LMFDB - Embedded newform 6009.2.a.b.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6009,2,Mod(1,6009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6009, 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("6009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6009 = 3 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6009.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:	$47.9821065746$
Analytic rank:	$1$
Dimension:	$74$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.52631 q^{2} -1.00000 q^{3} +0.329628 q^{4} -3.83581 q^{5} +1.52631 q^{6} +1.78836 q^{7} +2.54951 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.52631 q^{2} -1.00000 q^{3} +0.329628 q^{4} -3.83581 q^{5} +1.52631 q^{6} +1.78836 q^{7} +2.54951 q^{8} +1.00000 q^{9} +5.85464 q^{10} +2.88174 q^{11} -0.329628 q^{12} -4.98346 q^{13} -2.72959 q^{14} +3.83581 q^{15} -4.55060 q^{16} +0.835797 q^{17} -1.52631 q^{18} +4.19145 q^{19} -1.26439 q^{20} -1.78836 q^{21} -4.39843 q^{22} -6.35409 q^{23} -2.54951 q^{24} +9.71342 q^{25} +7.60632 q^{26} -1.00000 q^{27} +0.589494 q^{28} +5.67107 q^{29} -5.85464 q^{30} -0.398969 q^{31} +1.84662 q^{32} -2.88174 q^{33} -1.27569 q^{34} -6.85980 q^{35} +0.329628 q^{36} -11.1449 q^{37} -6.39746 q^{38} +4.98346 q^{39} -9.77942 q^{40} -4.93141 q^{41} +2.72959 q^{42} -6.03801 q^{43} +0.949901 q^{44} -3.83581 q^{45} +9.69833 q^{46} +9.10551 q^{47} +4.55060 q^{48} -3.80177 q^{49} -14.8257 q^{50} -0.835797 q^{51} -1.64269 q^{52} +9.09832 q^{53} +1.52631 q^{54} -11.0538 q^{55} +4.55944 q^{56} -4.19145 q^{57} -8.65582 q^{58} +9.25771 q^{59} +1.26439 q^{60} -8.50568 q^{61} +0.608951 q^{62} +1.78836 q^{63} +6.28268 q^{64} +19.1156 q^{65} +4.39843 q^{66} +3.15826 q^{67} +0.275502 q^{68} +6.35409 q^{69} +10.4702 q^{70} -5.86579 q^{71} +2.54951 q^{72} +11.1746 q^{73} +17.0107 q^{74} -9.71342 q^{75} +1.38162 q^{76} +5.15358 q^{77} -7.60632 q^{78} -14.4714 q^{79} +17.4552 q^{80} +1.00000 q^{81} +7.52687 q^{82} +11.3822 q^{83} -0.589494 q^{84} -3.20596 q^{85} +9.21588 q^{86} -5.67107 q^{87} +7.34701 q^{88} -17.2826 q^{89} +5.85464 q^{90} -8.91222 q^{91} -2.09449 q^{92} +0.398969 q^{93} -13.8978 q^{94} -16.0776 q^{95} -1.84662 q^{96} +8.50787 q^{97} +5.80269 q^{98} +2.88174 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 74 q - 3 q^{2} - 74 q^{3} + 57 q^{4} + 14 q^{5} + 3 q^{6} - 26 q^{7} - 9 q^{8} + 74 q^{9}+O(q^{10}) $ 74 * q - 3 * q^2 - 74 * q^3 + 57 * q^4 + 14 * q^5 + 3 * q^6 - 26 * q^7 - 9 * q^8 + 74 * q^9	\( 74 q - 3 q^{2} - 74 q^{3} + 57 q^{4} + 14 q^{5} + 3 q^{6} - 26 q^{7} - 9 q^{8} + 74 q^{9} - 21 q^{10} - 16 q^{11} - 57 q^{12} - 16 q^{13} - 17 q^{14} - 14 q^{15} + 15 q^{16} + 33 q^{17} - 3 q^{18} - 46 q^{19} + 17 q^{20} + 26 q^{21} - 28 q^{22} - 31 q^{23} + 9 q^{24} + 42 q^{25} - 8 q^{26} - 74 q^{27} - 46 q^{28} - 7 q^{29} + 21 q^{30} - 60 q^{31} - 16 q^{32} + 16 q^{33} - 42 q^{34} - 46 q^{35} + 57 q^{36} - 22 q^{37} + 10 q^{38} + 16 q^{39} - 67 q^{40} - 11 q^{41} + 17 q^{42} - 56 q^{43} - 25 q^{44} + 14 q^{45} - 59 q^{46} - q^{47} - 15 q^{48} + 12 q^{49} - 24 q^{50} - 33 q^{51} - 37 q^{52} + 25 q^{53} + 3 q^{54} - 90 q^{55} - 46 q^{56} + 46 q^{57} - 20 q^{58} - 60 q^{59} - 17 q^{60} - 55 q^{61} + 40 q^{62} - 26 q^{63} - 55 q^{64} - 12 q^{65} + 28 q^{66} - 64 q^{67} + 75 q^{68} + 31 q^{69} - 23 q^{70} - 128 q^{71} - 9 q^{72} - 31 q^{73} - 51 q^{74} - 42 q^{75} - 109 q^{76} + 70 q^{77} + 8 q^{78} - 193 q^{79} + 39 q^{80} + 74 q^{81} - 26 q^{82} - 5 q^{83} + 46 q^{84} - 60 q^{85} - 36 q^{86} + 7 q^{87} - 56 q^{88} - 21 q^{90} - 99 q^{91} - 54 q^{92} + 60 q^{93} - 66 q^{94} - 101 q^{95} + 16 q^{96} - 36 q^{97} - 21 q^{98} - 16 q^{99}+O(q^{100}) \) 74 * q - 3 * q^2 - 74 * q^3 + 57 * q^4 + 14 * q^5 + 3 * q^6 - 26 * q^7 - 9 * q^8 + 74 * q^9 - 21 * q^10 - 16 * q^11 - 57 * q^12 - 16 * q^13 - 17 * q^14 - 14 * q^15 + 15 * q^16 + 33 * q^17 - 3 * q^18 - 46 * q^19 + 17 * q^20 + 26 * q^21 - 28 * q^22 - 31 * q^23 + 9 * q^24 + 42 * q^25 - 8 * q^26 - 74 * q^27 - 