LMFDB - Embedded newform 4033.2.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4033,2,Mod(1,4033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4033, 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("4033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4033 = 37 \cdot 109 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4033.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.2036671352$
Analytic rank:	$0$
Dimension:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	4033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58504 q^{2} -2.45542 q^{3} +4.68242 q^{4} +2.00515 q^{5} +6.34735 q^{6} -0.0308722 q^{7} -6.93416 q^{8} +3.02908 q^{9} +O(q^{10})$	\(q-2.58504 q^{2} -2.45542 q^{3} +4.68242 q^{4} +2.00515 q^{5} +6.34735 q^{6} -0.0308722 q^{7} -6.93416 q^{8} +3.02908 q^{9} -5.18339 q^{10} +0.327701 q^{11} -11.4973 q^{12} +3.31247 q^{13} +0.0798059 q^{14} -4.92348 q^{15} +8.56022 q^{16} +7.26922 q^{17} -7.83029 q^{18} +5.88886 q^{19} +9.38895 q^{20} +0.0758042 q^{21} -0.847119 q^{22} +2.33512 q^{23} +17.0263 q^{24} -0.979373 q^{25} -8.56286 q^{26} -0.0714089 q^{27} -0.144557 q^{28} -3.65164 q^{29} +12.7274 q^{30} +4.44783 q^{31} -8.26017 q^{32} -0.804643 q^{33} -18.7912 q^{34} -0.0619034 q^{35} +14.1834 q^{36} -1.00000 q^{37} -15.2229 q^{38} -8.13350 q^{39} -13.9040 q^{40} +2.57553 q^{41} -0.195957 q^{42} +4.45341 q^{43} +1.53443 q^{44} +6.07376 q^{45} -6.03637 q^{46} +11.5605 q^{47} -21.0189 q^{48} -6.99905 q^{49} +2.53172 q^{50} -17.8490 q^{51} +15.5104 q^{52} +12.6593 q^{53} +0.184595 q^{54} +0.657089 q^{55} +0.214073 q^{56} -14.4596 q^{57} +9.43962 q^{58} +8.79436 q^{59} -23.0538 q^{60} -5.33862 q^{61} -11.4978 q^{62} -0.0935145 q^{63} +4.23241 q^{64} +6.64200 q^{65} +2.08003 q^{66} +12.9845 q^{67} +34.0375 q^{68} -5.73370 q^{69} +0.160023 q^{70} +7.77834 q^{71} -21.0041 q^{72} +3.78593 q^{73} +2.58504 q^{74} +2.40477 q^{75} +27.5741 q^{76} -0.0101169 q^{77} +21.0254 q^{78} -12.2458 q^{79} +17.1645 q^{80} -8.91191 q^{81} -6.65783 q^{82} +2.08176 q^{83} +0.354947 q^{84} +14.5759 q^{85} -11.5122 q^{86} +8.96630 q^{87} -2.27233 q^{88} +12.3813 q^{89} -15.7009 q^{90} -0.102263 q^{91} +10.9340 q^{92} -10.9213 q^{93} -29.8843 q^{94} +11.8080 q^{95} +20.2822 q^{96} +2.81251 q^{97} +18.0928 q^{98} +0.992633 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9}+O(q^{10}) $ 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9} + 13 q^{10} + 2 q^{11} + 36 q^{12} + 23 q^{13} + 24 q^{14} + 35 q^{15} + 104 q^{16} + 43 q^{17} + 42 q^{18} + 15 q^{19} + 59 q^{20} + 9 q^{21} + 6 q^{22} + 70 q^{23} + 15 q^{24} + 98 q^{25} + 10 q^{26} + 65 q^{27} + 37 q^{28} + 27 q^{29} + 17 q^{30} + 59 q^{31} + 46 q^{32} + 16 q^{33} - 16 q^{34} + 80 q^{35} + 88 q^{36} - 82 q^{37} + 82 q^{38} + 13 q^{39} + 14 q^{40} + 3 q^{41} + 62 q^{42} + 7 q^{43} - 11 q^{44} + 42 q^{45} - 11 q^{46} + 123 q^{47} + 45 q^{48} + 105 q^{49} + 27 q^{50} + 3 q^{51} - 30 q^{52} + 82 q^{53} - 27 q^{54} + 37 q^{55} + 66 q^{56} + 29 q^{57} - 34 q^{58} + 60 q^{59} + 94 q^{60} + 9 q^{61} - 2 q^{62} + 106 q^{63} + 93 q^{64} + 9 q^{65} + 63 q^{66} + 113 q^{68} + 48 q^{69} + 47 q^{70} + 59 q^{71} + 63 q^{72} + 21 q^{73} - 10 q^{74} + 77 q^{75} + 22 q^{76} + 30 q^{77} + 29 q^{78} + 55 q^{79} + 88 q^{80} + 42 q^{81} + 4 q^{82} + 92 q^{83} + 43 q^{84} - 7 q^{85} + 17 q^{86} + 147 q^{87} - 13 q^{88} + 100 q^{89} + 91 q^{90} + 28 q^{91} + 127 q^{92} + 3 q^{93} + 30 q^{94} + 48 q^{95} - 31 q^{96} + 53 q^{97} + 101 q^{98} - 20 q^{99}+O(q^{100}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9 + 13 * q^10 + 2 * q^11 + 36 * q^12 + 23 * q^13 + 24 * q^14 + 35 * q^15 + 104 * q^16 + 43 * q^17 + 42 * q^18 + 15 * q^19 + 59 * q^20 + 9 * q^21 + 6 * q^22 + 70 * q^23 + 15 * q^24 + 98 * q^25 + 10 * q^26 + 65 * q^27 + 37 * q^28 + 27 * q^29 + 17 * q^30 + 59 * q^31 + 46 * q^32 + 16 * q^33 - 16 * q^34 + 80 * q^35 + 88 * q^36 - 82 * q^37 + 82 * q^38 + 13 * q^39 + 14 * q^40 + 3 * q^41 + 62 * q^42 + 7 * q^43 - 11 * q^44 + 42 * q^45 - 11 * q^46 + 123 * q^47 + 45 * q^48 + 105 * q^49 + 27 * q^50 + 3 * q^51 - 30 * q^52 + 82 * q^53 - 27 * q^54 + 37 * q^55 + 66 * q^56 + 29 * q^57 - 34 * q^58 + 60 * q^59 + 94 * q^60 + 9 * q^61 - 2 * q^62 + 106 * q^63 + 93 * q^64 + 9 * q^65 + 63 * q^66 + 113 * q^68 + 48 * q^69 + 47 * q^70 + 59 * q^71 + 63 * q^72 + 21 * q^73 - 10 * q^74 + 77 * q^75 + 22 * q^76 + 30 * q^77 + 29 * q^78 + 55 * q^79 + 88 * q^80 + 42 * q^81 + 4 * q^82 + 92 * q^83 + 43 * q^84 - 7 * q^85 + 17 * q^86 + 147 * q^87 - 13 * q^88 + 100 * q^89 + 91 * q^90 + 28 * q^91 + 127 * q^92 + 3 * q^93 + 30 * q^94 + 48 * q^95 - 31 * q^96 + 53 * q^97 + 101 * q^98 - 20 * 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 $

$2$	−2.58504	−1.82790	−0.913949	−	0.405829i	$-0.866983\pi$
$2$	−2.58504	−1.82790	−0.913949	+	0.405829i	$0.866983\pi$
$3$	−2.45542	−1.41764	−0.708818	−	0.705391i	$-0.750771\pi$
$3$	−2.45542	−1.41764	−0.708818	+	0.705391i	$0.750771\pi$
$4$	4.68242	2.34121
$5$	2.00515	0.896730	0.448365	−	0.893850i	$-0.352006\pi$
$5$	2.00515	0.896730	0.448365	+	0.893850i	$0.352006\pi$
$6$	6.34735	2.59129
$7$	−0.0308722	−0.0116686	−0.00583430	−	0.999983i	$-0.501857\pi$
$7$	−0.0308722	−0.0116686	−0.00583430	+	0.999983i	$0.501857\pi$
$8$	−6.93416	−2.45159
$9$	3.02908	1.00969
$10$	−5.18339	−1.63913
$11$	0.327701	0.0988055	0.0494028	−	0.998779i	$-0.484268\pi$
$11$	0.327701	0.0988055	0.0494028	+	0.998779i	$0.484268\pi$
$12$	−11.4973	−3.31899
$13$	3.31247	0.918713	0.459357	−	0.888252i	$-0.348080\pi$
$13$	3.31247	0.918713	0.459357	+	0.888252i	$0.348080\pi$
$14$	0.0798059	0.0213290
$15$	−4.92348	−1.27124
$16$	8.56022	2.14005
$17$	7.26922	1.76304	0.881522	−	0.472143i	$-0.156520\pi$
$17$	7.26922	1.76304	0.881522	+	0.472143i	$0.156520\pi$
$18$	−7.83029	−1.84562
$19$	5.88886	1.35100	0.675498	−	0.737361i	$-0.263929\pi$
$19$	5.88886	1.35100	0.675498	+	0.737361i	$0.263929\pi$
$20$	9.38895	2.09943
$21$	0.0758042	0.0165418
$22$	−0.847119	−0.180606
$23$	2.33512	0.486906	0.243453	−	0.969913i	$-0.421720\pi$
$23$	2.33512	0.486906	0.243453	+	0.969913i	$0.421720\pi$
$24$	17.0263	3.47547
$25$	−0.979373	−0.195875
$26$	−8.56286	−1.67931
$27$	−0.0714089	−0.0137426
$28$	−0.144557	−0.0273186
