LMFDB - Embedded newform 6014.2.a.f.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.17019 q^{3} +1.00000 q^{4} +1.18841 q^{5} -2.17019 q^{6} -1.11869 q^{7} -1.00000 q^{8} +1.70972 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.17019 q^{3} +1.00000 q^{4} +1.18841 q^{5} -2.17019 q^{6} -1.11869 q^{7} -1.00000 q^{8} +1.70972 q^{9} -1.18841 q^{10} -1.35322 q^{11} +2.17019 q^{12} +1.19858 q^{13} +1.11869 q^{14} +2.57908 q^{15} +1.00000 q^{16} -2.91731 q^{17} -1.70972 q^{18} -6.09920 q^{19} +1.18841 q^{20} -2.42776 q^{21} +1.35322 q^{22} -2.71260 q^{23} -2.17019 q^{24} -3.58767 q^{25} -1.19858 q^{26} -2.80015 q^{27} -1.11869 q^{28} +6.09455 q^{29} -2.57908 q^{30} +1.00000 q^{31} -1.00000 q^{32} -2.93674 q^{33} +2.91731 q^{34} -1.32946 q^{35} +1.70972 q^{36} +8.60335 q^{37} +6.09920 q^{38} +2.60116 q^{39} -1.18841 q^{40} +8.96153 q^{41} +2.42776 q^{42} +3.76837 q^{43} -1.35322 q^{44} +2.03186 q^{45} +2.71260 q^{46} -9.20207 q^{47} +2.17019 q^{48} -5.74854 q^{49} +3.58767 q^{50} -6.33112 q^{51} +1.19858 q^{52} -13.3580 q^{53} +2.80015 q^{54} -1.60818 q^{55} +1.11869 q^{56} -13.2364 q^{57} -6.09455 q^{58} +9.22880 q^{59} +2.57908 q^{60} -5.54150 q^{61} -1.00000 q^{62} -1.91264 q^{63} +1.00000 q^{64} +1.42441 q^{65} +2.93674 q^{66} +6.43204 q^{67} -2.91731 q^{68} -5.88686 q^{69} +1.32946 q^{70} -1.35885 q^{71} -1.70972 q^{72} -10.6441 q^{73} -8.60335 q^{74} -7.78593 q^{75} -6.09920 q^{76} +1.51383 q^{77} -2.60116 q^{78} -8.70496 q^{79} +1.18841 q^{80} -11.2060 q^{81} -8.96153 q^{82} -8.14525 q^{83} -2.42776 q^{84} -3.46698 q^{85} -3.76837 q^{86} +13.2263 q^{87} +1.35322 q^{88} -8.48040 q^{89} -2.03186 q^{90} -1.34084 q^{91} -2.71260 q^{92} +2.17019 q^{93} +9.20207 q^{94} -7.24837 q^{95} -2.17019 q^{96} +1.00000 q^{97} +5.74854 q^{98} -2.31362 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9}+O(q^{10}) $ 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9	$ 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9} - 8 q^{13} + 11 q^{14} + q^{15} + 22 q^{16} - 4 q^{17} - 8 q^{18} - 23 q^{19} - 12 q^{21} + 2 q^{23} - 12 q^{25} + 8 q^{26} + 3 q^{27} - 11 q^{28} + 9 q^{29} - q^{30} + 22 q^{31} - 22 q^{32} + 4 q^{34} + 4 q^{35} + 8 q^{36} - 17 q^{37} + 23 q^{38} + 8 q^{39} - 21 q^{41} + 12 q^{42} - 7 q^{43} + 9 q^{45} - 2 q^{46} - 10 q^{47} - 27 q^{49} + 12 q^{50} - q^{51} - 8 q^{52} + 9 q^{53} - 3 q^{54} - 6 q^{55} + 11 q^{56} - q^{57} - 9 q^{58} - 12 q^{59} + q^{60} - 34 q^{61} - 22 q^{62} - 5 q^{63} + 22 q^{64} + 4 q^{65} - 31 q^{67} - 4 q^{68} - 51 q^{69} - 4 q^{70} - 15 q^{71} - 8 q^{72} + 3 q^{73} + 17 q^{74} - 24 q^{75} - 23 q^{76} + 24 q^{77} - 8 q^{78} - 23 q^{79} - 26 q^{81} + 21 q^{82} + 22 q^{83} - 12 q^{84} - 42 q^{85} + 7 q^{86} - 9 q^{87} - 36 q^{89} - 9 q^{90} - 6 q^{91} + 2 q^{92} + 10 q^{94} + 2 q^{95} + 22 q^{97} + 27 q^{98} - 25 q^{99}+O(q^{100}) $ 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9 - 8 * q^13 + 11 * q^14 + q^15 + 22 * q^16 - 4 * q^17 - 8 * q^18 - 23 * q^19 - 12 * q^21 + 2 * q^23 - 12 * q^25 + 8 * q^26 + 3 * q^27 - 11 * q^28 + 9 * q^29 - q^30 + 22 * q^31 - 22 * q^32 + 4 * q^34 + 4 * q^35 + 8 * q^36 - 17 * q^37 + 23 * q^38 + 8 * q^39 - 21 * q^41 + 12 * q^42 - 7 * q^43 + 9 * q^45 - 2 * q^46 - 10 * q^47 - 27 * q^49 + 12 * q^50 - q^51 - 8 * q^52 + 9 * q^53 - 3 * q^54 - 6 * q^55 + 11 * q^56 - q^57 - 9 * q^58 - 12 * q^59 + q^60 - 34 * q^61 - 22 * q^62 - 5 * q^63 + 22 * q^64 + 4 * q^65 - 31 * q^67 - 4 * q^68 - 51 * q^69 - 4 * q^70 - 15 * q^71 - 8 * q^72 + 3 * q^73 + 17 * q^74 - 24 * q^75 - 23 * q^76 + 24 * q^77 - 8 * q^78 - 23 * q^79 - 26 * q^81 + 21 * q^82 + 22 * q^83 - 12 * q^84 - 42 * q^85 + 7 * q^86 - 9 * q^87 - 36 * q^89 - 9 * q^90 - 6 * q^91 + 2 * q^92 + 10 * q^94 + 2 * q^95 + 22 * q^97 + 27 * q^98 - 25 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.17019	1.25296	0.626480	−	0.779438i	$-0.284495\pi$
$3$	2.17019	1.25296	0.626480	+	0.779438i	$0.284495\pi$
$4$	1.00000	0.500000
$5$	1.18841	0.531475	0.265737	−	0.964045i	$-0.414385\pi$
$5$	1.18841	0.531475	0.265737	+	0.964045i	$0.414385\pi$
$6$	−2.17019	−0.885976
$7$	−1.11869	−0.422824	−0.211412	−	0.977397i	$-0.567806\pi$
$7$	−1.11869	−0.422824	−0.211412	+	0.977397i	$0.567806\pi$
$8$	−1.00000	−0.353553
$9$	1.70972	0.569907
$10$	−1.18841	−0.375809
$11$	−1.35322	−0.408010	−0.204005	−	0.978970i	$-0.565396\pi$
$11$	−1.35322	−0.408010	−0.204005	+	0.978970i	$0.565396\pi$
$12$	2.17019	0.626480
$13$	1.19858	0.332428	0.166214	−	0.986090i	$-0.446846\pi$
$13$	1.19858	0.332428	0.166214	+	0.986090i	$0.446846\pi$
$14$	1.11869	0.298982
$15$	2.57908	0.665916
$16$	1.00000	0.250000
$17$	−2.91731	−0.707553	−0.353776	−	0.935330i	$-0.615103\pi$
$17$	−2.91731	−0.707553	−0.353776	+	0.935330i	$0.615103\pi$
$18$	−1.70972	−0.402985
$19$	−6.09920	−1.39925	−0.699626	−	0.714509i	$-0.746650\pi$
$19$	−6.09920	−1.39925	−0.699626	+	0.714509i	$0.746650\pi$
$20$	1.18841	0.265737
$21$	−2.42776	−0.529781
$22$	1.35322	0.288507
$23$	−2.71260	−0.565616	−0.282808	−	0.959176i	$-0.591266\pi$
$23$	−2.71260	−0.565616	−0.282808	+	0.959176i	$0.591266\pi$
$24$	−2.17019	−0.442988
$25$	−3.58767	−0.717535
$26$	−1.19858	−0.235062
$27$	−2.80015	−0.538889
$28$	−1.11869	−0.211412
$29$	6.09455	1.13173	0.565865	−	0.824498i	$-0.308542\pi$
$29$	6.09455	1.13173	0.565865	+	0.824498i	$0.308542\pi$
$30$	−2.57908	−0.470874
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−1.00000	−0.176777
$33$	−2.93674	−0.511220
$34$	2.91731	0.500315
$35$	−1.32946	−0.224720
$36$	1.70972	0.284954
$37$	8.60335	1.41438	0.707191	−	0.707022i	$-0.249962\pi$
$37$	8.60335	1.41438	0.707191	+	0.707022i	$0.249962\pi$
$38$	6.09920	0.989421
$39$	2.60116	0.416518
$40$	−1.18841	−0.187905
$41$	8.96153	1.39956	0.699778	−	0.714360i	$-0.253282\pi$
$41$	8.96153	1.39956	0.699778	+	0.714360i	$0.253282\pi$
$42$	2.42776	0.374612
$43$	3.76837	0.574671	0.287335	−	0.957830i	$-0.407231\pi$
$43$	3.76837	0.574671	0.287335	+	0.957830i	$0.407231\pi$
$44$	−1.35322	−0.204005
$45$	2.03186	0.302891
$46$	2.71260	0.399951