46 * q^28 - 7 * q^29 + 21 * q^30 - 60 * q^31 - 16 * q^32 + 16 * q^33 - 42 * q^34 - 46 * q^35 + 57 * q^36 - 22 * q^37 + 10 * q^38 + 16 * q^39 - 67 * q^40 - 11 * q^41 + 17 * q^42 - 56 * q^43 - 25 * q^44 + 14 * q^45 - 59 * q^46 - q^47 - 15 * q^48 + 12 * q^49 - 24 * q^50 - 33 * q^51 - 37 * q^52 + 25 * q^53 + 3 * q^54 - 90 * q^55 - 46 * q^56 + 46 * q^57 - 20 * q^58 - 60 * q^59 - 17 * q^60 - 55 * q^61 + 40 * q^62 - 26 * q^63 - 55 * q^64 - 12 * q^65 + 28 * q^66 - 64 * q^67 + 75 * q^68 + 31 * q^69 - 23 * q^70 - 128 * q^71 - 9 * q^72 - 31 * q^73 - 51 * q^74 - 42 * q^75 - 109 * q^76 + 70 * q^77 + 8 * q^78 - 193 * q^79 + 39 * q^80 + 74 * q^81 - 26 * q^82 - 5 * q^83 + 46 * q^84 - 60 * q^85 - 36 * q^86 + 7 * q^87 - 56 * q^88 - 21 * q^90 - 99 * q^91 - 54 * q^92 + 60 * q^93 - 66 * q^94 - 101 * q^95 + 16 * q^96 - 36 * q^97 - 21 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.52631	−1.07927	−0.539633	−	0.841901i	$-0.681437\pi$
$2$	−1.52631	−1.07927	−0.539633	+	0.841901i	$0.681437\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.329628	0.164814
$5$	−3.83581	−1.71543	−0.857713	−	0.514129i	$-0.828115\pi$
$5$	−3.83581	−1.71543	−0.857713	+	0.514129i	$0.828115\pi$
$6$	1.52631	0.623114
$7$	1.78836	0.675936	0.337968	−	0.941158i	$-0.390260\pi$
$7$	1.78836	0.675936	0.337968	+	0.941158i	$0.390260\pi$
$8$	2.54951	0.901387
$9$	1.00000	0.333333
$10$	5.85464	1.85140
$11$	2.88174	0.868876	0.434438	−	0.900702i	$-0.356947\pi$
$11$	2.88174	0.868876	0.434438	+	0.900702i	$0.356947\pi$
$12$	−0.329628	−0.0951555
$13$	−4.98346	−1.38216	−0.691082	−	0.722776i	$-0.742866\pi$
$13$	−4.98346	−1.38216	−0.691082	+	0.722776i	$0.742866\pi$
$14$	−2.72959	−0.729515
$15$	3.83581	0.990401
$16$	−4.55060	−1.13765
$17$	0.835797	0.202711	0.101355	−	0.994850i	$-0.467682\pi$
$17$	0.835797	0.202711	0.101355	+	0.994850i	$0.467682\pi$
$18$	−1.52631	−0.359755
$19$	4.19145	0.961584	0.480792	−	0.876835i	$-0.340349\pi$
$19$	4.19145	0.961584	0.480792	+	0.876835i	$0.340349\pi$
$20$	−1.26439	−0.282726
$21$	−1.78836	−0.390252
$22$	−4.39843	−0.937748
$23$	−6.35409	−1.32492	−0.662460	−	0.749097i	$-0.730487\pi$
$23$	−6.35409	−1.32492	−0.662460	+	0.749097i	$0.730487\pi$
$24$	−2.54951	−0.520416
$25$	9.71342	1.94268
$26$	7.60632	1.49172
$27$	−1.00000	−0.192450
$28$	0.589494	0.111404
$29$	5.67107	1.05309	0.526546	−	0.850147i	$-0.323487\pi$
$29$	5.67107	1.05309	0.526546	+	0.850147i	$0.323487\pi$
$30$	−5.85464	−1.06891
$31$	−0.398969	−0.0716570	−0.0358285	−	0.999358i	$-0.511407\pi$
$31$	−0.398969	−0.0716570	−0.0358285	+	0.999358i	$0.511407\pi$
$32$	1.84662	0.326440
$33$	−2.88174	−0.501646
$34$	−1.27569	−0.218779
$35$	−6.85980	−1.15952
$36$	0.329628	0.0549380
$37$	−11.1449	−1.83222	−0.916109	−	0.400930i	$-0.868687\pi$
$37$	−11.1449	−1.83222	−0.916109	+	0.400930i	$0.868687\pi$
$38$	−6.39746	−1.03780
$39$	4.98346	0.797993
$40$	−9.77942	−1.54626
$41$	−4.93141	−0.770157	−0.385078	−	0.922884i	$-0.625826\pi$
$41$	−4.93141	−0.770157	−0.385078	+	0.922884i	$0.625826\pi$
$42$	2.72959	0.421186
$43$	−6.03801	−0.920787	−0.460394	−	0.887715i	$-0.652292\pi$
$43$	−6.03801	−0.920787	−0.460394	+	0.887715i	$0.652292\pi$
$44$	0.949901	0.143203
$45$	−3.83581	−0.571808
$46$	9.69833	1.42994
$47$	9.10551	1.32818	0.664088	−	0.747655i	$-0.268820\pi$
$47$	9.10551	1.32818	0.664088	+	0.747655i	$0.268820\pi$
$48$	4.55060	0.656823
$49$	−3.80177	−0.543110
$50$	−14.8257	−2.09667
$51$	−0.835797	−0.117035
$52$	−1.64269	−0.227800
$53$	9.09832	1.24975	0.624875	−	0.780725i	$-0.285150\pi$
$53$	9.09832	1.24975	0.624875	+	0.780725i	$0.285150\pi$
$54$	1.52631	0.207705
$55$	−11.0538	−1.49049
$56$	4.55944	0.609280
$57$	−4.19145	−0.555171
$58$	−8.65582	−1.13657
$59$	9.25771	1.20525	0.602626	−	0.798024i	$-0.294121\pi$
$59$	9.25771	1.20525	0.602626	+	0.798024i	$0.294121\pi$
$60$	1.26439	0.163232
$61$	−8.50568	−1.08904	−0.544520	−	0.838748i	$-0.683288\pi$
$61$	−8.50568	−1.08904	−0.544520	+	0.838748i	$0.683288\pi$
$62$	0.608951	0.0773369
$63$	1.78836	0.225312
$64$	6.28268	0.785335