$29$	−3.65164	−0.678092	−0.339046	−	0.940770i	$-0.610104\pi$
$29$	−3.65164	−0.678092	−0.339046	+	0.940770i	$0.610104\pi$
$30$	12.7274	2.32369
$31$	4.44783	0.798854	0.399427	−	0.916765i	$-0.369209\pi$
$31$	4.44783	0.798854	0.399427	+	0.916765i	$0.369209\pi$
$32$	−8.26017	−1.46021
$33$	−0.804643	−0.140070
$34$	−18.7912	−3.22266
$35$	−0.0619034	−0.0104636
$36$	14.1834	2.36391
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−15.2229	−2.46948
$39$	−8.13350	−1.30240
$40$	−13.9040	−2.19842
$41$	2.57553	0.402230	0.201115	−	0.979568i	$-0.435544\pi$
$41$	2.57553	0.402230	0.201115	+	0.979568i	$0.435544\pi$
$42$	−0.195957	−0.0302368
$43$	4.45341	0.679138	0.339569	−	0.940581i	$-0.389719\pi$
$43$	4.45341	0.679138	0.339569	+	0.940581i	$0.389719\pi$
$44$	1.53443	0.231324
$45$	6.07376	0.905423
$46$	−6.03637	−0.890015
$47$	11.5605	1.68627	0.843136	−	0.537700i	$-0.180707\pi$
$47$	11.5605	1.68627	0.843136	+	0.537700i	$0.180707\pi$
$48$	−21.0189	−3.03382
$49$	−6.99905	−0.999864
$50$	2.53172	0.358039
$51$	−17.8490	−2.49936
$52$	15.5104	2.15090
$53$	12.6593	1.73889	0.869445	−	0.494030i	$-0.164477\pi$
$53$	12.6593	1.73889	0.869445	+	0.494030i	$0.164477\pi$
$54$	0.184595	0.0251202
$55$	0.657089	0.0886019
$56$	0.214073	0.0286067
$57$	−14.4596	−1.91522
$58$	9.43962	1.23948
$59$	8.79436	1.14493	0.572464	−	0.819930i	$-0.305988\pi$
$59$	8.79436	1.14493	0.572464	+	0.819930i	$0.305988\pi$
$60$	−23.0538	−2.97623
$61$	−5.33862	−0.683541	−0.341770	−	0.939783i	$-0.611027\pi$
$61$	−5.33862	−0.683541	−0.341770	+	0.939783i	$0.611027\pi$
$62$	−11.4978	−1.46022
$63$	−0.0935145	−0.0117817
$64$	4.23241	0.529052
$65$	6.64200	0.823838
$66$	2.08003	0.256034
$67$	12.9845	1.58630	0.793152	−	0.609023i	$-0.208438\pi$
$67$	12.9845	1.58630	0.793152	+	0.609023i	$0.208438\pi$
$68$	34.0375	4.12766
$69$	−5.73370	−0.690256
$70$	0.160023	0.0191264
$71$	7.77834	0.923119	0.461559	−	0.887109i	$-0.347290\pi$
$71$	7.77834	0.923119	0.461559	+	0.887109i	$0.347290\pi$
$72$	−21.0041	−2.47536
$73$	3.78593	0.443109	0.221555	−	0.975148i	$-0.428887\pi$
$73$	3.78593	0.443109	0.221555	+	0.975148i	$0.428887\pi$
$74$	2.58504	0.300505
$75$	2.40477	0.277679
$76$	27.5741	3.16297
$77$	−0.0101169	−0.00115292
$78$	21.0254	2.38066
$79$	−12.2458	−1.37776	−0.688882	−	0.724873i	$-0.741898\pi$
$79$	−12.2458	−1.37776	−0.688882	+	0.724873i	$0.741898\pi$
$80$	17.1645	1.91905
$81$	−8.91191	−0.990212
$82$	−6.65783	−0.735234
$83$	2.08176	0.228503	0.114252	−	0.993452i	$-0.463553\pi$
$83$	2.08176	0.228503	0.114252	+	0.993452i	$0.463553\pi$
$84$	0.354947	0.0387279
$85$	14.5759	1.58097
$86$	−11.5122	−1.24140
$87$	8.96630	0.961288
$88$	−2.27233	−0.242231
$89$	12.3813	1.31241	0.656207	−	0.754581i	$-0.272160\pi$
$89$	12.3813	1.31241	0.656207	+	0.754581i	$0.272160\pi$
$90$	−15.7009	−1.65502
$91$	−0.102263	−0.0107201
$92$	10.9340	1.13995
$93$	−10.9213	−1.13248
$94$	−29.8843	−3.08233
$95$	11.8080	1.21148
$96$	20.2822	2.07004
$97$	2.81251	0.285567	0.142784	−	0.989754i	$-0.454395\pi$
$97$	2.81251	0.285567	0.142784	+	0.989754i	$0.454395\pi$
$98$	18.0928	1.82765
$99$	0.992633	0.0997633
$100$	−4.58584	−0.458584
$101$	−10.5518	−1.04994	−0.524972	−	0.851119i	$-0.675924\pi$
$101$	−10.5518	−1.04994	−0.524972	+	0.851119i	$0.675924\pi$
$102$	46.1403	4.56857
$103$	3.41194	0.336189	0.168094	−	0.985771i	$-0.446239\pi$
$103$	3.41194	0.336189	0.168094	+	0.985771i	$0.446239\pi$
$104$	−22.9692	−2.25231
$105$	0.151999	0.0148336
$106$	−32.7248	−3.17851
$107$	10.2458	0.990500	0.495250	−	0.868751i	$-0.335076\pi$
$107$	10.2458	0.990500	0.495250	+	0.868751i	$0.335076\pi$
$108$	−0.334366	−0.0321744
$109$	1.00000	0.0957826
$109$	1.00000	0.0957826
$110$	−1.69860	−0.161955
$111$	2.45542	0.233058
$112$	−0.264273	−0.0249714
$113$	−6.97804	−0.656439	−0.328219	−	0.944602i	$-0.606449\pi$
$113$	−6.97804	−0.656439	−0.328219	+	0.944602i	$0.606449\pi$
$114$	37.3787	3.50083
$115$	4.68227	0.436624
$116$	−17.0985	−1.58756
$117$	10.0337	0.927620
$118$	−22.7338	−2.09281
$119$	−0.224417	−0.0205723
$120$	34.1402	3.11656
$121$	−10.8926	−0.990237
$122$	13.8005	1.24944
$123$	−6.32399	−0.570215
$124$	20.8266	1.87028
$125$	−11.9895	−1.07238
$126$	0.241739	0.0215358
$127$	−2.94058	−0.260934	−0.130467	−	0.991453i	$-0.541648\pi$
$127$	−2.94058	−0.260934	−0.130467	+	0.991453i	$0.541648\pi$
$128$	5.57939	0.493153
$129$	−10.9350	−0.962772
$130$	−17.1698	−1.50589
$131$	−20.0421	−1.75109	−0.875543	−	0.483140i	$-0.839496\pi$
$131$	−20.0421	−1.75109	−0.875543	+	0.483140i	$0.839496\pi$
$132$	−3.76767	−0.327934
$133$	−0.181802	−0.0157642
$134$	−33.5653	−2.89960
$135$	−0.143186	−0.0123235
$136$	−50.4059	−4.32227
$137$	−6.05327	−0.517166	−0.258583	−	0.965989i	$-0.583256\pi$
$137$	−6.05327	−0.517166	−0.258583	+	0.965989i	$0.583256\pi$
$138$	14.8218	1.26172
$139$	11.2572	0.954822	0.477411	−	0.878680i	$-0.341575\pi$
$139$	11.2572	0.954822	0.477411	+	0.878680i	$0.341575\pi$
$140$	−0.289858	−0.0244975
$141$	−28.3859	−2.39052
$142$	−20.1073	−1.68737
$143$	1.08550	0.0907739
$144$	25.9296	2.16080
$145$	−7.32208	−0.608066
$146$	−9.78676	−0.809958
$147$	17.1856	1.41744
$148$	−4.68242	−0.384893
$149$	1.87781	0.153836	0.0769181	−	0.997037i	$-0.475492\pi$
$149$	1.87781	0.153836	0.0769181	+	0.997037i	$0.475492\pi$
$150$	−6.21643	−0.507569
$151$	23.4945	1.91196	0.955978	−	0.293439i	$-0.0947997\pi$
$151$	23.4945	1.91196	0.955978	+	0.293439i	$0.0947997\pi$
$152$	−40.8343	−3.31210
$153$	22.0190	1.78013
$154$	0.0261524	0.00210742
$155$	8.91857	0.716357
$156$	−38.0845	−3.04920
$157$	−19.5887	−1.56335	−0.781676	−	0.623685i	$-0.785635\pi$
$157$	−19.5887	−1.56335	−0.781676	+	0.623685i	$0.785635\pi$
$158$	31.6560	2.51841
$159$	−31.0839	−2.46511
$160$	−16.5629	−1.30941
$161$	−0.0720903	−0.00568151
$162$	23.0376	1.81001
$163$	−8.72800	−0.683629	−0.341815	−	0.939767i	$-0.611042\pi$
$163$	−8.72800	−0.683629	−0.341815	+	0.939767i	$0.611042\pi$
$164$	12.0597	0.941704
$165$	−1.61343	−0.125605
$166$	−5.38143	−0.417680
$167$	−0.00954901	−0.000738924 0	−0.000369462	−	1.00000i	$-0.500118\pi$
$167$	−0.00954901	−0.000738924 0	−0.000369462		1.00000i	$0.500118\pi$
$168$	−0.525638	−0.0405539
$169$	−2.02755	−0.155966
$170$	−37.6792	−2.88986
$171$	17.8378	1.36409
$172$	20.8527	1.59001
