.545600	−0.0195356
$781$	10.7290	0.383914
$782$	39.1166	1.39881
$783$	0.885289	0.0316376
$784$	−3.59832	−0.128511
$785$	42.9331	1.53235
$786$	21.4895	0.766503
$787$	−26.4778	−0.943833	−0.471916	−	0.881643i	$-0.656438\pi$
$787$	−26.4778	−0.943833	−0.471916	+	0.881643i	$0.656438\pi$
$788$	−0.518078	−0.0184558
$789$	28.6223	1.01898
$790$	−6.88698	−0.245028
$791$	7.64379	0.271782
$792$	13.2996	0.472581
$793$	1.81494	0.0644503
$794$	−35.4305	−1.25738
$795$	11.9927	0.425339
$796$	2.93158	0.103907
$797$	−15.8025	−0.559754	−0.279877	−	0.960036i	$-0.590294\pi$
$797$	−15.8025	−0.559754	−0.279877	+	0.960036i	$0.590294\pi$
$798$	−4.63937	−0.164232
$799$	50.8654	1.79949
$800$	8.70602	0.307804
$801$	−7.63510	−0.269773
$802$	18.3738	0.648800
$803$	8.54712	0.301621
$804$	0.874481	0.0308406
$805$	−18.2718	−0.643997
$806$	−6.68098	−0.235328
$807$	7.71000	0.271405
$808$	−21.3655	−0.751634
$809$	7.92502	0.278629	0.139314	−	0.990248i	$-0.455510\pi$
$809$	7.92502	0.278629	0.139314	+	0.990248i	$0.455510\pi$
$810$	−4.93219	−0.173300
$811$	31.0437	1.09009	0.545047	−	0.838406i	$-0.316512\pi$
$811$	31.0437	1.09009	0.545047	+	0.838406i	$0.316512\pi$
$812$	−0.162827	−0.00571412
$813$	16.5694	0.581116
$814$	47.3096	1.65820
$815$	1.30613	0.0457516
$816$	−20.9211	−0.732387
$817$	−5.25060	−0.183695
$818$	41.1122	1.43745
$819$	−0.810511	−0.0283216
$820$	1.04612	0.0365320
$821$	4.40571	0.153760	0.0768802	−	0.997040i	$-0.475504\pi$
$821$	4.40571	0.153760	0.0768802	+	0.997040i	$0.475504\pi$
$822$	−23.6445	−0.824696
$823$	45.3304	1.58012	0.790059	−	0.613030i	$-0.210050\pi$
$823$	45.3304	1.58012	0.790059	+	0.613030i	$0.210050\pi$
$824$	4.32145	0.150545
$825$	37.9368	1.32079
$826$	9.51327	0.331009
$827$	10.5769	0.367794	0.183897	−	0.982946i	$-0.441129\pi$
$827$	10.5769	0.367794	0.183897	+	0.982946i	$0.441129\pi$
$828$	0.918229	0.0319107
$829$	−17.2257	−0.598275	−0.299137	−	0.954210i	$-0.596699\pi$
$829$	−17.2257	−0.598275	−0.299137	+	0.954210i	$0.596699\pi$
$830$	−52.0167	−1.80553
$831$	12.1366	0.421014
$832$	6.96567	0.241491
$833$	−5.81414	−0.201448
$834$	16.3378	0.565730
$835$	53.7885	1.86143
$836$	−2.86133	−0.0989612
$837$	6.11666	0.211423
$838$	−8.83493	−0.305198
$839$	21.4489	0.740499	0.370250	−	0.928932i	$-0.379272\pi$
$839$	21.4489	0.740499	0.370250	+	0.928932i	$0.379272\pi$
$840$	10.7715	0.371653
$841$	−28.2163	−0.972975
$842$	3.09733	0.106741
$843$	22.2539	0.766464
$844$	−3.52695	−0.121403
$845$	45.1748	1.55406
$846$	−11.7897	−0.405339
$847$	−9.42059	−0.323695
$848$	−11.7909	−0.404900
$849$	−11.7920	−0.404699
$850$	−65.7777	−2.25616
$851$	38.7844	1.32951
$852$	−0.436684	−0.0149605
