LMFDB - Embedded newform 845.2.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(1,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, 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("845.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.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:	$6.74735897080$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.24698$ of defining polynomial
Character	$\chi$	$=$	845.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.24698 q^{2} -0.198062 q^{3} -0.445042 q^{4} -1.00000 q^{5} +0.246980 q^{6} +0.198062 q^{7} +3.04892 q^{8} -2.96077 q^{9} +O(q^{10})$	\(q-1.24698 q^{2} -0.198062 q^{3} -0.445042 q^{4} -1.00000 q^{5} +0.246980 q^{6} +0.198062 q^{7} +3.04892 q^{8} -2.96077 q^{9} +1.24698 q^{10} +4.04892 q^{11} +0.0881460 q^{12} -0.246980 q^{14} +0.198062 q^{15} -2.91185 q^{16} -5.40581 q^{17} +3.69202 q^{18} +2.18598 q^{19} +0.445042 q^{20} -0.0392287 q^{21} -5.04892 q^{22} +7.23490 q^{23} -0.603875 q^{24} +1.00000 q^{25} +1.18060 q^{27} -0.0881460 q^{28} -7.07606 q^{29} -0.246980 q^{30} +0.0217703 q^{31} -2.46681 q^{32} -0.801938 q^{33} +6.74094 q^{34} -0.198062 q^{35} +1.31767 q^{36} +1.49396 q^{37} -2.72587 q^{38} -3.04892 q^{40} -10.9608 q^{41} +0.0489173 q^{42} -7.55496 q^{43} -1.80194 q^{44} +2.96077 q^{45} -9.02177 q^{46} +1.03923 q^{47} +0.576728 q^{48} -6.96077 q^{49} -1.24698 q^{50} +1.07069 q^{51} -0.554958 q^{53} -1.47219 q^{54} -4.04892 q^{55} +0.603875 q^{56} -0.432960 q^{57} +8.82371 q^{58} +3.89008 q^{59} -0.0881460 q^{60} -5.55496 q^{61} -0.0271471 q^{62} -0.586417 q^{63} +8.89977 q^{64} +1.00000 q^{66} -5.67025 q^{67} +2.40581 q^{68} -1.43296 q^{69} +0.246980 q^{70} -9.52111 q^{71} -9.02715 q^{72} -11.5797 q^{73} -1.86294 q^{74} -0.198062 q^{75} -0.972853 q^{76} +0.801938 q^{77} -15.8291 q^{79} +2.91185 q^{80} +8.64848 q^{81} +13.6679 q^{82} +17.3448 q^{83} +0.0174584 q^{84} +5.40581 q^{85} +9.42088 q^{86} +1.40150 q^{87} +12.3448 q^{88} -3.05429 q^{89} -3.69202 q^{90} -3.21983 q^{92} -0.00431187 q^{93} -1.29590 q^{94} -2.18598 q^{95} +0.488582 q^{96} +5.02177 q^{97} +8.67994 q^{98} -11.9879 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} - 5 q^{3} - q^{4} - 3 q^{5} - 4 q^{6} + 5 q^{7} + 4 q^{9}+O(q^{10}) $ 3 * q + q^2 - 5 * q^3 - q^4 - 3 * q^5 - 4 * q^6 + 5 * q^7 + 4 * q^9	$ 3 q + q^{2} - 5 q^{3} - q^{4} - 3 q^{5} - 4 q^{6} + 5 q^{7} + 4 q^{9} - q^{10} + 3 q^{11} + 4 q^{12} + 4 q^{14} + 5 q^{15} - 5 q^{16} - 3 q^{17} + 6 q^{18} - 8 q^{19} + q^{20} - 13 q^{21} - 6 q^{22} - 2 q^{23} + 7 q^{24} + 3 q^{25} - 8 q^{27} - 4 q^{28} - 6 q^{29} + 4 q^{30} - 3 q^{31} - 4 q^{32} + 2 q^{33} + 6 q^{34} - 5 q^{35} - 13 q^{36} - 5 q^{37} - 19 q^{38} - 20 q^{41} - 9 q^{42} - 23 q^{43} - q^{44} - 4 q^{45} - 24 q^{46} + 16 q^{47} - q^{48} - 8 q^{49} + q^{50} - 9 q^{51} - 2 q^{53} + 2 q^{54} - 3 q^{55} - 7 q^{56} + 18 q^{57} + 19 q^{58} + 11 q^{59} - 4 q^{60} - 17 q^{61} + 6 q^{62} + 23 q^{63} + 4 q^{64} + 3 q^{66} - 15 q^{67} - 6 q^{68} + 15 q^{69} - 4 q^{70} - 13 q^{71} - 21 q^{72} + 12 q^{73} - 11 q^{74} - 5 q^{75} - 9 q^{76} - 2 q^{77} - 37 q^{79} + 5 q^{80} + 27 q^{81} - 2 q^{82} + 29 q^{83} + 16 q^{84} + 3 q^{85} - 10 q^{86} + 10 q^{87} + 14 q^{88} + 3 q^{89} - 6 q^{90} - 11 q^{92} + 19 q^{93} + 10 q^{94} + 8 q^{95} - 5 q^{96} + 12 q^{97} + 2 q^{98} - 17 q^{99}+O(q^{100}) $ 3 * q + q^2 - 5 * q^3 - q^4 - 3 * q^5 - 4 * q^6 + 5 * q^7 + 4 * q^9 - q^10 + 3 * q^11 + 4 * q^12 + 4 * q^14 + 5 * q^15 - 5 * q^16 - 3 * q^17 + 6 * q^18 - 8 * q^19 + q^20 - 13 * q^21 - 6 * q^22 - 2 * q^23 + 7 * q^24 + 3 * q^25 - 8 * q^27 - 4 * q^28 - 6 * q^29 + 4 * q^30 - 3 * q^31 - 4 * q^32 + 2 * q^33 + 6 * q^34 - 5 * q^35 - 13 * q^36 - 5 * q^37 - 19 * q^38 - 20 * q^41 - 9 * q^42 - 23 * q^43 - q^44 - 4 * q^45 - 24 * q^46 + 16 * q^47 - q^48 - 8 * q^49 + q^50 - 9 * q^51 - 2 * q^53 + 2 * q^54 - 3 * q^55 - 7 * q^56 + 18 * q^57 + 19 * q^58 + 11 * q^59 - 4 * q^60 - 17 * q^61 + 6 * q^62 + 23 * q^63 + 4 * q^64 + 3 * q^66 - 15 * q^67 - 6 * q^68 + 15 * q^69 - 4 * q^70 - 13 * q^71 - 21 * q^72 + 12 * q^73 - 11 * q^74 - 5 * q^75 - 9 * q^76 - 2 * q^77 - 37 * q^79 + 5 * q^80 + 27 * q^81 - 2 * q^82 + 29 * q^83 + 16 * q^84 + 3 * q^85 - 10 * q^86 + 10 * q^87 + 14 * q^88 + 3 * q^89 - 6 * q^90 - 11 * q^92 + 19 * q^93 + 10 * q^94 + 8 * q^95 - 5 * q^96 + 12 * q^97 + 2 * q^98 - 17 * 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 $

$2$	−1.24698	−0.881748	−0.440874	−	0.897569i	$-0.645331\pi$
$2$	−1.24698	−0.881748	−0.440874	+	0.897569i	$0.645331\pi$
$3$	−0.198062	−0.114351	−0.0571757	−	0.998364i	$-0.518210\pi$
$3$	−0.198062	−0.114351	−0.0571757	+	0.998364i	$0.518210\pi$
$4$	−0.445042	−0.222521
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.246980	0.100829
$7$	0.198062	0.0748605	0.0374302	−	0.999299i	$-0.488083\pi$
$7$	0.198062	0.0748605	0.0374302	+	0.999299i	$0.488083\pi$
$8$	3.04892	1.07796
$9$	−2.96077	−0.986924
$10$	1.24698	0.394330
$11$	4.04892	1.22079	0.610397	−	0.792095i	$-0.291010\pi$
$11$	4.04892	1.22079	0.610397	+	0.792095i	$0.291010\pi$
$12$	0.0881460	0.0254456
$13$	0	0
$13$	0	0
$14$	−0.246980	−0.0660081
$15$	0.198062	0.0511395
$16$	−2.91185	−0.727963
$17$	−5.40581	−1.31110	−0.655551	−	0.755151i	$-0.727564\pi$
$17$	−5.40581	−1.31110	−0.655551	+	0.755151i	$0.727564\pi$
$18$	3.69202	0.870218
$19$	2.18598	0.501498	0.250749	−	0.968052i	$-0.419323\pi$
$19$	2.18598	0.501498	0.250749	+	0.968052i	$0.419323\pi$
$20$	0.445042	0.0995144
$21$	−0.0392287	−0.00856040
$22$	−5.04892	−1.07643
$23$	7.23490	1.50858	0.754290	−	0.656541i	$-0.227981\pi$
$23$	7.23490	1.50858	0.754290	+	0.656541i	$0.227981\pi$
$24$	−0.603875	−0.123266
$25$	1.00000	0.200000
$26$	0	0
$27$	1.18060	0.227207
$28$	−0.0881460	−0.0166580
$29$	−7.07606	−1.31399	−0.656996	−	0.753894i	$-0.728173\pi$
$29$	−7.07606	−1.31399	−0.656996	+	0.753894i	$0.728173\pi$
$30$	−0.246980	−0.0450921
$31$	0.0217703	0.00391005	0.00195503	−	0.999998i	$-0.499378\pi$
$31$	0.0217703	0.00391005	0.00195503	+	0.999998i	$0.499378\pi$
$32$	−2.46681	−0.436075
$33$	−0.801938	−0.139599
$34$	6.74094	1.15606
$35$	−0.198062	−0.0334786
$36$	1.31767	0.219611
$37$	1.49396	0.245605	0.122803	−	0.992431i	$-0.460812\pi$