$173$	−8.48065	−0.644772	−0.322386	−	0.946608i	$-0.604485\pi$
$173$	−8.48065	−0.644772	−0.322386	+	0.946608i	$0.604485\pi$
$174$	−23.1782	−1.75714
$175$	0.0302354	0.00228558
$176$	2.80519	0.211449
$177$	−21.5938	−1.62309
$178$	−32.0061	−2.39896
$179$	−7.12289	−0.532390	−0.266195	−	0.963919i	$-0.585766\pi$
$179$	−7.12289	−0.532390	−0.266195	+	0.963919i	$0.585766\pi$
$180$	28.4399	2.11979
$181$	−13.5897	−1.01012	−0.505059	−	0.863085i	$-0.668529\pi$
$181$	−13.5897	−1.01012	−0.505059	+	0.863085i	$0.668529\pi$
$182$	0.264354	0.0195953
$183$	13.1086	0.969012
$184$	−16.1921	−1.19370
$185$	−2.00515	−0.147422
$186$	28.2319	2.07007
$187$	2.38213	0.174198
$188$	54.1311	3.94792
$189$	0.00220455	0.000160358 0
$190$	−30.5242	−2.21446
$191$	−26.1632	−1.89310	−0.946551	−	0.322555i	$-0.895458\pi$
$191$	−26.1632	−1.89310	−0.946551	+	0.322555i	$0.895458\pi$
$192$	−10.3923	−0.750003
$193$	−5.62381	−0.404811	−0.202405	−	0.979302i	$-0.564876\pi$
$193$	−5.62381	−0.404811	−0.202405	+	0.979302i	$0.564876\pi$
$194$	−7.27045	−0.521988
$195$	−16.3089	−1.16790
$196$	−32.7725	−2.34089
$197$	15.0610	1.07305	0.536525	−	0.843885i	$-0.319737\pi$
$197$	15.0610	1.07305	0.536525	+	0.843885i	$0.319737\pi$
$198$	−2.56599	−0.182357
$199$	−21.2591	−1.50702	−0.753510	−	0.657437i	$-0.771641\pi$
$199$	−21.2591	−1.50702	−0.753510	+	0.657437i	$0.771641\pi$
$200$	6.79113	0.480205
$201$	−31.8823	−2.24880
$202$	27.2768	1.91919
$203$	0.112734	0.00791239
$204$	−83.5764	−5.85152
$205$	5.16432	0.360691
$206$	−8.82000	−0.614518
$207$	7.07327	0.491626
$208$	28.3554	1.96610
$209$	1.92978	0.133486
$210$	−0.392923	−0.0271143
$211$	17.0506	1.17381	0.586907	−	0.809654i	$-0.300345\pi$
$211$	17.0506	1.17381	0.586907	+	0.809654i	$0.300345\pi$
$212$	59.2762	4.07111
$213$	−19.0991	−1.30865
$214$	−26.4858	−1.81053
$215$	8.92975	0.609004
$216$	0.495160	0.0336914
$217$	−0.137314	−0.00932151
$218$	−2.58504	−0.175081
$219$	−9.29603	−0.628168
$220$	3.07677	0.207436
$221$	24.0790	1.61973
$222$	−6.34735	−0.426006
$223$	−17.0895	−1.14440	−0.572199	−	0.820115i	$-0.693910\pi$
$223$	−17.0895	−1.14440	−0.572199	+	0.820115i	$0.693910\pi$
$224$	0.255010	0.0170386
$225$	−2.96660	−0.197773
$226$	18.0385	1.19990
$227$	−25.7875	−1.71157	−0.855787	−	0.517328i	$-0.826927\pi$
$227$	−25.7875	−1.71157	−0.855787	+	0.517328i	$0.826927\pi$
$228$	−67.7060	−4.48394
$229$	−4.08771	−0.270124	−0.135062	−	0.990837i	$-0.543123\pi$
$229$	−4.08771	−0.270124	−0.135062	+	0.990837i	$0.543123\pi$
$230$	−12.1038	−0.798103
$231$	0.0248411	0.00163442
$232$	25.3210	1.66241
$233$	−13.7927	−0.903592	−0.451796	−	0.892121i	$-0.649217\pi$
$233$	−13.7927	−0.903592	−0.451796	+	0.892121i	$0.649217\pi$
$234$	−25.9376	−1.69559
$235$	23.1805	1.51213
$236$	41.1789	2.68052
$237$	30.0687	1.95317
$238$	0.580126	0.0376040
$239$	21.3738	1.38256	0.691279	−	0.722588i	$-0.257048\pi$
$239$	21.3738	1.38256	0.691279	+	0.722588i	$0.257048\pi$
$240$	−42.1461	−2.72052
$241$	−6.56472	−0.422871	−0.211436	−	0.977392i	$-0.567814\pi$
$241$	−6.56472	−0.422871	−0.211436	+	0.977392i	$0.567814\pi$
$242$	28.1578	1.81005
$243$	22.0967	1.41750
$244$	−24.9977	−1.60031
$245$	−14.0341	−0.896608
$246$	16.3478	1.04230
$247$	19.5067	1.24118
$248$	−30.8420	−1.95847
$249$	−5.11160	−0.323934
$250$	30.9934	1.96020
$251$	16.7212	1.05543	0.527715	−	0.849421i	$-0.323049\pi$
$251$	16.7212	1.05543	0.527715	+	0.849421i	$0.323049\pi$
$252$	−0.437874	−0.0275835
$253$	0.765221	0.0481090
$254$	7.60151	0.476961
$255$	−35.7899	−2.24125
$256$	−22.8878	−1.43048
$257$	−1.95392	−0.121882	−0.0609412	−	0.998141i	$-0.519410\pi$
$257$	−1.95392	−0.121882	−0.0609412	+	0.998141i	$0.519410\pi$
$258$	28.2673	1.75985
$259$	0.0308722	0.00191831
$260$	31.1006	1.92878
$261$	−11.0611	−0.684666
$262$	51.8096	3.20081
$263$	26.0118	1.60396	0.801978	−	0.597354i	$-0.203781\pi$
$263$	26.0118	1.60396	0.801978	+	0.597354i	$0.203781\pi$
$264$	5.57952	0.343396
$265$	25.3838	1.55932
$266$	0.469965	0.0288154
$267$	−30.4013	−1.86053
$268$	60.7987	3.71387
$269$	1.37655	0.0839296	0.0419648	−	0.999119i	$-0.486638\pi$
$269$	1.37655	0.0839296	0.0419648	+	0.999119i	$0.486638\pi$
$270$	0.370140	0.0225260
$271$	20.5145	1.24617	0.623083	−	0.782156i	$-0.285880\pi$
$271$	20.5145	1.24617	0.623083	+	0.782156i	$0.285880\pi$
$272$	62.2260	3.77301
$273$	0.251099	0.0151972
$274$	15.6479	0.945326
$275$	−0.320941	−0.0193535
$276$	−26.8476	−1.61603
$277$	5.51540	0.331388	0.165694	−	0.986177i	$-0.447014\pi$
$277$	5.51540	0.331388	0.165694	+	0.986177i	$0.447014\pi$
$278$	−29.1002	−1.74532
$279$	13.4728	0.806598
$280$	0.429248	0.0256525
$281$	−15.8991	−0.948461	−0.474231	−	0.880401i	$-0.657274\pi$
$281$	−15.8991	−0.948461	−0.474231	+	0.880401i	$0.657274\pi$
$282$	73.3785	4.36963
$283$	−30.0789	−1.78800	−0.894001	−	0.448064i	$-0.852114\pi$
$283$	−30.0789	−1.78800	−0.894001	+	0.448064i	$0.852114\pi$
$284$	36.4214	2.16122
$285$	−28.9937	−1.71744
$286$	−2.80605	−0.165925
$287$	−0.0795122	−0.00469346
$288$	−25.0207	−1.47436
$289$	35.8415	2.10832
$290$	18.9279	1.11148
$291$	−6.90589	−0.404831
$292$	17.7273	1.03741
$293$	−0.418065	−0.0244236	−0.0122118	−	0.999925i	$-0.503887\pi$
$293$	−0.418065	−0.0244236	−0.0122118	+	0.999925i	$0.503887\pi$
$294$	−44.4254	−2.59094
$295$	17.6340	1.02669
$296$	6.93416	0.403040
$297$	−0.0234008	−0.00135785
$298$	−4.85421	−0.281197
$299$	7.73501	0.447327
$300$	11.2602	0.650105
$301$	−0.137487	−0.00792460
$302$	−60.7342	−3.49486
$303$	25.9091	1.48844
$304$	50.4099	2.89121
$305$	−10.7047	−0.612952
$306$	−56.9201	−3.25390
$307$	−28.4652	−1.62459	−0.812296	−	0.583245i	$-0.801783\pi$
$307$	−28.4652	−1.62459	−0.812296	+	0.583245i	$0.801783\pi$
$308$	−0.0473713	−0.00269923
$309$	−8.37774	−0.476593
$310$	−23.0548	−1.30943
$311$	−10.4077	−0.590166	−0.295083	−	0.955472i	$-0.595347\pi$
$311$	−10.4077	−0.590166	−0.295083	+	0.955472i	$0.595347\pi$
$312$	56.3989	3.19296
$313$	2.02786	0.114621	0.0573107	−	0.998356i	$-0.481747\pi$
$313$	2.02786	0.114621	0.0573107	+	0.998356i	$0.481747\pi$
$314$	50.6376	2.85765
$315$	−0.187511	−0.0105650
$316$	−57.3402	−3.22564
$317$	33.7364	1.89482	0.947411	−	0.320018i	$-0.103689\pi$
$317$	33.7364	1.89482	0.947411	+	0.320018i	$0.103689\pi$
$318$	80.3531	4.50598
$319$	−1.19664	−0.0669992
$320$	8.48662	0.474417