$853$	17.3290	0.593333	0.296666	−	0.954981i	$-0.404125\pi$
$853$	17.3290	0.593333	0.296666	+	0.954981i	$0.404125\pi$
$854$	−3.01766	−0.103262
$855$	12.5998	0.430905
$856$	41.3377	1.41289
$857$	9.24242	0.315715	0.157858	−	0.987462i	$-0.449541\pi$
$857$	9.24242	0.315715	0.157858	+	0.987462i	$0.449541\pi$
$858$	4.93583	0.168506
$859$	57.4719	1.96092	0.980458	−	0.196727i	$-0.0630311\pi$
$859$	57.4719	1.96092	0.980458	+	0.196727i	$0.0630311\pi$
$860$	1.02667	0.0350093
$861$	1.55405	0.0529619
$862$	−5.66874	−0.193078
$863$	−52.6303	−1.79156	−0.895778	−	0.444502i	$-0.853381\pi$
$863$	−52.6303	−1.79156	−0.895778	+	0.444502i	$0.853381\pi$
$864$	−1.03703	−0.0352806
$865$	53.9798	1.83537
$866$	−43.6178	−1.48219
$867$	−16.8043	−0.570702
$868$	−1.12501	−0.0381854
$869$	−6.30991	−0.214049
$870$	−4.36641	−0.148035
$871$	3.85360	0.130574
$872$	−50.7903	−1.71998
$873$	−0.647152	−0.0219028
$874$	23.1615	0.783451
$875$	12.4259	0.420071
$876$	−0.347879	−0.0117537
$877$	10.7409	0.362693	0.181347	−	0.983419i	$-0.441954\pi$
$877$	10.7409	0.362693	0.181347	+	0.983419i	$0.441954\pi$
$878$	−24.7784	−0.836230
$879$	15.2212	0.513398
$880$	−59.5124	−2.00616
$881$	−26.4537	−0.891249	−0.445625	−	0.895220i	$-0.647018\pi$
$881$	−26.4537	−0.891249	−0.445625	+	0.895220i	$0.647018\pi$
$882$	1.34762	0.0453767
$883$	−33.5160	−1.12790	−0.563952	−	0.825807i	$-0.690720\pi$
$883$	−33.5160	−1.12790	−0.563952	+	0.825807i	$0.690720\pi$
$884$	0.866736	0.0291515
$885$	−25.8366	−0.868489
$886$	−24.4770	−0.822321
$887$	−21.2996	−0.715170	−0.357585	−	0.933881i	$-0.616400\pi$
$887$	−21.2996	−0.715170	−0.357585	+	0.933881i	$0.616400\pi$
$888$	−22.8640	−0.767266
$889$	−10.9492	−0.367225
$890$	37.6578	1.26229
$891$	−4.51891	−0.151389
$892$	0.262935	0.00880371
$893$	30.1182	1.00787
$894$	−2.10407	−0.0703705
$895$	38.5108	1.28727
$896$	−9.50758	−0.317626
$897$	4.04639	0.135105
$898$	−15.7771	−0.526489
$899$	5.41501	0.180601
$900$	−1.54408	−0.0514692
$901$	−19.0516	−0.634701
$902$	−9.46380	−0.315110
$903$	1.52517	0.0507544
$904$	22.4964	0.748220
$905$	−43.0290	−1.43033
$906$	5.99390	0.199134
$907$	−46.7532	−1.55241	−0.776207	−	0.630478i	$-0.782859\pi$
$907$	−46.7532	−1.55241	−0.776207	+	0.630478i	$0.782859\pi$
$908$	−2.73198	−0.0906639
$909$	7.25952	0.240783
$910$	3.99760	0.132519
$911$	−41.8215	−1.38561	−0.692804	−	0.721126i	$-0.743625\pi$
$911$	−41.8215	−1.38561	−0.692804	+	0.721126i	$0.743625\pi$
$912$	−12.3877	−0.410199
$913$	−47.6582	−1.57725
$914$	−18.6648	−0.617378
$915$	8.19551	0.270935
$916$	−0.124022	−0.00409781
$917$	15.9463	0.526592
$918$	7.83524	0.258602
$919$	35.6738	1.17677	0.588386	−	0.808581i	$-0.299764\pi$