$47$	−9.20207	−1.34226	−0.671130	−	0.741340i	$-0.734191\pi$
$47$	−9.20207	−1.34226	−0.671130	+	0.741340i	$0.734191\pi$
$48$	2.17019	0.313240
$49$	−5.74854	−0.821220
$50$	3.58767	0.507374
$51$	−6.33112	−0.886535
$52$	1.19858	0.166214
$53$	−13.3580	−1.83486	−0.917432	−	0.397891i	$-0.869742\pi$
$53$	−13.3580	−1.83486	−0.917432	+	0.397891i	$0.869742\pi$
$54$	2.80015	0.381052
$55$	−1.60818	−0.216847
$56$	1.11869	0.149491
$57$	−13.2364	−1.75321
$58$	−6.09455	−0.800253
$59$	9.22880	1.20149	0.600744	−	0.799442i	$-0.294871\pi$
$59$	9.22880	1.20149	0.600744	+	0.799442i	$0.294871\pi$
$60$	2.57908	0.332958
$61$	−5.54150	−0.709517	−0.354758	−	0.934958i	$-0.615437\pi$
$61$	−5.54150	−0.709517	−0.354758	+	0.934958i	$0.615437\pi$
$62$	−1.00000	−0.127000
$63$	−1.91264	−0.240971
$64$	1.00000	0.125000
$65$	1.42441	0.176677
$66$	2.93674	0.361487
$67$	6.43204	0.785799	0.392899	−	0.919581i	$-0.371472\pi$
$67$	6.43204	0.785799	0.392899	+	0.919581i	$0.371472\pi$
$68$	−2.91731	−0.353776
$69$	−5.88686	−0.708694
$70$	1.32946	0.158901
$71$	−1.35885	−0.161266	−0.0806328	−	0.996744i	$-0.525694\pi$
$71$	−1.35885	−0.161266	−0.0806328	+	0.996744i	$0.525694\pi$
$72$	−1.70972	−0.201493
$73$	−10.6441	−1.24580	−0.622901	−	0.782301i	$-0.714046\pi$
$73$	−10.6441	−1.24580	−0.622901	+	0.782301i	$0.714046\pi$
$74$	−8.60335	−1.00012
$75$	−7.78593	−0.899042
$76$	−6.09920	−0.699626
$77$	1.51383	0.172517
$78$	−2.60116	−0.294523
$79$	−8.70496	−0.979385	−0.489692	−	0.871895i	$-0.662891\pi$
$79$	−8.70496	−0.979385	−0.489692	+	0.871895i	$0.662891\pi$
$80$	1.18841	0.132869
$81$	−11.2060	−1.24511
$82$	−8.96153	−0.989635
$83$	−8.14525	−0.894057	−0.447028	−	0.894520i	$-0.647518\pi$
$83$	−8.14525	−0.894057	−0.447028	+	0.894520i	$0.647518\pi$
$84$	−2.42776	−0.264891
$85$	−3.46698	−0.376046
$86$	−3.76837	−0.406354
$87$	13.2263	1.41801
$88$	1.35322	0.144253
$89$	−8.48040	−0.898920	−0.449460	−	0.893300i	$-0.648384\pi$
$89$	−8.48040	−0.898920	−0.449460	+	0.893300i	$0.648384\pi$
$90$	−2.03186	−0.214177
$91$	−1.34084	−0.140558
$92$	−2.71260	−0.282808
$93$	2.17019	0.225038
$94$	9.20207	0.949121
$95$	−7.24837	−0.743667
$96$	−2.17019	−0.221494
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	5.74854	0.580690
$99$	−2.31362	−0.232528
$100$	−3.58767	−0.358767
$101$	−14.3018	−1.42308	−0.711542	−	0.702643i	$-0.752003\pi$
$101$	−14.3018	−1.42308	−0.711542	+	0.702643i	$0.752003\pi$
$102$	6.33112	0.626875
$103$	0.212057	0.0208946	0.0104473	−	0.999945i	$-0.496674\pi$
$103$	0.212057	0.0208946	0.0104473	+	0.999945i	$0.496674\pi$
$104$	−1.19858	−0.117531
$105$	−2.88519	−0.281565
$106$	13.3580	1.29745
$107$	6.80438	0.657804	0.328902	−	0.944364i	$-0.393321\pi$
$107$	6.80438	0.657804	0.328902	+	0.944364i	$0.393321\pi$
$108$	−2.80015	−0.269444
$109$	−1.29965	−0.124484	−0.0622419	−	0.998061i	$-0.519825\pi$
$109$	−1.29965	−0.124484	−0.0622419	+	0.998061i	$0.519825\pi$
$110$	1.60818	0.153334
$111$	18.6709	1.77216
$112$	−1.11869	−0.105706
$113$	19.9239	1.87428	0.937139	−	0.348955i	$-0.113463\pi$
$113$	19.9239	1.87428	0.937139	+	0.348955i	$0.113463\pi$
$114$	13.2364	1.23970
$115$	−3.22369	−0.300611
$116$	6.09455	0.565865
$117$	2.04925	0.189453
$118$	−9.22880	−0.849580
$119$	3.26356	0.299170
$120$	−2.57908	−0.235437
$121$	−9.16881	−0.833528
$122$	5.54150	0.501704
$123$	19.4482	1.75359
$124$	1.00000	0.0898027
$125$	−10.2057	−0.912826
$126$	1.91264	0.170392
$127$	0.362181	0.0321383	0.0160692	−	0.999871i	$-0.494885\pi$
$127$	0.362181	0.0321383	0.0160692	+	0.999871i	$0.494885\pi$
$128$	−1.00000	−0.0883883
$129$	8.17807	0.720039
$130$	−1.42441	−0.124929
$131$	0.245991	0.0214924	0.0107462	−	0.999942i	$-0.496579\pi$
$131$	0.245991	0.0214924	0.0107462	+	0.999942i	$0.496579\pi$
$132$	−2.93674	−0.255610
$133$	6.82310	0.591638
$134$	−6.43204	−0.555644
$135$	−3.32773	−0.286406
$136$	2.91731	0.250158
$137$	−9.07313	−0.775170	−0.387585	−	0.921834i	$-0.626691\pi$
$137$	−9.07313	−0.775170	−0.387585	+	0.921834i	$0.626691\pi$
$138$	5.88686	0.501123
$139$	15.5188	1.31629	0.658143	−	0.752893i	$-0.271342\pi$
$139$	15.5188	1.31629	0.658143	+	0.752893i	$0.271342\pi$
$140$	−1.32946	−0.112360
$141$	−19.9702	−1.68180
$142$	1.35885	0.114032
$143$	−1.62194	−0.135634
$144$	1.70972	0.142477
$145$	7.24284	0.601486
$146$	10.6441	0.880915
$147$	−12.4754	−1.02896
$148$	8.60335	0.707191
$149$	−14.7519	−1.20852	−0.604262	−	0.796785i	$-0.706532\pi$
$149$	−14.7519	−1.20852	−0.604262	+	0.796785i	$0.706532\pi$
$150$	7.78593	0.635718
$151$	−5.13130	−0.417579	−0.208789	−	0.977961i	$-0.566952\pi$
$151$	−5.13130	−0.417579	−0.208789	+	0.977961i	$0.566952\pi$
$152$	6.09920	0.494710
$153$	−4.98780	−0.403239
$154$	−1.51383	−0.121988
$155$	1.18841	0.0954557
$156$	2.60116	0.208259
$157$	−12.5064	−0.998122	−0.499061	−	0.866567i	$-0.666322\pi$
$157$	−12.5064	−0.998122	−0.499061	+	0.866567i	$0.666322\pi$
$158$	8.70496	0.692530
$159$	−28.9894	−2.29901
$160$	−1.18841	−0.0939524
$161$	3.03455	0.239156
$162$	11.2060	0.880428
$163$	−5.97329	−0.467864	−0.233932	−	0.972253i	$-0.575159\pi$
$163$	−5.97329	−0.467864	−0.233932	+	0.972253i	$0.575159\pi$
$164$	8.96153	0.699778
$165$	−3.49006	−0.271701
$166$	8.14525	0.632194
$167$	0.186213	0.0144096	0.00720479	−	0.999974i	$-0.497707\pi$
$167$	0.186213	0.0144096	0.00720479	+	0.999974i	$0.497707\pi$
$168$	2.42776	0.187306
$169$	−11.5634	−0.889492
$170$	3.46698	0.265905
$171$	−10.4279	−0.797444
$172$	3.76837	0.287335
$173$	−18.7401	−1.42478	−0.712392	−	0.701782i	$-0.752388\pi$
$173$	−18.7401	−1.42478	−0.712392	+	0.701782i	$0.752388\pi$
$174$	−13.2263	−1.00269
$175$	4.01348	0.303391
$176$	−1.35322	−0.102003
$177$	20.0282	1.50542
$178$	8.48040	0.635632
$179$	−2.32768	−0.173979	−0.0869895	−	0.996209i	$-0.527725\pi$
$179$	−2.32768	−0.173979	−0.0869895	+	0.996209i	$0.527725\pi$
$180$	2.03186	0.151446
$181$	−25.1743	−1.87119	−0.935596	−	0.353073i	$-0.885137\pi$
$181$	−25.1743	−1.87119	−0.935596	+	0.353073i	$0.885137\pi$
$182$	1.34084	0.0993898
$183$	−12.0261	−0.888996
$184$	2.71260	0.199976
$185$	10.2243	0.751709
$186$	−2.17019	−0.159126