$321$	−25.1578	−1.40417
$322$	0.186356	0.0103852
$323$	42.8074	2.38187
$324$	−41.7293	−2.31829
$325$	−3.24414	−0.179953
$326$	22.5622	1.24960
$327$	−2.45542	−0.135785
$328$	−17.8591	−0.986104
$329$	−0.356898	−0.0196764
$330$	4.17078	0.229594
$331$	26.9124	1.47924	0.739618	−	0.673026i	$-0.235006\pi$
$331$	26.9124	1.47924	0.739618	+	0.673026i	$0.235006\pi$
$332$	9.74768	0.534974
$333$	−3.02908	−0.165993
$334$	0.0246845	0.00135068
$335$	26.0358	1.42249
$336$	0.648901	0.0354004
$337$	−18.8112	−1.02471	−0.512355	−	0.858774i	$-0.671227\pi$
$337$	−18.8112	−1.02471	−0.512355	+	0.858774i	$0.671227\pi$
$338$	5.24130	0.285089
$339$	17.1340	0.930592
$340$	68.2503	3.70139
$341$	1.45756	0.0789312
$342$	−46.1115	−2.49342
$343$	0.432182	0.0233356
$344$	−30.8806	−1.66497
$345$	−11.4969	−0.618974
$346$	21.9228	1.17858
$347$	−12.7204	−0.682869	−0.341434	−	0.939906i	$-0.610913\pi$
$347$	−12.7204	−0.682869	−0.341434	+	0.939906i	$0.610913\pi$
$348$	41.9840	2.25058
$349$	−15.2989	−0.818932	−0.409466	−	0.912325i	$-0.634285\pi$
$349$	−15.2989	−0.818932	−0.409466	+	0.912325i	$0.634285\pi$
$350$	−0.0781597	−0.00417781
$351$	−0.236540	−0.0126256
$352$	−2.70686	−0.144276
$353$	15.6866	0.834916	0.417458	−	0.908696i	$-0.362921\pi$
$353$	15.6866	0.834916	0.417458	+	0.908696i	$0.362921\pi$
$354$	55.8209	2.96685
$355$	15.5967	0.827789
$356$	57.9744	3.07264
$357$	0.551037	0.0291640
$358$	18.4129	0.973154
$359$	−1.35820	−0.0716831	−0.0358415	−	0.999357i	$-0.511411\pi$
$359$	−1.35820	−0.0716831	−0.0358415	+	0.999357i	$0.511411\pi$
$360$	−42.1164	−2.21973
$361$	15.6787	0.825192
$362$	35.1300	1.84639
$363$	26.7459	1.40380
$364$	−0.478840	−0.0250980
$365$	7.59135	0.397349
$366$	−33.8861	−1.77126
$367$	−28.1628	−1.47008	−0.735042	−	0.678022i	$-0.762838\pi$
$367$	−28.1628	−1.47008	−0.735042	+	0.678022i	$0.762838\pi$
$368$	19.9891	1.04201
$369$	7.80148	0.406129
$370$	5.18339	0.269472
$371$	−0.390821	−0.0202904
$372$	−51.1381	−2.65138
$373$	−19.3856	−1.00375	−0.501874	−	0.864941i	$-0.667356\pi$
$373$	−19.3856	−1.00375	−0.501874	+	0.864941i	$0.667356\pi$
$374$	−6.15789	−0.318417
$375$	29.4393	1.52024
$376$	−80.1623	−4.13406
$377$	−12.0959	−0.622972
$378$	−0.00569885	−0.000293117 0
$379$	−1.39076	−0.0714386	−0.0357193	−	0.999362i	$-0.511372\pi$
$379$	−1.39076	−0.0714386	−0.0357193	+	0.999362i	$0.511372\pi$
$380$	55.2902	2.83633
$381$	7.22035	0.369910
$382$	67.6328	3.46040
$383$	−29.3118	−1.49776	−0.748882	−	0.662704i	$-0.769409\pi$
$383$	−29.3118	−1.49776	−0.748882	+	0.662704i	$0.769409\pi$
$384$	−13.6997	−0.699112
$385$	−0.0202858	−0.00103386
$386$	14.5378	0.739952
$387$	13.4897	0.685722
$388$	13.1694	0.668573
$389$	−8.74937	−0.443610	−0.221805	−	0.975091i	$-0.571195\pi$
$389$	−8.74937	−0.443610	−0.221805	+	0.975091i	$0.571195\pi$
$390$	42.1591	2.13481
$391$	16.9745	0.858437
$392$	48.5325	2.45126
$393$	49.2117	2.48240
$394$	−38.9332	−1.96142
$395$	−24.5547	−1.23548
$396$	4.64792	0.233567
$397$	−11.7655	−0.590496	−0.295248	−	0.955421i	$-0.595402\pi$
$397$	−11.7655	−0.590496	−0.295248	+	0.955421i	$0.595402\pi$
$398$	54.9556	2.75468
$399$	0.446400	0.0223480
$400$	−8.38365	−0.419182
$401$	20.4862	1.02303	0.511517	−	0.859273i	$-0.329084\pi$
$401$	20.4862	1.02303	0.511517	+	0.859273i	$0.329084\pi$
$402$	82.4169	4.11058
$403$	14.7333	0.733918
$404$	−49.4080	−2.45814
$405$	−17.8697	−0.887953
$406$	−0.291422	−0.0144630
$407$	−0.327701	−0.0162435
$408$	123.768	6.12741
$409$	11.1729	0.552466	0.276233	−	0.961091i	$-0.410914\pi$
$409$	11.1729	0.552466	0.276233	+	0.961091i	$0.410914\pi$
$410$	−13.3499	−0.659307
$411$	14.8633	0.733153
$412$	15.9761	0.787088
$413$	−0.271501	−0.0133597
$414$	−18.2847	−0.898642
$415$	4.17425	0.204906
$416$	−27.3615	−1.34151
$417$	−27.6411	−1.35359
$418$	−4.98856	−0.243999
$419$	10.6117	0.518415	0.259208	−	0.965822i	$-0.416539\pi$
$419$	10.6117	0.518415	0.259208	+	0.965822i	$0.416539\pi$
$420$	0.711723	0.0347285
$421$	−17.6971	−0.862504	−0.431252	−	0.902231i	$-0.641928\pi$
$421$	−17.6971	−0.862504	−0.431252	+	0.902231i	$0.641928\pi$
$422$	−44.0766	−2.14561
$423$	35.0177	1.70262
$424$	−87.7816	−4.26305
$425$	−7.11928	−0.345336
$426$	49.3718	2.39207
$427$	0.164815	0.00797597
$428$	47.9752	2.31897
$429$	−2.66535	−0.128684
$430$	−23.0837	−1.11320
$431$	24.0762	1.15971	0.579855	−	0.814720i	$-0.303109\pi$
$431$	24.0762	1.15971	0.579855	+	0.814720i	$0.303109\pi$
$432$	−0.611276	−0.0294100
$433$	−16.0509	−0.771358	−0.385679	−	0.922633i	$-0.626033\pi$
$433$	−16.0509	−0.771358	−0.385679	+	0.922633i	$0.626033\pi$
$434$	0.354963	0.0170388
$435$	17.9788	0.862017
$436$	4.68242	0.224247
$437$	13.7512	0.657809
$438$	24.0306	1.14823
$439$	−25.0571	−1.19591	−0.597956	−	0.801529i	$-0.704020\pi$
$439$	−25.0571	−1.19591	−0.597956	+	0.801529i	$0.704020\pi$
$440$	−4.55636	−0.217216
$441$	−21.2007	−1.00956
$442$	−62.2452	−2.96070
$443$	−23.1288	−1.09888	−0.549442	−	0.835532i	$-0.685160\pi$
$443$	−23.1288	−1.09888	−0.549442	+	0.835532i	$0.685160\pi$
$444$	11.4973	0.545638
$445$	24.8264	1.17688
$446$	44.1770	2.09184
$447$	−4.61081	−0.218084
$448$	−0.130664	−0.00617329
$449$	18.1841	0.858160	0.429080	−	0.903267i	$-0.358838\pi$
$449$	18.1841	0.858160	0.429080	+	0.903267i	$0.358838\pi$
$450$	7.66878	0.361510
$451$	0.844002	0.0397425
$452$	−32.6741	−1.53686
$453$	−57.6889	−2.71046
$454$	66.6616	3.12858
$455$	−0.205053	−0.00961304
$456$	100.265	4.69535
$457$	36.4645	1.70574	0.852869	−	0.522126i	$-0.174861\pi$
$457$	36.4645	1.70574	0.852869	+	0.522126i	$0.174861\pi$
$458$	10.5669	0.493759
$459$	−0.519087	−0.0242289
$460$	21.9243	1.02223
$461$	20.6072	0.959774	0.479887	−	0.877330i	$-0.340678\pi$
$461$	20.6072	0.959774	0.479887	+	0.877330i	$0.340678\pi$
$462$	−0.0642152	−0.00298756
$463$	−16.7322	−0.777613	−0.388806	−	0.921319i	$-0.627113\pi$
$463$	−16.7322	−0.777613	−0.388806	+	0.921319i	$0.627113\pi$
$464$	−31.2588	−1.45115
$465$	−21.8988	−1.01553
$466$	35.6547	1.65167
$467$	36.2810	1.67889	0.839443	−	0.543447i	$-0.182881\pi$
$467$	36.2810	1.67889	0.839443	+	0.543447i	$0.182881\pi$
$468$	46.9822	2.17175
$469$	−0.400859	−0.0185100
$470$	−59.9226	−2.76402
$471$	48.0986	2.21626
$472$	−60.9815	−2.80690
$473$	1.45939	0.0671026
$474$	−77.7286	−3.57019