$919$	35.6738	1.17677	0.588386	+	0.808581i	$0.299764\pi$
$920$	−53.7758	−1.77294
$921$	27.1315	0.894014
$922$	4.62630	0.152359
$923$	−1.92435	−0.0633407
$924$	0.831144	0.0273426
$925$	−65.2190	−2.14439
$926$	55.5953	1.82698
$927$	−1.46833	−0.0482264
$928$	−0.918074	−0.0301373
$929$	−42.9951	−1.41062	−0.705312	−	0.708897i	$-0.749193\pi$
$929$	−42.9951	−1.41062	−0.705312	+	0.708897i	$0.749193\pi$
$930$	−30.1685	−0.989266
$931$	−3.44264	−0.112828
$932$	−0.728260	−0.0238549
$933$	28.6466	0.937847
$934$	−0.842409	−0.0275645
$935$	−96.1597	−3.14476
$936$	−2.38541	−0.0779697
$937$	41.8128	1.36597	0.682983	−	0.730434i	$-0.260682\pi$
$937$	41.8128	1.36597	0.682983	+	0.730434i	$0.260682\pi$
$938$	−6.40730	−0.209206
$939$	0.270231	0.00881864
$940$	−5.88915	−0.192083
$941$	41.2213	1.34378	0.671888	−	0.740652i	$-0.265483\pi$
$941$	41.2213	1.34378	0.671888	+	0.740652i	$0.265483\pi$
$942$	15.8083	0.515063
$943$	−7.75843	−0.252649
$944$	25.4017	0.826755
$945$	−3.65993	−0.119058
$946$	−9.28792	−0.301976
$947$	50.1701	1.63031	0.815154	−	0.579244i	$-0.196652\pi$
$947$	50.1701	1.63031	0.815154	+	0.579244i	$0.196652\pi$
$948$	0.256821	0.00834117
$949$	−1.53301	−0.0497636
$950$	−38.9480	−1.26364
$951$	−14.7483	−0.478247
$952$	−17.1116	−0.554590
$953$	34.7738	1.12643	0.563216	−	0.826310i	$-0.309564\pi$
$953$	34.7738	1.12643	0.563216	+	0.826310i	$0.309564\pi$
$954$	4.41583	0.142968
$955$	−3.65993	−0.118433
$956$	−3.44725	−0.111492
$957$	−4.00054	−0.129319
$958$	−52.4195	−1.69360
$959$	−17.5454	−0.566570
$960$	31.4541	1.01518
$961$	6.41355	0.206889
$962$	−8.48543	−0.273581
$963$	−14.0456	−0.452615
$964$	−3.43836	−0.110742
$965$	56.5327	1.81985
$966$	−6.72784	−0.216465
$967$	43.3939	1.39546	0.697728	−	0.716363i	$-0.254195\pi$
$967$	43.3939	1.39546	0.697728	+	0.716363i	$0.254195\pi$
$968$	−27.7257	−0.891138
$969$	−20.0160	−0.643007
$970$	3.19188	0.102485
$971$	−20.6795	−0.663636	−0.331818	−	0.943343i	$-0.607662\pi$
$971$	−20.6795	−0.663636	−0.331818	+	0.943343i	$0.607662\pi$
$972$	0.183926	0.00589942
$973$	12.1234	0.388659
$974$	38.4545	1.23216
$975$	−6.80433	−0.217913
$976$	−8.05754	−0.257916
$977$	−57.9741	−1.85476	−0.927378	−	0.374126i	$-0.877943\pi$
$977$	−57.9741	−1.85476	−0.927378	+	0.374126i	$0.877943\pi$
$978$	0.480927	0.0153784
$979$	34.5024	1.10270
$980$	0.673156	0.0215032
$981$	17.2574	0.550987
$982$	35.3906	1.12936
$983$	−3.37484	−0.107641	−0.0538204	−	0.998551i	$-0.517140\pi$
$983$	−3.37484	−0.107641	−0.0538204	+	0.998551i	$0.517140\pi$
$984$	4.57372	0.145805
$985$	−10.3092	−0.328480
$986$	6.93645	0.220902
$987$	−8.74857	−0.278470
$988$	0.513208	0.0163273