$187$	3.94776	0.288689
$188$	−9.20207	−0.671130
$189$	3.13249	0.227855
$190$	7.24837	0.525852
$191$	0.713523	0.0516287	0.0258144	−	0.999667i	$-0.491782\pi$
$191$	0.713523	0.0516287	0.0258144	+	0.999667i	$0.491782\pi$
$192$	2.17019	0.156620
$193$	−18.2246	−1.31183	−0.655917	−	0.754833i	$-0.727718\pi$
$193$	−18.2246	−1.31183	−0.655917	+	0.754833i	$0.727718\pi$
$194$	−1.00000	−0.0717958
$195$	3.09125	0.221369
$196$	−5.74854	−0.410610
$197$	17.2978	1.23242	0.616208	−	0.787583i	$-0.288668\pi$
$197$	17.2978	1.23242	0.616208	+	0.787583i	$0.288668\pi$
$198$	2.31362	0.164422
$199$	11.3332	0.803387	0.401693	−	0.915774i	$-0.368422\pi$
$199$	11.3332	0.803387	0.401693	+	0.915774i	$0.368422\pi$
$200$	3.58767	0.253687
$201$	13.9587	0.984574
$202$	14.3018	1.00627
$203$	−6.81790	−0.478522
$204$	−6.33112	−0.443267
$205$	10.6500	0.743829
$206$	−0.212057	−0.0147747
$207$	−4.63779	−0.322349
$208$	1.19858	0.0831069
$209$	8.25353	0.570909
$210$	2.88519	0.199097
$211$	−10.3555	−0.712899	−0.356449	−	0.934315i	$-0.616013\pi$
$211$	−10.3555	−0.712899	−0.356449	+	0.934315i	$0.616013\pi$
$212$	−13.3580	−0.917432
$213$	−2.94896	−0.202059
$214$	−6.80438	−0.465138
$215$	4.47838	0.305423
$216$	2.80015	0.190526
$217$	−1.11869	−0.0759415
$218$	1.29965	0.0880233
$219$	−23.0998	−1.56094
$220$	−1.60818	−0.108424
$221$	−3.49665	−0.235210
$222$	−18.6709	−1.25311
$223$	9.63500	0.645207	0.322604	−	0.946534i	$-0.395442\pi$
$223$	9.63500	0.645207	0.322604	+	0.946534i	$0.395442\pi$
$224$	1.11869	0.0747455
$225$	−6.13392	−0.408928
$226$	−19.9239	−1.32532
$227$	−5.05561	−0.335553	−0.167776	−	0.985825i	$-0.553659\pi$
$227$	−5.05561	−0.335553	−0.167776	+	0.985825i	$0.553659\pi$
$228$	−13.2364	−0.876603
$229$	−11.5631	−0.764110	−0.382055	−	0.924140i	$-0.624784\pi$
$229$	−11.5631	−0.764110	−0.382055	+	0.924140i	$0.624784\pi$
$230$	3.22369	0.212564
$231$	3.28529	0.216156
$232$	−6.09455	−0.400127
$233$	1.40930	0.0923262	0.0461631	−	0.998934i	$-0.485301\pi$
$233$	1.40930	0.0923262	0.0461631	+	0.998934i	$0.485301\pi$
$234$	−2.04925	−0.133963
$235$	−10.9359	−0.713377
$236$	9.22880	0.600744
$237$	−18.8914	−1.22713
$238$	−3.26356	−0.211545
$239$	−1.10954	−0.0717700	−0.0358850	−	0.999356i	$-0.511425\pi$
$239$	−1.10954	−0.0717700	−0.0358850	+	0.999356i	$0.511425\pi$
$240$	2.57908	0.166479
$241$	12.4506	0.802012	0.401006	−	0.916075i	$-0.368661\pi$
$241$	12.4506	0.802012	0.401006	+	0.916075i	$0.368661\pi$
$242$	9.16881	0.589393
$243$	−15.9187	−1.02119
$244$	−5.54150	−0.354758
$245$	−6.83164	−0.436458
$246$	−19.4482	−1.23997
$247$	−7.31041	−0.465150
$248$	−1.00000	−0.0635001
$249$	−17.6767	−1.12022
$250$	10.2057	0.645466
$251$	−3.25951	−0.205738	−0.102869	−	0.994695i	$-0.532802\pi$
$251$	−3.25951	−0.205738	−0.102869	+	0.994695i	$0.532802\pi$
$252$	−1.91264	−0.120485
$253$	3.67074	0.230777
$254$	−0.362181	−0.0227252
$255$	−7.52399	−0.471171
$256$	1.00000	0.0625000
$257$	3.17761	0.198214	0.0991070	−	0.995077i	$-0.468401\pi$
$257$	3.17761	0.198214	0.0991070	+	0.995077i	$0.468401\pi$
$258$	−8.17807	−0.509145
$259$	−9.62446	−0.598035
$260$	1.42441	0.0883385
$261$	10.4200	0.644981
$262$	−0.245991	−0.0151974
$263$	26.9478	1.66167	0.830835	−	0.556519i	$-0.187863\pi$
$263$	26.9478	1.66167	0.830835	+	0.556519i	$0.187863\pi$
$264$	2.93674	0.180744
$265$	−15.8749	−0.975184
$266$	−6.82310	−0.418351
$267$	−18.4041	−1.12631
$268$	6.43204	0.392899
$269$	−9.21431	−0.561807	−0.280903	−	0.959736i	$-0.590634\pi$
$269$	−9.21431	−0.561807	−0.280903	+	0.959736i	$0.590634\pi$
$270$	3.32773	0.202519
$271$	−8.05685	−0.489419	−0.244709	−	0.969596i	$-0.578693\pi$
$271$	−8.05685	−0.489419	−0.244709	+	0.969596i	$0.578693\pi$
$272$	−2.91731	−0.176888
$273$	−2.90988	−0.176114
$274$	9.07313	0.548128
$275$	4.85490	0.292761
$276$	−5.88686	−0.354347
$277$	20.9889	1.26110	0.630552	−	0.776147i	$-0.282829\pi$
$277$	20.9889	1.26110	0.630552	+	0.776147i	$0.282829\pi$
$278$	−15.5188	−0.930755
$279$	1.70972	0.102358
$280$	1.32946	0.0794506
$281$	14.4530	0.862194	0.431097	−	0.902306i	$-0.358127\pi$
$281$	14.4530	0.862194	0.431097	+	0.902306i	$0.358127\pi$
$282$	19.9702	1.18921
$283$	23.5738	1.40132	0.700660	−	0.713495i	$-0.252889\pi$
$283$	23.5738	1.40132	0.700660	+	0.713495i	$0.252889\pi$
$284$	−1.35885	−0.0806328
$285$	−15.7303	−0.931785
$286$	1.62194	0.0959076
$287$	−10.0252	−0.591766
$288$	−1.70972	−0.100746
$289$	−8.48928	−0.499369
$290$	−7.24284	−0.425315
$291$	2.17019	0.127219
$292$	−10.6441	−0.622901
$293$	−0.944817	−0.0551968	−0.0275984	−	0.999619i	$-0.508786\pi$
$293$	−0.944817	−0.0551968	−0.0275984	+	0.999619i	$0.508786\pi$
$294$	12.4754	0.727581
$295$	10.9676	0.638560
$296$	−8.60335	−0.500060
$297$	3.78921	0.219872
$298$	14.7519	0.854556
$299$	−3.25128	−0.188027
$300$	−7.78593	−0.449521
$301$	−4.21563	−0.242985
$302$	5.13130	0.295273
$303$	−31.0377	−1.78307
$304$	−6.09920	−0.349813
$305$	−6.58560	−0.377090
$306$	4.98780	0.285133
$307$	−16.9320	−0.966359	−0.483180	−	0.875521i	$-0.660518\pi$
$307$	−16.9320	−0.966359	−0.483180	+	0.875521i	$0.660518\pi$
$308$	1.51383	0.0862583
$309$	0.460205	0.0261801
$310$	−1.18841	−0.0674974
$311$	−7.35825	−0.417248	−0.208624	−	0.977996i	$-0.566899\pi$
$311$	−7.35825	−0.417248	−0.208624	+	0.977996i	$0.566899\pi$
$312$	−2.60116	−0.147261
$313$	−14.5183	−0.820622	−0.410311	−	0.911946i	$-0.634580\pi$
$313$	−14.5183	−0.820622	−0.410311	+	0.911946i	$0.634580\pi$
$314$	12.5064	0.705779
$315$	−2.27301	−0.128070
$316$	−8.70496	−0.489692
$317$	11.8160	0.663651	0.331825	−	0.943341i	$-0.392336\pi$
$317$	11.8160	0.663651	0.331825	+	0.943341i	$0.392336\pi$
$318$	28.9894	1.62565
$319$	−8.24724	−0.461757
$320$	1.18841	0.0664343
$321$	14.7668	0.824202
$322$	−3.03455	−0.169109
$323$	17.7933	0.990044
$324$	−11.2060	−0.622556
$325$	−4.30013	−0.238528
$326$	5.97329	0.330830
$327$	−2.82048	−0.155973
$328$	−8.96153	−0.494818
$329$	10.2942	0.567540
$330$	3.49006	0.192121
$331$	15.4853	0.851148	0.425574	−	0.904924i	$-0.360072\pi$
$331$	15.4853	0.851148	0.425574	+	0.904924i	$0.360072\pi$
