LMFDB - Embedded newform 8049.2.a.a.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8049,2,Mod(1,8049)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8049, 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("8049.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8049 = 3 \cdot 2683 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8049.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:	$64.2715885869$
Analytic rank:	$1$
Dimension:	$95$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	8049.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49336 q^{2} +1.00000 q^{3} +4.21683 q^{4} -1.71250 q^{5} -2.49336 q^{6} -4.18090 q^{7} -5.52734 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.49336 q^{2} +1.00000 q^{3} +4.21683 q^{4} -1.71250 q^{5} -2.49336 q^{6} -4.18090 q^{7} -5.52734 q^{8} +1.00000 q^{9} +4.26986 q^{10} +0.800933 q^{11} +4.21683 q^{12} +4.41419 q^{13} +10.4245 q^{14} -1.71250 q^{15} +5.34798 q^{16} +3.75657 q^{17} -2.49336 q^{18} -2.89911 q^{19} -7.22130 q^{20} -4.18090 q^{21} -1.99701 q^{22} +1.04731 q^{23} -5.52734 q^{24} -2.06736 q^{25} -11.0062 q^{26} +1.00000 q^{27} -17.6301 q^{28} -1.52982 q^{29} +4.26986 q^{30} -0.854333 q^{31} -2.27973 q^{32} +0.800933 q^{33} -9.36647 q^{34} +7.15977 q^{35} +4.21683 q^{36} +2.31715 q^{37} +7.22851 q^{38} +4.41419 q^{39} +9.46555 q^{40} +5.39426 q^{41} +10.4245 q^{42} -1.70476 q^{43} +3.37740 q^{44} -1.71250 q^{45} -2.61133 q^{46} -5.56905 q^{47} +5.34798 q^{48} +10.4799 q^{49} +5.15466 q^{50} +3.75657 q^{51} +18.6139 q^{52} -0.666895 q^{53} -2.49336 q^{54} -1.37159 q^{55} +23.1092 q^{56} -2.89911 q^{57} +3.81439 q^{58} -11.7019 q^{59} -7.22130 q^{60} -9.93054 q^{61} +2.13016 q^{62} -4.18090 q^{63} -5.01177 q^{64} -7.55929 q^{65} -1.99701 q^{66} -6.27074 q^{67} +15.8408 q^{68} +1.04731 q^{69} -17.8519 q^{70} +11.1546 q^{71} -5.52734 q^{72} -8.44504 q^{73} -5.77748 q^{74} -2.06736 q^{75} -12.2250 q^{76} -3.34862 q^{77} -11.0062 q^{78} +5.79211 q^{79} -9.15839 q^{80} +1.00000 q^{81} -13.4498 q^{82} -7.95428 q^{83} -17.6301 q^{84} -6.43311 q^{85} +4.25059 q^{86} -1.52982 q^{87} -4.42703 q^{88} +10.8687 q^{89} +4.26986 q^{90} -18.4553 q^{91} +4.41635 q^{92} -0.854333 q^{93} +13.8856 q^{94} +4.96471 q^{95} -2.27973 q^{96} +3.88873 q^{97} -26.1301 q^{98} +0.800933 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 95 q - 9 q^{2} + 95 q^{3} + 65 q^{4} - 15 q^{5} - 9 q^{6} - 36 q^{7} - 27 q^{8} + 95 q^{9}+O(q^{10}) $ 95 * q - 9 * q^2 + 95 * q^3 + 65 * q^4 - 15 * q^5 - 9 * q^6 - 36 * q^7 - 27 * q^8 + 95 * q^9	\( 95 q - 9 q^{2} + 95 q^{3} + 65 q^{4} - 15 q^{5} - 9 q^{6} - 36 q^{7} - 27 q^{8} + 95 q^{9} - 36 q^{10} - 48 q^{11} + 65 q^{12} - 73 q^{13} - 17 q^{14} - 15 q^{15} + 13 q^{16} - 9 q^{17} - 9 q^{18} - 66 q^{19} - 35 q^{20} - 36 q^{21} - 37 q^{22} - 58 q^{23} - 27 q^{24} + 24 q^{25} - 25 q^{26} + 95 q^{27} - 75 q^{28} - 31 q^{29} - 36 q^{30} - 129 q^{31} - 53 q^{32} - 48 q^{33} - 61 q^{34} - 38 q^{35} + 65 q^{36} - 127 q^{37} + q^{38} - 73 q^{39} - 74 q^{40} - 31 q^{41} - 17 q^{42} - 62 q^{43} - 76 q^{44} - 15 q^{45} - 60 q^{46} - 75 q^{47} + 13 q^{48} + 5 q^{49} - 30 q^{50} - 9 q^{51} - 137 q^{52} - 28 q^{53} - 9 q^{54} - 117 q^{55} - 23 q^{56} - 66 q^{57} - 90 q^{58} - 60 q^{59} - 35 q^{60} - 96 q^{61} + 10 q^{62} - 36 q^{63} - 75 q^{64} - 28 q^{65} - 37 q^{66} - 116 q^{67} + 3 q^{68} - 58 q^{69} - 73 q^{70} - 144 q^{71} - 27 q^{72} - 121 q^{73} - 16 q^{74} + 24 q^{75} - 118 q^{76} - 3 q^{77} - 25 q^{78} - 135 q^{79} - 36 q^{80} + 95 q^{81} - 102 q^{82} - 21 q^{83} - 75 q^{84} - 129 q^{85} - 46 q^{86} - 31 q^{87} - 77 q^{88} - 63 q^{89} - 36 q^{90} - 123 q^{91} - 42 q^{92} - 129 q^{93} - 44 q^{94} - 80 q^{95} - 53 q^{96} - 144 q^{97} + 10 q^{98} - 48 q^{99}+O(q^{100}) \) 95 * q - 9 * q^2 + 95 * q^3 + 65 * q^4 - 15 * q^5 - 9 * q^6 - 36 * q^7 - 27 * q^8 + 95 * q^9 - 36 * q^10 - 48 * q^11 + 65 * q^12 - 73 * q^13 - 17 * q^14 - 15 * q^15 + 13 * q^16 - 9 * q^17 - 9 * q^18 - 66 * q^19 - 35 * q^20 - 36 * q^21 - 37 * q^22 - 58 * q^23 - 27 * q^24 + 24 * q^25 - 25 * q^26 + 95 * q^27 - 75 * q^28 - 31 * q^29 - 36 * q^30 - 129 * q^31 - 53 * q^32 - 48 * q^33 - 61 * q^34 - 38 * q^35 + 65 * q^36 - 127 * q^37 + q^38 - 73 * q^39 - 74 * q^40 - 31 * q^41 - 17 * q^42 - 62 * q^43 - 76 * q^44 - 15 * q^45 - 60 * q^46 - 75 * q^47 + 13 * q^48 + 5 * q^49 - 30 * q^50 - 9 * q^51 - 137 * q^52 - 28 * q^53 - 9 * q^54 - 117 * q^55 - 23 * q^56 - 66 * q^57 - 90 * q^58 - 60 * q^59 - 35 * q^60 - 96 * q^61 + 10 * q^62 - 36 * q^63 - 75 * q^64 - 28 * q^65 - 37 * q^66 - 116 * q^67 + 3 * q^68 - 58 * q^69 - 73 * q^70 - 144 * q^71 - 27 * q^72 - 121 * q^73 - 16 * q^74 + 24 * q^75 - 118 * q^76 - 3 * q^77 - 25 * q^78 - 135 * q^79 - 36 * q^80 + 95 * q^81 - 102 * q^82 - 21 * q^83 - 75 * q^84 - 129 * q^85 - 46 * q^86 - 31 * q^87 - 77 * q^88 - 63 * q^89 - 36 * q^90 - 123 * q^91 - 42 * q^92 - 129 * q^93 - 44 * q^94 - 80 * q^95 - 53 * q^96 - 144 * q^97 + 10 * q^98 - 48 * 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 $

$2$	−2.49336	−1.76307	−0.881535	−	0.472119i	$-0.843489\pi$
$2$	−2.49336	−1.76307	−0.881535	+	0.472119i	$0.843489\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.21683	2.10841
$5$	−1.71250	−0.765852	−0.382926	−	0.923779i	$-0.625084\pi$
$5$	−1.71250	−0.765852	−0.382926	+	0.923779i	$0.625084\pi$
$6$	−2.49336	−1.01791
$7$	−4.18090	−1.58023	−0.790115	−	0.612958i	$-0.789979\pi$
$7$	−4.18090	−1.58023	−0.790115	+	0.612958i	$0.789979\pi$
$8$	−5.52734	−1.95421
$9$	1.00000	0.333333
$10$	4.26986	1.35025
$11$	0.800933	0.241490	0.120745	−	0.992684i	$-0.461472\pi$
$11$	0.800933	0.241490	0.120745	+	0.992684i	$0.461472\pi$
$12$	4.21683	1.21729
$13$	4.41419	1.22428	0.612138	−	0.790751i	$-0.290310\pi$
$13$	4.41419	1.22428	0.612138	+	0.790751i	$0.290310\pi$
$14$	10.4245	2.78606
$15$	−1.71250	−0.442165
$16$	5.34798	1.33699
$17$	3.75657	0.911103	0.455551	−	0.890210i	$-0.349442\pi$
$17$	3.75657	0.911103	0.455551	+	0.890210i	$0.349442\pi$
$18$	−2.49336	−0.587690
$19$	−2.89911	−0.665101	−0.332550	−	0.943086i	$-0.607909\pi$
$19$	−2.89911	−0.665101	−0.332550	+	0.943086i	$0.607909\pi$
$20$	−7.22130	−1.61473
$21$	−4.18090	−0.912347
$22$	−1.99701	−0.425764
$23$	1.04731	0.218380	0.109190	−	0.994021i	$-0.465174\pi$