$989$	−7.61424	−0.242119
$990$	22.2882	0.708364
$991$	−36.7135	−1.16624	−0.583121	−	0.812385i	$-0.698169\pi$
$991$	−36.7135	−1.16624	−0.583121	+	0.812385i	$0.698169\pi$
$992$	−6.34319	−0.201396
$993$	11.5274	0.365810
$994$	3.19957	0.101484
$995$	58.3355	1.84936
$996$	1.93975	0.0614633
$997$	−5.70775	−0.180766	−0.0903832	−	0.995907i	$-0.528809\pi$
$997$	−5.70775	−0.180766	−0.0903832	+	0.995907i	$0.528809\pi$
$998$	−5.32537	−0.168572
$999$	7.76869	0.245791

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.j.1.19	✓	26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.j.1.19	✓	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)

\(f(q)\)	\(=\)	\(q+1.34762 q^{2} -1.00000 q^{3} -0.183926 q^{4} -3.65993 q^{5} -1.34762 q^{6} -1.00000 q^{7} -2.94310 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.34762 q^{2} -1.00000 q^{3} -0.183926 q^{4} -3.65993 q^{5} -1.34762 q^{6} -1.00000 q^{7} -2.94310 q^{8} +1.00000 q^{9} -4.93219 q^{10} -4.51891 q^{11} +0.183926 q^{12} +0.810511 q^{13} -1.34762 q^{14} +3.65993 q^{15} -3.59832 q^{16} -5.81414 q^{17} +1.34762 q^{18} -3.44264 q^{19} +0.673156 q^{20} +1.00000 q^{21} -6.08977 q^{22} -4.99239 q^{23} +2.94310 q^{24} +8.39511 q^{25} +1.09226 q^{26} -1.00000 q^{27} +0.183926 q^{28} -0.885289 q^{29} +4.93219 q^{30} -6.11666 q^{31} +1.03703 q^{32} +4.51891 q^{33} -7.83524 q^{34} +3.65993 q^{35} -0.183926 q^{36} -7.76869 q^{37} -4.63937 q^{38} -0.810511 q^{39} +10.7715 q^{40} +1.55405 q^{41} +1.34762 q^{42} +1.52517 q^{43} +0.831144 q^{44} -3.65993 q^{45} -6.72784 q^{46} -8.74857 q^{47} +3.59832 q^{48} +1.00000 q^{49} +11.3134 q^{50} +5.81414 q^{51} -0.149074 q^{52} +3.27677 q^{53} -1.34762 q^{54} +16.5389 q^{55} +2.94310 q^{56} +3.44264 q^{57} -1.19303 q^{58} -7.05932 q^{59} -0.673156 q^{60} +2.23925 q^{61} -8.24292 q^{62} -1.00000 q^{63} +8.59417 q^{64} -2.96642 q^{65} +6.08977 q^{66} +4.75453 q^{67} +1.06937 q^{68} +4.99239 q^{69} +4.93219 q^{70} -2.37424 q^{71} -2.94310 q^{72} -1.89141 q^{73} -10.4692 q^{74} -8.39511 q^{75} +0.633190 q^{76} +4.51891 q^{77} -1.09226 q^{78} +1.39633 q^{79} +13.1696 q^{80} +1.00000 q^{81} +2.09426 q^{82} +10.5464 q^{83} -0.183926 q^{84} +21.2794 q^{85} +2.05534 q^{86} +0.885289 q^{87} +13.2996 q^{88} -7.63510 q^{89} -4.93219 q^{90} -0.810511 q^{91} +0.918229 q^{92} +6.11666 q^{93} -11.7897 q^{94} +12.5998 q^{95} -1.03703 q^{96} -0.647152 q^{97} +1.34762 q^{98} -4.51891 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 26 q^{3} + 34 q^{4} + 2 q^{5} - 26 q^{7} + 26 q^{9}+O(q^{10}) \) 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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