$332$	−8.14525	−0.447028
$333$	14.7093	0.806067
$334$	−0.186213	−0.0101891
$335$	7.64392	0.417632
$336$	−2.42776	−0.132445
$337$	13.1494	0.716295	0.358147	−	0.933665i	$-0.383409\pi$
$337$	13.1494	0.716295	0.358147	+	0.933665i	$0.383409\pi$
$338$	11.5634	0.628966
$339$	43.2385	2.34840
$340$	−3.46698	−0.188023
$341$	−1.35322	−0.0732808
$342$	10.4279	0.563878
$343$	14.2616	0.770056
$344$	−3.76837	−0.203177
$345$	−6.99602	−0.376653
$346$	18.7401	1.00747
$347$	25.5656	1.37243	0.686215	−	0.727398i	$-0.259271\pi$
$347$	25.5656	1.37243	0.686215	+	0.727398i	$0.259271\pi$
$348$	13.2263	0.709005
$349$	35.0322	1.87523	0.937616	−	0.347673i	$-0.113028\pi$
$349$	35.0322	1.87523	0.937616	+	0.347673i	$0.113028\pi$
$350$	−4.01348	−0.214530
$351$	−3.35621	−0.179141
$352$	1.35322	0.0721267
$353$	24.3886	1.29808	0.649038	−	0.760756i	$-0.275172\pi$
$353$	24.3886	1.29808	0.649038	+	0.760756i	$0.275172\pi$
$354$	−20.0282	−1.06449
$355$	−1.61487	−0.0857086
$356$	−8.48040	−0.449460
$357$	7.08255	0.374848
$358$	2.32768	0.123022
$359$	8.62793	0.455365	0.227682	−	0.973735i	$-0.426885\pi$
$359$	8.62793	0.455365	0.227682	+	0.973735i	$0.426885\pi$
$360$	−2.03186	−0.107088
$361$	18.2002	0.957906
$362$	25.1743	1.32313
$363$	−19.8980	−1.04438
$364$	−1.34084	−0.0702792
$365$	−12.6496	−0.662112
$366$	12.0261	0.628615
$367$	5.71091	0.298107	0.149054	−	0.988829i	$-0.452377\pi$
$367$	5.71091	0.298107	0.149054	+	0.988829i	$0.452377\pi$
$368$	−2.71260	−0.141404
$369$	15.3217	0.797617
$370$	−10.2243	−0.531538
$371$	14.9434	0.775825
$372$	2.17019	0.112519
$373$	14.4867	0.750092	0.375046	−	0.927006i	$-0.377627\pi$
$373$	14.4867	0.750092	0.375046	+	0.927006i	$0.377627\pi$
$374$	−3.94776	−0.204134
$375$	−22.1483	−1.14373
$376$	9.20207	0.474560
$377$	7.30483	0.376218
$378$	−3.13249	−0.161118
$379$	19.7457	1.01427	0.507133	−	0.861868i	$-0.330705\pi$
$379$	19.7457	1.01427	0.507133	+	0.861868i	$0.330705\pi$
$380$	−7.24837	−0.371834
$381$	0.786000	0.0402680
$382$	−0.713523	−0.0365070
$383$	6.02817	0.308025	0.154013	−	0.988069i	$-0.450780\pi$
$383$	6.02817	0.308025	0.154013	+	0.988069i	$0.450780\pi$
$384$	−2.17019	−0.110747
$385$	1.79905	0.0916882
$386$	18.2246	0.927606
$387$	6.44286	0.327509
$388$	1.00000	0.0507673
$389$	−9.89076	−0.501481	−0.250741	−	0.968054i	$-0.580674\pi$
$389$	−9.89076	−0.501481	−0.250741	+	0.968054i	$0.580674\pi$
$390$	−3.09125	−0.156532
$391$	7.91351	0.400203
$392$	5.74854	0.290345
$393$	0.533848	0.0269290
$394$	−17.2978	−0.871450
$395$	−10.3451	−0.520518
$396$	−2.31362	−0.116264
$397$	−36.6684	−1.84033	−0.920166	−	0.391529i	$-0.871946\pi$
$397$	−36.6684	−1.84033	−0.920166	+	0.391529i	$0.871946\pi$
$398$	−11.3332	−0.568080
$399$	14.8074	0.741298
$400$	−3.58767	−0.179384
$401$	17.4763	0.872726	0.436363	−	0.899771i	$-0.356266\pi$
$401$	17.4763	0.872726	0.436363	+	0.899771i	$0.356266\pi$
$402$	−13.9587	−0.696199
$403$	1.19858	0.0597058
$404$	−14.3018	−0.711542
$405$	−13.3174	−0.661746
$406$	6.81790	0.338366
$407$	−11.6422	−0.577082
$408$	6.33112	0.313437
$409$	10.0882	0.498829	0.249415	−	0.968397i	$-0.419762\pi$
$409$	10.0882	0.498829	0.249415	+	0.968397i	$0.419762\pi$
$410$	−10.6500	−0.525966
$411$	−19.6904	−0.971256
$412$	0.212057	0.0104473
$413$	−10.3241	−0.508018
$414$	4.63779	0.227935
$415$	−9.67992	−0.475169
$416$	−1.19858	−0.0587655
$417$	33.6787	1.64925
$418$	−8.25353	−0.403694
$419$	9.11876	0.445481	0.222740	−	0.974878i	$-0.428500\pi$
$419$	9.11876	0.445481	0.222740	+	0.974878i	$0.428500\pi$
$420$	−2.88519	−0.140783
$421$	1.75851	0.0857045	0.0428523	−	0.999081i	$-0.486356\pi$
$421$	1.75851	0.0857045	0.0428523	+	0.999081i	$0.486356\pi$
$422$	10.3555	0.504096
$423$	−15.7330	−0.764963
$424$	13.3580	0.648723
$425$	10.4664	0.507693
$426$	2.94896	0.142877
$427$	6.19921	0.300001
$428$	6.80438	0.328902
$429$	−3.51993	−0.169944
$430$	−4.47838	−0.215967
$431$	4.77447	0.229978	0.114989	−	0.993367i	$-0.463317\pi$
$431$	4.77447	0.229978	0.114989	+	0.993367i	$0.463317\pi$
$432$	−2.80015	−0.134722
$433$	−11.4008	−0.547889	−0.273944	−	0.961746i	$-0.588328\pi$
$433$	−11.4008	−0.547889	−0.273944	+	0.961746i	$0.588328\pi$
$434$	1.11869	0.0536987
$435$	15.7183	0.753637
$436$	−1.29965	−0.0622419
$437$	16.5447	0.791440
$438$	23.0998	1.10375
$439$	14.9821	0.715055	0.357527	−	0.933903i	$-0.383620\pi$
$439$	14.9821	0.715055	0.357527	+	0.933903i	$0.383620\pi$
$440$	1.60818	0.0766670
$441$	−9.82840	−0.468019
$442$	3.49665	0.166319
$443$	−32.0704	−1.52371	−0.761855	−	0.647748i	$-0.775711\pi$
$443$	−32.0704	−1.52371	−0.761855	+	0.647748i	$0.775711\pi$
$444$	18.6709	0.886082
$445$	−10.0782	−0.477753
$446$	−9.63500	−0.456231
$447$	−32.0145	−1.51423
$448$	−1.11869	−0.0528530
$449$	−29.0916	−1.37292	−0.686459	−	0.727169i	$-0.740836\pi$
$449$	−29.0916	−1.37292	−0.686459	+	0.727169i	$0.740836\pi$
$450$	6.13392	0.289156
$451$	−12.1269	−0.571033
$452$	19.9239	0.937139
$453$	−11.1359	−0.523209
$454$	5.05561	0.237272
$455$	−1.59347	−0.0747033
$456$	13.2364	0.619852
$457$	−26.9717	−1.26168	−0.630841	−	0.775912i	$-0.717290\pi$
$457$	−26.9717	−1.26168	−0.630841	+	0.775912i	$0.717290\pi$
$458$	11.5631	0.540307
$459$	8.16891	0.381292
$460$	−3.22369	−0.150305
$461$	−22.1479	−1.03153	−0.515766	−	0.856729i	$-0.672493\pi$
$461$	−22.1479	−1.03153	−0.515766	+	0.856729i	$0.672493\pi$
$462$	−3.28529	−0.152846
$463$	0.935057	0.0434558	0.0217279	−	0.999764i	$-0.493083\pi$
$463$	0.935057	0.0434558	0.0217279	+	0.999764i	$0.493083\pi$
$464$	6.09455	0.282932
$465$	2.57908	0.119602
$466$	−1.40930	−0.0652845
$467$	13.0409	0.603459	0.301730	−	0.953394i	$-0.402436\pi$
$467$	13.0409	0.603459	0.301730	+	0.953394i	$0.402436\pi$
$468$	2.04925	0.0947265
$469$	−7.19544	−0.332255
$470$	10.9359	0.504434
$471$	−27.1413	−1.25061
$472$	−9.22880	−0.424790
$473$	−5.09942	−0.234472
$474$	18.8914	0.867711
$475$	21.8819	1.00401
$476$	3.26356	0.149585
$477$	−22.8385	−1.04570
$478$	1.10954	0.0507491
$479$	−7.59986	−0.347246	−0.173623	−	0.984812i	$-0.555547\pi$
$479$	−7.59986	−0.347246	−0.173623	+	0.984812i	$0.555547\pi$