$475$	−5.76739	−0.264626
$476$	−1.05081	−0.0481640
$477$	38.3461	1.75575
$478$	−55.2521	−2.52717
$479$	−16.9936	−0.776457	−0.388228	−	0.921563i	$-0.626913\pi$
$479$	−16.9936	−0.776457	−0.388228	+	0.921563i	$0.626913\pi$
$480$	40.6688	1.85627
$481$	−3.31247	−0.151036
$482$	16.9701	0.772965
$483$	0.177012	0.00805432
$484$	−51.0038	−2.31835
$485$	5.63951	0.256077
$486$	−57.1208	−2.59105
$487$	36.6218	1.65949	0.829746	−	0.558141i	$-0.188485\pi$
$487$	36.6218	1.65949	0.829746	+	0.558141i	$0.188485\pi$
$488$	37.0189	1.67576
$489$	21.4309	0.969138
$490$	36.2788	1.63891
$491$	16.5228	0.745663	0.372831	−	0.927899i	$-0.378387\pi$
$491$	16.5228	0.745663	0.372831	+	0.927899i	$0.378387\pi$
$492$	−29.6116	−1.33499
$493$	−26.5445	−1.19551
$494$	−50.4254	−2.26875
$495$	1.99038	0.0894608
$496$	38.0744	1.70959
$497$	−0.240135	−0.0107715
$498$	13.2137	0.592119
$499$	2.21458	0.0991382	0.0495691	−	0.998771i	$-0.484215\pi$
$499$	2.21458	0.0991382	0.0495691	+	0.998771i	$0.484215\pi$
$500$	−56.1401	−2.51066
$501$	0.0234468	0.00104753
$502$	−43.2248	−1.92922
$503$	16.1553	0.720328	0.360164	−	0.932889i	$-0.382721\pi$
$503$	16.1553	0.720328	0.360164	+	0.932889i	$0.382721\pi$
$504$	0.648444	0.0288840
$505$	−21.1580	−0.941517
$506$	−1.97812	−0.0879383
$507$	4.97849	0.221103
$508$	−13.7690	−0.610902
$509$	22.3220	0.989404	0.494702	−	0.869063i	$-0.335277\pi$
$509$	22.3220	0.989404	0.494702	+	0.869063i	$0.335277\pi$
$510$	92.5181	4.09677
$511$	−0.116880	−0.00517046
$512$	48.0069	2.12163
$513$	−0.420517	−0.0185663
$514$	5.05096	0.222788
$515$	6.84145	0.301470
$516$	−51.2022	−2.25405
$517$	3.78838	0.166613
$518$	−0.0798059	−0.00350647
$519$	20.8235	0.914052
$520$	−46.0566	−2.01972
$521$	−8.68469	−0.380483	−0.190242	−	0.981737i	$-0.560927\pi$
$521$	−8.68469	−0.380483	−0.190242	+	0.981737i	$0.560927\pi$
$522$	28.5934	1.25150
$523$	25.6892	1.12331	0.561654	−	0.827372i	$-0.310165\pi$
$523$	25.6892	1.12331	0.561654	+	0.827372i	$0.310165\pi$
$524$	−93.8455	−4.09966
$525$	−0.0742406	−0.00324013
$526$	−67.2415	−2.93187
$527$	32.3322	1.40841
$528$	−6.88792	−0.299758
$529$	−17.5472	−0.762922
$530$	−65.6181	−2.85027
$531$	26.6388	1.15603
$532$	−0.851274	−0.0369074
$533$	8.53135	0.369534
$534$	78.5884	3.40085
$535$	20.5444	0.888211
$536$	−90.0363	−3.88898
$537$	17.4897	0.754735
$538$	−3.55843	−0.153415
$539$	−2.29359	−0.0987921
$540$	−0.670455	−0.0288518
$541$	−17.9178	−0.770344	−0.385172	−	0.922845i	$-0.625858\pi$
$541$	−17.9178	−0.770344	−0.385172	+	0.922845i	$0.625858\pi$
$542$	−53.0307	−2.27786
$543$	33.3685	1.43198
$544$	−60.0449	−2.57441
$545$	2.00515	0.0858912
$546$	−0.649101	−0.0277789
$547$	−2.58936	−0.110713	−0.0553565	−	0.998467i	$-0.517630\pi$
$547$	−2.58936	−0.110713	−0.0553565	+	0.998467i	$0.517630\pi$
$548$	−28.3439	−1.21079
$549$	−16.1711	−0.690167
$550$	0.829646	0.0353762
$551$	−21.5040	−0.916100
$552$	39.7584	1.69223
$553$	0.378056	0.0160766
$554$	−14.2575	−0.605743
$555$	4.92348	0.208990
$556$	52.7109	2.23544
$557$	1.89386	0.0802452	0.0401226	−	0.999195i	$-0.487225\pi$
$557$	1.89386	0.0802452	0.0401226	+	0.999195i	$0.487225\pi$
$558$	−34.8278	−1.47438
$559$	14.7518	0.623934
$560$	−0.529907	−0.0223926
$561$	−5.84912	−0.246950
$562$	41.0998	1.73369
$563$	41.5766	1.75225	0.876123	−	0.482088i	$-0.160122\pi$
$563$	41.5766	1.75225	0.876123	+	0.482088i	$0.160122\pi$
$564$	−132.915	−5.59671
$565$	−13.9920	−0.588649
$566$	77.7550	3.26829
$567$	0.275130	0.0115544
$568$	−53.9362	−2.26311
$569$	13.6832	0.573630	0.286815	−	0.957986i	$-0.407404\pi$
$569$	13.6832	0.573630	0.286815	+	0.957986i	$0.407404\pi$
$570$	74.9498	3.13930
$571$	−39.5155	−1.65367	−0.826835	−	0.562444i	$-0.809861\pi$
$571$	−39.5155	−1.65367	−0.826835	+	0.562444i	$0.809861\pi$
$572$	5.08276	0.212521
$573$	64.2416	2.68373
$574$	0.205542	0.00857916
$575$	−2.28695	−0.0953726
$576$	12.8203	0.534180
$577$	−14.7448	−0.613833	−0.306916	−	0.951736i	$-0.599297\pi$
$577$	−14.7448	−0.613833	−0.306916	+	0.951736i	$0.599297\pi$
$578$	−92.6516	−3.85380
$579$	13.8088	0.573874
$580$	−34.2851	−1.42361
$581$	−0.0642686	−0.00266631
$582$	17.8520	0.739989
$583$	4.14847	0.171812
$584$	−26.2522	−1.08632
$585$	20.1192	0.831825
$586$	1.08071	0.0446439
$587$	−39.7638	−1.64123	−0.820614	−	0.571483i	$-0.806368\pi$
$587$	−39.7638	−1.64123	−0.820614	+	0.571483i	$0.806368\pi$
$588$	80.4702	3.31853
$589$	26.1926	1.07925
$590$	−45.5846	−1.87669
$591$	−36.9810	−1.52119
$592$	−8.56022	−0.351823
$593$	16.1017	0.661217	0.330609	−	0.943768i	$-0.392746\pi$
$593$	16.1017	0.661217	0.330609	+	0.943768i	$0.392746\pi$
$594$	0.0604918	0.00248201
$595$	−0.449989	−0.0184478
$596$	8.79270	0.360163
$597$	52.2001	2.13641
$598$	−19.9953	−0.817668
$599$	12.3786	0.505777	0.252889	−	0.967495i	$-0.418619\pi$
$599$	12.3786	0.505777	0.252889	+	0.967495i	$0.418619\pi$
$600$	−16.6751	−0.680757
$601$	16.3073	0.665187	0.332593	−	0.943070i	$-0.392076\pi$
$601$	16.3073	0.665187	0.332593	+	0.943070i	$0.392076\pi$
$602$	0.355408	0.0144854
$603$	39.3310	1.60168
$604$	110.011	4.47629
$605$	−21.8413	−0.887976
$606$	−66.9761	−2.72072
$607$	17.7017	0.718490	0.359245	−	0.933243i	$-0.383034\pi$
$607$	17.7017	0.718490	0.359245	+	0.933243i	$0.383034\pi$
$608$	−48.6430	−1.97273
$609$	−0.276810	−0.0112169
$610$	27.6722	1.12041
$611$	38.2938	1.54920
$612$	103.102	4.16767
$613$	−25.1349	−1.01519	−0.507595	−	0.861596i	$-0.669465\pi$
$613$	−25.1349	−1.01519	−0.507595	+	0.861596i	$0.669465\pi$
$614$	73.5835	2.96959
$615$	−12.6806	−0.511329
$616$	0.0701518	0.00282650
$617$	−3.00461	−0.120961	−0.0604805	−	0.998169i	$-0.519263\pi$
$617$	−3.00461	−0.120961	−0.0604805	+	0.998169i	$0.519263\pi$
$618$	21.6568	0.871164
$619$	−5.53822	−0.222600	−0.111300	−	0.993787i	$-0.535501\pi$
$619$	−5.53822	−0.222600	−0.111300	+	0.993787i	$0.535501\pi$
$620$	41.7605	1.67714
$621$	−0.166748	−0.00669138
$622$	26.9043	1.07876
$623$	−0.382238	−0.0153140
$624$	−69.6245	−2.78721
$625$	−19.1440	−0.765758
$626$	−5.24209	−0.209516
$627$	−4.73843	−0.189235
$628$	−91.7227	−3.66013
$629$	−7.26922	−0.289843
$630$	0.484722	0.0193118
$631$	−12.9287	−0.514682	−0.257341	−	0.966321i	$-0.582846\pi$
$631$	−12.9287	−0.514682	−0.257341	+	0.966321i	$0.582846\pi$
$632$	84.9146	3.37772
$633$	−41.8665	−1.66404