$37$	1.49396	0.245605	0.122803	+	0.992431i	$0.460812\pi$
$38$	−2.72587	−0.442195
$39$	0	0
$40$	−3.04892	−0.482076
$41$	−10.9608	−1.71178	−0.855892	−	0.517154i	$-0.826991\pi$
$41$	−10.9608	−1.71178	−0.855892	+	0.517154i	$0.826991\pi$
$42$	0.0489173	0.00754811
$43$	−7.55496	−1.15212	−0.576060	−	0.817407i	$-0.695411\pi$
$43$	−7.55496	−1.15212	−0.576060	+	0.817407i	$0.695411\pi$
$44$	−1.80194	−0.271652
$45$	2.96077	0.441366
$46$	−9.02177	−1.33019
$47$	1.03923	0.151587	0.0757935	−	0.997124i	$-0.475851\pi$
$47$	1.03923	0.151587	0.0757935	+	0.997124i	$0.475851\pi$
$48$	0.576728	0.0832436
$49$	−6.96077	−0.994396
$50$	−1.24698	−0.176350
$51$	1.07069	0.149926
$52$	0	0
$53$	−0.554958	−0.0762294	−0.0381147	−	0.999273i	$-0.512135\pi$
$53$	−0.554958	−0.0762294	−0.0381147	+	0.999273i	$0.512135\pi$
$54$	−1.47219	−0.200340
$55$	−4.04892	−0.545956
$56$	0.603875	0.0806963
$57$	−0.432960	−0.0573470
$58$	8.82371	1.15861
$59$	3.89008	0.506446	0.253223	−	0.967408i	$-0.418509\pi$
$59$	3.89008	0.506446	0.253223	+	0.967408i	$0.418509\pi$
$60$	−0.0881460	−0.0113796
$61$	−5.55496	−0.711240	−0.355620	−	0.934631i	$-0.615730\pi$
$61$	−5.55496	−0.711240	−0.355620	+	0.934631i	$0.615730\pi$
$62$	−0.0271471	−0.00344768
$63$	−0.586417	−0.0738816
$64$	8.89977	1.11247
$65$	0	0
$66$	1.00000	0.123091
$67$	−5.67025	−0.692731	−0.346366	−	0.938100i	$-0.612584\pi$
$67$	−5.67025	−0.692731	−0.346366	+	0.938100i	$0.612584\pi$
$68$	2.40581	0.291748
$69$	−1.43296	−0.172508
$70$	0.246980	0.0295197
$71$	−9.52111	−1.12995	−0.564974	−	0.825109i	$-0.691114\pi$
$71$	−9.52111	−1.12995	−0.564974	+	0.825109i	$0.691114\pi$
$72$	−9.02715	−1.06386
$73$	−11.5797	−1.35530	−0.677651	−	0.735383i	$-0.737002\pi$
$73$	−11.5797	−1.35530	−0.677651	+	0.735383i	$0.737002\pi$
$74$	−1.86294	−0.216562
$75$	−0.198062	−0.0228703
$76$	−0.972853	−0.111594
$77$	0.801938	0.0913893
$78$	0	0
$79$	−15.8291	−1.78091	−0.890456	−	0.455070i	$-0.849614\pi$
$79$	−15.8291	−1.78091	−0.890456	+	0.455070i	$0.849614\pi$
$80$	2.91185	0.325555
$81$	8.64848	0.960942
$82$	13.6679	1.50936
$83$	17.3448	1.90384	0.951920	−	0.306346i	$-0.0991063\pi$
$83$	17.3448	1.90384	0.951920	+	0.306346i	$0.0991063\pi$
$84$	0.0174584	0.00190487
$85$	5.40581	0.586343
$86$	9.42088	1.01588
$87$	1.40150	0.150257
$88$	12.3448	1.31596
$89$	−3.05429	−0.323755	−0.161877	−	0.986811i	$-0.551755\pi$
$89$	−3.05429	−0.323755	−0.161877	+	0.986811i	$0.551755\pi$
$90$	−3.69202	−0.389173
$91$	0	0
$92$	−3.21983	−0.335691
$93$	−0.00431187	−0.000447120 0
$94$	−1.29590	−0.133662
$95$	−2.18598	−0.224277
$96$	0.488582	0.0498657
$97$	5.02177	0.509884	0.254942	−	0.966956i	$-0.417944\pi$
$97$	5.02177	0.509884	0.254942	+	0.966956i	$0.417944\pi$
$98$	8.67994	0.876806
$99$	−11.9879	−1.20483
$100$	−0.445042	−0.0445042
$101$	−12.9487	−1.28844	−0.644221	−	0.764839i	$-0.722818\pi$
$101$	−12.9487	−1.28844	−0.644221	+	0.764839i	$0.722818\pi$
$102$	−1.33513	−0.132197
$103$	−13.4058	−1.32091	−0.660457	−	0.750864i	$-0.729637\pi$
$103$	−13.4058	−1.32091	−0.660457	+	0.750864i	$0.729637\pi$
$104$	0	0
$105$	0.0392287	0.00382833
$106$	0.692021	0.0672151
$107$	0.994623	0.0961539	0.0480769	−	0.998844i	$-0.484691\pi$
$107$	0.994623	0.0961539	0.0480769	+	0.998844i	$0.484691\pi$
$108$	−0.525418	−0.0505584
$109$	−19.3056	−1.84914	−0.924570	−	0.381013i	$-0.875575\pi$
$109$	−19.3056	−1.84914	−0.924570	+	0.381013i	$0.875575\pi$
$110$	5.04892	0.481395
$111$	−0.295897	−0.0280853
$112$	−0.576728	−0.0544957
$113$	19.6136	1.84509	0.922544	−	0.385891i	$-0.126106\pi$
$113$	19.6136	1.84509	0.922544	+	0.385891i	$0.126106\pi$
$114$	0.539893	0.0505656
$115$	−7.23490	−0.674658
$116$	3.14914	0.292391
$117$	0	0
$118$	−4.85086	−0.446557
$119$	−1.07069	−0.0981498
$120$	0.603875	0.0551260
$121$	5.39373	0.490339
$122$	6.92692	0.627134
$123$	2.17092	0.195745
$124$	−0.00968868	−0.000870069 0
$125$	−1.00000	−0.0894427
$126$	0.731250	0.0651449
$127$	−9.76271	−0.866300	−0.433150	−	0.901322i	$-0.642598\pi$
$127$	−9.76271	−0.866300	−0.433150	+	0.901322i	$0.642598\pi$
$128$	−6.16421	−0.544844
$129$	1.49635	0.131746
$130$	0	0
$131$	14.6189	1.27726	0.638631	−	0.769513i	$-0.279501\pi$
$131$	14.6189	1.27726	0.638631	+	0.769513i	$0.279501\pi$
$132$	0.356896	0.0310638
$133$	0.432960	0.0375424
$134$	7.07069	0.610814
$135$	−1.18060	−0.101610
$136$	−16.4819	−1.41331
$137$	−5.54288	−0.473560	−0.236780	−	0.971563i	$-0.576092\pi$
$137$	−5.54288	−0.473560	−0.236780	+	0.971563i	$0.576092\pi$
$138$	1.78687	0.152109
$139$	−0.545269	−0.0462492	−0.0231246	−	0.999733i	$-0.507361\pi$
$139$	−0.545269	−0.0462492	−0.0231246	+	0.999733i	$0.507361\pi$
$140$	0.0881460	0.00744970
$141$	−0.205832	−0.0173342
$142$	11.8726	0.996329
$143$	0	0
$144$	8.62133	0.718444
$145$	7.07606	0.587635
$146$	14.4397	1.19504
$147$	1.37867	0.113710
$148$	−0.664874	−0.0546523
$149$	0.768086	0.0629240	0.0314620	−	0.999505i	$-0.489984\pi$
$149$	0.768086	0.0629240	0.0314620	+	0.999505i	$0.489984\pi$
$150$	0.246980	0.0201658
$151$	−14.0097	−1.14009	−0.570046	−	0.821613i	$-0.693075\pi$
$151$	−14.0097	−1.14009	−0.570046	+	0.821613i	$0.693075\pi$
$152$	6.66487	0.540593
$153$	16.0054	1.29396
$154$	−1.00000	−0.0805823
$155$	−0.0217703	−0.00174863
$156$	0	0
$157$	16.2620	1.29785	0.648926	−	0.760851i	$-0.275218\pi$
$157$	16.2620	1.29785	0.648926	+	0.760851i	$0.275218\pi$
$158$	19.7385	1.57031
$159$	0.109916	0.00871693
$160$	2.46681	0.195019
$161$	1.43296	0.112933
$162$	−10.7845	−0.847309
$163$	12.3666	0.968626	0.484313	−	0.874895i	$-0.339070\pi$
$163$	12.3666	0.968626	0.484313	+	0.874895i	$0.339070\pi$
$164$	4.87800	0.380908
$165$	0.801938	0.0624308
$166$	−21.6286	−1.67871
$167$	21.4523	1.66003	0.830016	−	0.557740i	$-0.188331\pi$
$167$	21.4523	1.66003	0.830016	+	0.557740i	$0.188331\pi$
$168$	−0.119605	−0.00922772
$169$	0	0
$170$	−6.74094	−0.517006
$171$	−6.47219	−0.494941
$172$	3.36227	0.256371
$173$	−2.57002	−0.195395	−0.0976976	−	0.995216i	$-0.531148\pi$
$173$	−2.57002	−0.195395	−0.0976976	+	0.995216i	$0.531148\pi$
$174$	−1.74764	−0.132489
$175$	0.198062	0.0149721
$176$	−11.7899	−0.888694
$177$	−0.770479	−0.0579127
$178$	3.80864	0.285470
$179$	−15.1981	−1.13596	−0.567978	−	0.823044i	$-0.692274\pi$