$23$	1.04731	0.218380	0.109190	+	0.994021i	$0.465174\pi$
$24$	−5.52734	−1.12826
$25$	−2.06736	−0.413471
$26$	−11.0062	−2.15848
$27$	1.00000	0.192450
$28$	−17.6301	−3.33178
$29$	−1.52982	−0.284081	−0.142040	−	0.989861i	$-0.545366\pi$
$29$	−1.52982	−0.284081	−0.142040	+	0.989861i	$0.545366\pi$
$30$	4.26986	0.779567
$31$	−0.854333	−0.153443	−0.0767214	−	0.997053i	$-0.524445\pi$
$31$	−0.854333	−0.153443	−0.0767214	+	0.997053i	$0.524445\pi$
$32$	−2.27973	−0.403004
$33$	0.800933	0.139425
$34$	−9.36647	−1.60634
$35$	7.15977	1.21022
$36$	4.21683	0.702805
$37$	2.31715	0.380937	0.190468	−	0.981693i	$-0.438999\pi$
$37$	2.31715	0.380937	0.190468	+	0.981693i	$0.438999\pi$
$38$	7.22851	1.17262
$39$	4.41419	0.706837
$40$	9.46555	1.49663
$41$	5.39426	0.842442	0.421221	−	0.906958i	$-0.361602\pi$
$41$	5.39426	0.842442	0.421221	+	0.906958i	$0.361602\pi$
$42$	10.4245	1.60853
$43$	−1.70476	−0.259974	−0.129987	−	0.991516i	$-0.541494\pi$
$43$	−1.70476	−0.259974	−0.129987	+	0.991516i	$0.541494\pi$
$44$	3.37740	0.509162
$45$	−1.71250	−0.255284
$46$	−2.61133	−0.385019
$47$	−5.56905	−0.812329	−0.406165	−	0.913800i	$-0.633134\pi$
$47$	−5.56905	−0.812329	−0.406165	+	0.913800i	$0.633134\pi$
$48$	5.34798	0.771914
$49$	10.4799	1.49713
$50$	5.15466	0.728979
$51$	3.75657	0.526025
$52$	18.6139	2.58128
$53$	−0.666895	−0.0916051	−0.0458026	−	0.998951i	$-0.514585\pi$
$53$	−0.666895	−0.0916051	−0.0458026	+	0.998951i	$0.514585\pi$
$54$	−2.49336	−0.339303
$55$	−1.37159	−0.184946
$56$	23.1092	3.08810
$57$	−2.89911	−0.383996
$58$	3.81439	0.500854
$59$	−11.7019	−1.52346	−0.761731	−	0.647893i	$-0.775650\pi$
$59$	−11.7019	−1.52346	−0.761731	+	0.647893i	$0.775650\pi$
$60$	−7.22130	−0.932266
$61$	−9.93054	−1.27148	−0.635738	−	0.771905i	$-0.719304\pi$
$61$	−9.93054	−1.27148	−0.635738	+	0.771905i	$0.719304\pi$
$62$	2.13016	0.270530
$63$	−4.18090	−0.526744
$64$	−5.01177	−0.626471
$65$	−7.55929	−0.937614
$66$	−1.99701	−0.245815
$67$	−6.27074	−0.766093	−0.383047	−	0.923729i	$-0.625125\pi$
$67$	−6.27074	−0.766093	−0.383047	+	0.923729i	$0.625125\pi$
$68$	15.8408	1.92098
$69$	1.04731	0.126082
$70$	−17.8519	−2.13371
$71$	11.1546	1.32381	0.661903	−	0.749590i	$-0.269749\pi$
$71$	11.1546	1.32381	0.661903	+	0.749590i	$0.269749\pi$
$72$	−5.52734	−0.651403
$73$	−8.44504	−0.988417	−0.494208	−	0.869344i	$-0.664542\pi$
$73$	−8.44504	−0.988417	−0.494208	+	0.869344i	$0.664542\pi$
$74$	−5.77748	−0.671618
$75$	−2.06736	−0.238718
$76$	−12.2250	−1.40231
$77$	−3.34862	−0.381611
$78$	−11.0062	−1.24620
$79$	5.79211	0.651663	0.325832	−	0.945428i	$-0.394356\pi$
$79$	5.79211	0.651663	0.325832	+	0.945428i	$0.394356\pi$
$80$	−9.15839	−1.02394
$81$	1.00000	0.111111
$82$	−13.4498	−1.48528
$83$	−7.95428	−0.873096	−0.436548	−	0.899681i	$-0.643799\pi$
$83$	−7.95428	−0.873096	−0.436548	+	0.899681i	$0.643799\pi$
$84$	−17.6301	−1.92360
$85$	−6.43311	−0.697769
$86$	4.25059	0.458352
$87$	−1.52982	−0.164014
$88$	−4.42703	−0.471923
$89$	10.8687	1.15208	0.576040	−	0.817422i	$-0.304597\pi$
$89$	10.8687	1.15208	0.576040	+	0.817422i	$0.304597\pi$
$90$	4.26986	0.450083
$91$	−18.4553	−1.93464
$92$	4.41635	0.460436
$93$	−0.854333	−0.0885902
$94$	13.8856	1.43219
$95$	4.96471	0.509368
$96$	−2.27973	−0.232674
$97$	3.88873	0.394841	0.197421	−	0.980319i	$-0.436744\pi$
$97$	3.88873	0.394841	0.197421	+	0.980319i	$0.436744\pi$
$98$	−26.1301	−2.63954
$99$	0.800933	0.0804968
$100$	−8.71769	−0.871769
$101$	1.44051	0.143336	0.0716678	−	0.997429i	$-0.477168\pi$
$101$	1.44051	0.143336	0.0716678	+	0.997429i	$0.477168\pi$
$102$	−9.36647	−0.927419
$103$	12.2013	1.20223	0.601115	−	0.799163i	$-0.294723\pi$
$103$	12.2013	1.20223	0.601115	+	0.799163i	$0.294723\pi$
$104$	−24.3987	−2.39249
$105$	7.15977	0.698722
$106$	1.66281	0.161506
$107$	11.7945	1.14022	0.570109	−	0.821569i	$-0.306901\pi$
$107$	11.7945	1.14022	0.570109	+	0.821569i	$0.306901\pi$
$108$	4.21683	0.405764
$109$	1.71973	0.164720	0.0823601	−	0.996603i	$-0.473754\pi$
$109$	1.71973	0.164720	0.0823601	+	0.996603i	$0.473754\pi$
$110$	3.41988	0.326072
$111$	2.31715	0.219934
$112$	−22.3593	−2.11276
$113$	0.951374	0.0894978	0.0447489	−	0.998998i	$-0.485751\pi$
$113$	0.951374	0.0894978	0.0447489	+	0.998998i	$0.485751\pi$
$114$	7.22851	0.677012
$115$	−1.79352	−0.167247
$116$	−6.45100	−0.598960
$117$	4.41419	0.408092
$118$	29.1771	2.68597
$119$	−15.7058	−1.43975
$120$	9.46555	0.864083
$121$	−10.3585	−0.941682
$122$	24.7604	2.24170
$123$	5.39426	0.486384
$124$	−3.60257	−0.323521
$125$	12.1028	1.08251
$126$	10.4245	0.928685
$127$	−0.910420	−0.0807867	−0.0403934	−	0.999184i	$-0.512861\pi$
$127$	−0.910420	−0.0807867	−0.0403934	+	0.999184i	$0.512861\pi$
$128$	17.0556	1.50752
$129$	−1.70476	−0.150096
$130$	18.8480	1.65308
$131$	14.9045	1.30221	0.651105	−	0.758987i	$-0.274306\pi$
$131$	14.9045	1.30221	0.651105	+	0.758987i	$0.274306\pi$
$132$	3.37740	0.293965
$133$	12.1209	1.05101
$134$	15.6352	1.35068
$135$	−1.71250	−0.147388
$136$	−20.7639	−1.78049
$137$	15.1888	1.29767	0.648834	−	0.760930i	$-0.275257\pi$
$137$	15.1888	1.29767	0.648834	+	0.760930i	$0.275257\pi$
$138$	−2.61133	−0.222291
$139$	14.7476	1.25088	0.625438	−	0.780274i	$-0.284920\pi$
$139$	14.7476	1.25088	0.625438	+	0.780274i	$0.284920\pi$
$140$	30.1915	2.55165
$141$	−5.56905	−0.468999
$142$	−27.8123	−2.33396
$143$	3.53547	0.295651
$144$	5.34798	0.445665
$145$	2.61982	0.217564
$146$	21.0565	1.74265
$147$	10.4799	0.864368
$148$	9.77101	0.803172
$149$	16.5156	1.35301	0.676506	−	0.736437i	$-0.263493\pi$
$149$	16.5156	1.35301	0.676506	+	0.736437i	$0.263493\pi$
$150$	5.15466	0.420876
$151$	−9.18963	−0.747841	−0.373921	−	0.927461i	$-0.621987\pi$
$151$	−9.18963	−0.747841	−0.373921	+	0.927461i	$0.621987\pi$
$152$	16.0244	1.29975
$153$	3.75657	0.303701
$154$	8.34930	0.672806
$155$	1.46304	0.117514
$156$	18.6139	1.49030
$157$	−5.24454	−0.418559	−0.209280	−	0.977856i	$-0.567112\pi$
$157$	−5.24454	−0.418559	−0.209280	+	0.977856i	$0.567112\pi$
$158$	−14.4418	−1.14893
$159$	−0.666895	−0.0528882
$160$	3.90403	0.308641
$161$	−4.37872	−0.345091
$162$	−2.49336	−0.195897
$163$	−4.32384	−0.338669	−0.169335	−	0.985559i	$-0.554162\pi$
$163$	−4.32384	−0.338669	−0.169335	+	0.985559i	$0.554162\pi$
$164$	22.7467	1.77622
$165$	−1.37159	−0.106779
$166$	19.8329	1.53933
$167$	−8.96116	−0.693436	−0.346718	−	0.937970i	$-0.612704\pi$