$634$	−87.2098	−3.46354
$635$	−5.89630	−0.233988
$636$	−145.548	−5.77135
$637$	−23.1841	−0.918588
$638$	3.09337	0.122468
$639$	23.5612	0.932068
$640$	11.1875	0.442225
$641$	−34.0921	−1.34656	−0.673278	−	0.739390i	$-0.735114\pi$
$641$	−34.0921	−1.34656	−0.673278	+	0.739390i	$0.735114\pi$
$642$	65.0338	2.56668
$643$	16.4979	0.650615	0.325308	−	0.945608i	$-0.394532\pi$
$643$	16.4979	0.650615	0.325308	+	0.945608i	$0.394532\pi$
$644$	−0.337557	−0.0133016
$645$	−21.9263	−0.863347
$646$	−110.659	−4.35381
$647$	−27.9559	−1.09906	−0.549530	−	0.835474i	$-0.685193\pi$
$647$	−27.9559	−1.09906	−0.549530	+	0.835474i	$0.685193\pi$
$648$	61.7966	2.42760
$649$	2.88192	0.113125
$650$	8.38623	0.328935
$651$	0.337164	0.0132145
$652$	−40.8681	−1.60052
$653$	14.5353	0.568810	0.284405	−	0.958704i	$-0.408204\pi$
$653$	14.5353	0.568810	0.284405	+	0.958704i	$0.408204\pi$
$654$	6.34735	0.248201
$655$	−40.1874	−1.57025
$656$	22.0471	0.860793
$657$	11.4679	0.447405
$658$	0.922595	0.0359665
$659$	−33.8466	−1.31848	−0.659238	−	0.751934i	$-0.729121\pi$
$659$	−33.8466	−1.31848	−0.659238	+	0.751934i	$0.729121\pi$
$660$	−7.55475	−0.294068
$661$	32.5014	1.26416	0.632079	−	0.774904i	$-0.282202\pi$
$661$	32.5014	1.26416	0.632079	+	0.774904i	$0.282202\pi$
$662$	−69.5695	−2.70389
$663$	−59.1241	−2.29619
$664$	−14.4353	−0.560197
$665$	−0.364541	−0.0141363
$666$	7.83029	0.303418
$667$	−8.52701	−0.330167
$668$	−0.0447125	−0.00172998
$669$	41.9619	1.62234
$670$	−67.3035	−2.60016
$671$	−1.74947	−0.0675376
$672$	−0.626156	−0.0241545
$673$	−0.929324	−0.0358228	−0.0179114	−	0.999840i	$-0.505702\pi$
$673$	−0.929324	−0.0358228	−0.0179114	+	0.999840i	$0.505702\pi$
$674$	48.6276	1.87306
$675$	0.0699360	0.00269184
$676$	−9.49385	−0.365148
$677$	11.0012	0.422811	0.211406	−	0.977398i	$-0.432196\pi$
$677$	11.0012	0.422811	0.211406	+	0.977398i	$0.432196\pi$
$678$	−44.2921	−1.70103
$679$	−0.0868285	−0.00333217
$680$	−101.071	−3.87591
$681$	63.3190	2.42639
$682$	−3.76784	−0.144278
$683$	−26.2714	−1.00525	−0.502623	−	0.864506i	$-0.667632\pi$
$683$	−26.2714	−1.00525	−0.502623	+	0.864506i	$0.667632\pi$
$684$	83.5242	3.19363
$685$	−12.1377	−0.463758
$686$	−1.11721	−0.0426551
$687$	10.0370	0.382937
$688$	38.1221	1.45339
$689$	41.9336	1.59754
$690$	29.7200	1.13142
$691$	−15.1800	−0.577476	−0.288738	−	0.957408i	$-0.593236\pi$
$691$	−15.1800	−0.577476	−0.288738	+	0.957408i	$0.593236\pi$
$692$	−39.7100	−1.50955
$693$	−0.0306448	−0.00116410
$694$	32.8828	1.24821
$695$	22.5723	0.856218
$696$	−62.1737	−2.35669
$697$	18.7220	0.709148
$698$	39.5483	1.49692
$699$	33.8669	1.28097
$700$	0.141575	0.00535103
$701$	4.54006	0.171476	0.0857378	−	0.996318i	$-0.472675\pi$
$701$	4.54006	0.171476	0.0857378	+	0.996318i	$0.472675\pi$
$702$	0.611464	0.0230782
$703$	−5.88886	−0.222103
$704$	1.38697	0.0522732
$705$	−56.9179	−2.14365
$706$	−40.5506	−1.52614
$707$	0.325758	0.0122514
$708$	−101.111	−3.80000
$709$	−4.82477	−0.181198	−0.0905991	−	0.995887i	$-0.528878\pi$
$709$	−4.82477	−0.181198	−0.0905991	+	0.995887i	$0.528878\pi$
$710$	−40.3181	−1.51311
$711$	−37.0936	−1.39112
$712$	−85.8538	−3.21751
$713$	10.3862	0.388967
$714$	−1.42445	−0.0533088
$715$	2.17659	0.0813998
$716$	−33.3523	−1.24644
$717$	−52.4817	−1.95996
$718$	3.51100	0.131029
$719$	52.7524	1.96733	0.983666	−	0.180002i	$-0.0576106\pi$
$719$	52.7524	1.96733	0.983666	+	0.180002i	$0.0576106\pi$
$720$	51.9927	1.93765
$721$	−0.105334	−0.00392285
$722$	−40.5299	−1.50837
$723$	16.1191	0.599478
$724$	−63.6329	−2.36490
$725$	3.57632	0.132821
$726$	−69.1392	−2.56600
$727$	28.0042	1.03862	0.519308	−	0.854587i	$-0.326190\pi$
$727$	28.0042	1.03862	0.519308	+	0.854587i	$0.326190\pi$
$728$	0.709109	0.0262813
$729$	−27.5209	−1.01929
$730$	−19.6239	−0.726314
$731$	32.3728	1.19735
$732$	61.3798	2.26866
$733$	2.25332	0.0832281	0.0416141	−	0.999134i	$-0.486750\pi$
$733$	2.25332	0.0832281	0.0416141	+	0.999134i	$0.486750\pi$
$734$	72.8018	2.68716
$735$	34.4597	1.27106
$736$	−19.2885	−0.710983
$737$	4.25502	0.156736
$738$	−20.1671	−0.742362
$739$	27.0807	0.996181	0.498091	−	0.867125i	$-0.334035\pi$
$739$	27.0807	0.996181	0.498091	+	0.867125i	$0.334035\pi$
$740$	−9.38895	−0.345145
$741$	−47.8970	−1.75954
$742$	1.01029	0.0370888
$743$	27.5506	1.01073	0.505366	−	0.862905i	$-0.331357\pi$
$743$	27.5506	1.01073	0.505366	+	0.862905i	$0.331357\pi$
$744$	75.7299	2.77639
$745$	3.76529	0.137950
$746$	50.1125	1.83475
$747$	6.30583	0.230718
$748$	11.1541	0.407835
$749$	−0.316311	−0.0115578
$750$	−76.1018	−2.77885
$751$	11.5720	0.422268	0.211134	−	0.977457i	$-0.432284\pi$
$751$	11.5720	0.422268	0.211134	+	0.977457i	$0.432284\pi$
$752$	98.9604	3.60871
$753$	−41.0575	−1.49622
$754$	31.2685	1.13873
$755$	47.1100	1.71451
$756$	0.0103226	0.000375431 0
$757$	34.2111	1.24342	0.621711	−	0.783247i	$-0.286438\pi$
$757$	34.2111	1.24342	0.621711	+	0.783247i	$0.286438\pi$
$758$	3.59517	0.130582
$759$	−1.87894	−0.0682011
$760$	−81.8788	−2.97006
$761$	−15.5053	−0.562067	−0.281033	−	0.959698i	$-0.590677\pi$
$761$	−15.5053	−0.562067	−0.281033	+	0.959698i	$0.590677\pi$
$762$	−18.6649	−0.676158
$763$	−0.0308722	−0.00111765
$764$	−122.507	−4.43215
$765$	44.1515	1.59630
$766$	75.7721	2.73776
$767$	29.1310	1.05186
$768$	56.1990	2.02791
$769$	−22.2619	−0.802786	−0.401393	−	0.915906i	$-0.631474\pi$
$769$	−22.2619	−0.802786	−0.401393	+	0.915906i	$0.631474\pi$
$770$	0.0524396	0.00188979
$771$	4.79770	0.172785
$772$	−26.3330	−0.947747
$773$	50.4206	1.81350	0.906751	−	0.421667i	$-0.138555\pi$
$773$	50.4206	1.81350	0.906751	+	0.421667i	$0.138555\pi$
$774$	−34.8715	−1.25343
$775$	−4.35609	−0.156475
$776$	−19.5024	−0.700095
$777$	−0.0758042	−0.00271946
$778$	22.6174	0.810875
$779$	15.1669	0.543411
$780$	−76.3650	−2.73431
$781$	2.54897	0.0912092
$782$	−43.8797	−1.56913
$783$	0.260759	0.00931878
$784$	−59.9134	−2.13976
$785$	−39.2784	−1.40190
$786$	−127.214	−4.53758
$787$	2.47860	0.0883525	0.0441762	−	0.999024i	$-0.485934\pi$
$787$	2.47860	0.0883525	0.0441762	+	0.999024i	$0.485934\pi$
$788$	70.5217	2.51223
$789$	−63.8698	−2.27383
$790$	63.4749	2.25834
$791$	0.215428	0.00765972
$792$	−6.88307	−0.244579
$793$	−17.6840	−0.627978
$794$	30.4144	1.07937
$795$	−62.3279	−2.21054
$796$	−99.5441	−3.52825