$480$	−2.57908	−0.117718
$481$	10.3118	0.470180
$482$	−12.4506	−0.567108
$483$	6.58555	0.299653
$484$	−9.16881	−0.416764
$485$	1.18841	0.0539631
$486$	15.9187	0.722089
$487$	−19.4678	−0.882171	−0.441085	−	0.897465i	$-0.645406\pi$
$487$	−19.4678	−0.882171	−0.441085	+	0.897465i	$0.645406\pi$
$488$	5.54150	0.250852
$489$	−12.9632	−0.586215
$490$	6.83164	0.308622
$491$	12.8463	0.579745	0.289873	−	0.957065i	$-0.406387\pi$
$491$	12.8463	0.579745	0.289873	+	0.957065i	$0.406387\pi$
$492$	19.4482	0.876793
$493$	−17.7797	−0.800758
$494$	7.31041	0.328911
$495$	−2.74954	−0.123583
$496$	1.00000	0.0449013
$497$	1.52013	0.0681870
$498$	17.6767	0.792113
$499$	−15.5697	−0.696997	−0.348499	−	0.937309i	$-0.613308\pi$
$499$	−15.5697	−0.696997	−0.348499	+	0.937309i	$0.613308\pi$
$500$	−10.2057	−0.456413
$501$	0.404117	0.0180546
$502$	3.25951	0.145479
$503$	29.9551	1.33563	0.667817	−	0.744326i	$-0.267229\pi$
$503$	29.9551	1.33563	0.667817	+	0.744326i	$0.267229\pi$
$504$	1.91264	0.0851960
$505$	−16.9965	−0.756333
$506$	−3.67074	−0.163184
$507$	−25.0948	−1.11450
$508$	0.362181	0.0160692
$509$	1.05996	0.0469818	0.0234909	−	0.999724i	$-0.492522\pi$
$509$	1.05996	0.0469818	0.0234909	+	0.999724i	$0.492522\pi$
$510$	7.52399	0.333168
$511$	11.9075	0.526755
$512$	−1.00000	−0.0441942
$513$	17.0787	0.754041
$514$	−3.17761	−0.140158
$515$	0.252012	0.0111050
$516$	8.17807	0.360020
$517$	12.4524	0.547655
$518$	9.62446	0.422875
$519$	−40.6696	−1.78520
$520$	−1.42441	−0.0624647
$521$	32.3605	1.41774	0.708870	−	0.705339i	$-0.249205\pi$
$521$	32.3605	1.41774	0.708870	+	0.705339i	$0.249205\pi$
$522$	−10.4200	−0.456070
$523$	−36.2305	−1.58425	−0.792126	−	0.610358i	$-0.791026\pi$
$523$	−36.2305	−1.58425	−0.792126	+	0.610358i	$0.791026\pi$
$524$	0.245991	0.0107462
$525$	8.71002	0.380137
$526$	−26.9478	−1.17498
$527$	−2.91731	−0.127080
$528$	−2.93674	−0.127805
$529$	−15.6418	−0.680078
$530$	15.8749	0.689560
$531$	15.7787	0.684737
$532$	6.82310	0.295819
$533$	10.7412	0.465251
$534$	18.4041	0.796422
$535$	8.08642	0.349606
$536$	−6.43204	−0.277822
$537$	−5.05151	−0.217989
$538$	9.21431	0.397257
$539$	7.77902	0.335066
$540$	−3.32773	−0.143203
$541$	43.1756	1.85626	0.928131	−	0.372253i	$-0.121415\pi$
$541$	43.1756	1.85626	0.928131	+	0.372253i	$0.121415\pi$
$542$	8.05685	0.346071
$543$	−54.6330	−2.34453
$544$	2.91731	0.125079
$545$	−1.54452	−0.0661600
$546$	2.90988	0.124531
$547$	1.52079	0.0650242	0.0325121	−	0.999471i	$-0.489649\pi$
$547$	1.52079	0.0650242	0.0325121	+	0.999471i	$0.489649\pi$
$548$	−9.07313	−0.387585
$549$	−9.47443	−0.404359
$550$	−4.85490	−0.207014
$551$	−37.1719	−1.58357
$552$	5.88686	0.250561
$553$	9.73813	0.414108
$554$	−20.9889	−0.891735
$555$	22.1888	0.941860
$556$	15.5188	0.658143
$557$	13.4188	0.568573	0.284286	−	0.958739i	$-0.408243\pi$
$557$	13.4188	0.568573	0.284286	+	0.958739i	$0.408243\pi$
$558$	−1.70972	−0.0723783
$559$	4.51671	0.191036
$560$	−1.32946	−0.0561801
$561$	8.56738	0.361715
$562$	−14.4530	−0.609663
$563$	−3.17860	−0.133962	−0.0669811	−	0.997754i	$-0.521337\pi$
$563$	−3.17860	−0.133962	−0.0669811	+	0.997754i	$0.521337\pi$
$564$	−19.9702	−0.840898
$565$	23.6778	0.996132
$566$	−23.5738	−0.990883
$567$	12.5360	0.526464
$568$	1.35885	0.0570160
$569$	1.77942	0.0745973	0.0372986	−	0.999304i	$-0.488125\pi$
$569$	1.77942	0.0745973	0.0372986	+	0.999304i	$0.488125\pi$
$570$	15.7303	0.658871
$571$	3.43823	0.143886	0.0719428	−	0.997409i	$-0.477080\pi$
$571$	3.43823	0.143886	0.0719428	+	0.997409i	$0.477080\pi$
$572$	−1.62194	−0.0678169
$573$	1.54848	0.0646887
$574$	10.0252	0.418442
$575$	9.73192	0.405849
$576$	1.70972	0.0712384
$577$	−26.3147	−1.09550	−0.547748	−	0.836644i	$-0.684515\pi$
$577$	−26.3147	−1.09550	−0.547748	+	0.836644i	$0.684515\pi$
$578$	8.48928	0.353107
$579$	−39.5508	−1.64367
$580$	7.24284	0.300743
$581$	9.11198	0.378029
$582$	−2.17019	−0.0899572
$583$	18.0763	0.748643
$584$	10.6441	0.440458
$585$	2.43535	0.100689
$586$	0.944817	0.0390300
$587$	40.1410	1.65680	0.828399	−	0.560139i	$-0.189252\pi$
$587$	40.1410	1.65680	0.828399	+	0.560139i	$0.189252\pi$
$588$	−12.4754	−0.514478
$589$	−6.09920	−0.251313
$590$	−10.9676	−0.451530
$591$	37.5395	1.54417
$592$	8.60335	0.353596
$593$	−28.3673	−1.16491	−0.582454	−	0.812864i	$-0.697907\pi$
$593$	−28.3673	−1.16491	−0.582454	+	0.812864i	$0.697907\pi$
$594$	−3.78921	−0.155473
$595$	3.87846	0.159001
$596$	−14.7519	−0.604262
$597$	24.5951	1.00661
$598$	3.25128	0.132955
$599$	26.6032	1.08698	0.543488	−	0.839417i	$-0.317103\pi$
$599$	26.6032	1.08698	0.543488	+	0.839417i	$0.317103\pi$
$600$	7.78593	0.317859
$601$	−19.2012	−0.783232	−0.391616	−	0.920129i	$-0.628084\pi$
$601$	−19.2012	−0.783232	−0.391616	+	0.920129i	$0.628084\pi$
$602$	4.21563	0.171816
$603$	10.9970	0.447832
$604$	−5.13130	−0.208789
$605$	−10.8963	−0.442999
$606$	31.0377	1.26082
$607$	−5.20034	−0.211075	−0.105538	−	0.994415i	$-0.533656\pi$
$607$	−5.20034	−0.211075	−0.105538	+	0.994415i	$0.533656\pi$
$608$	6.09920	0.247355
$609$	−14.7961	−0.599569
$610$	6.58560	0.266643
$611$	−11.0295	−0.446204
$612$	−4.98780	−0.201620
$613$	−10.0958	−0.407767	−0.203883	−	0.978995i	$-0.565356\pi$
$613$	−10.0958	−0.407767	−0.203883	+	0.978995i	$0.565356\pi$
$614$	16.9320	0.683319
$615$	23.1125	0.931987
$616$	−1.51383	−0.0609938
$617$	−35.5300	−1.43038	−0.715191	−	0.698929i	$-0.753660\pi$
$617$	−35.5300	−1.43038	−0.715191	+	0.698929i	$0.753660\pi$
$618$	−0.460205	−0.0185122
$619$	−31.3484	−1.26000	−0.630000	−	0.776596i	$-0.716945\pi$
$619$	−31.3484	−1.26000	−0.630000	+	0.776596i	$0.716945\pi$
$620$	1.18841	0.0477278
$621$	7.59568	0.304804
$622$	7.35825	0.295039
$623$	9.48691	0.380085
$624$	2.60116	0.104130
$625$	5.80976	0.232390
$626$	14.5183	0.580268
$627$	17.9117	0.715326
$628$	−12.5064	−0.499061
$629$	−25.0987	−1.00075
$630$	2.27301	0.0905590
$631$	13.4814	0.536686	0.268343	−	0.963323i	$-0.413524\pi$
$631$	13.4814	0.536686	0.268343	+	0.963323i	$0.413524\pi$
$632$	8.70496	0.346265
$633$	−22.4733	−0.893233
$634$	−11.8160	−0.469272