$167$	−8.96116	−0.693436	−0.346718	+	0.937970i	$0.612704\pi$
$168$	23.1092	1.78292
$169$	6.48510	0.498854
$170$	16.0400	1.23022
$171$	−2.89911	−0.221700
$172$	−7.18870	−0.548133
$173$	5.51986	0.419667	0.209833	−	0.977737i	$-0.432708\pi$
$173$	5.51986	0.419667	0.209833	+	0.977737i	$0.432708\pi$
$174$	3.81439	0.289168
$175$	8.64341	0.653380
$176$	4.28337	0.322871
$177$	−11.7019	−0.879571
$178$	−27.0995	−2.03120
$179$	18.5129	1.38372	0.691858	−	0.722034i	$-0.256792\pi$
$179$	18.5129	1.38372	0.691858	+	0.722034i	$0.256792\pi$
$180$	−7.22130	−0.538244
$181$	−21.2615	−1.58036	−0.790179	−	0.612876i	$-0.790012\pi$
$181$	−21.2615	−1.58036	−0.790179	+	0.612876i	$0.790012\pi$
$182$	46.0156	3.41090
$183$	−9.93054	−0.734087
$184$	−5.78887	−0.426761
$185$	−3.96811	−0.291741
$186$	2.13016	0.156191
$187$	3.00876	0.220023
$188$	−23.4837	−1.71273
$189$	−4.18090	−0.304116
$190$	−12.3788	−0.898052
$191$	−3.25454	−0.235490	−0.117745	−	0.993044i	$-0.537567\pi$
$191$	−3.25454	−0.235490	−0.117745	+	0.993044i	$0.537567\pi$
$192$	−5.01177	−0.361693
$193$	6.76124	0.486685	0.243342	−	0.969940i	$-0.421756\pi$
$193$	6.76124	0.486685	0.243342	+	0.969940i	$0.421756\pi$
$194$	−9.69600	−0.696132
$195$	−7.55929	−0.541332
$196$	44.1919	3.15657
$197$	−3.77426	−0.268905	−0.134452	−	0.990920i	$-0.542928\pi$
$197$	−3.77426	−0.268905	−0.134452	+	0.990920i	$0.542928\pi$
$198$	−1.99701	−0.141921
$199$	−19.0443	−1.35002	−0.675008	−	0.737810i	$-0.735860\pi$
$199$	−19.0443	−1.35002	−0.675008	+	0.737810i	$0.735860\pi$
$200$	11.4270	0.808010
$201$	−6.27074	−0.442304
$202$	−3.59169	−0.252711
$203$	6.39603	0.448914
$204$	15.8408	1.10908
$205$	−9.23765	−0.645185
$206$	−30.4222	−2.11961
$207$	1.04731	0.0727934
$208$	23.6070	1.63685
$209$	−2.32199	−0.160615
$210$	−17.8519	−1.23190
$211$	−15.2056	−1.04680	−0.523399	−	0.852088i	$-0.675336\pi$
$211$	−15.2056	−1.04680	−0.523399	+	0.852088i	$0.675336\pi$
$212$	−2.81218	−0.193142
$213$	11.1546	0.764299
$214$	−29.4079	−2.01028
$215$	2.91940	0.199102
$216$	−5.52734	−0.376088
$217$	3.57188	0.242475
$218$	−4.28790	−0.290413
$219$	−8.44504	−0.570663
$220$	−5.78378	−0.389942
$221$	16.5822	1.11544
$222$	−5.77748	−0.387759
$223$	13.4959	0.903753	0.451876	−	0.892081i	$-0.350755\pi$
$223$	13.4959	0.903753	0.451876	+	0.892081i	$0.350755\pi$
$224$	9.53133	0.636839
$225$	−2.06736	−0.137824
$226$	−2.37212	−0.157791
$227$	−2.20160	−0.146125	−0.0730626	−	0.997327i	$-0.523277\pi$
$227$	−2.20160	−0.146125	−0.0730626	+	0.997327i	$0.523277\pi$
$228$	−12.2250	−0.809623
$229$	21.3693	1.41212	0.706062	−	0.708150i	$-0.250470\pi$
$229$	21.3693	1.41212	0.706062	+	0.708150i	$0.250470\pi$
$230$	4.47189	0.294868
$231$	−3.34862	−0.220323
$232$	8.45585	0.555154
$233$	2.94144	0.192700	0.0963500	−	0.995348i	$-0.469283\pi$
$233$	2.94144	0.192700	0.0963500	+	0.995348i	$0.469283\pi$
$234$	−11.0062	−0.719495
$235$	9.53698	0.622124
$236$	−49.3450	−3.21209
$237$	5.79211	0.376238
$238$	39.1603	2.53838
$239$	−25.5998	−1.65592	−0.827958	−	0.560791i	$-0.810497\pi$
$239$	−25.5998	−1.65592	−0.827958	+	0.560791i	$0.810497\pi$
$240$	−9.15839	−0.591172
$241$	−13.9930	−0.901368	−0.450684	−	0.892683i	$-0.648820\pi$
$241$	−13.9930	−0.901368	−0.450684	+	0.892683i	$0.648820\pi$
$242$	25.8274	1.66025
$243$	1.00000	0.0641500
$244$	−41.8754	−2.68080
$245$	−17.9468	−1.14658
$246$	−13.4498	−0.857528
$247$	−12.7972	−0.814267
$248$	4.72219	0.299859
$249$	−7.95428	−0.504082
$250$	−30.1767	−1.90854
$251$	−7.02136	−0.443184	−0.221592	−	0.975139i	$-0.571125\pi$
$251$	−7.02136	−0.443184	−0.221592	+	0.975139i	$0.571125\pi$
$252$	−17.6301	−1.11059
$253$	0.838829	0.0527367
$254$	2.27000	0.142433
$255$	−6.43311	−0.402857
$256$	−32.5021	−2.03138
$257$	18.6916	1.16595	0.582974	−	0.812491i	$-0.301889\pi$
$257$	18.6916	1.16595	0.582974	+	0.812491i	$0.301889\pi$
$258$	4.25059	0.264630
$259$	−9.68776	−0.601968
$260$	−31.8762	−1.97688
$261$	−1.52982	−0.0946937
$262$	−37.1622	−2.29589
$263$	−12.4262	−0.766231	−0.383116	−	0.923700i	$-0.625149\pi$
$263$	−12.4262	−0.766231	−0.383116	+	0.923700i	$0.625149\pi$
$264$	−4.42703	−0.272465
$265$	1.14206	0.0701559
$266$	−30.2216	−1.85301
$267$	10.8687	0.665154
$268$	−26.4426	−1.61524
$269$	18.3235	1.11720	0.558601	−	0.829437i	$-0.311338\pi$
$269$	18.3235	1.11720	0.558601	+	0.829437i	$0.311338\pi$
$270$	4.26986	0.259856
$271$	3.23595	0.196570	0.0982851	−	0.995158i	$-0.468664\pi$
$271$	3.23595	0.196570	0.0982851	+	0.995158i	$0.468664\pi$
$272$	20.0901	1.21814
$273$	−18.4553	−1.11696
$274$	−37.8711	−2.28788
$275$	−1.65581	−0.0998494
$276$	4.41635	0.265833
$277$	−11.3492	−0.681905	−0.340953	−	0.940080i	$-0.610750\pi$
$277$	−11.3492	−0.681905	−0.340953	+	0.940080i	$0.610750\pi$
$278$	−36.7711	−2.20538
$279$	−0.854333	−0.0511476
$280$	−39.5745	−2.36503
$281$	−10.2294	−0.610236	−0.305118	−	0.952315i	$-0.598696\pi$
$281$	−10.2294	−0.610236	−0.305118	+	0.952315i	$0.598696\pi$
$282$	13.8856	0.826877
$283$	2.31229	0.137451	0.0687257	−	0.997636i	$-0.478107\pi$
$283$	2.31229	0.137451	0.0687257	+	0.997636i	$0.478107\pi$
$284$	47.0369	2.79113
$285$	4.96471	0.294084
$286$	−8.81520	−0.521253
$287$	−22.5528	−1.33125
$288$	−2.27973	−0.134335
$289$	−2.88817	−0.169892
$290$	−6.53214	−0.383580
$291$	3.88873	0.227962
$292$	−35.6113	−2.08399
$293$	−15.1692	−0.886192	−0.443096	−	0.896474i	$-0.646120\pi$
$293$	−15.1692	−0.886192	−0.443096	+	0.896474i	$0.646120\pi$
$294$	−26.1301	−1.52394
$295$	20.0395	1.16675
$296$	−12.8077	−0.744431
$297$	0.800933	0.0464749
$298$	−41.1793	−2.38545
$299$	4.62305	0.267358
$300$	−8.71769	−0.503316
$301$	7.12745	0.410819
$302$	22.9130	1.31850
$303$	1.44051	0.0827549
$304$	−15.5044	−0.889236
$305$	17.0060	0.973762
$306$	−9.36647	−0.535446
$307$	−2.06613	−0.117920	−0.0589600	−	0.998260i	$-0.518778\pi$
$307$	−2.06613	−0.117920	−0.0589600	+	0.998260i	$0.518778\pi$
$308$	−14.1205	−0.804593
$309$	12.2013	0.694108
$310$	−3.64788	−0.207186
$311$	0.934138	0.0529701	0.0264850	−	0.999649i	$-0.491569\pi$
$311$	0.934138	0.0529701	0.0264850	+	0.999649i	$0.491569\pi$
$312$	−24.3987	−1.38131
$313$	−1.10809	−0.0626332	−0.0313166	−	0.999510i	$-0.509970\pi$
$313$	−1.10809	−0.0626332	−0.0313166	+	0.999510i	$0.509970\pi$
$314$	13.0765	0.737949
$315$	7.15977	0.403407
$316$	24.4243	1.37398