$65$	19.1156	2.37100
$66$	4.39843	0.541409
$67$	3.15826	0.385842	0.192921	−	0.981214i	$-0.438204\pi$
$67$	3.15826	0.385842	0.192921	+	0.981214i	$0.438204\pi$
$68$	0.275502	0.0334096
$69$	6.35409	0.764943
$70$	10.4702	1.25143
$71$	−5.86579	−0.696141	−0.348070	−	0.937468i	$-0.613163\pi$
$71$	−5.86579	−0.696141	−0.348070	+	0.937468i	$0.613163\pi$
$72$	2.54951	0.300462
$73$	11.1746	1.30789	0.653947	−	0.756541i	$-0.273112\pi$
$73$	11.1746	1.30789	0.653947	+	0.756541i	$0.273112\pi$
$74$	17.0107	1.97745
$75$	−9.71342	−1.12161
$76$	1.38162	0.158483
$77$	5.15358	0.587305
$78$	−7.60632	−0.861246
$79$	−14.4714	−1.62816	−0.814082	−	0.580750i	$-0.802760\pi$
$79$	−14.4714	−1.62816	−0.814082	+	0.580750i	$0.802760\pi$
$80$	17.4552	1.95155
$81$	1.00000	0.111111
$82$	7.52687	0.831204
$83$	11.3822	1.24936	0.624680	−	0.780881i	$-0.285230\pi$
$83$	11.3822	1.24936	0.624680	+	0.780881i	$0.285230\pi$
$84$	−0.589494	−0.0643190
$85$	−3.20596	−0.347735
$86$	9.21588	0.993774
$87$	−5.67107	−0.608003
$88$	7.34701	0.783194
$89$	−17.2826	−1.83196	−0.915978	−	0.401229i	$-0.868583\pi$
$89$	−17.2826	−1.83196	−0.915978	+	0.401229i	$0.868583\pi$
$90$	5.85464	0.617133
$91$	−8.91222	−0.934255
$92$	−2.09449	−0.218366
$93$	0.398969	0.0413712
$94$	−13.8978	−1.43345
$95$	−16.0776	−1.64953
$96$	−1.84662	−0.188470
$97$	8.50787	0.863843	0.431922	−	0.901911i	$-0.357836\pi$
$97$	8.50787	0.863843	0.431922	+	0.901911i	$0.357836\pi$
$98$	5.80269	0.586160
$99$	2.88174	0.289625
$100$	3.20182	0.320182
$101$	−6.80272	−0.676896	−0.338448	−	0.940985i	$-0.609902\pi$
$101$	−6.80272	−0.676896	−0.338448	+	0.940985i	$0.609902\pi$
$102$	1.27569	0.126312
$103$	4.09752	0.403741	0.201870	−	0.979412i	$-0.435298\pi$
$103$	4.09752	0.403741	0.201870	+	0.979412i	$0.435298\pi$
$104$	−12.7054	−1.24587
$105$	6.85980	0.669448
$106$	−13.8869	−1.34881
$107$	15.6627	1.51417	0.757084	−	0.653317i	$-0.226623\pi$
$107$	15.6627	1.51417	0.757084	+	0.653317i	$0.226623\pi$
$108$	−0.329628	−0.0317185
$109$	8.07989	0.773913	0.386956	−	0.922098i	$-0.373526\pi$
$109$	8.07989	0.773913	0.386956	+	0.922098i	$0.373526\pi$
$110$	16.8715	1.60864
$111$	11.1449	1.05783
$112$	−8.13811	−0.768979
$113$	2.56290	0.241097	0.120549	−	0.992707i	$-0.461535\pi$
$113$	2.56290	0.241097	0.120549	+	0.992707i	$0.461535\pi$
$114$	6.39746	0.599177
$115$	24.3731	2.27280
$116$	1.86935	0.173564
$117$	−4.98346	−0.460721
$118$	−14.1302	−1.30079
$119$	1.49471	0.137019
$120$	9.77942	0.892735
$121$	−2.69560	−0.245055
$122$	12.9823	1.17536
$123$	4.93141	0.444650
$124$	−0.131512	−0.0118101
$125$	−18.0798	−1.61710
$126$	−2.72959	−0.243172
$127$	5.28991	0.469404	0.234702	−	0.972067i	$-0.424589\pi$
$127$	5.28991	0.469404	0.234702	+	0.972067i	$0.424589\pi$
$128$	−13.2826	−1.17403
$129$	6.03801	0.531617
$130$	−29.1764	−2.55894
$131$	20.6522	1.80439	0.902197	−	0.431325i	$-0.141954\pi$
$131$	20.6522	1.80439	0.902197	+	0.431325i	$0.141954\pi$
$132$	−0.949901	−0.0826783
$133$	7.49582	0.649970
$134$	−4.82048	−0.416426
$135$	3.83581	0.330134
$136$	2.13087	0.182721
$137$	15.1307	1.29270	0.646352	−	0.763039i	$-0.276294\pi$
$137$	15.1307	1.29270	0.646352	+	0.763039i	$0.276294\pi$
$138$	−9.69833	−0.825576
$139$	14.7144	1.24806	0.624028	−	0.781402i	$-0.285495\pi$
$139$	14.7144	1.24806	0.624028	+	0.781402i	$0.285495\pi$
$140$	−2.26118	−0.191105
$141$	−9.10551	−0.766822
$142$	8.95302	0.751321
$143$	−14.3610	−1.20093
$144$	−4.55060	−0.379217
$145$	−21.7531	−1.80650
$146$	−17.0560	−1.41156
$147$	3.80177	0.313565
$148$	−3.67369	−0.301975
$149$	−19.5916	−1.60501	−0.802505	−	0.596645i	$-0.796500\pi$
$149$	−19.5916	−1.60501	−0.802505	+	0.596645i	$0.796500\pi$
$150$	14.8257	1.21051
$151$	−16.2746	−1.32441	−0.662203	−	0.749324i	$-0.730379\pi$
$151$	−16.2746	−1.32441	−0.662203	+	0.749324i	$0.730379\pi$
$152$	10.6861	0.866760
$153$	0.835797	0.0675702
$154$	−7.86597	−0.633858
$155$	1.53037	0.122922
$156$	1.64269	0.131521
$157$	−4.35410	−0.347495	−0.173747	−	0.984790i	$-0.555588\pi$
$157$	−4.35410	−0.347495	−0.173747	+	0.984790i	$0.555588\pi$