$797$	44.2765	1.56836	0.784178	−	0.620536i	$-0.213085\pi$
$797$	44.2765	1.56836	0.784178	+	0.620536i	$0.213085\pi$
$798$	−1.15396	−0.0408498
$799$	84.0357	2.97297
$800$	8.08979	0.286017
$801$	37.5040	1.32514
$802$	−52.9577	−1.87000
$803$	1.24065	0.0437816
$804$	−149.286	−5.26492
$805$	−0.144552	−0.00509479
$806$	−38.0861	−1.34153
$807$	−3.38000	−0.118982
$808$	73.1679	2.57404
$809$	−22.4586	−0.789601	−0.394800	−	0.918767i	$-0.629186\pi$
$809$	−22.4586	−0.789601	−0.394800	+	0.918767i	$0.629186\pi$
$810$	46.1939	1.62309
$811$	−24.5322	−0.861444	−0.430722	−	0.902485i	$-0.641741\pi$
$811$	−24.5322	−0.861444	−0.430722	+	0.902485i	$0.641741\pi$
$812$	0.527869	0.0185246
$813$	−50.3716	−1.76661
$814$	0.847119	0.0296915
$815$	−17.5009	−0.613031
$816$	−152.791	−5.34876
$817$	26.2255	0.917514
$818$	−28.8825	−1.00985
$819$	−0.309764	−0.0108240
$820$	24.1815	0.844454
$821$	−13.6013	−0.474690	−0.237345	−	0.971425i	$-0.576277\pi$
$821$	−13.6013	−0.474690	−0.237345	+	0.971425i	$0.576277\pi$
$822$	−38.4222	−1.34013
$823$	−11.0766	−0.386105	−0.193052	−	0.981188i	$-0.561839\pi$
$823$	−11.0766	−0.386105	−0.193052	+	0.981188i	$0.561839\pi$
$824$	−23.6589	−0.824198
$825$	0.788046	0.0274362
$826$	0.701842	0.0244202
$827$	−43.7387	−1.52094	−0.760472	−	0.649370i	$-0.775032\pi$
$827$	−43.7387	−1.52094	−0.760472	+	0.649370i	$0.775032\pi$
$828$	33.1200	1.15100
$829$	21.9321	0.761732	0.380866	−	0.924630i	$-0.375626\pi$
$829$	21.9321	0.761732	0.380866	+	0.924630i	$0.375626\pi$
$830$	−10.7906	−0.374547
$831$	−13.5426	−0.469788
$832$	14.0197	0.486047
$833$	−50.8776	−1.76280
$834$	71.4533	2.47423
$835$	−0.0191472	−0.000662616 0
$836$	9.03606	0.312519
$837$	−0.317615	−0.0109784
$838$	−27.4316	−0.947610
$839$	−30.9753	−1.06939	−0.534694	−	0.845046i	$-0.679573\pi$
$839$	−30.9753	−1.06939	−0.534694	+	0.845046i	$0.679573\pi$
$840$	−1.05398	−0.0363659
$841$	−15.6655	−0.540191
$842$	45.7477	1.57657
$843$	39.0390	1.34457
$844$	79.8383	2.74815
$845$	−4.06555	−0.139859
$846$	−90.5221	−3.11221
$847$	0.336279	0.0115547
$848$	108.366	3.72132
$849$	73.8562	2.53474
$850$	18.4036	0.631238
$851$	−2.33512	−0.0800469
$852$	−89.4299	−3.06382
$853$	−40.6818	−1.39292	−0.696459	−	0.717596i	$-0.745242\pi$
$853$	−40.6818	−1.39292	−0.696459	+	0.717596i	$0.745242\pi$
$854$	−0.426053	−0.0145792
$855$	35.7675	1.22322
$856$	−71.0461	−2.42830
$857$	21.4582	0.732999	0.366499	−	0.930418i	$-0.380556\pi$
$857$	21.4582	0.732999	0.366499	+	0.930418i	$0.380556\pi$
$858$	6.89004	0.235222
$859$	−3.91419	−0.133551	−0.0667753	−	0.997768i	$-0.521271\pi$
$859$	−3.91419	−0.133551	−0.0667753	+	0.997768i	$0.521271\pi$
$860$	41.8128	1.42581
$861$	0.195236	0.00665362
$862$	−62.2379	−2.11983
$863$	−8.83078	−0.300603	−0.150302	−	0.988640i	$-0.548024\pi$
$863$	−8.83078	−0.300603	−0.150302	+	0.988640i	$0.548024\pi$
$864$	0.589849	0.0200671
$865$	−17.0050	−0.578187
$866$	41.4922	1.40996
$867$	−88.0059	−2.98884
$868$	−0.642964	−0.0218236
$869$	−4.01297	−0.136131
$870$	−46.4758	−1.57568
$871$	43.0106	1.45736
$872$	−6.93416	−0.234820
$873$	8.51933	0.288336
$874$	−35.5473	−1.20241
$875$	0.370144	0.0125131
$876$	−43.5279	−1.47067
$877$	−24.7100	−0.834399	−0.417200	−	0.908815i	$-0.636988\pi$
$877$	−24.7100	−0.834399	−0.417200	+	0.908815i	$0.636988\pi$
$878$	64.7736	2.18600
$879$	1.02652	0.0346238
$880$	5.62483	0.189613
$881$	51.6598	1.74046	0.870232	−	0.492642i	$-0.163969\pi$
$881$	51.6598	1.74046	0.870232	+	0.492642i	$0.163969\pi$
$882$	54.8046	1.84537
$883$	−19.6688	−0.661909	−0.330955	−	0.943647i	$-0.607371\pi$
$883$	−19.6688	−0.661909	−0.330955	+	0.943647i	$0.607371\pi$
$884$	112.748	3.79213
$885$	−43.2989	−1.45548
$886$	59.7889	2.00865
$887$	15.3652	0.515914	0.257957	−	0.966156i	$-0.416951\pi$
$887$	15.3652	0.515914	0.257957	+	0.966156i	$0.416951\pi$
$888$	−17.0263	−0.571364
$889$	0.0907822	0.00304474
$890$	−64.1771	−2.15122
$891$	−2.92044	−0.0978384
$892$	−80.0203	−2.67928
$893$	68.0781	2.27815
$894$	11.9191	0.398635
$895$	−14.2825	−0.477410
$896$	−0.172248	−0.00575440
$897$	−18.9927	−0.634148
$898$	−47.0065	−1.56863
$899$	−16.2419	−0.541697
$900$	−13.8909	−0.463029
$901$	92.0232	3.06574
$902$	−2.18178	−0.0726452
$903$	0.337587	0.0112342
$904$	48.3868	1.60932
$905$	−27.2495	−0.905803
$906$	149.128	4.95444
$907$	11.1064	0.368783	0.184391	−	0.982853i	$-0.440969\pi$
$907$	11.1064	0.368783	0.184391	+	0.982853i	$0.440969\pi$
$908$	−120.748	−4.00715
$909$	−31.9623	−1.06012
$910$	0.530070	0.0175717
$911$	−44.0801	−1.46044	−0.730220	−	0.683212i	$-0.760583\pi$
$911$	−44.0801	−1.46044	−0.730220	+	0.683212i	$0.760583\pi$
$912$	−123.777	−4.09868
$913$	0.682195	0.0225774
$914$	−94.2621	−3.11791
$915$	26.2846	0.868943
$916$	−19.1404	−0.632416
$917$	0.618744	0.0204327
$918$	1.34186	0.0442879
$919$	30.9260	1.02015	0.510077	−	0.860129i	$-0.329617\pi$
$919$	30.9260	1.02015	0.510077	+	0.860129i	$0.329617\pi$
$920$	−32.4676	−1.07042
$921$	69.8939	2.30308
$922$	−53.2704	−1.75437
$923$	25.7655	0.848082
$924$	0.116316	0.00382653
$925$	0.979373	0.0322016
$926$	43.2535	1.42140
$927$	10.3350	0.339448
$928$	30.1631	0.990154
$929$	−24.6419	−0.808474	−0.404237	−	0.914654i	$-0.632463\pi$
$929$	−24.6419	−0.808474	−0.404237	+	0.914654i	$0.632463\pi$
$930$	56.6093	1.85629
$931$	−41.2164	−1.35081
$932$	−64.5834	−2.11550
$933$	25.5553	0.836642
$934$	−93.7879	−3.06883
$935$	4.77652	0.156209
$936$	−69.5755	−2.27415
$937$	34.5941	1.13014	0.565070	−	0.825043i	$-0.308849\pi$
$937$	34.5941	1.13014	0.565070	+	0.825043i	$0.308849\pi$
$938$	1.03624	0.0338343
$939$	−4.97924	−0.162491
$940$	108.541	3.54022
$941$	−20.4602	−0.666983	−0.333492	−	0.942753i	$-0.608227\pi$
$941$	−20.4602	−0.666983	−0.333492	+	0.942753i	$0.608227\pi$
$942$	−124.337	−4.05110
$943$	6.01416	0.195848
$944$	75.2816	2.45021
$945$	0.00442046	0.000143797 0
$946$	−3.77257	−0.122657
$947$	16.3300	0.530654	0.265327	−	0.964158i	$-0.414520\pi$
$947$	16.3300	0.530654	0.265327	+	0.964158i	$0.414520\pi$
$948$	140.794	4.57278
$949$	12.5408	0.407090
$950$	14.9089	0.483709
$951$	−82.8369	−2.68617
$952$	1.55614	0.0504348
$953$	−22.2463	−0.720629	−0.360314	−	0.932831i	$-0.617331\pi$
$953$	−22.2463	−0.720629	−0.360314	+	0.932831i	$0.617331\pi$
$954$	−99.1261	−3.20933