$179$	−15.1981	−1.13596	−0.567978	+	0.823044i	$0.692274\pi$
$180$	−1.31767	−0.0982131
$181$	0.686645	0.0510379	0.0255189	−	0.999674i	$-0.491876\pi$
$181$	0.686645	0.0510379	0.0255189	+	0.999674i	$0.491876\pi$
$182$	0	0
$183$	1.10023	0.0813312
$184$	22.0586	1.62618
$185$	−1.49396	−0.109838
$186$	0.00537681	0.000394247 0
$187$	−21.8877	−1.60059
$188$	−0.462500	−0.0337313
$189$	0.233833	0.0170089
$190$	2.72587	0.197756
$191$	3.47219	0.251239	0.125619	−	0.992079i	$-0.459908\pi$
$191$	3.47219	0.251239	0.125619	+	0.992079i	$0.459908\pi$
$192$	−1.76271	−0.127213
$193$	−8.80625	−0.633888	−0.316944	−	0.948444i	$-0.602657\pi$
$193$	−8.80625	−0.633888	−0.316944	+	0.948444i	$0.602657\pi$
$194$	−6.26205	−0.449589
$195$	0	0
$196$	3.09783	0.221274
$197$	12.3284	0.878364	0.439182	−	0.898398i	$-0.355268\pi$
$197$	12.3284	0.878364	0.439182	+	0.898398i	$0.355268\pi$
$198$	14.9487	1.06236
$199$	6.48188	0.459488	0.229744	−	0.973251i	$-0.426211\pi$
$199$	6.48188	0.459488	0.229744	+	0.973251i	$0.426211\pi$
$200$	3.04892	0.215591
$201$	1.12306	0.0792147
$202$	16.1468	1.13608
$203$	−1.40150	−0.0983661
$204$	−0.476501	−0.0333617
$205$	10.9608	0.765533
$206$	16.7168	1.16471
$207$	−21.4209	−1.48885
$208$	0	0
$209$	8.85086	0.612226
$210$	−0.0489173	−0.00337562
$211$	−14.6160	−1.00620	−0.503102	−	0.864227i	$-0.667808\pi$
$211$	−14.6160	−1.00620	−0.503102	+	0.864227i	$0.667808\pi$
$212$	0.246980	0.0169626
$213$	1.88577	0.129211
$214$	−1.24027	−0.0847834
$215$	7.55496	0.515244
$216$	3.59956	0.244919
$217$	0.00431187	0.000292709 0
$218$	24.0737	1.63047
$219$	2.29350	0.154981
$220$	1.80194	0.121487
$221$	0	0
$222$	0.368977	0.0247641
$223$	25.4644	1.70522	0.852612	−	0.522545i	$-0.175017\pi$
$223$	25.4644	1.70522	0.852612	+	0.522545i	$0.175017\pi$
$224$	−0.488582	−0.0326448
$225$	−2.96077	−0.197385
$226$	−24.4577	−1.62690
$227$	−20.7332	−1.37611	−0.688054	−	0.725659i	$-0.741535\pi$
$227$	−20.7332	−1.37611	−0.688054	+	0.725659i	$0.741535\pi$
$228$	0.192685	0.0127609
$229$	7.28621	0.481486	0.240743	−	0.970589i	$-0.422609\pi$
$229$	7.28621	0.481486	0.240743	+	0.970589i	$0.422609\pi$
$230$	9.02177	0.594878
$231$	−0.158834	−0.0104505
$232$	−21.5743	−1.41642
$233$	−6.06638	−0.397421	−0.198711	−	0.980058i	$-0.563675\pi$
$233$	−6.06638	−0.397421	−0.198711	+	0.980058i	$0.563675\pi$
$234$	0	0
$235$	−1.03923	−0.0677918
$236$	−1.73125	−0.112695
$237$	3.13514	0.203650
$238$	1.33513	0.0865433
$239$	12.8213	0.829342	0.414671	−	0.909971i	$-0.363897\pi$
$239$	12.8213	0.829342	0.414671	+	0.909971i	$0.363897\pi$
$240$	−0.576728	−0.0372277
$241$	5.66919	0.365184	0.182592	−	0.983189i	$-0.441551\pi$
$241$	5.66919	0.365184	0.182592	+	0.983189i	$0.441551\pi$
$242$	−6.72587	−0.432356
$243$	−5.25475	−0.337092
$244$	2.47219	0.158266
$245$	6.96077	0.444707
$246$	−2.70709	−0.172598
$247$	0	0
$248$	0.0663757	0.00421486
$249$	−3.43535	−0.217707
$250$	1.24698	0.0788659
$251$	15.3642	0.969779	0.484890	−	0.874575i	$-0.338860\pi$
$251$	15.3642	0.969779	0.484890	+	0.874575i	$0.338860\pi$
$252$	0.260980	0.0164402
$253$	29.2935	1.84167
$254$	12.1739	0.763858
$255$	−1.07069	−0.0670491
$256$	−10.1129	−0.632056
$257$	−16.8659	−1.05207	−0.526034	−	0.850464i	$-0.676321\pi$
$257$	−16.8659	−1.05207	−0.526034	+	0.850464i	$0.676321\pi$
$258$	−1.86592	−0.116167
$259$	0.295897	0.0183861
$260$	0	0
$261$	20.9506	1.29681
$262$	−18.2295	−1.12622
$263$	−6.03923	−0.372395	−0.186197	−	0.982512i	$-0.559616\pi$
$263$	−6.03923	−0.372395	−0.186197	+	0.982512i	$0.559616\pi$
$264$	−2.44504	−0.150482
$265$	0.554958	0.0340908
$266$	−0.539893	−0.0331029
$267$	0.604940	0.0370218
$268$	2.52350	0.154147
$269$	15.6963	0.957022	0.478511	−	0.878081i	$-0.341177\pi$
$269$	15.6963	0.957022	0.478511	+	0.878081i	$0.341177\pi$
$270$	1.47219	0.0895946
$271$	15.6310	0.949517	0.474758	−	0.880116i	$-0.342535\pi$
$271$	15.6310	0.949517	0.474758	+	0.880116i	$0.342535\pi$
$272$	15.7409	0.954435
$273$	0	0
$274$	6.91185	0.417560
$275$	4.04892	0.244159
$276$	0.637727	0.0383867
$277$	−17.6189	−1.05862	−0.529310	−	0.848429i	$-0.677549\pi$
$277$	−17.6189	−1.05862	−0.529310	+	0.848429i	$0.677549\pi$
$278$	0.679940	0.0407801
$279$	−0.0644568	−0.00385893
$280$	−0.603875	−0.0360885
$281$	4.04461	0.241281	0.120640	−	0.992696i	$-0.461505\pi$
$281$	4.04461	0.241281	0.120640	+	0.992696i	$0.461505\pi$
$282$	0.256668	0.0152844
$283$	−16.7409	−0.995146	−0.497573	−	0.867422i	$-0.665775\pi$
$283$	−16.7409	−0.995146	−0.497573	+	0.867422i	$0.665775\pi$
$284$	4.23729	0.251437
$285$	0.432960	0.0256464
$286$	0	0
$287$	−2.17092	−0.128145
$288$	7.30367	0.430373
$289$	12.2228	0.718989
$290$	−8.82371	−0.518146
$291$	−0.994623	−0.0583058
$292$	5.15346	0.301583
$293$	8.67456	0.506773	0.253387	−	0.967365i	$-0.418455\pi$
$293$	8.67456	0.506773	0.253387	+	0.967365i	$0.418455\pi$
$294$	−1.71917	−0.100264
$295$	−3.89008	−0.226489
$296$	4.55496	0.264752
$297$	4.78017	0.277373
$298$	−0.957787	−0.0554831
$299$	0	0
$300$	0.0881460	0.00508911
$301$	−1.49635	−0.0862483
$302$	17.4698	1.00527
$303$	2.56465	0.147335
$304$	−6.36526	−0.365073
$305$	5.55496	0.318076
$306$	−19.9584	−1.14094
$307$	15.6069	0.890731	0.445365	−	0.895349i	$-0.353074\pi$
$307$	15.6069	0.890731	0.445365	+	0.895349i	$0.353074\pi$
$308$	−0.356896	−0.0203360
$309$	2.65519	0.151048
$310$	0.0271471	0.00154185
$311$	22.0965	1.25298	0.626489	−	0.779430i	$-0.284491\pi$
$311$	22.0965	1.25298	0.626489	+	0.779430i	$0.284491\pi$
$312$	0	0
$313$	−19.6015	−1.10794	−0.553971	−	0.832536i	$-0.686888\pi$
$313$	−19.6015	−1.10794	−0.553971	+	0.832536i	$0.686888\pi$
$314$	−20.2784	−1.14438
$315$	0.586417	0.0330409
$316$	7.04461	0.396290
$317$	13.2470	0.744024	0.372012	−	0.928228i	$-0.378668\pi$
$317$	13.2470	0.744024	0.372012	+	0.928228i	$0.378668\pi$
$318$	−0.137063	−0.00768613
$319$	−28.6504	−1.60411
$320$	−8.89977	−0.497512
$321$	−0.196997	−0.0109953
$322$	−1.78687	−0.0995785
$323$	−11.8170	−0.657516
$324$	−3.84894	−0.213830
$325$	0	0
$326$	−15.4209	−0.854083
$327$	3.82371	0.211452
$328$	−33.4185	−1.84523
$329$	0.205832	0.0113479
$330$	−1.00000	−0.0550482
$331$	−12.2121	−0.671236	−0.335618	−	0.941998i	$-0.608945\pi$
$331$	−12.2121	−0.671236	−0.335618	+	0.941998i	$0.608945\pi$