$317$	−28.2086	−1.58435	−0.792177	−	0.610292i	$-0.791052\pi$
$317$	−28.2086	−1.58435	−0.792177	+	0.610292i	$0.791052\pi$
$318$	1.66281	0.0932456
$319$	−1.22529	−0.0686028
$320$	8.58263	0.479784
$321$	11.7945	0.658305
$322$	10.9177	0.608420
$323$	−10.8907	−0.605975
$324$	4.21683	0.234268
$325$	−9.12571	−0.506203
$326$	10.7809	0.597098
$327$	1.71973	0.0951012
$328$	−29.8159	−1.64631
$329$	23.2836	1.28367
$330$	3.41988	0.188258
$331$	−27.4101	−1.50660	−0.753298	−	0.657679i	$-0.771538\pi$
$331$	−27.4101	−1.50660	−0.753298	+	0.657679i	$0.771538\pi$
$332$	−33.5418	−1.84085
$333$	2.31715	0.126979
$334$	22.3434	1.22257
$335$	10.7386	0.586714
$336$	−22.3593	−1.21980
$337$	20.6022	1.12227	0.561137	−	0.827723i	$-0.310364\pi$
$337$	20.6022	1.12227	0.561137	+	0.827723i	$0.310364\pi$
$338$	−16.1697	−0.879514
$339$	0.951374	0.0516716
$340$	−27.1273	−1.47119
$341$	−0.684264	−0.0370549
$342$	7.22851	0.390873
$343$	−14.5491	−0.785579
$344$	9.42281	0.508044
$345$	−1.79352	−0.0965600
$346$	−13.7630	−0.739902
$347$	33.5916	1.80329	0.901645	−	0.432476i	$-0.142360\pi$
$347$	33.5916	1.80329	0.901645	+	0.432476i	$0.142360\pi$
$348$	−6.45100	−0.345810
$349$	6.57779	0.352101	0.176050	−	0.984381i	$-0.443668\pi$
$349$	6.57779	0.352101	0.176050	+	0.984381i	$0.443668\pi$
$350$	−21.5511	−1.15195
$351$	4.41419	0.235612
$352$	−1.82591	−0.0973215
$353$	−27.8787	−1.48383	−0.741916	−	0.670493i	$-0.766083\pi$
$353$	−27.8787	−1.48383	−0.741916	+	0.670493i	$0.766083\pi$
$354$	29.1771	1.55074
$355$	−19.1022	−1.01384
$356$	45.8314	2.42906
$357$	−15.7058	−0.831241
$358$	−46.1592	−2.43959
$359$	−9.53059	−0.503005	−0.251503	−	0.967857i	$-0.580925\pi$
$359$	−9.53059	−0.503005	−0.251503	+	0.967857i	$0.580925\pi$
$360$	9.46555	0.498878
$361$	−10.5952	−0.557641
$362$	53.0126	2.78628
$363$	−10.3585	−0.543681
$364$	−77.8228	−4.07902
$365$	14.4621	0.756980
$366$	24.7604	1.29425
$367$	−21.0717	−1.09993	−0.549967	−	0.835186i	$-0.685360\pi$
$367$	−21.0717	−1.09993	−0.549967	+	0.835186i	$0.685360\pi$
$368$	5.60102	0.291973
$369$	5.39426	0.280814
$370$	9.89391	0.514360
$371$	2.78822	0.144757
$372$	−3.60257	−0.186785
$373$	16.3985	0.849081	0.424540	−	0.905409i	$-0.360436\pi$
$373$	16.3985	0.849081	0.424540	+	0.905409i	$0.360436\pi$
$374$	−7.50192	−0.387915
$375$	12.1028	0.624987
$376$	30.7820	1.58746
$377$	−6.75293	−0.347794
$378$	10.4245	0.536177
$379$	−17.6269	−0.905436	−0.452718	−	0.891654i	$-0.649545\pi$
$379$	−17.6269	−0.905436	−0.452718	+	0.891654i	$0.649545\pi$
$380$	20.9353	1.07396
$381$	−0.910420	−0.0466422
$382$	8.11472	0.415185
$383$	−33.8270	−1.72848	−0.864239	−	0.503082i	$-0.832199\pi$
$383$	−33.8270	−1.72848	−0.864239	+	0.503082i	$0.832199\pi$
$384$	17.0556	0.870364
$385$	5.73450	0.292257
$386$	−16.8582	−0.858059
$387$	−1.70476	−0.0866580
$388$	16.3981	0.832488
$389$	−2.70928	−0.137366	−0.0686829	−	0.997639i	$-0.521880\pi$
$389$	−2.70928	−0.137366	−0.0686829	+	0.997639i	$0.521880\pi$
$390$	18.8480	0.954406
$391$	3.93431	0.198967
$392$	−57.9260	−2.92570
$393$	14.9045	0.751832
$394$	9.41057	0.474098
$395$	−9.91897	−0.499077
$396$	3.37740	0.169721
$397$	−16.9819	−0.852298	−0.426149	−	0.904653i	$-0.640130\pi$
$397$	−16.9819	−0.852298	−0.426149	+	0.904653i	$0.640130\pi$
$398$	47.4843	2.38017
$399$	12.1209	0.606802
$400$	−11.0562	−0.552809
$401$	−17.4582	−0.871822	−0.435911	−	0.899990i	$-0.643574\pi$
$401$	−17.4582	−0.871822	−0.435911	+	0.899990i	$0.643574\pi$
$402$	15.6352	0.779813
$403$	−3.77119	−0.187856
$404$	6.07436	0.302211
$405$	−1.71250	−0.0850946
$406$	−15.9476	−0.791466
$407$	1.85588	0.0919926
$408$	−20.7639	−1.02796
$409$	−26.7014	−1.32030	−0.660149	−	0.751134i	$-0.729507\pi$
$409$	−26.7014	−1.32030	−0.660149	+	0.751134i	$0.729507\pi$
$410$	23.0327	1.13751
$411$	15.1888	0.749208
$412$	51.4508	2.53480
$413$	48.9246	2.40742
$414$	−2.61133	−0.128340
$415$	13.6217	0.668662
$416$	−10.0632	−0.493388
$417$	14.7476	0.722194
$418$	5.78955	0.283176
$419$	−12.7102	−0.620934	−0.310467	−	0.950584i	$-0.600485\pi$
$419$	−12.7102	−0.620934	−0.310467	+	0.950584i	$0.600485\pi$
$420$	30.1915	1.47320
$421$	−6.05279	−0.294995	−0.147497	−	0.989062i	$-0.547122\pi$
$421$	−6.05279	−0.294995	−0.147497	+	0.989062i	$0.547122\pi$
$422$	37.9130	1.84558
$423$	−5.56905	−0.270776
$424$	3.68616	0.179016
$425$	−7.76618	−0.376715
$426$	−27.8123	−1.34751
$427$	41.5186	2.00923
$428$	49.7354	2.40405
$429$	3.53547	0.170694
$430$	−7.27911	−0.351030
$431$	−39.3575	−1.89578	−0.947892	−	0.318593i	$-0.896790\pi$
$431$	−39.3575	−1.89578	−0.947892	+	0.318593i	$0.896790\pi$
$432$	5.34798	0.257305
$433$	−4.66862	−0.224359	−0.112180	−	0.993688i	$-0.535783\pi$
$433$	−4.66862	−0.224359	−0.112180	+	0.993688i	$0.535783\pi$
$434$	−8.90597	−0.427500
$435$	2.61982	0.125611
$436$	7.25180	0.347298
$437$	−3.03628	−0.145245
$438$	21.0565	1.00612
$439$	13.4969	0.644172	0.322086	−	0.946710i	$-0.395616\pi$
$439$	13.4969	0.644172	0.322086	+	0.946710i	$0.395616\pi$
$440$	7.58127	0.361423
$441$	10.4799	0.499043
$442$	−41.3454	−1.96660
$443$	6.13660	0.291559	0.145779	−	0.989317i	$-0.453431\pi$
$443$	6.13660	0.291559	0.145779	+	0.989317i	$0.453431\pi$
$444$	9.77101	0.463712
$445$	−18.6126	−0.882322
$446$	−33.6501	−1.59338
$447$	16.5156	0.781162
$448$	20.9537	0.989969
$449$	−18.5623	−0.876011	−0.438005	−	0.898972i	$-0.644315\pi$
$449$	−18.5623	−0.876011	−0.438005	+	0.898972i	$0.644315\pi$
$450$	5.15466	0.242993
$451$	4.32044	0.203442
$452$	4.01178	0.188698
$453$	−9.18963	−0.431766
$454$	5.48937	0.257629
$455$	31.6046	1.48165
$456$	16.0244	0.750409
$457$	23.7692	1.11187	0.555937	−	0.831224i	$-0.312359\pi$
$457$	23.7692	1.11187	0.555937	+	0.831224i	$0.312359\pi$
$458$	−53.2813	−2.48967
$459$	3.75657	0.175342
$460$	−7.56297	−0.352625
$461$	16.5649	0.771502	0.385751	−	0.922603i	$-0.373942\pi$
$461$	16.5649	0.771502	0.385751	+	0.922603i	$0.373942\pi$
$462$	8.34930	0.388445
$463$	26.7373	1.24259	0.621294	−	0.783578i	$-0.286607\pi$
$463$	26.7373	1.24259	0.621294	+	0.783578i	$0.286607\pi$
$464$	−8.18146	−0.379815
$465$	1.46304	0.0678469
$466$	−7.33405	−0.339743
$467$	19.7637	0.914554	0.457277	−	0.889324i	$-0.348825\pi$
$467$	19.7637	0.914554	0.457277	+	0.889324i	$0.348825\pi$
$468$	18.6139	0.860427
$469$	26.2173	1.21060
$470$	−23.7791	−1.09685
$471$	−5.24454	−0.241655
$472$	64.6806	2.97716