$635$	0.430420	0.0170807
$636$	−28.9894	−1.14951
$637$	−6.89011	−0.272996
$638$	8.24724	0.326511
$639$	−2.32325	−0.0919065
$640$	−1.18841	−0.0469762
$641$	3.12606	0.123472	0.0617359	−	0.998093i	$-0.480336\pi$
$641$	3.12606	0.123472	0.0617359	+	0.998093i	$0.480336\pi$
$642$	−14.7668	−0.582799
$643$	−38.7136	−1.52671	−0.763357	−	0.645976i	$-0.776450\pi$
$643$	−38.7136	−1.52671	−0.763357	+	0.645976i	$0.776450\pi$
$644$	3.03455	0.119578
$645$	9.71894	0.382683
$646$	−17.7933	−0.700067
$647$	10.7987	0.424540	0.212270	−	0.977211i	$-0.431914\pi$
$647$	10.7987	0.424540	0.212270	+	0.977211i	$0.431914\pi$
$648$	11.2060	0.440214
$649$	−12.4886	−0.490219
$650$	4.30013	0.168665
$651$	−2.42776	−0.0951516
$652$	−5.97329	−0.233932
$653$	15.2761	0.597801	0.298900	−	0.954284i	$-0.403380\pi$
$653$	15.2761	0.597801	0.298900	+	0.954284i	$0.403380\pi$
$654$	2.82048	0.110290
$655$	0.292339	0.0114226
$656$	8.96153	0.349889
$657$	−18.1985	−0.709992
$658$	−10.2942	−0.401311
$659$	3.91520	0.152515	0.0762573	−	0.997088i	$-0.475703\pi$
$659$	3.91520	0.152515	0.0762573	+	0.997088i	$0.475703\pi$
$660$	−3.49006	−0.135850
$661$	33.0151	1.28414	0.642069	−	0.766647i	$-0.278076\pi$
$661$	33.0151	1.28414	0.642069	+	0.766647i	$0.278076\pi$
$662$	−15.4853	−0.601852
$663$	−7.58839	−0.294709
$664$	8.14525	0.316097
$665$	8.10866	0.314440
$666$	−14.7093	−0.569975
$667$	−16.5321	−0.640125
$668$	0.186213	0.00720479
$669$	20.9098	0.808419
$670$	−7.64392	−0.295311
$671$	7.49885	0.289490
$672$	2.42776	0.0936530
$673$	−19.8432	−0.764897	−0.382449	−	0.923977i	$-0.624919\pi$
$673$	−19.8432	−0.764897	−0.382449	+	0.923977i	$0.624919\pi$
$674$	−13.1494	−0.506497
$675$	10.0460	0.386671
$676$	−11.5634	−0.444746
$677$	−22.6270	−0.869625	−0.434812	−	0.900521i	$-0.643185\pi$
$677$	−22.6270	−0.869625	−0.434812	+	0.900521i	$0.643185\pi$
$678$	−43.2385	−1.66057
$679$	−1.11869	−0.0429313
$680$	3.46698	0.132952
$681$	−10.9716	−0.420434
$682$	1.35322	0.0518173
$683$	1.50916	0.0577464	0.0288732	−	0.999583i	$-0.490808\pi$
$683$	1.50916	0.0577464	0.0288732	+	0.999583i	$0.490808\pi$
$684$	−10.4279	−0.398722
$685$	−10.7826	−0.411983
$686$	−14.2616	−0.544512
$687$	−25.0941	−0.957399
$688$	3.76837	0.143668
$689$	−16.0107	−0.609960
$690$	6.99602	0.266334
$691$	13.1362	0.499723	0.249861	−	0.968282i	$-0.419615\pi$
$691$	13.1362	0.499723	0.249861	+	0.968282i	$0.419615\pi$
$692$	−18.7401	−0.712392
$693$	2.58822	0.0983184
$694$	−25.5656	−0.970455
$695$	18.4427	0.699573
$696$	−13.2263	−0.501343
$697$	−26.1436	−0.990259
$698$	−35.0322	−1.32599
$699$	3.05844	0.115681
$700$	4.01348	0.151695
$701$	14.2407	0.537865	0.268932	−	0.963159i	$-0.413329\pi$
$701$	14.2407	0.537865	0.268932	+	0.963159i	$0.413329\pi$
$702$	3.35621	0.126672
$703$	−52.4735	−1.97908
$704$	−1.35322	−0.0510013
$705$	−23.7329	−0.893832
$706$	−24.3886	−0.917879
$707$	15.9993	0.601714
$708$	20.0282	0.752708
$709$	−27.1310	−1.01893	−0.509463	−	0.860493i	$-0.670156\pi$
$709$	−27.1310	−1.01893	−0.509463	+	0.860493i	$0.670156\pi$
$710$	1.61487	0.0606051
$711$	−14.8831	−0.558159
$712$	8.48040	0.317816
$713$	−2.71260	−0.101588
$714$	−7.08255	−0.265058
$715$	−1.92754	−0.0720860
$716$	−2.32768	−0.0869895
$717$	−2.40791	−0.0899249
$718$	−8.62793	−0.321991
$719$	3.83276	0.142938	0.0714689	−	0.997443i	$-0.477231\pi$
$719$	3.83276	0.142938	0.0714689	+	0.997443i	$0.477231\pi$
$720$	2.03186	0.0757228
$721$	−0.237226	−0.00883476
$722$	−18.2002	−0.677342
$723$	27.0201	1.00489
$724$	−25.1743	−0.935596
$725$	−21.8652	−0.812055
$726$	19.8980	0.738486
$727$	30.0973	1.11625	0.558124	−	0.829758i	$-0.311522\pi$
$727$	30.0973	1.11625	0.558124	+	0.829758i	$0.311522\pi$
$728$	1.34084	0.0496949
$729$	−0.928621	−0.0343934
$730$	12.6496	0.468184
$731$	−10.9935	−0.406610
$732$	−12.0261	−0.444498
$733$	13.5412	0.500157	0.250078	−	0.968226i	$-0.419544\pi$
$733$	13.5412	0.500157	0.250078	+	0.968226i	$0.419544\pi$
$734$	−5.71091	−0.210794
$735$	−14.8260	−0.546864
$736$	2.71260	0.0999878
$737$	−8.70394	−0.320614
$738$	−15.3217	−0.564000
$739$	13.8426	0.509207	0.254604	−	0.967046i	$-0.418055\pi$
$739$	13.8426	0.509207	0.254604	+	0.967046i	$0.418055\pi$
$740$	10.2243	0.375854
$741$	−15.8650	−0.582814
$742$	−14.9434	−0.548591
$743$	16.5452	0.606984	0.303492	−	0.952834i	$-0.401847\pi$
$743$	16.5452	0.606984	0.303492	+	0.952834i	$0.401847\pi$
$744$	−2.17019	−0.0795630
$745$	−17.5314	−0.642300
$746$	−14.4867	−0.530395
$747$	−13.9261	−0.509530
$748$	3.94776	0.144344
$749$	−7.61198	−0.278136
$750$	22.1483	0.808742
$751$	33.9474	1.23876	0.619378	−	0.785093i	$-0.287385\pi$
$751$	33.9474	1.23876	0.619378	+	0.785093i	$0.287385\pi$
$752$	−9.20207	−0.335565
$753$	−7.07375	−0.257782
$754$	−7.30483	−0.266026
$755$	−6.09810	−0.221933
$756$	3.13249	0.113928
$757$	−16.6064	−0.603569	−0.301785	−	0.953376i	$-0.597582\pi$
$757$	−16.6064	−0.603569	−0.301785	+	0.953376i	$0.597582\pi$
$758$	−19.7457	−0.717195
$759$	7.96619	0.289154
$760$	7.24837	0.262926
$761$	54.1956	1.96459	0.982294	−	0.187346i	$-0.0599885\pi$
$761$	54.1956	1.96459	0.982294	+	0.187346i	$0.0599885\pi$
$762$	−0.786000	−0.0284738
$763$	1.45390	0.0526347
$764$	0.713523	0.0258144
$765$	−5.92757	−0.214312
$766$	−6.02817	−0.217807
$767$	11.0615	0.399408
$768$	2.17019	0.0783100
$769$	2.76321	0.0996439	0.0498219	−	0.998758i	$-0.484135\pi$
$769$	2.76321	0.0996439	0.0498219	+	0.998758i	$0.484135\pi$
$770$	−1.79905	−0.0648333
$771$	6.89602	0.248354
$772$	−18.2246	−0.655917
$773$	5.83739	0.209956	0.104978	−	0.994475i	$-0.466523\pi$
$773$	5.83739	0.209956	0.104978	+	0.994475i	$0.466523\pi$
$774$	−6.44286	−0.231584
$775$	−3.58767	−0.128873
$776$	−1.00000	−0.0358979
$777$	−20.8869	−0.749314
$778$	9.89076	0.354601
$779$	−54.6581	−1.95833
$780$	3.09125	0.110684
$781$	1.83882	0.0657980
$782$	−7.91351	−0.282986
$783$	−17.0656	−0.609876
$784$	−5.74854	−0.205305
$785$	−14.8628	−0.530477
$786$	−0.533848	−0.0190417
$787$	22.2077	0.791619	0.395809	−	0.918333i	$-0.370464\pi$
$787$	22.2077	0.791619	0.395809	+	0.918333i	$0.370464\pi$
$788$	17.2978	0.616208