$332$	−7.71917	−0.423644
$333$	−4.42327	−0.242394
$334$	−26.7506	−1.46373
$335$	5.67025	0.309799
$336$	0.114228	0.00623166
$337$	5.59611	0.304839	0.152420	−	0.988316i	$-0.451293\pi$
$337$	5.59611	0.304839	0.152420	+	0.988316i	$0.451293\pi$
$338$	0	0
$339$	−3.88471	−0.210988
$340$	−2.40581	−0.130474
$341$	0.0881460	0.00477337
$342$	8.07069	0.436413
$343$	−2.76510	−0.149301
$344$	−23.0344	−1.24193
$345$	1.43296	0.0771480
$346$	3.20477	0.172289
$347$	−20.8649	−1.12008	−0.560042	−	0.828464i	$-0.689215\pi$
$347$	−20.8649	−1.12008	−0.560042	+	0.828464i	$0.689215\pi$
$348$	−0.623727	−0.0334353
$349$	−17.6082	−0.942545	−0.471272	−	0.881988i	$-0.656205\pi$
$349$	−17.6082	−0.942545	−0.471272	+	0.881988i	$0.656205\pi$
$350$	−0.246980	−0.0132016
$351$	0	0
$352$	−9.98792	−0.532358
$353$	−26.3043	−1.40003	−0.700017	−	0.714126i	$-0.746824\pi$
$353$	−26.3043	−1.40003	−0.700017	+	0.714126i	$0.746824\pi$
$354$	0.960771	0.0510644
$355$	9.52111	0.505328
$356$	1.35929	0.0720422
$357$	0.212063	0.0112236
$358$	18.9517	1.00163
$359$	−10.9685	−0.578897	−0.289449	−	0.957194i	$-0.593472\pi$
$359$	−10.9685	−0.578897	−0.289449	+	0.957194i	$0.593472\pi$
$360$	9.02715	0.475772
$361$	−14.2215	−0.748499
$362$	−0.856232	−0.0450025
$363$	−1.06829	−0.0560709
$364$	0	0
$365$	11.5797	0.606110
$366$	−1.37196	−0.0717136
$367$	−32.2693	−1.68445	−0.842223	−	0.539129i	$-0.818753\pi$
$367$	−32.2693	−1.68445	−0.842223	+	0.539129i	$0.818753\pi$
$368$	−21.0670	−1.09819
$369$	32.4523	1.68940
$370$	1.86294	0.0968495
$371$	−0.109916	−0.00570657
$372$	0.00191896	9.94935e−5 0
$373$	6.88338	0.356408	0.178204	−	0.983994i	$-0.442971\pi$
$373$	6.88338	0.356408	0.178204	+	0.983994i	$0.442971\pi$
$374$	27.2935	1.41131
$375$	0.198062	0.0102279
$376$	3.16852	0.163404
$377$	0	0
$378$	−0.291585	−0.0149975
$379$	−12.2784	−0.630701	−0.315351	−	0.948975i	$-0.602122\pi$
$379$	−12.2784	−0.630701	−0.315351	+	0.948975i	$0.602122\pi$
$380$	0.972853	0.0499063
$381$	1.93362	0.0990626
$382$	−4.32975	−0.221529
$383$	8.43296	0.430904	0.215452	−	0.976514i	$-0.430877\pi$
$383$	8.43296	0.430904	0.215452	+	0.976514i	$0.430877\pi$
$384$	1.22090	0.0623037
$385$	−0.801938	−0.0408705
$386$	10.9812	0.558929
$387$	22.3685	1.13705
$388$	−2.23490	−0.113460
$389$	−20.4198	−1.03533	−0.517663	−	0.855585i	$-0.673198\pi$
$389$	−20.4198	−1.03533	−0.517663	+	0.855585i	$0.673198\pi$
$390$	0	0
$391$	−39.1105	−1.97790
$392$	−21.2228	−1.07191
$393$	−2.89546	−0.146057
$394$	−15.3733	−0.774495
$395$	15.8291	0.796448
$396$	5.33513	0.268100
$397$	−18.6431	−0.935671	−0.467835	−	0.883816i	$-0.654966\pi$
$397$	−18.6431	−0.935671	−0.467835	+	0.883816i	$0.654966\pi$
$398$	−8.08277	−0.405153
$399$	−0.0857531	−0.00429302
$400$	−2.91185	−0.145593
$401$	−30.9831	−1.54722	−0.773612	−	0.633660i	$-0.781552\pi$
$401$	−30.9831	−1.54722	−0.773612	+	0.633660i	$0.781552\pi$
$402$	−1.40044	−0.0698474
$403$	0	0
$404$	5.76271	0.286705
$405$	−8.64848	−0.429746
$406$	1.74764	0.0867341
$407$	6.04892	0.299834
$408$	3.26444	0.161614
$409$	23.8073	1.17720	0.588598	−	0.808426i	$-0.299680\pi$
$409$	23.8073	1.17720	0.588598	+	0.808426i	$0.299680\pi$
$410$	−13.6679	−0.675007
$411$	1.09783	0.0541522
$412$	5.96615	0.293931
$413$	0.770479	0.0379128
$414$	26.7114	1.31279
$415$	−17.3448	−0.851423
$416$	0	0
$417$	0.107997	0.00528865
$418$	−11.0368	−0.539829
$419$	12.1153	0.591871	0.295935	−	0.955208i	$-0.404369\pi$
$419$	12.1153	0.591871	0.295935	+	0.955208i	$0.404369\pi$
$420$	−0.0174584	−0.000851883 0
$421$	11.2537	0.548471	0.274236	−	0.961663i	$-0.411575\pi$
$421$	11.2537	0.548471	0.274236	+	0.961663i	$0.411575\pi$
$422$	18.2258	0.887218
$423$	−3.07692	−0.149605
$424$	−1.69202	−0.0821718
$425$	−5.40581	−0.262220
$426$	−2.35152	−0.113931
$427$	−1.10023	−0.0532437
$428$	−0.442649	−0.0213962
$429$	0	0
$430$	−9.42088	−0.454315
$431$	−17.3575	−0.836081	−0.418040	−	0.908428i	$-0.637283\pi$
$431$	−17.3575	−0.836081	−0.418040	+	0.908428i	$0.637283\pi$
$432$	−3.43775	−0.165399
$433$	−7.17390	−0.344756	−0.172378	−	0.985031i	$-0.555145\pi$
$433$	−7.17390	−0.344756	−0.172378	+	0.985031i	$0.555145\pi$
$434$	−0.00537681	−0.000258095 0
$435$	−1.40150	−0.0671968
$436$	8.59179	0.411472
$437$	15.8153	0.756551
$438$	−2.85995	−0.136654
$439$	10.3207	0.492578	0.246289	−	0.969196i	$-0.420789\pi$
$439$	10.3207	0.492578	0.246289	+	0.969196i	$0.420789\pi$
$440$	−12.3448	−0.588516
$441$	20.6093	0.981393
$442$	0	0
$443$	−30.2271	−1.43613	−0.718067	−	0.695974i	$-0.754973\pi$
$443$	−30.2271	−1.43613	−0.718067	+	0.695974i	$0.754973\pi$
$444$	0.131687	0.00624957
$445$	3.05429	0.144787
$446$	−31.7536	−1.50358
$447$	−0.152129	−0.00719545
$448$	1.76271	0.0832802
$449$	−24.7006	−1.16570	−0.582848	−	0.812581i	$-0.698062\pi$
$449$	−24.7006	−1.16570	−0.582848	+	0.812581i	$0.698062\pi$
$450$	3.69202	0.174044
$451$	−44.3793	−2.08974
$452$	−8.72886	−0.410571
$453$	2.77479	0.130371
$454$	25.8538	1.21338
$455$	0	0
$456$	−1.32006	−0.0618175
$457$	15.2198	0.711954	0.355977	−	0.934495i	$-0.384148\pi$
$457$	15.2198	0.711954	0.355977	+	0.934495i	$0.384148\pi$
$458$	−9.08575	−0.424549
$459$	−6.38212	−0.297892
$460$	3.21983	0.150125
$461$	11.7995	0.549560	0.274780	−	0.961507i	$-0.411395\pi$
$461$	11.7995	0.549560	0.274780	+	0.961507i	$0.411395\pi$
$462$	0.198062	0.00921469
$463$	13.2325	0.614967	0.307483	−	0.951553i	$-0.400513\pi$
$463$	13.2325	0.614967	0.307483	+	0.951553i	$0.400513\pi$
$464$	20.6045	0.956538
$465$	0.00431187	0.000199958 0
$466$	7.56465	0.350425
$467$	−8.01507	−0.370893	−0.185446	−	0.982654i	$-0.559373\pi$
$467$	−8.01507	−0.370893	−0.185446	+	0.982654i	$0.559373\pi$
$468$	0	0
$469$	−1.12306	−0.0518582
$470$	1.29590	0.0597753
$471$	−3.22090	−0.148411
$472$	11.8605	0.545926
$473$	−30.5894	−1.40650
$474$	−3.90946	−0.179567
$475$	2.18598	0.100300
$476$	0.476501	0.0218404
$477$	1.64310	0.0752326
$478$	−15.9879	−0.731270
$479$	6.72886	0.307449	0.153725	−	0.988114i	$-0.450873\pi$
$479$	6.72886	0.307449	0.153725	+	0.988114i	$0.450873\pi$
$480$	−0.488582	−0.0223006
$481$	0	0
$482$	−7.06936	−0.322001
$483$	−0.283815	−0.0129140
$484$	−2.40044	−0.109111
$485$	−5.02177	−0.228027
$486$	6.55257	0.297230