$473$	−1.36540	−0.0627813
$474$	−14.4418	−0.663334
$475$	5.99349	0.275000
$476$	−66.2288	−3.03559
$477$	−0.666895	−0.0305350
$478$	63.8295	2.91949
$479$	−36.5053	−1.66797	−0.833984	−	0.551788i	$-0.813946\pi$
$479$	−36.5053	−1.66797	−0.833984	+	0.551788i	$0.813946\pi$
$480$	3.90403	0.178194
$481$	10.2283	0.466372
$482$	34.8895	1.58918
$483$	−4.37872	−0.199238
$484$	−43.6800	−1.98546
$485$	−6.65944	−0.302390
$486$	−2.49336	−0.113101
$487$	−30.2320	−1.36994	−0.684971	−	0.728570i	$-0.740185\pi$
$487$	−30.2320	−1.36994	−0.684971	+	0.728570i	$0.740185\pi$
$488$	54.8895	2.48473
$489$	−4.32384	−0.195531
$490$	44.7478	2.02150
$491$	−33.5063	−1.51212	−0.756058	−	0.654505i	$-0.772877\pi$
$491$	−33.5063	−1.51212	−0.756058	+	0.654505i	$0.772877\pi$
$492$	22.7467	1.02550
$493$	−5.74689	−0.258827
$494$	31.9080	1.43561
$495$	−1.37159	−0.0616486
$496$	−4.56895	−0.205152
$497$	−46.6362	−2.09192
$498$	19.8329	0.888732
$499$	17.9363	0.802939	0.401470	−	0.915872i	$-0.368500\pi$
$499$	17.9363	0.802939	0.401470	+	0.915872i	$0.368500\pi$
$500$	51.0355	2.28238
$501$	−8.96116	−0.400355
$502$	17.5068	0.781365
$503$	−37.0340	−1.65126	−0.825632	−	0.564209i	$-0.809181\pi$
$503$	−37.0340	−1.65126	−0.825632	+	0.564209i	$0.809181\pi$
$504$	23.1092	1.02937
$505$	−2.46686	−0.109774
$506$	−2.09150	−0.0929785
$507$	6.48510	0.288013
$508$	−3.83909	−0.170332
$509$	−6.90882	−0.306228	−0.153114	−	0.988209i	$-0.548930\pi$
$509$	−6.90882	−0.306228	−0.153114	+	0.988209i	$0.548930\pi$
$510$	16.0400	0.710265
$511$	35.3078	1.56193
$512$	46.9282	2.07395
$513$	−2.89911	−0.127999
$514$	−46.6047	−2.05565
$515$	−20.8947	−0.920729
$516$	−7.18870	−0.316465
$517$	−4.46044	−0.196170
$518$	24.1550	1.06131
$519$	5.51986	0.242295
$520$	41.7828	1.83230
$521$	8.54733	0.374465	0.187233	−	0.982316i	$-0.440048\pi$
$521$	8.54733	0.374465	0.187233	+	0.982316i	$0.440048\pi$
$522$	3.81439	0.166951
$523$	−14.3619	−0.628001	−0.314000	−	0.949423i	$-0.601669\pi$
$523$	−14.3619	−0.628001	−0.314000	+	0.949423i	$0.601669\pi$
$524$	62.8496	2.74560
$525$	8.64341	0.377229
$526$	30.9829	1.35092
$527$	−3.20936	−0.139802
$528$	4.28337	0.186410
$529$	−21.9031	−0.952310
$530$	−2.84755	−0.123690
$531$	−11.7019	−0.507821
$532$	51.1116	2.21597
$533$	23.8113	1.03138
$534$	−27.0995	−1.17271
$535$	−20.1980	−0.873237
$536$	34.6605	1.49711
$537$	18.5129	0.798889
$538$	−45.6869	−1.96970
$539$	8.39370	0.361542
$540$	−7.22130	−0.310755
$541$	−21.2560	−0.913867	−0.456934	−	0.889501i	$-0.651052\pi$
$541$	−21.2560	−0.913867	−0.456934	+	0.889501i	$0.651052\pi$
$542$	−8.06838	−0.346567
$543$	−21.2615	−0.912420
$544$	−8.56398	−0.367178
$545$	−2.94503	−0.126151
$546$	46.0156	1.96929
$547$	−11.8316	−0.505882	−0.252941	−	0.967482i	$-0.581398\pi$
$547$	−11.8316	−0.505882	−0.252941	+	0.967482i	$0.581398\pi$
$548$	64.0486	2.73602
$549$	−9.93054	−0.423825
$550$	4.12854	0.176041
$551$	4.43512	0.188942
$552$	−5.78887	−0.246390
$553$	−24.2162	−1.02978
$554$	28.2975	1.20225
$555$	−3.96811	−0.168437
$556$	62.1882	2.63737
$557$	−28.1678	−1.19351	−0.596753	−	0.802425i	$-0.703543\pi$
$557$	−28.1678	−1.19351	−0.596753	+	0.802425i	$0.703543\pi$
$558$	2.13016	0.0901767
$559$	−7.52516	−0.318280
$560$	38.2903	1.61806
$561$	3.00876	0.127030
$562$	25.5056	1.07589
$563$	0.925652	0.0390116	0.0195058	−	0.999810i	$-0.493791\pi$
$563$	0.925652	0.0390116	0.0195058	+	0.999810i	$0.493791\pi$
$564$	−23.4837	−0.988843
$565$	−1.62922	−0.0685420
$566$	−5.76537	−0.242336
$567$	−4.18090	−0.175581
$568$	−61.6552	−2.58699
$569$	7.70455	0.322992	0.161496	−	0.986873i	$-0.448368\pi$
$569$	7.70455	0.322992	0.161496	+	0.986873i	$0.448368\pi$
$570$	−12.3788	−0.518490
$571$	28.6063	1.19714	0.598569	−	0.801071i	$-0.295736\pi$
$571$	28.6063	1.19714	0.598569	+	0.801071i	$0.295736\pi$
$572$	14.9085	0.623355
$573$	−3.25454	−0.135960
$574$	56.2323	2.34709
$575$	−2.16517	−0.0902940
$576$	−5.01177	−0.208824
$577$	42.9757	1.78910	0.894551	−	0.446967i	$-0.147496\pi$
$577$	42.9757	1.78910	0.894551	+	0.446967i	$0.147496\pi$
$578$	7.20123	0.299532
$579$	6.76124	0.280988
$580$	11.0473	0.458715
$581$	33.2560	1.37969
$582$	−9.69600	−0.401912
$583$	−0.534139	−0.0221218
$584$	46.6786	1.93157
$585$	−7.55929	−0.312538
$586$	37.8221	1.56242
$587$	−5.16951	−0.213369	−0.106684	−	0.994293i	$-0.534023\pi$
$587$	−5.16951	−0.213369	−0.106684	+	0.994293i	$0.534023\pi$
$588$	44.1919	1.82245
$589$	2.47680	0.102055
$590$	−49.9657	−2.05705
$591$	−3.77426	−0.155252
$592$	12.3921	0.509310
$593$	39.5599	1.62453	0.812265	−	0.583288i	$-0.198234\pi$
$593$	39.5599	1.62453	0.812265	+	0.583288i	$0.198234\pi$
$594$	−1.99701	−0.0819384
$595$	26.8962	1.10264
$596$	69.6435	2.85271
$597$	−19.0443	−0.779432
$598$	−11.5269	−0.471370
$599$	−19.4714	−0.795578	−0.397789	−	0.917477i	$-0.630222\pi$
$599$	−19.4714	−0.795578	−0.397789	+	0.917477i	$0.630222\pi$
$600$	11.4270	0.466505
$601$	−28.1850	−1.14969	−0.574845	−	0.818263i	$-0.694938\pi$
$601$	−28.1850	−1.14969	−0.574845	+	0.818263i	$0.694938\pi$
$602$	−17.7713	−0.724303
$603$	−6.27074	−0.255364
$604$	−38.7511	−1.57676
$605$	17.7389	0.721189
$606$	−3.59169	−0.145903
$607$	−27.4614	−1.11462	−0.557311	−	0.830304i	$-0.688167\pi$
$607$	−27.4614	−1.11462	−0.557311	+	0.830304i	$0.688167\pi$
$608$	6.60919	0.268038
$609$	6.39603	0.259180
$610$	−42.4021	−1.71681
$611$	−24.5829	−0.994516
$612$	15.8408	0.640327
$613$	−0.0762193	−0.00307847	−0.00153923	−	0.999999i	$-0.500490\pi$
$613$	−0.0762193	−0.00307847	−0.00153923	+	0.999999i	$0.500490\pi$
$614$	5.15159	0.207901
$615$	−9.23765	−0.372498
$616$	18.5090	0.745747
$617$	−19.5678	−0.787770	−0.393885	−	0.919160i	$-0.628869\pi$
$617$	−19.5678	−0.787770	−0.393885	+	0.919160i	$0.628869\pi$
$618$	−30.4222	−1.22376
$619$	−14.7821	−0.594144	−0.297072	−	0.954855i	$-0.596010\pi$
$619$	−14.7821	−0.594144	−0.297072	+	0.954855i	$0.596010\pi$
$620$	6.16939	0.247769
$621$	1.04731	0.0420273
$622$	−2.32914	−0.0933900
$623$	−45.4409	−1.82055
$624$	23.6070	0.945036
$625$	−10.3893	−0.415570
$626$	2.76287	0.110427
$627$	−2.32199	−0.0927314
$628$	−22.1153	−0.882496
$629$	8.70453	0.347073
$630$	−17.8519	−0.711235
$631$	−16.2620	−0.647381	−0.323690	−	0.946163i	$-0.604924\pi$
$631$	−16.2620	−0.647381	−0.323690	+	0.946163i	$0.604924\pi$
$632$	−32.0150	−1.27349
$633$	−15.2056	−0.604369