$789$	58.4818	2.08201
$790$	10.3451	0.368062
$791$	−22.2886	−0.792490
$792$	2.31362	0.0822110
$793$	−6.64196	−0.235863
$794$	36.6684	1.30131
$795$	−34.4514	−1.22187
$796$	11.3332	0.401693
$797$	13.2763	0.470269	0.235135	−	0.971963i	$-0.424447\pi$
$797$	13.2763	0.470269	0.235135	+	0.971963i	$0.424447\pi$
$798$	−14.8074	−0.524177
$799$	26.8453	0.949719
$800$	3.58767	0.126843
$801$	−14.4991	−0.512301
$802$	−17.4763	−0.617111
$803$	14.4038	0.508300
$804$	13.9587	0.492287
$805$	3.60630	0.127106
$806$	−1.19858	−0.0422184
$807$	−19.9968	−0.703921
$808$	14.3018	0.503136
$809$	6.92446	0.243451	0.121726	−	0.992564i	$-0.461157\pi$
$809$	6.92446	0.243451	0.121726	+	0.992564i	$0.461157\pi$
$810$	13.3174	0.467925
$811$	−41.8949	−1.47113	−0.735564	−	0.677455i	$-0.763083\pi$
$811$	−41.8949	−1.47113	−0.735564	+	0.677455i	$0.763083\pi$
$812$	−6.81790	−0.239261
$813$	−17.4849	−0.613222
$814$	11.6422	0.408059
$815$	−7.09874	−0.248658
$816$	−6.33112	−0.221634
$817$	−22.9840	−0.804109
$818$	−10.0882	−0.352726
$819$	−2.29247	−0.0801053
$820$	10.6500	0.371914
$821$	23.2081	0.809969	0.404985	−	0.914324i	$-0.367277\pi$
$821$	23.2081	0.809969	0.404985	+	0.914324i	$0.367277\pi$
$822$	19.6904	0.686782
$823$	34.8265	1.21398	0.606988	−	0.794711i	$-0.292377\pi$
$823$	34.8265	1.21398	0.606988	+	0.794711i	$0.292377\pi$
$824$	−0.212057	−0.00738737
$825$	10.5360	0.366818
$826$	10.3241	0.359223
$827$	2.27776	0.0792054	0.0396027	−	0.999216i	$-0.487391\pi$
$827$	2.27776	0.0792054	0.0396027	+	0.999216i	$0.487391\pi$
$828$	−4.63779	−0.161174
$829$	−55.2713	−1.91965	−0.959827	−	0.280594i	$-0.909469\pi$
$829$	−55.2713	−1.91965	−0.959827	+	0.280594i	$0.909469\pi$
$830$	9.67992	0.335995
$831$	45.5500	1.58011
$832$	1.19858	0.0415535
$833$	16.7703	0.581056
$834$	−33.6787	−1.16620
$835$	0.221298	0.00765833
$836$	8.25353	0.285454
$837$	−2.80015	−0.0967873
$838$	−9.11876	−0.315002
$839$	−7.49315	−0.258692	−0.129346	−	0.991600i	$-0.541288\pi$
$839$	−7.49315	−0.258692	−0.129346	+	0.991600i	$0.541288\pi$
$840$	2.88519	0.0995484
$841$	8.14352	0.280811
$842$	−1.75851	−0.0606022
$843$	31.3658	1.08029
$844$	−10.3555	−0.356449
$845$	−13.7421	−0.472742
$846$	15.7330	0.540911
$847$	10.2570	0.352436
$848$	−13.3580	−0.458716
$849$	51.1597	1.75580
$850$	−10.4664	−0.358993
$851$	−23.3375	−0.799998
$852$	−2.94896	−0.101030
$853$	−33.4441	−1.14511	−0.572553	−	0.819868i	$-0.694047\pi$
$853$	−33.4441	−1.14511	−0.572553	+	0.819868i	$0.694047\pi$
$854$	−6.19921	−0.212133
$855$	−12.3927	−0.423821
$856$	−6.80438	−0.232569
$857$	12.6054	0.430591	0.215296	−	0.976549i	$-0.430928\pi$
$857$	12.6054	0.430591	0.215296	+	0.976549i	$0.430928\pi$
$858$	3.51993	0.120168
$859$	21.9559	0.749127	0.374563	−	0.927201i	$-0.377793\pi$
$859$	21.9559	0.749127	0.374563	+	0.927201i	$0.377793\pi$
$860$	4.47838	0.152712
$861$	−21.7565	−0.741459
$862$	−4.77447	−0.162619
$863$	19.8488	0.675662	0.337831	−	0.941207i	$-0.390307\pi$
$863$	19.8488	0.675662	0.337831	+	0.941207i	$0.390307\pi$
$864$	2.80015	0.0952630
$865$	−22.2710	−0.757237
$866$	11.4008	0.387416
$867$	−18.4233	−0.625690
$868$	−1.11869	−0.0379707
$869$	11.7797	0.399599
$870$	−15.7183	−0.532902
$871$	7.70935	0.261221
$872$	1.29965	0.0440116
$873$	1.70972	0.0578653
$874$	−16.5447	−0.559632
$875$	11.4170	0.385965
$876$	−23.0998	−0.780470
$877$	49.5301	1.67251	0.836257	−	0.548338i	$-0.184739\pi$
$877$	49.5301	1.67251	0.836257	+	0.548338i	$0.184739\pi$
$878$	−14.9821	−0.505620
$879$	−2.05043	−0.0691594
$880$	−1.60818	−0.0542118
$881$	23.9356	0.806410	0.403205	−	0.915110i	$-0.367896\pi$
$881$	23.9356	0.806410	0.403205	+	0.915110i	$0.367896\pi$
$882$	9.82840	0.330940
$883$	29.5050	0.992923	0.496462	−	0.868059i	$-0.334632\pi$
$883$	29.5050	0.992923	0.496462	+	0.868059i	$0.334632\pi$
$884$	−3.49665	−0.117605
$885$	23.8018	0.800090
$886$	32.0704	1.07743
$887$	25.6742	0.862055	0.431028	−	0.902339i	$-0.358151\pi$
$887$	25.6742	0.862055	0.431028	+	0.902339i	$0.358151\pi$
$888$	−18.6709	−0.626554
$889$	−0.405167	−0.0135889
$890$	10.0782	0.337823
$891$	15.1642	0.508019
$892$	9.63500	0.322604
$893$	56.1252	1.87816
$894$	32.0145	1.07072
$895$	−2.76625	−0.0924655
$896$	1.11869	0.0373727
$897$	−7.05590	−0.235590
$898$	29.0916	0.970800
$899$	6.09455	0.203265
$900$	−6.13392	−0.204464
$901$	38.9695	1.29826
$902$	12.1269	0.403781
$903$	−9.14871	−0.304450
$904$	−19.9239	−0.662658
$905$	−29.9175	−0.994491
$906$	11.1359	0.369965
$907$	−12.6968	−0.421589	−0.210795	−	0.977530i	$-0.567605\pi$
$907$	−12.6968	−0.421589	−0.210795	+	0.977530i	$0.567605\pi$
$908$	−5.05561	−0.167776
$909$	−24.4521	−0.811026
$910$	1.59347	0.0528232
$911$	24.7155	0.818862	0.409431	−	0.912341i	$-0.365727\pi$
$911$	24.7155	0.818862	0.409431	+	0.912341i	$0.365727\pi$
$912$	−13.2364	−0.438301
$913$	11.0223	0.364784
$914$	26.9717	0.892144
$915$	−14.2920	−0.472479
$916$	−11.5631	−0.382055
$917$	−0.275187	−0.00908749
$918$	−8.16891	−0.269614
$919$	−41.2587	−1.36100	−0.680500	−	0.732748i	$-0.738237\pi$
$919$	−41.2587	−1.36100	−0.680500	+	0.732748i	$0.738237\pi$
$920$	3.22369	0.106282
$921$	−36.7456	−1.21081
$922$	22.1479	0.729403
$923$	−1.62869	−0.0536091
$924$	3.28529	0.108078
$925$	−30.8660	−1.01487
$926$	−0.935057	−0.0307279
$927$	0.362559	0.0119080
$928$	−6.09455	−0.200063
$929$	−47.1353	−1.54646	−0.773230	−	0.634125i	$-0.781360\pi$
$929$	−47.1353	−1.54646	−0.773230	+	0.634125i	$0.781360\pi$
$930$	−2.57908	−0.0845715
$931$	35.0615	1.14909
$932$	1.40930	0.0461631
$933$	−15.9688	−0.522795
$934$	−13.0409	−0.426710
$935$	4.69157	0.153431
$936$	−2.04925	−0.0669817
$937$	−5.77248	−0.188579	−0.0942893	−	0.995545i	$-0.530058\pi$
$937$	−5.77248	−0.188579	−0.0942893	+	0.995545i	$0.530058\pi$
$938$	7.19544	0.234940
$939$	−31.5074	−1.02821
$940$	−10.9359	−0.356688
$941$	−18.5449	−0.604545	−0.302273	−	0.953221i	$-0.597745\pi$
$941$	−18.5449	−0.604545	−0.302273	+	0.953221i	$0.597745\pi$
$942$	27.1413	0.884313
$943$	−24.3091	−0.791612
$944$	9.22880	0.300372
$945$	3.72269	0.121099
$946$	5.09942	0.165796