$487$	9.27545	0.420311	0.210155	−	0.977668i	$-0.432603\pi$
$487$	9.27545	0.420311	0.210155	+	0.977668i	$0.432603\pi$
$488$	−16.9366	−0.766684
$489$	−2.44935	−0.110764
$490$	−8.67994	−0.392120
$491$	7.94630	0.358611	0.179306	−	0.983793i	$-0.442615\pi$
$491$	7.94630	0.358611	0.179306	+	0.983793i	$0.442615\pi$
$492$	−0.966148	−0.0435573
$493$	38.2519	1.72278
$494$	0	0
$495$	11.9879	0.538817
$496$	−0.0633918	−0.00284638
$497$	−1.88577	−0.0845884
$498$	4.28382	0.191962
$499$	22.0291	0.986156	0.493078	−	0.869985i	$-0.335872\pi$
$499$	22.0291	0.986156	0.493078	+	0.869985i	$0.335872\pi$
$500$	0.445042	0.0199029
$501$	−4.24890	−0.189827
$502$	−19.1588	−0.855101
$503$	−26.2693	−1.17129	−0.585646	−	0.810567i	$-0.699159\pi$
$503$	−26.2693	−1.17129	−0.585646	+	0.810567i	$0.699159\pi$
$504$	−1.78794	−0.0796411
$505$	12.9487	0.576209
$506$	−36.5284	−1.62389
$507$	0	0
$508$	4.34481	0.192770
$509$	−35.4784	−1.57255	−0.786277	−	0.617875i	$-0.787994\pi$
$509$	−35.4784	−1.57255	−0.786277	+	0.617875i	$0.787994\pi$
$510$	1.33513	0.0591204
$511$	−2.29350	−0.101459
$512$	24.9390	1.10216
$513$	2.58078	0.113944
$514$	21.0315	0.927658
$515$	13.4058	0.590731
$516$	−0.665939	−0.0293163
$517$	4.20775	0.185057
$518$	−0.368977	−0.0162119
$519$	0.509025	0.0223437
$520$	0	0
$521$	30.2295	1.32438	0.662190	−	0.749336i	$-0.269627\pi$
$521$	30.2295	1.32438	0.662190	+	0.749336i	$0.269627\pi$
$522$	−26.1250	−1.14346
$523$	2.23191	0.0975948	0.0487974	−	0.998809i	$-0.484461\pi$
$523$	2.23191	0.0975948	0.0487974	+	0.998809i	$0.484461\pi$
$524$	−6.50604	−0.284218
$525$	−0.0392287	−0.00171208
$526$	7.53079	0.328358
$527$	−0.117686	−0.00512648
$528$	2.33513	0.101623
$529$	29.3437	1.27582
$530$	−0.692021	−0.0300595
$531$	−11.5176	−0.499823
$532$	−0.192685	−0.00835397
$533$	0	0
$534$	−0.754348	−0.0326438
$535$	−0.994623	−0.0430013
$536$	−17.2881	−0.746733
$537$	3.01016	0.129898
$538$	−19.5730	−0.843852
$539$	−28.1836	−1.21395
$540$	0.525418	0.0226104
$541$	17.4306	0.749399	0.374699	−	0.927146i	$-0.377746\pi$
$541$	17.4306	0.749399	0.374699	+	0.927146i	$0.377746\pi$
$542$	−19.4916	−0.837234
$543$	−0.135998	−0.00583625
$544$	13.3351	0.571739
$545$	19.3056	0.826960
$546$	0	0
$547$	2.65578	0.113553	0.0567764	−	0.998387i	$-0.481918\pi$
$547$	2.65578	0.113553	0.0567764	+	0.998387i	$0.481918\pi$
$548$	2.46681	0.105377
$549$	16.4470	0.701939
$550$	−5.04892	−0.215287
$551$	−15.4681	−0.658965
$552$	−4.36898	−0.185956
$553$	−3.13514	−0.133320
$554$	21.9705	0.933435
$555$	0.295897	0.0125601
$556$	0.242668	0.0102914
$557$	30.4547	1.29041	0.645204	−	0.764010i	$-0.276772\pi$
$557$	30.4547	1.29041	0.645204	+	0.764010i	$0.276772\pi$
$558$	0.0803763	0.00340260
$559$	0	0
$560$	0.576728	0.0243712
$561$	4.33513	0.183029
$562$	−5.04354	−0.212749
$563$	37.8170	1.59380	0.796898	−	0.604113i	$-0.206473\pi$
$563$	37.8170	1.59380	0.796898	+	0.604113i	$0.206473\pi$
$564$	0.0916038	0.00385722
$565$	−19.6136	−0.825149
$566$	20.8756	0.877467
$567$	1.71294	0.0719366
$568$	−29.0291	−1.21803
$569$	21.3720	0.895959	0.447980	−	0.894044i	$-0.352144\pi$
$569$	21.3720	0.895959	0.447980	+	0.894044i	$0.352144\pi$
$570$	−0.539893	−0.0226136
$571$	−18.8412	−0.788478	−0.394239	−	0.919008i	$-0.628992\pi$
$571$	−18.8412	−0.788478	−0.394239	+	0.919008i	$0.628992\pi$
$572$	0	0
$573$	−0.687710	−0.0287295
$574$	2.70709	0.112992
$575$	7.23490	0.301716
$576$	−26.3502	−1.09792
$577$	−37.6407	−1.56700	−0.783502	−	0.621390i	$-0.786568\pi$
$577$	−37.6407	−1.56700	−0.783502	+	0.621390i	$0.786568\pi$
$578$	−15.2416	−0.633967
$579$	1.74419	0.0724859
$580$	−3.14914	−0.130761
$581$	3.43535	0.142522
$582$	1.24027	0.0514110
$583$	−2.24698	−0.0930604
$584$	−35.3056	−1.46096
$585$	0	0
$586$	−10.8170	−0.446846
$587$	39.9627	1.64944	0.824718	−	0.565544i	$-0.191334\pi$
$587$	39.9627	1.64944	0.824718	+	0.565544i	$0.191334\pi$
$588$	−0.613564	−0.0253030
$589$	0.0475894	0.00196089
$590$	4.85086	0.199707
$591$	−2.44179	−0.100442
$592$	−4.35019	−0.178792
$593$	28.0116	1.15030	0.575149	−	0.818048i	$-0.304944\pi$
$593$	28.0116	1.15030	0.575149	+	0.818048i	$0.304944\pi$
$594$	−5.96077	−0.244573
$595$	1.07069	0.0438939
$596$	−0.341830	−0.0140019
$597$	−1.28382	−0.0525431
$598$	0	0
$599$	−5.40880	−0.220997	−0.110499	−	0.993876i	$-0.535245\pi$
$599$	−5.40880	−0.220997	−0.110499	+	0.993876i	$0.535245\pi$
$600$	−0.603875	−0.0246531
$601$	−27.3263	−1.11466	−0.557331	−	0.830290i	$-0.688175\pi$
$601$	−27.3263	−1.11466	−0.557331	+	0.830290i	$0.688175\pi$
$602$	1.86592	0.0760492
$603$	16.7883	0.683673
$604$	6.23490	0.253694
$605$	−5.39373	−0.219286
$606$	−3.19806	−0.129912
$607$	27.8092	1.12874	0.564371	−	0.825521i	$-0.309119\pi$
$607$	27.8092	1.12874	0.564371	+	0.825521i	$0.309119\pi$
$608$	−5.39240	−0.218691
$609$	0.277585	0.0112483
$610$	−6.92692	−0.280463
$611$	0	0
$612$	−7.12306	−0.287933
$613$	11.5773	0.467604	0.233802	−	0.972284i	$-0.424883\pi$
$613$	11.5773	0.467604	0.233802	+	0.972284i	$0.424883\pi$
$614$	−19.4614	−0.785400
$615$	−2.17092	−0.0875397
$616$	2.44504	0.0985135
$617$	24.7192	0.995156	0.497578	−	0.867419i	$-0.334223\pi$
$617$	24.7192	0.995156	0.497578	+	0.867419i	$0.334223\pi$
$618$	−3.31096	−0.133186
$619$	−10.4983	−0.421961	−0.210981	−	0.977490i	$-0.567666\pi$
$619$	−10.4983	−0.421961	−0.210981	+	0.977490i	$0.567666\pi$
$620$	0.00968868	0.000389107 0
$621$	8.54155	0.342761
$622$	−27.5539	−1.10481
$623$	−0.604940	−0.0242364
$624$	0	0
$625$	1.00000	0.0400000
$626$	24.4426	0.976925
$627$	−1.75302	−0.0700089
$628$	−7.23729	−0.288799
$629$	−8.07606	−0.322014
$630$	−0.731250	−0.0291337
$631$	33.9124	1.35003	0.675017	−	0.737803i	$-0.264136\pi$
$631$	33.9124	1.35003	0.675017	+	0.737803i	$0.264136\pi$
$632$	−48.2616	−1.91974
$633$	2.89487	0.115061
$634$	−16.5187	−0.656042
$635$	9.76271	0.387421
$636$	−0.0489173	−0.00193970
$637$	0	0
$638$	35.7265	1.41442
$639$	28.1898	1.11517
$640$	6.16421	0.243662
$641$	11.8170	0.466744	0.233372	−	0.972388i	$-0.425024\pi$
$641$	11.8170	0.466744	0.233372	+	0.972388i	$0.425024\pi$
$642$	0.245652	0.00969510
$643$	−26.6746	−1.05194	−0.525971	−	0.850502i	$-0.676298\pi$
$643$	−26.6746	−1.05194	−0.525971	+	0.850502i	$0.676298\pi$
$644$	−0.637727	−0.0251300
$645$	−1.49635	−0.0589188