$634$	70.3341	2.79333
$635$	1.55909	0.0618706
$636$	−2.81218	−0.111510
$637$	46.2603	1.83290
$638$	3.05507	0.120952
$639$	11.1546	0.441268
$640$	−29.2076	−1.15453
$641$	3.57771	0.141311	0.0706556	−	0.997501i	$-0.477491\pi$
$641$	3.57771	0.141311	0.0706556	+	0.997501i	$0.477491\pi$
$642$	−29.4079	−1.16064
$643$	−2.64873	−0.104456	−0.0522278	−	0.998635i	$-0.516632\pi$
$643$	−2.64873	−0.104456	−0.0522278	+	0.998635i	$0.516632\pi$
$644$	−18.4643	−0.727595
$645$	2.91940	0.114951
$646$	27.1544	1.06838
$647$	24.9821	0.982147	0.491073	−	0.871118i	$-0.336605\pi$
$647$	24.9821	0.982147	0.491073	+	0.871118i	$0.336605\pi$
$648$	−5.52734	−0.217134
$649$	−9.37247	−0.367901
$650$	22.7537	0.892472
$651$	3.57188	0.139993
$652$	−18.2329	−0.714055
$653$	8.17737	0.320005	0.160003	−	0.987117i	$-0.448850\pi$
$653$	8.17737	0.320005	0.160003	+	0.987117i	$0.448850\pi$
$654$	−4.28790	−0.167670
$655$	−25.5239	−0.997300
$656$	28.8484	1.12634
$657$	−8.44504	−0.329472
$658$	−58.0544	−2.26320
$659$	−8.37877	−0.326391	−0.163195	−	0.986594i	$-0.552180\pi$
$659$	−8.37877	−0.326391	−0.163195	+	0.986594i	$0.552180\pi$
$660$	−5.78378	−0.225133
$661$	4.19867	0.163309	0.0816546	−	0.996661i	$-0.473980\pi$
$661$	4.19867	0.163309	0.0816546	+	0.996661i	$0.473980\pi$
$662$	68.3432	2.65623
$663$	16.5822	0.644001
$664$	43.9660	1.70621
$665$	−20.7569	−0.804920
$666$	−5.77748	−0.223873
$667$	−1.60221	−0.0620377
$668$	−37.7877	−1.46205
$669$	13.4959	0.521782
$670$	−26.7752	−1.03442
$671$	−7.95370	−0.307049
$672$	9.53133	0.367679
$673$	−1.41592	−0.0545797	−0.0272898	−	0.999628i	$-0.508688\pi$
$673$	−1.41592	−0.0545797	−0.0272898	+	0.999628i	$0.508688\pi$
$674$	−51.3687	−1.97865
$675$	−2.06736	−0.0795726
$676$	27.3465	1.05179
$677$	17.2535	0.663104	0.331552	−	0.943437i	$-0.392428\pi$
$677$	17.2535	0.663104	0.331552	+	0.943437i	$0.392428\pi$
$678$	−2.37212	−0.0911005
$679$	−16.2584	−0.623940
$680$	35.5580	1.36359
$681$	−2.20160	−0.0843654
$682$	1.70611	0.0653304
$683$	−28.5441	−1.09221	−0.546104	−	0.837717i	$-0.683890\pi$
$683$	−28.5441	−1.09221	−0.546104	+	0.837717i	$0.683890\pi$
$684$	−12.2250	−0.467436
$685$	−26.0108	−0.993820
$686$	36.2762	1.38503
$687$	21.3693	0.815290
$688$	−9.11704	−0.347584
$689$	−2.94381	−0.112150
$690$	4.47189	0.170242
$691$	−41.7092	−1.58669	−0.793347	−	0.608770i	$-0.791663\pi$
$691$	−41.7092	−1.58669	−0.793347	+	0.608770i	$0.791663\pi$
$692$	23.2763	0.884831
$693$	−3.34862	−0.127204
$694$	−83.7558	−3.17933
$695$	−25.2552	−0.957986
$696$	8.45585	0.320518
$697$	20.2639	0.767551
$698$	−16.4008	−0.620778
$699$	2.94144	0.111255
$700$	36.4478	1.37760
$701$	2.16083	0.0816134	0.0408067	−	0.999167i	$-0.487007\pi$
$701$	2.16083	0.0816134	0.0408067	+	0.999167i	$0.487007\pi$
$702$	−11.0062	−0.415401
$703$	−6.71766	−0.253361
$704$	−4.01409	−0.151287
$705$	9.53698	0.359183
$706$	69.5114	2.61610
$707$	−6.02261	−0.226503
$708$	−49.3450	−1.85450
$709$	−33.8706	−1.27204	−0.636018	−	0.771675i	$-0.719419\pi$
$709$	−33.8706	−1.27204	−0.636018	+	0.771675i	$0.719419\pi$
$710$	47.6285	1.78747
$711$	5.79211	0.217221
$712$	−60.0750	−2.25141
$713$	−0.894755	−0.0335089
$714$	39.1603	1.46554
$715$	−6.05448	−0.226425
$716$	78.0655	2.91745
$717$	−25.5998	−0.956043
$718$	23.7632	0.886833
$719$	−9.68412	−0.361157	−0.180578	−	0.983561i	$-0.557797\pi$
$719$	−9.68412	−0.361157	−0.180578	+	0.983561i	$0.557797\pi$
$720$	−9.15839	−0.341313
$721$	−51.0124	−1.89980
$722$	26.4176	0.983160
$723$	−13.9930	−0.520405
$724$	−89.6562	−3.33205
$725$	3.16269	0.117459
$726$	25.8274	0.958547
$727$	38.0407	1.41085	0.705426	−	0.708784i	$-0.250756\pi$
$727$	38.0407	1.41085	0.705426	+	0.708784i	$0.250756\pi$
$728$	102.009	3.78069
$729$	1.00000	0.0370370
$730$	−36.0591	−1.33461
$731$	−6.40407	−0.236863
$732$	−41.8754	−1.54776
$733$	−0.326170	−0.0120473	−0.00602367	−	0.999982i	$-0.501917\pi$
$733$	−0.326170	−0.0120473	−0.00602367	+	0.999982i	$0.501917\pi$
$734$	52.5393	1.93926
$735$	−17.9468	−0.661978
$736$	−2.38760	−0.0880080
$737$	−5.02245	−0.185004
$738$	−13.4498	−0.495094
$739$	21.0922	0.775891	0.387945	−	0.921682i	$-0.373185\pi$
$739$	21.0922	0.775891	0.387945	+	0.921682i	$0.373185\pi$
$740$	−16.7328	−0.615111
$741$	−12.7972	−0.470117
$742$	−6.95203	−0.255217
$743$	38.8761	1.42623	0.713113	−	0.701049i	$-0.247285\pi$
$743$	38.8761	1.42623	0.713113	+	0.701049i	$0.247285\pi$
$744$	4.72219	0.173124
$745$	−28.2829	−1.03621
$746$	−40.8873	−1.49699
$747$	−7.95428	−0.291032
$748$	12.6874	0.463898
$749$	−49.3116	−1.80181
$750$	−30.1767	−1.10190
$751$	7.55803	0.275796	0.137898	−	0.990446i	$-0.455965\pi$
$751$	7.55803	0.275796	0.137898	+	0.990446i	$0.455965\pi$
$752$	−29.7831	−1.08608
$753$	−7.02136	−0.255873
$754$	16.8375	0.613185
$755$	15.7372	0.572735
$756$	−17.6301	−0.641201
$757$	24.1251	0.876842	0.438421	−	0.898770i	$-0.355538\pi$
$757$	24.1251	0.876842	0.438421	+	0.898770i	$0.355538\pi$
$758$	43.9503	1.59635
$759$	0.838829	0.0304476
$760$	−27.4416	−0.995413
$761$	39.5516	1.43374	0.716872	−	0.697205i	$-0.245573\pi$
$761$	39.5516	1.43374	0.716872	+	0.697205i	$0.245573\pi$
$762$	2.27000	0.0822335
$763$	−7.19001	−0.260296
$764$	−13.7238	−0.496510
$765$	−6.43311	−0.232590
$766$	84.3427	3.04743
$767$	−51.6546	−1.86514
$768$	−32.5021	−1.17282
$769$	6.92315	0.249655	0.124828	−	0.992178i	$-0.460162\pi$
$769$	6.92315	0.249655	0.124828	+	0.992178i	$0.460162\pi$
$770$	−14.2981	−0.515269
$771$	18.6916	0.673160
$772$	28.5110	1.02613
$773$	−16.9567	−0.609890	−0.304945	−	0.952370i	$-0.598638\pi$
$773$	−16.9567	−0.609890	−0.304945	+	0.952370i	$0.598638\pi$
$774$	4.25059	0.152784
$775$	1.76621	0.0634442
$776$	−21.4944	−0.771603
$777$	−9.68776	−0.347546
$778$	6.75519	0.242185
$779$	−15.6385	−0.560308
$780$	−31.8762	−1.14135
$781$	8.93407	0.319686
$782$	−9.80965	−0.350792
$783$	−1.52982	−0.0546714
$784$	56.0463	2.00165
$785$	8.98125	0.320554
$786$	−37.1622	−1.32553
$787$	6.40161	0.228193	0.114096	−	0.993470i	$-0.463603\pi$
$787$	6.40161	0.228193	0.114096	+	0.993470i	$0.463603\pi$
$788$	−15.9154	−0.566962
$789$	−12.4262	−0.442384
$790$	24.7315	0.879908
$791$	−3.97760	−0.141427
$792$	−4.42703	−0.157308
$793$	−43.8353	−1.55664
$794$	42.3420	1.50266
$795$	1.14206	0.0405045
$796$	−80.3066	−2.84639
$797$	11.7884	0.417566	0.208783	−	0.977962i	$-0.433050\pi$