$947$	−30.6043	−0.994507	−0.497254	−	0.867605i	$-0.665658\pi$
$947$	−30.6043	−0.994507	−0.497254	+	0.867605i	$0.665658\pi$
$948$	−18.8914	−0.613565
$949$	−12.7579	−0.414139
$950$	−21.8819	−0.709943
$951$	25.6429	0.831527
$952$	−3.26356	−0.105773
$953$	−39.7476	−1.28755	−0.643776	−	0.765214i	$-0.722633\pi$
$953$	−39.7476	−1.28755	−0.643776	+	0.765214i	$0.722633\pi$
$954$	22.8385	0.739424
$955$	0.847961	0.0274394
$956$	−1.10954	−0.0358850
$957$	−17.8981	−0.578563
$958$	7.59986	0.245540
$959$	10.1500	0.327761
$960$	2.57908	0.0832395
$961$	1.00000	0.0322581
$962$	−10.3118	−0.332467
$963$	11.6336	0.374888
$964$	12.4506	0.401006
$965$	−21.6583	−0.697206
$966$	−6.58555	−0.211887
$967$	−38.0818	−1.22463	−0.612314	−	0.790615i	$-0.709761\pi$
$967$	−38.0818	−1.22463	−0.612314	+	0.790615i	$0.709761\pi$
$968$	9.16881	0.294697
$969$	38.6148	1.24049
$970$	−1.18841	−0.0381577
$971$	−36.6303	−1.17552	−0.587761	−	0.809035i	$-0.699990\pi$
$971$	−36.6303	−1.17552	−0.587761	+	0.809035i	$0.699990\pi$
$972$	−15.9187	−0.510594
$973$	−17.3607	−0.556557
$974$	19.4678	0.623789
$975$	−9.33210	−0.298866
$976$	−5.54150	−0.177379
$977$	47.2462	1.51154	0.755771	−	0.654836i	$-0.227262\pi$
$977$	47.2462	1.51154	0.755771	+	0.654836i	$0.227262\pi$
$978$	12.9632	0.414516
$979$	11.4758	0.366768
$980$	−6.83164	−0.218229
$981$	−2.22204	−0.0709442
$982$	−12.8463	−0.409942
$983$	−43.8665	−1.39912	−0.699561	−	0.714572i	$-0.746621\pi$
$983$	−43.8665	−1.39912	−0.699561	+	0.714572i	$0.746621\pi$
$984$	−19.4482	−0.619987
$985$	20.5569	0.654998
$986$	17.7797	0.566221
$987$	22.3404	0.711104
$988$	−7.31041	−0.232575
$989$	−10.2221	−0.325043
$990$	2.74954	0.0873862
$991$	−3.77474	−0.119909	−0.0599543	−	0.998201i	$-0.519096\pi$
$991$	−3.77474	−0.119909	−0.0599543	+	0.998201i	$0.519096\pi$
$992$	−1.00000	−0.0317500
$993$	33.6060	1.06645
$994$	−1.52013	−0.0482155
$995$	13.4685	0.426980
$996$	−17.6767	−0.560108
$997$	−12.3065	−0.389750	−0.194875	−	0.980828i	$-0.562430\pi$
$997$	−12.3065	−0.389750	−0.194875	+	0.980828i	$0.562430\pi$
$998$	15.5697	0.492852
$999$	−24.0907	−0.762195

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.f.1.19	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.f.1.19	✓	22	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.17019 q^{3} +1.00000 q^{4} +1.18841 q^{5} -2.17019 q^{6} -1.11869 q^{7} -1.00000 q^{8} +1.70972 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.17019 q^{3} +1.00000 q^{4} +1.18841 q^{5} -2.17019 q^{6} -1.11869 q^{7} -1.00000 q^{8} +1.70972 q^{9} -1.18841 q^{10} -1.35322 q^{11} +2.17019 q^{12} +1.19858 q^{13} +1.11869 q^{14} +2.57908 q^{15} +1.00000 q^{16} -2.91731 q^{17} -1.70972 q^{18} -6.09920 q^{19} +1.18841 q^{20} -2.42776 q^{21} +1.35322 q^{22} -2.71260 q^{23} -2.17019 q^{24} -3.58767 q^{25} -1.19858 q^{26} -2.80015 q^{27} -1.11869 q^{28} +6.09455 q^{29} -2.57908 q^{30} +1.00000 q^{31} -1.00000 q^{32} -2.93674 q^{33} +2.91731 q^{34} -1.32946 q^{35} +1.70972 q^{36} +8.60335 q^{37} +6.09920 q^{38} +2.60116 q^{39} -1.18841 q^{40} +8.96153 q^{41} +2.42776 q^{42} +3.76837 q^{43} -1.35322 q^{44} +2.03186 q^{45} +2.71260 q^{46} -9.20207 q^{47} +2.17019 q^{48} -5.74854 q^{49} +3.58767 q^{50} -6.33112 q^{51} +1.19858 q^{52} -13.3580 q^{53} +2.80015 q^{54} -1.60818 q^{55} +1.11869 q^{56} -13.2364 q^{57} -6.09455 q^{58} +9.22880 q^{59} +2.57908 q^{60} -5.54150 q^{61} -1.00000 q^{62} -1.91264 q^{63} +1.00000 q^{64} +1.42441 q^{65} +2.93674 q^{66} +6.43204 q^{67} -2.91731 q^{68} -5.88686 q^{69} +1.32946 q^{70} -1.35885 q^{71} -1.70972 q^{72} -10.6441 q^{73} -8.60335 q^{74} -7.78593 q^{75} -6.09920 q^{76} +1.51383 q^{77} -2.60116 q^{78} -8.70496 q^{79} +1.18841 q^{80} -11.2060 q^{81} -8.96153 q^{82} -8.14525 q^{83} -2.42776 q^{84} -3.46698 q^{85} -3.76837 q^{86} +13.2263 q^{87} +1.35322 q^{88} -8.48040 q^{89} -2.03186 q^{90} -1.34084 q^{91} -2.71260 q^{92} +2.17019 q^{93} +9.20207 q^{94} -7.24837 q^{95} -2.17019 q^{96} +1.00000 q^{97} +5.74854 q^{98} -2.31362 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9}+O(q^{10}) \) 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9	\( 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9} - 8 q^{13} + 11 q^{14} + q^{15} + 22 q^{16} - 4 q^{17} - 8 q^{18} - 23 q^{19} - 12 q^{21} + 2 q^{23} - 12 q^{25} + 8 q^{26} + 3 q^{27} - 11 q^{28} + 9 q^{29} - q^{30} + 22 q^{31} - 22 q^{32} + 4 q^{34} + 4 q^{35} + 8 q^{36} - 17 q^{37} + 23 q^{38} + 8 q^{39} - 21 q^{41} + 12 q^{42} - 7 q^{43} + 9 q^{45} - 2 q^{46} - 10 q^{47} - 27 q^{49} + 12 q^{50} - q^{51} - 8 q^{52} + 9 q^{53} - 3 q^{54} - 6 q^{55} + 11 q^{56} - q^{57} - 9 q^{58} - 12 q^{59} + q^{60} - 34 q^{61} - 22 q^{62} - 5 q^{63} + 22 q^{64} + 4 q^{65} - 31 q^{67} - 4 q^{68} - 51 q^{69} - 4 q^{70} - 15 q^{71} - 8 q^{72} + 3 q^{73} + 17 q^{74} - 24 q^{75} - 23 q^{76} + 24 q^{77} - 8 q^{78} - 23 q^{79} - 26 q^{81} + 21 q^{82} + 22 q^{83} - 12 q^{84} - 42 q^{85} + 7 q^{86} - 9 q^{87} - 36 q^{89} - 9 q^{90} - 6 q^{91} + 2 q^{92} + 10 q^{94} + 2 q^{95} + 22 q^{97} + 27 q^{98} - 25 q^{99}+O(q^{100}) \) 22 * q - 22 * q^2 + 22 * q^4 - 11 * q^7 - 22 * q^8 + 8 * q^9 - 8 * q^13 + 11 * q^14 + q^15 + 22 * q^16 - 4 * q^17 - 8 * q^18 - 23 * q^19 - 12 * q^21 + 2 * q^23 - 12 * q^25 + 8 * q^26 + 3 * q^27 - 11 * q^28 + 9 * q^29 - q^30 + 22 * q^31 - 22 * q^32 + 4 * q^34 + 4 * q^35 + 8 * q^36 - 17 * q^37 + 23 * q^38 + 8 * q^39 - 21 * q^41 + 12 * q^42 - 7 * q^43 + 9 * q^45 - 2 * q^46 - 10 * q^47 - 27 * q^49 + 12 * q^50 - q^51 - 8 * q^52 + 9 * q^53 - 3 * q^54 - 6 * q^55 + 11 * q^56 - q^57 - 9 * q^58 - 12 * q^59 + q^60 - 34 * q^61 - 22 * q^62 - 5 * q^63 + 22 * q^64 + 4 * q^65 - 31 * q^67 - 4 * q^68 - 51 * q^69 - 4 * q^70 - 15 * q^71 - 8 * q^72 + 3 * q^73 + 17 * q^74 - 24 * q^75 - 23 * q^76 + 24 * q^77 - 8 * q^78 - 23 * q^79 - 26 * q^81 + 21 * q^82 + 22 * q^83 - 12 * q^84 - 42 * q^85 + 7 * q^86 - 9 * q^87 - 36 * q^89 - 9 * q^90 - 6 * q^91 + 2 * q^92 + 10 * q^94 + 2 * q^95 + 22 * q^97 + 27 * q^98 - 25 * q^99

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