$158$	22.0879	1.75722
$159$	−9.09832	−0.721544
$160$	−7.08328	−0.559983
$161$	−11.3634	−0.895561
$162$	−1.52631	−0.119918
$163$	7.71271	0.604106	0.302053	−	0.953291i	$-0.402328\pi$
$163$	7.71271	0.604106	0.302053	+	0.953291i	$0.402328\pi$
$164$	−1.62553	−0.126933
$165$	11.0538	0.860536
$166$	−17.3728	−1.34839
$167$	−13.2638	−1.02638	−0.513191	−	0.858274i	$-0.671537\pi$
$167$	−13.2638	−1.02638	−0.513191	+	0.858274i	$0.671537\pi$
$168$	−4.55944	−0.351768
$169$	11.8349	0.910378
$170$	4.89329	0.375298
$171$	4.19145	0.320528
$172$	−1.99030	−0.151759
$173$	13.1480	0.999623	0.499811	−	0.866134i	$-0.333403\pi$
$173$	13.1480	0.999623	0.499811	+	0.866134i	$0.333403\pi$
$174$	8.65582	0.656196
$175$	17.3711	1.31313
$176$	−13.1136	−0.988477
$177$	−9.25771	−0.695852
$178$	26.3787	1.97717
$179$	11.9535	0.893447	0.446723	−	0.894672i	$-0.352591\pi$
$179$	11.9535	0.893447	0.446723	+	0.894672i	$0.352591\pi$
$180$	−1.26439	−0.0942421
$181$	−1.30977	−0.0973547	−0.0486774	−	0.998815i	$-0.515501\pi$
$181$	−1.30977	−0.0973547	−0.0486774	+	0.998815i	$0.515501\pi$
$182$	13.6028	1.00831
$183$	8.50568	0.628758
$184$	−16.1998	−1.19427
$185$	42.7498	3.14303
$186$	−0.608951	−0.0446505
$187$	2.40855	0.176130
$188$	3.00143	0.218902
$189$	−1.78836	−0.130084
$190$	24.5394	1.78028
$191$	13.7216	0.992863	0.496432	−	0.868076i	$-0.334643\pi$
$191$	13.7216	0.992863	0.496432	+	0.868076i	$0.334643\pi$
$192$	−6.28268	−0.453414
$193$	5.38589	0.387685	0.193842	−	0.981033i	$-0.437905\pi$
$193$	5.38589	0.387685	0.193842	+	0.981033i	$0.437905\pi$
$194$	−12.9857	−0.932316
$195$	−19.1156	−1.36890
$196$	−1.25317	−0.0895122
$197$	16.5247	1.17734	0.588669	−	0.808374i	$-0.299652\pi$
$197$	16.5247	1.17734	0.588669	+	0.808374i	$0.299652\pi$
$198$	−4.39843	−0.312583
$199$	14.3656	1.01835	0.509174	−	0.860663i	$-0.329951\pi$
$199$	14.3656	1.01835	0.509174	+	0.860663i	$0.329951\pi$
$200$	24.7644	1.75111
$201$	−3.15826	−0.222766
$202$	10.3831	0.730550
$203$	10.1419	0.711823
$204$	−0.275502	−0.0192890
$205$	18.9159	1.32115
$206$	−6.25410	−0.435744
$207$	−6.35409	−0.441640
$208$	22.6778	1.57242
$209$	12.0786	0.835497
$210$	−10.4702	−0.722512
$211$	−10.4394	−0.718676	−0.359338	−	0.933208i	$-0.616997\pi$
$211$	−10.4394	−0.718676	−0.359338	+	0.933208i	$0.616997\pi$
$212$	2.99906	0.205977
$213$	5.86579	0.401917
$214$	−23.9061	−1.63419
$215$	23.1606	1.57954
$216$	−2.54951	−0.173472
$217$	−0.713500	−0.0484355
$218$	−12.3324	−0.835257
$219$	−11.1746	−0.755112
$220$	−3.64364	−0.245654
$221$	−4.16516	−0.280179
$222$	−17.0107	−1.14168
$223$	9.38079	0.628184	0.314092	−	0.949393i	$-0.398300\pi$
$223$	9.38079	0.628184	0.314092	+	0.949393i	$0.398300\pi$
$224$	3.30242	0.220652
$225$	9.71342	0.647561
$226$	−3.91178	−0.260208
$227$	−1.81057	−0.120172	−0.0600860	−	0.998193i	$-0.519137\pi$
$227$	−1.81057	−0.120172	−0.0600860	+	0.998193i	$0.519137\pi$
$228$	−1.38162	−0.0915000
$229$	−17.5978	−1.16290	−0.581448	−	0.813583i	$-0.697514\pi$
$229$	−17.5978	−1.16290	−0.581448	+	0.813583i	$0.697514\pi$
$230$	−37.2009	−2.45296
$231$	−5.15358	−0.339081
$232$	14.4584	0.949243
$233$	−14.2539	−0.933807	−0.466903	−	0.884308i	$-0.654630\pi$
$233$	−14.2539	−0.933807	−0.466903	+	0.884308i	$0.654630\pi$
$234$	7.60632	0.497241
$235$	−34.9270	−2.27839
$236$	3.05160	0.198643
$237$	14.4714	0.940021
$238$	−2.28139	−0.147880
$239$	7.17886	0.464362	0.232181	−	0.972673i	$-0.425414\pi$
$239$	7.17886	0.464362	0.232181	+	0.972673i	$0.425414\pi$
$240$	−17.4552	−1.12673
$241$	−2.32260	−0.149612	−0.0748058	−	0.997198i	$-0.523834\pi$
$241$	−2.32260	−0.149612	−0.0748058	+	0.997198i	$0.523834\pi$
$242$	4.11433	0.264479
$243$	−1.00000	−0.0641500
$244$	−2.80371	−0.179489
$245$	14.5829	0.931665
$246$	−7.52687	−0.479896
$247$	−20.8879	−1.32907
$248$	−1.01718	−0.0645907
$249$	−11.3822	−0.721318
$250$	27.5954	1.74528
$251$	−2.02091	−0.127559	−0.0637793	−	0.997964i	$-0.520315\pi$
$251$	−2.02091	−0.127559	−0.0637793	+	0.997964i	$0.520315\pi$
$252$	0.589494	0.0371346