$797$	11.7884	0.417566	0.208783	+	0.977962i	$0.433050\pi$
$798$	−30.2216	−1.06983
$799$	−20.9205	−0.740115
$800$	4.71302	0.166630
$801$	10.8687	0.384027
$802$	43.5296	1.53708
$803$	−6.76391	−0.238693
$804$	−26.4426	−0.932560
$805$	7.49853	0.264289
$806$	9.40292	0.331204
$807$	18.3235	0.645017
$808$	−7.96216	−0.280108
$809$	39.0402	1.37258	0.686290	−	0.727328i	$-0.259238\pi$
$809$	39.0402	1.37258	0.686290	+	0.727328i	$0.259238\pi$
$810$	4.26986	0.150028
$811$	9.94985	0.349386	0.174693	−	0.984623i	$-0.444107\pi$
$811$	9.94985	0.349386	0.174693	+	0.984623i	$0.444107\pi$
$812$	26.9710	0.946495
$813$	3.23595	0.113490
$814$	−4.62737	−0.162189
$815$	7.40456	0.259371
$816$	20.0901	0.703293
$817$	4.94229	0.172909
$818$	66.5761	2.32778
$819$	−18.4553	−0.644880
$820$	−38.9536	−1.36032
$821$	−15.7035	−0.548054	−0.274027	−	0.961722i	$-0.588356\pi$
$821$	−15.7035	−0.548054	−0.274027	+	0.961722i	$0.588356\pi$
$822$	−37.8711	−1.32091
$823$	−31.1419	−1.08554	−0.542769	−	0.839882i	$-0.682624\pi$
$823$	−31.1419	−1.08554	−0.542769	+	0.839882i	$0.682624\pi$
$824$	−67.4407	−2.34941
$825$	−1.65581	−0.0576481
$826$	−121.986	−4.24445
$827$	24.1006	0.838060	0.419030	−	0.907972i	$-0.362370\pi$
$827$	24.1006	0.838060	0.419030	+	0.907972i	$0.362370\pi$
$828$	4.41635	0.153479
$829$	9.17824	0.318773	0.159387	−	0.987216i	$-0.449048\pi$
$829$	9.17824	0.318773	0.159387	+	0.987216i	$0.449048\pi$
$830$	−33.9637	−1.17890
$831$	−11.3492	−0.393698
$832$	−22.1229	−0.766974
$833$	39.3685	1.36404
$834$	−36.7711	−1.27328
$835$	15.3460	0.531069
$836$	−9.79143	−0.338644
$837$	−0.854333	−0.0295301
$838$	31.6911	1.09475
$839$	−42.8007	−1.47764	−0.738821	−	0.673901i	$-0.764617\pi$
$839$	−42.8007	−1.47764	−0.738821	+	0.673901i	$0.764617\pi$
$840$	−39.5745	−1.36545
$841$	−26.6596	−0.919298
$842$	15.0918	0.520096
$843$	−10.2294	−0.352320
$844$	−64.1195	−2.20708
$845$	−11.1057	−0.382048
$846$	13.8856	0.477398
$847$	43.3079	1.48808
$848$	−3.56654	−0.122476
$849$	2.31229	0.0793576
$850$	19.3638	0.664174
$851$	2.42678	0.0831891
$852$	47.0369	1.61146
$853$	39.8107	1.36309	0.681547	−	0.731775i	$-0.261308\pi$
$853$	39.8107	1.36309	0.681547	+	0.731775i	$0.261308\pi$
$854$	−103.521	−3.54240
$855$	4.96471	0.169789
$856$	−65.1922	−2.22822
$857$	46.4148	1.58550	0.792750	−	0.609547i	$-0.208649\pi$
$857$	46.4148	1.58550	0.792750	+	0.609547i	$0.208649\pi$
$858$	−8.81520	−0.300946
$859$	−20.5521	−0.701227	−0.350613	−	0.936520i	$-0.614027\pi$
$859$	−20.5521	−0.701227	−0.350613	+	0.936520i	$0.614027\pi$
$860$	12.3106	0.419789
$861$	−22.5528	−0.768599
$862$	98.1322	3.34240
$863$	−33.6394	−1.14510	−0.572550	−	0.819870i	$-0.694046\pi$
$863$	−33.6394	−1.14510	−0.572550	+	0.819870i	$0.694046\pi$
$864$	−2.27973	−0.0775581
$865$	−9.45273	−0.321402
$866$	11.6405	0.395561
$867$	−2.88817	−0.0980873
$868$	15.0620	0.511237
$869$	4.63909	0.157370
$870$	−6.53214	−0.221460
$871$	−27.6803	−0.937910
$872$	−9.50553	−0.321898
$873$	3.88873	0.131614
$874$	7.57052	0.256077
$875$	−50.6007	−1.71061
$876$	−35.6113	−1.20319
$877$	−7.93513	−0.267950	−0.133975	−	0.990985i	$-0.542774\pi$
$877$	−7.93513	−0.267950	−0.133975	+	0.990985i	$0.542774\pi$
$878$	−33.6526	−1.13572
$879$	−15.1692	−0.511643
$880$	−7.33526	−0.247272
$881$	−34.3737	−1.15808	−0.579040	−	0.815299i	$-0.696572\pi$
$881$	−34.3737	−1.15808	−0.579040	+	0.815299i	$0.696572\pi$
$882$	−26.1301	−0.879848
$883$	47.6040	1.60200	0.801001	−	0.598662i	$-0.204301\pi$
$883$	47.6040	1.60200	0.801001	+	0.598662i	$0.204301\pi$
$884$	69.9244	2.35181
$885$	20.0395	0.673621
$886$	−15.3007	−0.514038
$887$	−4.98664	−0.167435	−0.0837175	−	0.996490i	$-0.526679\pi$
$887$	−4.98664	−0.167435	−0.0837175	+	0.996490i	$0.526679\pi$
$888$	−12.8077	−0.429797
$889$	3.80637	0.127662
$890$	46.4079	1.55560
$891$	0.800933	0.0268323
$892$	56.9099	1.90548
$893$	16.1453	0.540281
$894$	−41.1793	−1.37724
$895$	−31.7032	−1.05972
$896$	−71.3077	−2.38222
$897$	4.62305	0.154359
$898$	46.2825	1.54447
$899$	1.30698	0.0435902
$900$	−8.71769	−0.290590
$901$	−2.50524	−0.0834617
$902$	−10.7724	−0.358682
$903$	7.12745	0.237187
$904$	−5.25857	−0.174897
$905$	36.4103	1.21032
$906$	22.9130	0.761234
$907$	15.3831	0.510788	0.255394	−	0.966837i	$-0.417795\pi$
$907$	15.3831	0.510788	0.255394	+	0.966837i	$0.417795\pi$
$908$	−9.28376	−0.308092
$909$	1.44051	0.0477786
$910$	−78.8016	−2.61225
$911$	22.4267	0.743030	0.371515	−	0.928427i	$-0.378839\pi$
$911$	22.4267	0.743030	0.371515	+	0.928427i	$0.378839\pi$
$912$	−15.5044	−0.513401
$913$	−6.37085	−0.210844
$914$	−59.2650	−1.96031
$915$	17.0060	0.562202
$916$	90.1107	2.97734
$917$	−62.3141	−2.05779
$918$	−9.36647	−0.309140
$919$	−25.8802	−0.853709	−0.426855	−	0.904320i	$-0.640378\pi$
$919$	−25.8802	−0.853709	−0.426855	+	0.904320i	$0.640378\pi$
$920$	9.91341	0.326835
$921$	−2.06613	−0.0680812
$922$	−41.3021	−1.36021
$923$	49.2385	1.62070
$924$	−14.1205	−0.464532
$925$	−4.79037	−0.157506
$926$	−66.6656	−2.19077
$927$	12.2013	0.400743
$928$	3.48759	0.114486
$929$	−23.4961	−0.770884	−0.385442	−	0.922732i	$-0.625951\pi$
$929$	−23.4961	−0.770884	−0.385442	+	0.922732i	$0.625951\pi$
$930$	−3.64788	−0.119619
$931$	−30.3824	−0.995742
$932$	12.4035	0.406291
$933$	0.934138	0.0305823
$934$	−49.2779	−1.61242
$935$	−5.15249	−0.168505
$936$	−24.3987	−0.797498
$937$	21.2470	0.694108	0.347054	−	0.937845i	$-0.387182\pi$
$937$	21.2470	0.694108	0.347054	+	0.937845i	$0.387182\pi$
$938$	−65.3692	−2.13438
$939$	−1.10809	−0.0361613
$940$	40.2158	1.31169
$941$	−48.7663	−1.58974	−0.794868	−	0.606782i	$-0.792460\pi$
$941$	−48.7663	−1.58974	−0.794868	+	0.606782i	$0.792460\pi$
$942$	13.0765	0.426055
$943$	5.64949	0.183973
$944$	−62.5817	−2.03686
$945$	7.15977	0.232907
$946$	3.40443	0.110688
$947$	28.4806	0.925495	0.462748	−	0.886490i	$-0.346864\pi$
$947$	28.4806	0.925495	0.462748	+	0.886490i	$0.346864\pi$
$948$	24.4243	0.793265
$949$	−37.2780	−1.21010
$950$	−14.9439	−0.484844
$951$	−28.2086	−0.914727
$952$	86.8115	2.81358
$953$	18.8848	0.611739	0.305870	−	0.952073i	$-0.401053\pi$
$953$	18.8848	0.611739	0.305870	+	0.952073i	$0.401053\pi$
$954$	1.66281	0.0538354
$955$	5.57338	0.180350
$956$	−107.950	−3.49135
$957$	−1.22529	−0.0396079
$958$	91.0207	2.94074
$959$	−63.5028	−2.05061
$960$	8.58263	0.277003
$961$	−30.2701	−0.976455