$646$	14.7356	0.579763
$647$	32.6485	1.28354	0.641772	−	0.766895i	$-0.278200\pi$
$647$	32.6485	1.28354	0.641772	+	0.766895i	$0.278200\pi$
$648$	26.3685	1.03585
$649$	15.7506	0.618266
$650$	0	0
$651$	−0.000854018 0	−3.34716e−5 0
$652$	−5.50365	−0.215539
$653$	4.06936	0.159246	0.0796232	−	0.996825i	$-0.474628\pi$
$653$	4.06936	0.159246	0.0796232	+	0.996825i	$0.474628\pi$
$654$	−4.76809	−0.186447
$655$	−14.6189	−0.571209
$656$	31.9162	1.24612
$657$	34.2849	1.33758
$658$	−0.256668	−0.0100060
$659$	−21.9909	−0.856644	−0.428322	−	0.903626i	$-0.640895\pi$
$659$	−21.9909	−0.856644	−0.428322	+	0.903626i	$0.640895\pi$
$660$	−0.356896	−0.0138922
$661$	−11.8562	−0.461154	−0.230577	−	0.973054i	$-0.574061\pi$
$661$	−11.8562	−0.461154	−0.230577	+	0.973054i	$0.574061\pi$
$662$	15.2282	0.591861
$663$	0	0
$664$	52.8829	2.05225
$665$	−0.432960	−0.0167895
$666$	5.51573	0.213730
$667$	−51.1946	−1.98226
$668$	−9.54719	−0.369392
$669$	−5.04354	−0.194995
$670$	−7.07069	−0.273164
$671$	−22.4916	−0.868277
$672$	0.0967697	0.00373297
$673$	−24.1943	−0.932623	−0.466312	−	0.884621i	$-0.654417\pi$
$673$	−24.1943	−0.932623	−0.466312	+	0.884621i	$0.654417\pi$
$674$	−6.97823	−0.268791
$675$	1.18060	0.0454415
$676$	0	0
$677$	25.3806	0.975455	0.487728	−	0.872996i	$-0.337826\pi$
$677$	25.3806	0.975455	0.487728	+	0.872996i	$0.337826\pi$
$678$	4.84415	0.186038
$679$	0.994623	0.0381701
$680$	16.4819	0.632051
$681$	4.10646	0.157360
$682$	−0.109916	−0.00420891
$683$	−19.2741	−0.737504	−0.368752	−	0.929528i	$-0.620215\pi$
$683$	−19.2741	−0.737504	−0.368752	+	0.929528i	$0.620215\pi$
$684$	2.88040	0.110135
$685$	5.54288	0.211782
$686$	3.44803	0.131646
$687$	−1.44312	−0.0550586
$688$	21.9989	0.838702
$689$	0	0
$690$	−1.78687	−0.0680251
$691$	33.8049	1.28600	0.643000	−	0.765866i	$-0.277690\pi$
$691$	33.8049	1.28600	0.643000	+	0.765866i	$0.277690\pi$
$692$	1.14377	0.0434795
$693$	−2.37435	−0.0901943
$694$	26.0180	0.987632
$695$	0.545269	0.0206832
$696$	4.27306	0.161970
$697$	59.2519	2.24433
$698$	21.9571	0.831087
$699$	1.20152	0.0454457
$700$	−0.0881460	−0.00333161
$701$	15.5907	0.588854	0.294427	−	0.955674i	$-0.404871\pi$
$701$	15.5907	0.588854	0.294427	+	0.955674i	$0.404871\pi$
$702$	0	0
$703$	3.26577	0.123171
$704$	36.0344	1.35810
$705$	0.205832	0.00775208
$706$	32.8009	1.23448
$707$	−2.56465	−0.0964535
$708$	0.342895	0.0128868
$709$	6.09485	0.228897	0.114448	−	0.993429i	$-0.463490\pi$
$709$	6.09485	0.228897	0.114448	+	0.993429i	$0.463490\pi$
$710$	−11.8726	−0.445572
$711$	46.8663	1.75762
$712$	−9.31229	−0.348993
$713$	0.157506	0.00589863
$714$	−0.264438	−0.00989634
$715$	0	0
$716$	6.76377	0.252774
$717$	−2.53942	−0.0948363
$718$	13.6775	0.510442
$719$	26.5961	0.991867	0.495934	−	0.868360i	$-0.334826\pi$
$719$	26.5961	0.991867	0.495934	+	0.868360i	$0.334826\pi$
$720$	−8.62133	−0.321298
$721$	−2.65519	−0.0988843
$722$	17.7339	0.659988
$723$	−1.12285	−0.0417593
$724$	−0.305586	−0.0113570
$725$	−7.07606	−0.262798
$726$	1.33214	0.0494404
$727$	−9.91915	−0.367881	−0.183940	−	0.982937i	$-0.558885\pi$
$727$	−9.91915	−0.367881	−0.183940	+	0.982937i	$0.558885\pi$
$728$	0	0
$729$	−24.9047	−0.922395
$730$	−14.4397	−0.534436
$731$	40.8407	1.51055
$732$	−0.489647	−0.0180979
$733$	−26.2194	−0.968434	−0.484217	−	0.874948i	$-0.660895\pi$
$733$	−26.2194	−0.968434	−0.484217	+	0.874948i	$0.660895\pi$
$734$	40.2392	1.48526
$735$	−1.37867	−0.0508529
$736$	−17.8471	−0.657854
$737$	−22.9584	−0.845683
$738$	−40.4674	−1.48963
$739$	−3.50471	−0.128923	−0.0644615	−	0.997920i	$-0.520533\pi$
$739$	−3.50471	−0.128923	−0.0644615	+	0.997920i	$0.520533\pi$
$740$	0.664874	0.0244413
$741$	0	0
$742$	0.137063	0.00503175
$743$	−17.7138	−0.649856	−0.324928	−	0.945739i	$-0.605340\pi$
$743$	−17.7138	−0.649856	−0.324928	+	0.945739i	$0.605340\pi$
$744$	−0.0131465	−0.000481975 0
$745$	−0.768086	−0.0281405
$746$	−8.58343	−0.314262
$747$	−51.3540	−1.87895
$748$	9.74094	0.356164
$749$	0.196997	0.00719813
$750$	−0.246980	−0.00901842
$751$	50.1879	1.83138	0.915691	−	0.401883i	$-0.131644\pi$
$751$	50.1879	1.83138	0.915691	+	0.401883i	$0.131644\pi$
$752$	−3.02608	−0.110350
$753$	−3.04307	−0.110896
$754$	0	0
$755$	14.0097	0.509865
$756$	−0.104066	−0.00378483
$757$	37.8256	1.37480	0.687398	−	0.726281i	$-0.258753\pi$
$757$	37.8256	1.37480	0.687398	+	0.726281i	$0.258753\pi$
$758$	15.3110	0.556119
$759$	−5.80194	−0.210597
$760$	−6.66487	−0.241760
$761$	−13.3080	−0.482414	−0.241207	−	0.970474i	$-0.577543\pi$
$761$	−13.3080	−0.482414	−0.241207	+	0.970474i	$0.577543\pi$
$762$	−2.41119	−0.0873482
$763$	−3.82371	−0.138428
$764$	−1.54527	−0.0559059
$765$	−16.0054	−0.578676
$766$	−10.5157	−0.379949
$767$	0	0
$768$	2.00298	0.0722765
$769$	9.45904	0.341102	0.170551	−	0.985349i	$-0.445445\pi$
$769$	9.45904	0.341102	0.170551	+	0.985349i	$0.445445\pi$
$770$	1.00000	0.0360375
$771$	3.34050	0.120305
$772$	3.91915	0.141053
$773$	−50.2137	−1.80606	−0.903031	−	0.429575i	$-0.858663\pi$
$773$	−50.2137	−1.80606	−0.903031	+	0.429575i	$0.858663\pi$
$774$	−27.8931	−1.00260
$775$	0.0217703	0.000782011 0
$776$	15.3110	0.549632
$777$	−0.0586060	−0.00210248
$778$	25.4631	0.912896
$779$	−23.9600	−0.858457
$780$	0	0
$781$	−38.5502	−1.37943
$782$	48.7700	1.74401
$783$	−8.35403	−0.298549
$784$	20.2687	0.723884
$785$	−16.2620	−0.580417
$786$	3.61058	0.128785
$787$	5.07175	0.180788	0.0903942	−	0.995906i	$-0.471187\pi$
$787$	5.07175	0.180788	0.0903942	+	0.995906i	$0.471187\pi$
$788$	−5.48666	−0.195454
$789$	1.19614	0.0425838
$790$	−19.7385	−0.702266
$791$	3.88471	0.138124
$792$	−36.5502	−1.29875
$793$	0	0
$794$	23.2476	0.825025
$795$	−0.109916	−0.00389833
$796$	−2.88471	−0.102246
$797$	−9.07798	−0.321559	−0.160779	−	0.986990i	$-0.551401\pi$
$797$	−9.07798	−0.321559	−0.160779	+	0.986990i	$0.551401\pi$
$798$	0.106932	0.00378536
$799$	−5.61788	−0.198746
$800$	−2.46681	−0.0872150
$801$	9.04307	0.319521
$802$	38.6353	1.36426
$803$	−46.8853	−1.65455
$804$	−0.499810	−0.0176269
$805$	−1.43296	−0.0505052
$806$	0	0
$807$	−3.10885	−0.109437
$808$	−39.4795	−1.38888
$809$	33.2553	1.16920	0.584598	−	0.811323i	$-0.301252\pi$
$809$	33.2553	1.16920	0.584598	+	0.811323i	$0.301252\pi$
$810$	10.7845	0.378928