$253$	−18.3108	−1.15119
$254$	−8.07406	−0.506612
$255$	3.20596	0.200765
$256$	7.70799	0.481749
$257$	21.7673	1.35781	0.678903	−	0.734228i	$-0.262456\pi$
$257$	21.7673	1.35781	0.678903	+	0.734228i	$0.262456\pi$
$258$	−9.21588	−0.573756
$259$	−19.9312	−1.23846
$260$	6.30105	0.390774
$261$	5.67107	0.351030
$262$	−31.5217	−1.94742
$263$	15.9607	0.984182	0.492091	−	0.870544i	$-0.336233\pi$
$263$	15.9607	0.984182	0.492091	+	0.870544i	$0.336233\pi$
$264$	−7.34701	−0.452177
$265$	−34.8994	−2.14385
$266$	−11.4410	−0.701490
$267$	17.2826	1.05768
$268$	1.04105	0.0635923
$269$	−26.6937	−1.62754	−0.813772	−	0.581184i	$-0.802590\pi$
$269$	−26.6937	−1.62754	−0.813772	+	0.581184i	$0.802590\pi$
$270$	−5.85464	−0.356302
$271$	−2.98310	−0.181210	−0.0906052	−	0.995887i	$-0.528880\pi$
$271$	−2.98310	−0.181210	−0.0906052	+	0.995887i	$0.528880\pi$
$272$	−3.80338	−0.230614
$273$	8.91222	0.539392
$274$	−23.0942	−1.39517
$275$	27.9915	1.68795
$276$	2.09449	0.126073
$277$	−18.5206	−1.11279	−0.556397	−	0.830917i	$-0.687817\pi$
$277$	−18.5206	−1.11279	−0.556397	+	0.830917i	$0.687817\pi$
$278$	−22.4587	−1.34698
$279$	−0.398969	−0.0238857
$280$	−17.4891	−1.04517
$281$	−18.7561	−1.11890	−0.559448	−	0.828865i	$-0.688987\pi$
$281$	−18.7561	−1.11890	−0.559448	+	0.828865i	$0.688987\pi$
$282$	13.8978	0.827605
$283$	−17.0995	−1.01646	−0.508230	−	0.861221i	$-0.669700\pi$
$283$	−17.0995	−1.01646	−0.508230	+	0.861221i	$0.669700\pi$
$284$	−1.93353	−0.114734
$285$	16.0776	0.952354
$286$	21.9194	1.29612
$287$	−8.81913	−0.520577
$288$	1.84662	0.108813
$289$	−16.3014	−0.958908
$290$	33.2021	1.94969
$291$	−8.50787	−0.498740
$292$	3.68348	0.215559
$293$	−24.1211	−1.40917	−0.704585	−	0.709619i	$-0.748867\pi$
$293$	−24.1211	−1.40917	−0.704585	+	0.709619i	$0.748867\pi$
$294$	−5.80269	−0.338420
$295$	−35.5108	−2.06752
$296$	−28.4141	−1.65154
$297$	−2.88174	−0.167215
$298$	29.9030	1.73223
$299$	31.6654	1.83126
$300$	−3.20182	−0.184857
$301$	−10.7981	−0.622393
$302$	24.8401	1.42939
$303$	6.80272	0.390806
$304$	−19.0736	−1.09395
$305$	32.6262	1.86817
$306$	−1.27569	−0.0729262
$307$	17.7188	1.01127	0.505634	−	0.862748i	$-0.331259\pi$
$307$	17.7188	1.01127	0.505634	+	0.862748i	$0.331259\pi$
$308$	1.69877	0.0967961
$309$	−4.09752	−0.233100
$310$	−2.33582	−0.132666
$311$	−20.9912	−1.19030	−0.595150	−	0.803614i	$-0.702907\pi$
$311$	−20.9912	−1.19030	−0.595150	+	0.803614i	$0.702907\pi$
$312$	12.7054	0.719301
$313$	9.51265	0.537687	0.268843	−	0.963184i	$-0.413359\pi$
$313$	9.51265	0.537687	0.268843	+	0.963184i	$0.413359\pi$
$314$	6.64571	0.375039
$315$	−6.85980	−0.386506
$316$	−4.77020	−0.268345
$317$	−8.33184	−0.467963	−0.233981	−	0.972241i	$-0.575176\pi$
$317$	−8.33184	−0.467963	−0.233981	+	0.972241i	$0.575176\pi$
$318$	13.8869	0.778737
$319$	16.3425	0.915006
$320$	−24.0992	−1.34718
$321$	−15.6627	−0.874206
$322$	17.3441	0.966548
$323$	3.50320	0.194923
$324$	0.329628	0.0183127
$325$	−48.4065	−2.68511
$326$	−11.7720	−0.651991
$327$	−8.07989	−0.446819
$328$	−12.5727	−0.694210
$329$	16.2839	0.897762
$330$	−16.8715	−0.928747
$331$	7.05034	0.387522	0.193761	−	0.981049i	$-0.437931\pi$
$331$	7.05034	0.387522	0.193761	+	0.981049i	$0.437931\pi$
$332$	3.75190	0.205912
$333$	−11.1449	−0.610739
$334$	20.2447	1.10774
$335$	−12.1145	−0.661884
$336$	8.13811	0.443970
$337$	−28.9958	−1.57950	−0.789751	−	0.613428i	$-0.789790\pi$
$337$	−28.9958	−1.57950	−0.789751	+	0.613428i	$0.789790\pi$
$338$	−18.0638	−0.982540
$339$	−2.56290	−0.139197
$340$	−1.05677	−0.0573116
$341$	−1.14972	−0.0622610
$342$	−6.39746	−0.345935
$343$	−19.3174	−1.04304
$344$	−15.3939	−0.829986
$345$	−24.3731	−1.31220
$346$	−20.0679	−1.07886
$347$	−5.71739	−0.306925	−0.153463	−	0.988154i	$-0.549042\pi$
$347$	−5.71739	−0.306925	−0.153463	+	0.988154i	$0.549042\pi$
$348$	−1.86935	−0.100207
$349$	−9.11808	−0.488080	−0.244040	−	0.969765i	$-0.578473\pi$
$349$	−9.11808	−0.488080	−0.244040	+	0.969765i	$0.578473\pi$
$350$	−26.5137	−1.41722
$351$	4.98346	0.265998
$352$	5.32147	0.283636