$955$	−52.4611	−1.69760
$956$	100.081	3.23686
$957$	2.93826	0.0949806
$958$	43.9291	1.41928
$959$	0.186878	0.00603460
$960$	−20.8382	−0.672551
$961$	−11.2168	−0.361832
$962$	8.56286	0.276078
$963$	31.0354	1.00010
$964$	−30.7388	−0.990030
$965$	−11.2766	−0.363006
$966$	−0.457583	−0.0147225
$967$	35.1870	1.13154	0.565769	−	0.824564i	$-0.308579\pi$
$967$	35.1870	1.13154	0.565769	+	0.824564i	$0.308579\pi$
$968$	75.5311	2.42766
$969$	−105.110	−3.37662
$970$	−14.5783	−0.468082
$971$	−29.9423	−0.960893	−0.480447	−	0.877024i	$-0.659525\pi$
$971$	−29.9423	−0.960893	−0.480447	+	0.877024i	$0.659525\pi$
$972$	103.466	3.31867
$973$	−0.347534	−0.0111414
$974$	−94.6687	−3.03338
$975$	7.96573	0.255108
$976$	−45.6998	−1.46281
$977$	−11.1671	−0.357266	−0.178633	−	0.983916i	$-0.557167\pi$
$977$	−11.1671	−0.357266	−0.178633	+	0.983916i	$0.557167\pi$
$978$	−55.3996	−1.77149
$979$	4.05736	0.129674
$980$	−65.7137	−2.09915
$981$	3.02908	0.0967112
$982$	−42.7120	−1.36300
$983$	−24.1843	−0.771358	−0.385679	−	0.922633i	$-0.626033\pi$
$983$	−24.1843	−0.771358	−0.385679	+	0.922633i	$0.626033\pi$
$984$	43.8516	1.39794
$985$	30.1995	0.962236
$986$	68.6186	2.18526
$987$	0.876335	0.0278940
$988$	91.3384	2.90586
$989$	10.3992	0.330677
$990$	−5.14520	−0.163525
$991$	41.3732	1.31426	0.657132	−	0.753776i	$-0.271769\pi$
$991$	41.3732	1.31426	0.657132	+	0.753776i	$0.271769\pi$
$992$	−36.7398	−1.16649
$993$	−66.0811	−2.09702
$994$	0.620757	0.0196892
$995$	−42.6277	−1.35139
$996$	−23.9346	−0.758398
$997$	25.5885	0.810397	0.405198	−	0.914229i	$-0.367202\pi$
$997$	25.5885	0.810397	0.405198	+	0.914229i	$0.367202\pi$
$998$	−5.72477	−0.181215
$999$	0.0714089	0.00225928

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4033.2.a.e.1.3	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4033.2.a.e.1.3	✓	82	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:	\( N \)	\(=\)	\( 4033 = 37 \cdot 109 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58504 q^{2} -2.45542 q^{3} +4.68242 q^{4} +2.00515 q^{5} +6.34735 q^{6} -0.0308722 q^{7} -6.93416 q^{8} +3.02908 q^{9} +O(q^{10})\)	\(q-2.58504 q^{2} -2.45542 q^{3} +4.68242 q^{4} +2.00515 q^{5} +6.34735 q^{6} -0.0308722 q^{7} -6.93416 q^{8} +3.02908 q^{9} -5.18339 q^{10} +0.327701 q^{11} -11.4973 q^{12} +3.31247 q^{13} +0.0798059 q^{14} -4.92348 q^{15} +8.56022 q^{16} +7.26922 q^{17} -7.83029 q^{18} +5.88886 q^{19} +9.38895 q^{20} +0.0758042 q^{21} -0.847119 q^{22} +2.33512 q^{23} +17.0263 q^{24} -0.979373 q^{25} -8.56286 q^{26} -0.0714089 q^{27} -0.144557 q^{28} -3.65164 q^{29} +12.7274 q^{30} +4.44783 q^{31} -8.26017 q^{32} -0.804643 q^{33} -18.7912 q^{34} -0.0619034 q^{35} +14.1834 q^{36} -1.00000 q^{37} -15.2229 q^{38} -8.13350 q^{39} -13.9040 q^{40} +2.57553 q^{41} -0.195957 q^{42} +4.45341 q^{43} +1.53443 q^{44} +6.07376 q^{45} -6.03637 q^{46} +11.5605 q^{47} -21.0189 q^{48} -6.99905 q^{49} +2.53172 q^{50} -17.8490 q^{51} +15.5104 q^{52} +12.6593 q^{53} +0.184595 q^{54} +0.657089 q^{55} +0.214073 q^{56} -14.4596 q^{57} +9.43962 q^{58} +8.79436 q^{59} -23.0538 q^{60} -5.33862 q^{61} -11.4978 q^{62} -0.0935145 q^{63} +4.23241 q^{64} +6.64200 q^{65} +2.08003 q^{66} +12.9845 q^{67} +34.0375 q^{68} -5.73370 q^{69} +0.160023 q^{70} +7.77834 q^{71} -21.0041 q^{72} +3.78593 q^{73} +2.58504 q^{74} +2.40477 q^{75} +27.5741 q^{76} -0.0101169 q^{77} +21.0254 q^{78} -12.2458 q^{79} +17.1645 q^{80} -8.91191 q^{81} -6.65783 q^{82} +2.08176 q^{83} +0.354947 q^{84} +14.5759 q^{85} -11.5122 q^{86} +8.96630 q^{87} -2.27233 q^{88} +12.3813 q^{89} -15.7009 q^{90} -0.102263 q^{91} +10.9340 q^{92} -10.9213 q^{93} -29.8843 q^{94} +11.8080 q^{95} +20.2822 q^{96} +2.81251 q^{97} +18.0928 q^{98} +0.992633 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9}+O(q^{10}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9	\( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9} + 13 q^{10} + 2 q^{11} + 36 q^{12} + 23 q^{13} + 24 q^{14} + 35 q^{15} + 104 q^{16} + 43 q^{17} + 42 q^{18} + 15 q^{19} + 59 q^{20} + 9 q^{21} + 6 q^{22} + 70 q^{23} + 15 q^{24} + 98 q^{25} + 10 q^{26} + 65 q^{27} + 37 q^{28} + 27 q^{29} + 17 q^{30} + 59 q^{31} + 46 q^{32} + 16 q^{33} - 16 q^{34} + 80 q^{35} + 88 q^{36} - 82 q^{37} + 82 q^{38} + 13 q^{39} + 14 q^{40} + 3 q^{41} + 62 q^{42} + 7 q^{43} - 11 q^{44} + 42 q^{45} - 11 q^{46} + 123 q^{47} + 45 q^{48} + 105 q^{49} + 27 q^{50} + 3 q^{51} - 30 q^{52} + 82 q^{53} - 27 q^{54} + 37 q^{55} + 66 q^{56} + 29 q^{57} - 34 q^{58} + 60 q^{59} + 94 q^{60} + 9 q^{61} - 2 q^{62} + 106 q^{63} + 93 q^{64} + 9 q^{65} + 63 q^{66} + 113 q^{68} + 48 q^{69} + 47 q^{70} + 59 q^{71} + 63 q^{72} + 21 q^{73} - 10 q^{74} + 77 q^{75} + 22 q^{76} + 30 q^{77} + 29 q^{78} + 55 q^{79} + 88 q^{80} + 42 q^{81} + 4 q^{82} + 92 q^{83} + 43 q^{84} - 7 q^{85} + 17 q^{86} + 147 q^{87} - 13 q^{88} + 100 q^{89} + 91 q^{90} + 28 q^{91} + 127 q^{92} + 3 q^{93} + 30 q^{94} + 48 q^{95} - 31 q^{96} + 53 q^{97} + 101 q^{98} - 20 q^{99}+O(q^{100}) \) 82 * q + 10 * q^2 + 17 * q^3 + 88 * q^4 + 22 * q^5 + 4 * q^6 + 15 * q^7 + 33 * q^8 + 91 * q^9 + 13 * q^10 + 2 * q^11 + 36 * q^12 + 23 * q^13 + 24 * q^14 + 35 * q^15 + 104 * q^16 + 43 * q^17 + 42 * q^18 + 15 * q^19 + 59 * q^20 + 9 * q^21 + 6 * q^22 + 70 * q^23 + 15 * q^24 + 98 * q^25 + 10 * q^26 + 65 * q^27 + 37 * q^28 + 27 * q^29 + 17 * q^30 + 59 * q^31 + 46 * q^32 + 16 * q^33 - 16 * q^34 + 80 * q^35 + 88 * q^36 - 82 * q^37 + 82 * q^38 + 13 * q^39 + 14 * q^40 + 3 * q^41 + 62 * q^42 + 7 * q^43 - 11 * q^44 + 42 * q^45 - 11 * q^46 + 123 * q^47 + 45 * q^48 + 105 * q^49 + 27 * q^50 + 3 * q^51 - 30 * q^52 + 82 * q^53 - 27 * q^54 + 37 * q^55 + 66 * q^56 + 29 * q^57 - 34 * q^58 + 60 * q^59 + 94 * q^60 + 9 * q^61 - 2 * q^62 + 106 * q^63 + 93 * q^64 + 9 * q^65 + 63 * q^66 + 113 * q^68 + 48 * q^69 + 47 * q^70 + 59 * q^71 + 63 * q^72 + 21 * q^73 - 10 * q^74 + 77 * q^75 + 22 * q^76 + 30 * q^77 + 29 * q^78 + 55 * q^79 + 88 * q^80 + 42 * q^81 + 4 * q^82 + 92 * q^83 + 43 * q^84 - 7 * q^85 + 17 * q^86 + 147 * q^87 - 13 * q^88 + 100 * q^89 + 91 * q^90 + 28 * q^91 + 127 * q^92 + 3 * q^93 + 30 * q^94 + 48 * q^95 - 31 * q^96 + 53 * q^97 + 101 * q^98 - 20 * q^99

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