$962$	−25.5029	−0.822246
$963$	11.7945	0.380072
$964$	−59.0061	−1.90046
$965$	−11.5786	−0.372728
$966$	10.9177	0.351271
$967$	−29.0479	−0.934119	−0.467059	−	0.884226i	$-0.654687\pi$
$967$	−29.0479	−0.934119	−0.467059	+	0.884226i	$0.654687\pi$
$968$	57.2550	1.84025
$969$	−10.8907	−0.349860
$970$	16.6044	0.533134
$971$	−4.47172	−0.143504	−0.0717521	−	0.997422i	$-0.522859\pi$
$971$	−4.47172	−0.143504	−0.0717521	+	0.997422i	$0.522859\pi$
$972$	4.21683	0.135255
$973$	−61.6583	−1.97667
$974$	75.3792	2.41530
$975$	−9.12571	−0.292257
$976$	−53.1083	−1.69996
$977$	2.20085	0.0704113	0.0352056	−	0.999380i	$-0.488791\pi$
$977$	2.20085	0.0704113	0.0352056	+	0.999380i	$0.488791\pi$
$978$	10.7809	0.344735
$979$	8.70510	0.278216
$980$	−75.6785	−2.41746
$981$	1.71973	0.0549067
$982$	83.5430	2.66597
$983$	−8.92440	−0.284644	−0.142322	−	0.989820i	$-0.545457\pi$
$983$	−8.92440	−0.284644	−0.142322	+	0.989820i	$0.545457\pi$
$984$	−29.8159	−0.950496
$985$	6.46340	0.205941
$986$	14.3290	0.456330
$987$	23.2836	0.741126
$988$	−53.9636	−1.71681
$989$	−1.78542	−0.0567732
$990$	3.41988	0.108691
$991$	8.82850	0.280446	0.140223	−	0.990120i	$-0.455218\pi$
$991$	8.82850	0.280446	0.140223	+	0.990120i	$0.455218\pi$
$992$	1.94765	0.0618380
$993$	−27.4101	−0.869834
$994$	116.281	3.68820
$995$	32.6133	1.03391
$996$	−33.5418	−1.06281
$997$	9.30347	0.294644	0.147322	−	0.989089i	$-0.452935\pi$
$997$	9.30347	0.294644	0.147322	+	0.989089i	$0.452935\pi$
$998$	−44.7216	−1.41564
$999$	2.31715	0.0733113

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.a.1.7	✓	95

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.a.1.7	✓	95	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:	\( N \)	\(=\)	\( 8049 = 3 \cdot 2683 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8049.a (trivial)

\(f(q)\)	\(=\)	\(q-2.49336 q^{2} +1.00000 q^{3} +4.21683 q^{4} -1.71250 q^{5} -2.49336 q^{6} -4.18090 q^{7} -5.52734 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.49336 q^{2} +1.00000 q^{3} +4.21683 q^{4} -1.71250 q^{5} -2.49336 q^{6} -4.18090 q^{7} -5.52734 q^{8} +1.00000 q^{9} +4.26986 q^{10} +0.800933 q^{11} +4.21683 q^{12} +4.41419 q^{13} +10.4245 q^{14} -1.71250 q^{15} +5.34798 q^{16} +3.75657 q^{17} -2.49336 q^{18} -2.89911 q^{19} -7.22130 q^{20} -4.18090 q^{21} -1.99701 q^{22} +1.04731 q^{23} -5.52734 q^{24} -2.06736 q^{25} -11.0062 q^{26} +1.00000 q^{27} -17.6301 q^{28} -1.52982 q^{29} +4.26986 q^{30} -0.854333 q^{31} -2.27973 q^{32} +0.800933 q^{33} -9.36647 q^{34} +7.15977 q^{35} +4.21683 q^{36} +2.31715 q^{37} +7.22851 q^{38} +4.41419 q^{39} +9.46555 q^{40} +5.39426 q^{41} +10.4245 q^{42} -1.70476 q^{43} +3.37740 q^{44} -1.71250 q^{45} -2.61133 q^{46} -5.56905 q^{47} +5.34798 q^{48} +10.4799 q^{49} +5.15466 q^{50} +3.75657 q^{51} +18.6139 q^{52} -0.666895 q^{53} -2.49336 q^{54} -1.37159 q^{55} +23.1092 q^{56} -2.89911 q^{57} +3.81439 q^{58} -11.7019 q^{59} -7.22130 q^{60} -9.93054 q^{61} +2.13016 q^{62} -4.18090 q^{63} -5.01177 q^{64} -7.55929 q^{65} -1.99701 q^{66} -6.27074 q^{67} +15.8408 q^{68} +1.04731 q^{69} -17.8519 q^{70} +11.1546 q^{71} -5.52734 q^{72} -8.44504 q^{73} -5.77748 q^{74} -2.06736 q^{75} -12.2250 q^{76} -3.34862 q^{77} -11.0062 q^{78} +5.79211 q^{79} -9.15839 q^{80} +1.00000 q^{81} -13.4498 q^{82} -7.95428 q^{83} -17.6301 q^{84} -6.43311 q^{85} +4.25059 q^{86} -1.52982 q^{87} -4.42703 q^{88} +10.8687 q^{89} +4.26986 q^{90} -18.4553 q^{91} +4.41635 q^{92} -0.854333 q^{93} +13.8856 q^{94} +4.96471 q^{95} -2.27973 q^{96} +3.88873 q^{97} -26.1301 q^{98} +0.800933 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 95 q - 9 q^{2} + 95 q^{3} + 65 q^{4} - 15 q^{5} - 9 q^{6} - 36 q^{7} - 27 q^{8} + 95 q^{9}+O(q^{10}) \) 95 * q - 9 * q^2 + 95 * q^3 + 65 * q^4 - 15 * q^5 - 9 * q^6 - 36 * q^7 - 27 * q^8 + 95 * q^9	\( 95 q - 9 q^{2} + 95 q^{3} + 65 q^{4} - 15 q^{5} - 9 q^{6} - 36 q^{7} - 27 q^{8} + 95 q^{9} - 36 q^{10} - 48 q^{11} + 65 q^{12} - 73 q^{13} - 17 q^{14} - 15 q^{15} + 13 q^{16} - 9 q^{17} - 9 q^{18} - 66 q^{19} - 35 q^{20} - 36 q^{21} - 37 q^{22} - 58 q^{23} - 27 q^{24} + 24 q^{25} - 25 q^{26} + 95 q^{27} - 75 q^{28} - 31 q^{29} - 36 q^{30} - 129 q^{31} - 53 q^{32} - 48 q^{33} - 61 q^{34} - 38 q^{35} + 65 q^{36} - 127 q^{37} + q^{38} - 73 q^{39} - 74 q^{40} - 31 q^{41} - 17 q^{42} - 62 q^{43} - 76 q^{44} - 15 q^{45} - 60 q^{46} - 75 q^{47} + 13 q^{48} + 5 q^{49} - 30 q^{50} - 9 q^{51} - 137 q^{52} - 28 q^{53} - 9 q^{54} - 117 q^{55} - 23 q^{56} - 66 q^{57} - 90 q^{58} - 60 q^{59} - 35 q^{60} - 96 q^{61} + 10 q^{62} - 36 q^{63} - 75 q^{64} - 28 q^{65} - 37 q^{66} - 116 q^{67} + 3 q^{68} - 58 q^{69} - 73 q^{70} - 144 q^{71} - 27 q^{72} - 121 q^{73} - 16 q^{74} + 24 q^{75} - 118 q^{76} - 3 q^{77} - 25 q^{78} - 135 q^{79} - 36 q^{80} + 95 q^{81} - 102 q^{82} - 21 q^{83} - 75 q^{84} - 129 q^{85} - 46 q^{86} - 31 q^{87} - 77 q^{88} - 63 q^{89} - 36 q^{90} - 123 q^{91} - 42 q^{92} - 129 q^{93} - 44 q^{94} - 80 q^{95} - 53 q^{96} - 144 q^{97} + 10 q^{98} - 48 q^{99}+O(q^{100}) \) 95 * q - 9 * q^2 + 95 * q^3 + 65 * q^4 - 15 * q^5 - 9 * q^6 - 36 * q^7 - 27 * q^8 + 95 * q^9 - 36 * q^10 - 48 * q^11 + 65 * q^12 - 73 * q^13 - 17 * q^14 - 15 * q^15 + 13 * q^16 - 9 * q^17 - 9 * q^18 - 66 * q^19 - 35 * q^20 - 36 * q^21 - 37 * q^22 - 58 * q^23 - 27 * q^24 + 24 * q^25 - 25 * q^26 + 95 * q^27 - 75 * q^28 - 31 * q^29 - 36 * q^30 - 129 * q^31 - 53 * q^32 - 48 * q^33 - 61 * q^34 - 38 * q^35 + 65 * q^36 - 127 * q^37 + q^38 - 73 * q^39 - 74 * q^40 - 31 * q^41 - 17 * q^42 - 62 * q^43 - 76 * q^44 - 15 * q^45 - 60 * q^46 - 75 * q^47 + 13 * q^48 + 5 * q^49 - 30 * q^50 - 9 * q^51 - 137 * q^52 - 28 * q^53 - 9 * q^54 - 117 * q^55 - 23 * q^56 - 66 * q^57 - 90 * q^58 - 60 * q^59 - 35 * q^60 - 96 * q^61 + 10 * q^62 - 36 * q^63 - 75 * q^64 - 28 * q^65 - 37 * q^66 - 116 * q^67 + 3 * q^68 - 58 * q^69 - 73 * q^70 - 144 * q^71 - 27 * q^72 - 121 * q^73 - 16 * q^74 + 24 * q^75 - 118 * q^76 - 3 * q^77 - 25 * q^78 - 135 * q^79 - 36 * q^80 + 95 * q^81 - 102 * q^82 - 21 * q^83 - 75 * q^84 - 129 * q^85 - 46 * q^86 - 31 * q^87 - 77 * q^88 - 63 * q^89 - 36 * q^90 - 123 * q^91 - 42 * q^92 - 129 * q^93 - 44 * q^94 - 80 * q^95 - 53 * q^96 - 144 * q^97 + 10 * q^98 - 48 * q^99

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