$811$	21.0258	0.738316	0.369158	−	0.929367i	$-0.379646\pi$
$811$	21.0258	0.738316	0.369158	+	0.929367i	$0.379646\pi$
$812$	0.623727	0.0218885
$813$	−3.09592	−0.108579
$814$	−7.54288	−0.264378
$815$	−12.3666	−0.433183
$816$	−3.11769	−0.109141
$817$	−16.5150	−0.577786
$818$	−29.6872	−1.03799
$819$	0	0
$820$	−4.87800	−0.170347
$821$	13.7463	0.479750	0.239875	−	0.970804i	$-0.422894\pi$
$821$	13.7463	0.479750	0.239875	+	0.970804i	$0.422894\pi$
$822$	−1.36898	−0.0477486
$823$	37.3159	1.30075	0.650375	−	0.759614i	$-0.274612\pi$
$823$	37.3159	1.30075	0.650375	+	0.759614i	$0.274612\pi$
$824$	−40.8732	−1.42389
$825$	−0.801938	−0.0279199
$826$	−0.960771	−0.0334295
$827$	−36.5478	−1.27089	−0.635445	−	0.772146i	$-0.719183\pi$
$827$	−36.5478	−1.27089	−0.635445	+	0.772146i	$0.719183\pi$
$828$	9.53319	0.331301
$829$	−32.4566	−1.12727	−0.563633	−	0.826025i	$-0.690597\pi$
$829$	−32.4566	−1.12727	−0.563633	+	0.826025i	$0.690597\pi$
$830$	21.6286	0.750741
$831$	3.48965	0.121055
$832$	0	0
$833$	37.6286	1.30375
$834$	−0.134670	−0.00466326
$835$	−21.4523	−0.742389
$836$	−3.93900	−0.136233
$837$	0.0257021	0.000888393 0
$838$	−15.1075	−0.521881
$839$	12.5670	0.433862	0.216931	−	0.976187i	$-0.430395\pi$
$839$	12.5670	0.433862	0.216931	+	0.976187i	$0.430395\pi$
$840$	0.119605	0.00412676
$841$	21.0707	0.726575
$842$	−14.0331	−0.483613
$843$	−0.801084	−0.0275908
$844$	6.50471	0.223901
$845$	0	0
$846$	3.83685	0.131914
$847$	1.06829	0.0367070
$848$	1.61596	0.0554922
$849$	3.31575	0.113796
$850$	6.74094	0.231212
$851$	10.8086	0.370515
$852$	−0.839247	−0.0287521
$853$	−38.3220	−1.31212	−0.656060	−	0.754709i	$-0.727778\pi$
$853$	−38.3220	−1.31212	−0.656060	+	0.754709i	$0.727778\pi$
$854$	1.37196	0.0469476
$855$	6.47219	0.221344
$856$	3.03252	0.103650
$857$	35.9081	1.22660	0.613299	−	0.789851i	$-0.289842\pi$
$857$	35.9081	1.22660	0.613299	+	0.789851i	$0.289842\pi$
$858$	0	0
$859$	−46.2881	−1.57933	−0.789665	−	0.613538i	$-0.789746\pi$
$859$	−46.2881	−1.57933	−0.789665	+	0.613538i	$0.789746\pi$
$860$	−3.36227	−0.114653
$861$	0.429976	0.0146536
$862$	21.6444	0.737212
$863$	7.86725	0.267804	0.133902	−	0.990995i	$-0.457249\pi$
$863$	7.86725	0.267804	0.133902	+	0.990995i	$0.457249\pi$
$864$	−2.91233	−0.0990794
$865$	2.57002	0.0873834
$866$	8.94571	0.303987
$867$	−2.42088	−0.0822174
$868$	−0.00191896	−6.51338e−5 0
$869$	−64.0907	−2.17413
$870$	1.74764	0.0592507
$871$	0	0
$872$	−58.8611	−1.99329
$873$	−14.8683	−0.503216
$874$	−19.7214	−0.667087
$875$	−0.198062	−0.00669573
$876$	−1.02071	−0.0344864
$877$	41.3913	1.39769	0.698843	−	0.715275i	$-0.253699\pi$
$877$	41.3913	1.39769	0.698843	+	0.715275i	$0.253699\pi$
$878$	−12.8696	−0.434329
$879$	−1.71810	−0.0579502
$880$	11.7899	0.397436
$881$	38.8558	1.30908	0.654542	−	0.756026i	$-0.272862\pi$
$881$	38.8558	1.30908	0.654542	+	0.756026i	$0.272862\pi$
$882$	−25.6993	−0.865341
$883$	−6.22713	−0.209560	−0.104780	−	0.994495i	$-0.533414\pi$
$883$	−6.22713	−0.209560	−0.104780	+	0.994495i	$0.533414\pi$
$884$	0	0
$885$	0.770479	0.0258994
$886$	37.6926	1.26631
$887$	36.3274	1.21975	0.609877	−	0.792496i	$-0.291219\pi$
$887$	36.3274	1.21975	0.609877	+	0.792496i	$0.291219\pi$
$888$	−0.902165	−0.0302747
$889$	−1.93362	−0.0648517
$890$	−3.80864	−0.127666
$891$	35.0170	1.17311
$892$	−11.3327	−0.379448
$893$	2.27173	0.0760207
$894$	0.189702	0.00634457
$895$	15.1981	0.508015
$896$	−1.22090	−0.0407873
$897$	0	0
$898$	30.8012	1.02785
$899$	−0.154048	−0.00513778
$900$	1.31767	0.0439222
$901$	3.00000	0.0999445
$902$	55.3400	1.84262
$903$	0.296371	0.00986261
$904$	59.8001	1.98892
$905$	−0.686645	−0.0228248
$906$	−3.46011	−0.114954
$907$	−4.34721	−0.144347	−0.0721733	−	0.997392i	$-0.522993\pi$
$907$	−4.34721	−0.144347	−0.0721733	+	0.997392i	$0.522993\pi$
$908$	9.22713	0.306213
$909$	38.3381	1.27159
$910$	0	0
$911$	−21.8866	−0.725136	−0.362568	−	0.931957i	$-0.618100\pi$
$911$	−21.8866	−0.725136	−0.362568	+	0.931957i	$0.618100\pi$
$912$	1.26072	0.0417465
$913$	70.2277	2.32420
$914$	−18.9788	−0.627764
$915$	−1.10023	−0.0363724
$916$	−3.24267	−0.107141
$917$	2.89546	0.0956165
$918$	7.95838	0.262666
$919$	25.6292	0.845430	0.422715	−	0.906263i	$-0.361077\pi$
$919$	25.6292	0.845430	0.422715	+	0.906263i	$0.361077\pi$
$920$	−22.0586	−0.727251
$921$	−3.09113	−0.101856
$922$	−14.7138	−0.484573
$923$	0	0
$924$	0.0706876	0.00232545
$925$	1.49396	0.0491211
$926$	−16.5007	−0.542245
$927$	39.6915	1.30364
$928$	17.4553	0.572999
$929$	−13.6635	−0.448286	−0.224143	−	0.974556i	$-0.571958\pi$
$929$	−13.6635	−0.448286	−0.224143	+	0.974556i	$0.571958\pi$
$930$	−0.00537681	−0.000176313 0
$931$	−15.2161	−0.498688
$932$	2.69979	0.0884346
$933$	−4.37648	−0.143280
$934$	9.99462	0.327034
$935$	21.8877	0.715804
$936$	0	0
$937$	17.1381	0.559878	0.279939	−	0.960018i	$-0.409686\pi$
$937$	17.1381	0.559878	0.279939	+	0.960018i	$0.409686\pi$
$938$	1.40044	0.0457259
$939$	3.88231	0.126695
$940$	0.462500	0.0150851
$941$	2.58775	0.0843581	0.0421790	−	0.999110i	$-0.486570\pi$
$941$	2.58775	0.0843581	0.0421790	+	0.999110i	$0.486570\pi$
$942$	4.01639	0.130861
$943$	−79.3001	−2.58237
$944$	−11.3274	−0.368674
$945$	−0.233833	−0.00760659
$946$	38.1444	1.24018
$947$	11.2078	0.364203	0.182101	−	0.983280i	$-0.441710\pi$
$947$	11.2078	0.364203	0.182101	+	0.983280i	$0.441710\pi$
$948$	−1.39527	−0.0453163
$949$	0	0
$950$	−2.72587	−0.0884390
$951$	−2.62373	−0.0850802
$952$	−3.26444	−0.105801
$953$	−38.2591	−1.23933	−0.619666	−	0.784865i	$-0.712732\pi$
$953$	−38.2591	−1.23933	−0.619666	+	0.784865i	$0.712732\pi$
$954$	−2.04892	−0.0663361
$955$	−3.47219	−0.112357
$956$	−5.70602	−0.184546
$957$	5.67456	0.183433
$958$	−8.39075	−0.271093
$959$	−1.09783	−0.0354509
$960$	1.76271	0.0568912
$961$	−30.9995	−0.999985
$962$	0	0
$963$	−2.94485	−0.0948965
$964$	−2.52303	−0.0812612
$965$	8.80625	0.283483
$966$	0.353912	0.0113869
$967$	−5.26875	−0.169432	−0.0847158	−	0.996405i	$-0.526998\pi$
$967$	−5.26875	−0.169432	−0.0847158	+	0.996405i	$0.526998\pi$
$968$	16.4450	0.528564
$969$	2.34050	0.0751878
$970$	6.26205	0.201062
$971$	−7.31203	−0.234654	−0.117327	−	0.993093i	$-0.537433\pi$
$971$	−7.31203	−0.234654	−0.117327	+	0.993093i	$0.537433\pi$