$353$	6.78561	0.361162	0.180581	−	0.983560i	$-0.442202\pi$
$353$	6.78561	0.361162	0.180581	+	0.983560i	$0.442202\pi$
$354$	14.1302	0.751010
$355$	22.5000	1.19418
$356$	−5.69684	−0.301932
$357$	−1.49471	−0.0791082
$358$	−18.2448	−0.964266
$359$	−30.7676	−1.62385	−0.811925	−	0.583762i	$-0.801580\pi$
$359$	−30.7676	−1.62385	−0.811925	+	0.583762i	$0.801580\pi$
$360$	−9.77942	−0.515421
$361$	−1.43175	−0.0753555
$362$	1.99912	0.105072
$363$	2.69560	0.141482
$364$	−2.93772	−0.153978
$365$	−42.8638	−2.24359
$366$	−12.9823	−0.678597
$367$	18.1987	0.949966	0.474983	−	0.879995i	$-0.342454\pi$
$367$	18.1987	0.949966	0.474983	+	0.879995i	$0.342454\pi$
$368$	28.9149	1.50730
$369$	−4.93141	−0.256719
$370$	−65.2496	−3.39217
$371$	16.2711	0.844751
$372$	0.131512	0.00681855
$373$	−16.6428	−0.861729	−0.430865	−	0.902417i	$-0.641791\pi$
$373$	−16.6428	−0.861729	−0.430865	+	0.902417i	$0.641791\pi$
$374$	−3.67619	−0.190091
$375$	18.0798	0.933635
$376$	23.2146	1.19720
$377$	−28.2616	−1.45555
$378$	2.72959	0.140395
$379$	31.8545	1.63625	0.818127	−	0.575037i	$-0.195012\pi$
$379$	31.8545	1.63625	0.818127	+	0.575037i	$0.195012\pi$
$380$	−5.29963	−0.271865
$381$	−5.28991	−0.271011
$382$	−20.9435	−1.07156
$383$	9.35309	0.477921	0.238960	−	0.971029i	$-0.423193\pi$
$383$	9.35309	0.477921	0.238960	+	0.971029i	$0.423193\pi$
$384$	13.2826	0.677824
$385$	−19.7681	−1.00748
$386$	−8.22055	−0.418415
$387$	−6.03801	−0.306929
$388$	2.80443	0.142374
$389$	29.5641	1.49896	0.749481	−	0.662026i	$-0.230303\pi$
$389$	29.5641	1.49896	0.749481	+	0.662026i	$0.230303\pi$
$390$	29.1764	1.47740
$391$	−5.31073	−0.268575
$392$	−9.69265	−0.489553
$393$	−20.6522	−1.04177
$394$	−25.2219	−1.27066
$395$	55.5097	2.79299
$396$	0.949901	0.0477343
$397$	−2.45548	−0.123237	−0.0616186	−	0.998100i	$-0.519626\pi$
$397$	−2.45548	−0.123237	−0.0616186	+	0.998100i	$0.519626\pi$
$398$	−21.9263	−1.09907
$399$	−7.49582	−0.375260
$400$	−44.2019	−2.21010
$401$	13.5037	0.674343	0.337171	−	0.941443i	$-0.390530\pi$
$401$	13.5037	0.674343	0.337171	+	0.941443i	$0.390530\pi$
$402$	4.82048	0.240424
$403$	1.98825	0.0990417
$404$	−2.24237	−0.111562
$405$	−3.83581	−0.190603
$406$	−15.4797	−0.768246
$407$	−32.1168	−1.59197
$408$	−2.13087	−0.105494
$409$	3.46840	0.171501	0.0857506	−	0.996317i	$-0.472671\pi$
$409$	3.46840	0.171501	0.0857506	+	0.996317i	$0.472671\pi$
$410$	−28.8716	−1.42587
$411$	−15.1307	−0.746343
$412$	1.35066	0.0665422
$413$	16.5561	0.814673
$414$	9.69833	0.476647
$415$	−43.6599	−2.14318
$416$	−9.20257	−0.451193
$417$	−14.7144	−0.720565
$418$	−18.4358	−0.901724
$419$	−2.49616	−0.121945	−0.0609727	−	0.998139i	$-0.519420\pi$
$419$	−2.49616	−0.121945	−0.0609727	+	0.998139i	$0.519420\pi$
$420$	2.26118	0.110335
$421$	−1.65187	−0.0805071	−0.0402535	−	0.999189i	$-0.512817\pi$
$421$	−1.65187	−0.0805071	−0.0402535	+	0.999189i	$0.512817\pi$
$422$	15.9337	0.775642
$423$	9.10551	0.442725
$424$	23.1962	1.12651
$425$	8.11845	0.393803
$426$	−8.95302	−0.433775
$427$	−15.2112	−0.736122
$428$	5.16286	0.249556
$429$	14.3610	0.693357
$430$	−35.3503	−1.70474
$431$	1.51018	0.0727430	0.0363715	−	0.999338i	$-0.488420\pi$
$431$	1.51018	0.0727430	0.0363715	+	0.999338i	$0.488420\pi$
$432$	4.55060	0.218941
$433$	−15.5360	−0.746610	−0.373305	−	0.927709i	$-0.621776\pi$
$433$	−15.5360	−0.746610	−0.373305	+	0.927709i	$0.621776\pi$
$434$	1.08902	0.0522748
$435$	21.7531	1.04298
$436$	2.66336	0.127552
$437$	−26.6329	−1.27402
$438$	17.0560	0.814967
$439$	−25.3992	−1.21224	−0.606118	−	0.795375i	$-0.707274\pi$
$439$	−25.3992	−1.21224	−0.606118	+	0.795375i	$0.707274\pi$
$440$	−28.1817	−1.34351
$441$	−3.80177	−0.181037
$442$	6.35734	0.302388
$443$	−13.6208	−0.647144	−0.323572	−	0.946204i	$-0.604884\pi$
$443$	−13.6208	−0.647144	−0.323572	+	0.946204i	$0.604884\pi$
$444$	3.67369	0.174346
$445$	66.2928	3.14258
$446$	−14.3180	−0.677977
$447$	19.5916	0.926653
$448$	11.2357	0.530837
$449$	−34.3822	−1.62260	−0.811298	−	0.584633i	$-0.801239\pi$
$449$	−34.3822	−1.62260	−0.811298	+	0.584633i	$0.801239\pi$
$450$	−14.8257	−0.698891
$451$	−14.2110	−0.669171
$452$	0.844803	0.0397362
$453$	16.2746	0.764647
$454$	2.76350	0.129698
$455$	34.1856	1.60264
$456$	−10.6861	−0.500424
$457$	−35.2294	−1.64796	−0.823980	−	0.566618i	$-0.808251\pi$
$457$	−35.2294	−1.64796	−0.823980	+	0.566618i	$0.808251\pi$
$458$	26.8598	1.25507
$459$	−0.835797	−0.0390117
$460$	8.03405	0.374590
$461$	−12.0504	−0.561242	−0.280621	−	0.959819i	$-0.590540\pi$
$461$	−12.0504	−0.561242	−0.280621	+	0.959819i	$0.590540\pi$
$462$	7.86597	0.365958
$463$	37.0652	1.72256	0.861282	−	0.508128i	$-0.169662\pi$
$463$	37.0652	1.72256	0.861282	+	0.508128i	$0.169662\pi$
$464$	−25.8068	−1.19805
$465$	−1.53037	−0.0709692
$466$	21.7560	1.00783
$467$	−7.24343	−0.335186	−0.167593	−	0.985856i	$-0.553599\pi$
$467$	−7.24343	−0.335186	−0.167593	+	0.985856i	$0.553599\pi$
$468$	−1.64269	−0.0759334
$469$	5.64810	0.260805
$470$	53.3095	2.45898
$471$	4.35410	0.200626
$472$	23.6026	1.08640
$473$	−17.3999	−0.800050
$474$	−22.0879	−1.01453
$475$	40.7133	1.86805
$476$	0.492697	0.0225827
$477$	9.09832	0.416583
$478$	−10.9572	−0.501170
$479$	37.5793	1.71704	0.858522	−	0.512776i	$-0.171383\pi$
$479$	37.5793	1.71704	0.858522	+	0.512776i	$0.171383\pi$
$480$	7.08328	0.323306
$481$	55.5404	2.53242
$482$	3.54501	0.161471
$483$	11.3634	0.517053
$484$	−0.888547	−0.0403885
$485$	−32.6346	−1.48186
$486$	1.52631	0.0692349
$487$	14.1898	0.643000	0.321500	−	0.946910i	$-0.395813\pi$
$487$	14.1898	0.643000	0.321500	+	0.946910i	$0.395813\pi$
$488$	−21.6853	−0.981648
$489$	−7.71271	−0.348781
$490$	−22.2580	−1.00551
$491$	19.5576	0.882623	0.441312	−	0.897354i	$-0.354513\pi$
$491$	19.5576	0.882623	0.441312	+	0.897354i	$0.354513\pi$
$492$	1.62553	0.0732847
$493$	4.73986	0.213473
$494$	31.8815	1.43442
$495$	−11.0538	−0.496831
$496$	1.81555	0.0815206
$497$	−10.4901	−0.470547
$498$	17.3728	0.778494
$499$	−24.4532	−1.09467	−0.547337	−	0.836912i	$-0.684358\pi$
$499$	−24.4532	−1.09467	−0.547337	+	0.836912i	$0.684358\pi$
$500$	−5.95960	−0.266522
$501$	13.2638	0.592582
$502$	3.08454	0.137670
$503$	20.7747	0.926298	0.463149	−	0.886280i	$-0.346719\pi$
$503$	20.7747	0.926298	0.463149	+	0.886280i	$0.346719\pi$
$504$	4.55944	0.203093
$505$	26.0939	1.16116
$506$	27.9480	1.24244
$507$	−11.8349	−0.525607
$508$	1.74371	0.0773644
$509$	−5.77125	−0.255806	−0.127903	−	0.991787i	$-0.540825\pi$
$509$	−5.77125	−0.255806	−0.127903	+	0.991787i	$0.540825\pi$
$510$	−4.89329	−0.216679
$511$	19.9843	0.884052
$512$	14.8004	0.654090
$513$	−4.19145	−0.185057
$514$	−33.2237	−1.46543
$515$	−15.7173	−0.692587
$516$	1.99030	0.0876180
$517$	26.2397	1.15402
$518$	30.4212	1.33663
$519$	−13.1480	−0.577133
$520$	48.7354	2.13719
$521$	−24.2835	−1.06388	−0.531939	−	0.846783i	$-0.678536\pi$
$521$	−24.2835	−1.06388	−0.531939	+	0.846783i	$0.678536\pi$
$522$	−8.65582	−0.378855
$523$	−15.4841	−0.677073	−0.338536	−	0.940953i	$-0.609932\pi$
$523$	−15.4841	−0.677073	−0.338536	+	0.940953i	$0.609932\pi$
$524$	6.80756	0.297390
$525$	−17.3711	−0.758136
$526$	−24.3611	−1.06219
$527$	−0.333457	−0.0145256
$528$	13.1136	0.570697
$529$	17.3745	0.755412
$530$	53.2674	2.31379
$531$	9.25771	0.401751
$532$	2.47083	0.107124
$533$	24.5755	1.06448
$534$	−26.3787	−1.14152
$535$	−60.0790	−2.59744
$536$	8.05200	0.347793
$537$	−11.9535	−0.515832
$538$	40.7429	1.75655
$539$	−10.9557	−0.471895
$540$	1.26439	0.0544107
$541$	−36.9415	−1.58824	−0.794119	−	0.607762i	$-0.792067\pi$
$541$	−36.9415	−1.58824	−0.794119	+	0.607762i	$0.792067\pi$
$542$	4.55314	0.195574
$543$	1.30977	0.0562078
$544$	1.54340	0.0661728
$545$	−30.9929	−1.32759
$546$	−13.6028	−0.582148
$547$	−20.5688	−0.879460	−0.439730	−	0.898130i	$-0.644926\pi$
$547$	−20.5688	−0.879460	−0.439730	+	0.898130i	$0.644926\pi$
$548$	4.98751	0.213056
$549$	−8.50568	−0.363014
$550$	−42.7238	−1.82175
$551$	23.7700	1.01264
$552$	16.1998	0.689510
$553$	−25.8801	−1.10054
$554$	28.2682	1.20100
$555$	−42.7498	−1.81463
$556$	4.85027	0.205697