$972$	2.33858	0.0750101
$973$	−0.107997	−0.00346223
$974$	−11.5663	−0.370608
$975$	0	0
$976$	16.1752	0.517756
$977$	31.3661	1.00349	0.501745	−	0.865015i	$-0.332691\pi$
$977$	31.3661	1.00349	0.501745	+	0.865015i	$0.332691\pi$
$978$	3.05429	0.0976656
$979$	−12.3666	−0.395238
$980$	−3.09783	−0.0989567
$981$	57.1594	1.82496
$982$	−9.90887	−0.316205
$983$	−35.9724	−1.14734	−0.573670	−	0.819086i	$-0.694481\pi$
$983$	−35.9724	−1.14734	−0.573670	+	0.819086i	$0.694481\pi$
$984$	6.61894	0.211004
$985$	−12.3284	−0.392816
$986$	−47.6993	−1.51906
$987$	−0.0407675	−0.00129765
$988$	0	0
$989$	−54.6594	−1.73807
$990$	−14.9487	−0.475101
$991$	21.2476	0.674951	0.337476	−	0.941334i	$-0.390427\pi$
$991$	21.2476	0.674951	0.337476	+	0.941334i	$0.390427\pi$
$992$	−0.0537032	−0.00170508
$993$	2.41875	0.0767567
$994$	2.35152	0.0745857
$995$	−6.48188	−0.205489
$996$	1.52888	0.0484443
$997$	38.4040	1.21627	0.608134	−	0.793835i	$-0.291918\pi$
$997$	38.4040	1.21627	0.608134	+	0.793835i	$0.291918\pi$
$998$	−27.4698	−0.869541
$999$	1.76377	0.0558033

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.a.j.1.1	yes	3
3.2	odd	2		7605.2.a.br.1.3		3
5.4	even	2		4225.2.a.bd.1.3		3
13.2	odd	12		845.2.m.i.316.2		12
13.3	even	3		845.2.e.j.191.3		6
13.4	even	6		845.2.e.l.146.1		6
13.5	odd	4		845.2.c.f.506.5		6
13.6	odd	12		845.2.m.i.361.5		12
13.7	odd	12		845.2.m.i.361.2		12
13.8	odd	4		845.2.c.f.506.2		6
13.9	even	3		845.2.e.j.146.3		6
13.10	even	6		845.2.e.l.191.1		6
13.11	odd	12		845.2.m.i.316.5		12
13.12	even	2		845.2.a.h.1.3	✓	3
39.38	odd	2		7605.2.a.by.1.1		3
65.64	even	2		4225.2.a.bf.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
845.2.a.h.1.3	✓	3	13.12	even	2
845.2.a.j.1.1	yes	3	1.1	even	1	trivial
845.2.c.f.506.2		6	13.8	odd	4
845.2.c.f.506.5		6	13.5	odd	4
845.2.e.j.146.3		6	13.9	even	3
845.2.e.j.191.3		6	13.3	even	3
845.2.e.l.146.1		6	13.4	even	6
845.2.e.l.191.1		6	13.10	even	6
845.2.m.i.316.2		12	13.2	odd	12
845.2.m.i.316.5		12	13.11	odd	12
845.2.m.i.361.2		12	13.7	odd	12
845.2.m.i.361.5		12	13.6	odd	12
4225.2.a.bd.1.3		3	5.4	even	2
4225.2.a.bf.1.1		3	65.64	even	2
7605.2.a.br.1.3		3	3.2	odd	2
7605.2.a.by.1.1		3	39.38	odd	2

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.a (trivial)

\(f(q)\)	\(=\)	\(q-1.24698 q^{2} -0.198062 q^{3} -0.445042 q^{4} -1.00000 q^{5} +0.246980 q^{6} +0.198062 q^{7} +3.04892 q^{8} -2.96077 q^{9} +O(q^{10})\)	\(q-1.24698 q^{2} -0.198062 q^{3} -0.445042 q^{4} -1.00000 q^{5} +0.246980 q^{6} +0.198062 q^{7} +3.04892 q^{8} -2.96077 q^{9} +1.24698 q^{10} +4.04892 q^{11} +0.0881460 q^{12} -0.246980 q^{14} +0.198062 q^{15} -2.91185 q^{16} -5.40581 q^{17} +3.69202 q^{18} +2.18598 q^{19} +0.445042 q^{20} -0.0392287 q^{21} -5.04892 q^{22} +7.23490 q^{23} -0.603875 q^{24} +1.00000 q^{25} +1.18060 q^{27} -0.0881460 q^{28} -7.07606 q^{29} -0.246980 q^{30} +0.0217703 q^{31} -2.46681 q^{32} -0.801938 q^{33} +6.74094 q^{34} -0.198062 q^{35} +1.31767 q^{36} +1.49396 q^{37} -2.72587 q^{38} -3.04892 q^{40} -10.9608 q^{41} +0.0489173 q^{42} -7.55496 q^{43} -1.80194 q^{44} +2.96077 q^{45} -9.02177 q^{46} +1.03923 q^{47} +0.576728 q^{48} -6.96077 q^{49} -1.24698 q^{50} +1.07069 q^{51} -0.554958 q^{53} -1.47219 q^{54} -4.04892 q^{55} +0.603875 q^{56} -0.432960 q^{57} +8.82371 q^{58} +3.89008 q^{59} -0.0881460 q^{60} -5.55496 q^{61} -0.0271471 q^{62} -0.586417 q^{63} +8.89977 q^{64} +1.00000 q^{66} -5.67025 q^{67} +2.40581 q^{68} -1.43296 q^{69} +0.246980 q^{70} -9.52111 q^{71} -9.02715 q^{72} -11.5797 q^{73} -1.86294 q^{74} -0.198062 q^{75} -0.972853 q^{76} +0.801938 q^{77} -15.8291 q^{79} +2.91185 q^{80} +8.64848 q^{81} +13.6679 q^{82} +17.3448 q^{83} +0.0174584 q^{84} +5.40581 q^{85} +9.42088 q^{86} +1.40150 q^{87} +12.3448 q^{88} -3.05429 q^{89} -3.69202 q^{90} -3.21983 q^{92} -0.00431187 q^{93} -1.29590 q^{94} -2.18598 q^{95} +0.488582 q^{96} +5.02177 q^{97} +8.67994 q^{98} -11.9879 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} - 5 q^{3} - q^{4} - 3 q^{5} - 4 q^{6} + 5 q^{7} + 4 q^{9}+O(q^{10}) \) 3 * q + q^2 - 5 * q^3 - q^4 - 3 * q^5 - 4 * q^6 + 5 * q^7 + 4 * q^9	\( 3 q + q^{2} - 5 q^{3} - q^{4} - 3 q^{5} - 4 q^{6} + 5 q^{7} + 4 q^{9} - q^{10} + 3 q^{11} + 4 q^{12} + 4 q^{14} + 5 q^{15} - 5 q^{16} - 3 q^{17} + 6 q^{18} - 8 q^{19} + q^{20} - 13 q^{21} - 6 q^{22} - 2 q^{23} + 7 q^{24} + 3 q^{25} - 8 q^{27} - 4 q^{28} - 6 q^{29} + 4 q^{30} - 3 q^{31} - 4 q^{32} + 2 q^{33} + 6 q^{34} - 5 q^{35} - 13 q^{36} - 5 q^{37} - 19 q^{38} - 20 q^{41} - 9 q^{42} - 23 q^{43} - q^{44} - 4 q^{45} - 24 q^{46} + 16 q^{47} - q^{48} - 8 q^{49} + q^{50} - 9 q^{51} - 2 q^{53} + 2 q^{54} - 3 q^{55} - 7 q^{56} + 18 q^{57} + 19 q^{58} + 11 q^{59} - 4 q^{60} - 17 q^{61} + 6 q^{62} + 23 q^{63} + 4 q^{64} + 3 q^{66} - 15 q^{67} - 6 q^{68} + 15 q^{69} - 4 q^{70} - 13 q^{71} - 21 q^{72} + 12 q^{73} - 11 q^{74} - 5 q^{75} - 9 q^{76} - 2 q^{77} - 37 q^{79} + 5 q^{80} + 27 q^{81} - 2 q^{82} + 29 q^{83} + 16 q^{84} + 3 q^{85} - 10 q^{86} + 10 q^{87} + 14 q^{88} + 3 q^{89} - 6 q^{90} - 11 q^{92} + 19 q^{93} + 10 q^{94} + 8 q^{95} - 5 q^{96} + 12 q^{97} + 2 q^{98} - 17 q^{99}+O(q^{100}) \) 3 * q + q^2 - 5 * q^3 - q^4 - 3 * q^5 - 4 * q^6 + 5 * q^7 + 4 * q^9 - q^10 + 3 * q^11 + 4 * q^12 + 4 * q^14 + 5 * q^15 - 5 * q^16 - 3 * q^17 + 6 * q^18 - 8 * q^19 + q^20 - 13 * q^21 - 6 * q^22 - 2 * q^23 + 7 * q^24 + 3 * q^25 - 8 * q^27 - 4 * q^28 - 6 * q^29 + 4 * q^30 - 3 * q^31 - 4 * q^32 + 2 * q^33 + 6 * q^34 - 5 * q^35 - 13 * q^36 - 5 * q^37 - 19 * q^38 - 20 * q^41 - 9 * q^42 - 23 * q^43 - q^44 - 4 * q^45 - 24 * q^46 + 16 * q^47 - q^48 - 8 * q^49 + q^50 - 9 * q^51 - 2 * q^53 + 2 * q^54 - 3 * q^55 - 7 * q^56 + 18 * q^57 + 19 * q^58 + 11 * q^59 - 4 * q^60 - 17 * q^61 + 6 * q^62 + 23 * q^63 + 4 * q^64 + 3 * q^66 - 15 * q^67 - 6 * q^68 + 15 * q^69 - 4 * q^70 - 13 * q^71 - 21 * q^72 + 12 * q^73 - 11 * q^74 - 5 * q^75 - 9 * q^76 - 2 * q^77 - 37 * q^79 + 5 * q^80 + 27 * q^81 - 2 * q^82 + 29 * q^83 + 16 * q^84 + 3 * q^85 - 10 * q^86 + 10 * q^87 + 14 * q^88 + 3 * q^89 - 6 * q^90 - 11 * q^92 + 19 * q^93 + 10 * q^94 + 8 * q^95 - 5 * q^96 + 12 * q^97 + 2 * q^98 - 17 * q^99

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