$557$	−18.4560	−0.782007	−0.391004	−	0.920389i	$-0.627872\pi$
$557$	−18.4560	−0.782007	−0.391004	+	0.920389i	$0.627872\pi$
$558$	0.608951	0.0257790
$559$	30.0902	1.27268
$560$	31.2162	1.31913
$561$	−2.40855	−0.101689
$562$	28.6277	1.20759
$563$	0.129802	0.00547050	0.00273525	−	0.999996i	$-0.499129\pi$
$563$	0.129802	0.00547050	0.00273525	+	0.999996i	$0.499129\pi$
$564$	−3.00143	−0.126383
$565$	−9.83078	−0.413584
$566$	26.0992	1.09703
$567$	1.78836	0.0751040
$568$	−14.9549	−0.627493
$569$	5.34161	0.223932	0.111966	−	0.993712i	$-0.464285\pi$
$569$	5.34161	0.223932	0.111966	+	0.993712i	$0.464285\pi$
$570$	−24.5394	−1.02784
$571$	12.0693	0.505084	0.252542	−	0.967586i	$-0.418733\pi$
$571$	12.0693	0.505084	0.252542	+	0.967586i	$0.418733\pi$
$572$	−4.73380	−0.197930
$573$	−13.7216	−0.573230
$574$	13.4608	0.561841
$575$	−61.7200	−2.57390
$576$	6.28268	0.261778
$577$	11.1315	0.463411	0.231706	−	0.972786i	$-0.425569\pi$
$577$	11.1315	0.463411	0.231706	+	0.972786i	$0.425569\pi$
$578$	24.8811	1.03492
$579$	−5.38589	−0.223830
$580$	−7.17045	−0.297737
$581$	20.3555	0.844487
$582$	12.9857	0.538273
$583$	26.2189	1.08588
$584$	28.4898	1.17892
$585$	19.1156	0.790333
$586$	36.8164	1.52087
$587$	−12.6907	−0.523802	−0.261901	−	0.965095i	$-0.584349\pi$
$587$	−12.6907	−0.523802	−0.261901	+	0.965095i	$0.584349\pi$
$588$	1.25317	0.0516799
$589$	−1.67226	−0.0689042
$590$	54.2006	2.23140
$591$	−16.5247	−0.679736
$592$	50.7162	2.08442
$593$	−24.9088	−1.02288	−0.511440	−	0.859319i	$-0.670888\pi$
$593$	−24.9088	−1.02288	−0.511440	+	0.859319i	$0.670888\pi$
$594$	4.39843	0.180470
$595$	−5.73340	−0.235047
$596$	−6.45796	−0.264528
$597$	−14.3656	−0.587944
$598$	−48.3313	−1.97641
$599$	−17.7207	−0.724046	−0.362023	−	0.932169i	$-0.617914\pi$
$599$	−17.7207	−0.724046	−0.362023	+	0.932169i	$0.617914\pi$
$600$	−24.7644	−1.01100
$601$	−8.27802	−0.337667	−0.168834	−	0.985645i	$-0.554000\pi$
$601$	−8.27802	−0.337667	−0.168834	+	0.985645i	$0.554000\pi$
$602$	16.4813	0.671728
$603$	3.15826	0.128614
$604$	−5.36456	−0.218281
$605$	10.3398	0.420373
$606$	−10.3831	−0.421783
$607$	27.5657	1.11886	0.559428	−	0.828879i	$-0.311021\pi$
$607$	27.5657	1.11886	0.559428	+	0.828879i	$0.311021\pi$
$608$	7.74002	0.313899
$609$	−10.1419	−0.410971
$610$	−49.7977	−2.01625
$611$	−45.3770	−1.83576
$612$	0.275502	0.0111365
$613$	−9.04476	−0.365315	−0.182657	−	0.983177i	$-0.558470\pi$
$613$	−9.04476	−0.365315	−0.182657	+	0.983177i	$0.558470\pi$
$614$	−27.0445	−1.09143
$615$	−18.9159	−0.762764
$616$	13.1391	0.529389
$617$	7.76154	0.312468	0.156234	−	0.987720i	$-0.450065\pi$
$617$	7.76154	0.312468	0.156234	+	0.987720i	$0.450065\pi$
$618$	6.25410	0.251577
$619$	0.991552	0.0398539	0.0199269	−	0.999801i	$-0.493657\pi$
$619$	0.991552	0.0398539	0.0199269	+	0.999801i	$0.493657\pi$
$620$	0.504453	0.0202593
$621$	6.35409	0.254981
$622$	32.0391	1.28465
$623$	−30.9076	−1.23829
$624$	−22.6778	−0.907837
$625$	20.7834	0.831337
$626$	−14.5193	−0.580307
$627$	−12.0786	−0.482375
$628$	−1.43523	−0.0572721
$629$	−9.31491	−0.371410
$630$	10.4702	0.417143
$631$	−42.0948	−1.67577	−0.837884	−	0.545848i	$-0.816207\pi$
$631$	−42.0948	−1.67577	−0.837884	+	0.545848i	$0.816207\pi$
$632$	−36.8951	−1.46761
$633$	10.4394	0.414928
$634$	12.7170	0.505056
$635$	−20.2911	−0.805228
$636$	−2.99906	−0.118921
$637$	18.9460	0.750667
$638$	−24.9438	−0.987534
$639$	−5.86579	−0.232047
$640$	50.9494	2.01395
$641$	−49.6772	−1.96213	−0.981065	−	0.193676i	$-0.937959\pi$
$641$	−49.6772	−1.96213	−0.981065	+	0.193676i	$0.937959\pi$
$642$	23.9061	0.943500
$643$	0.541789	0.0213661	0.0106830	−	0.999943i	$-0.496599\pi$
$643$	0.541789	0.0213661	0.0106830	+	0.999943i	$0.496599\pi$
$644$	−3.74570	−0.147601
$645$	−23.1606	−0.911949
$646$	−5.34698	−0.210374
$647$	41.6723	1.63831	0.819154	−	0.573573i	$-0.194443\pi$
$647$	41.6723	1.63831	0.819154	+	0.573573i	$0.194443\pi$
$648$	2.54951	0.100154
$649$	26.6783	1.04721
$650$	73.8834	2.89794
$651$	0.713500	0.0279643
$652$	2.54233	0.0995652
$653$	47.0370	1.84070	0.920351	−	0.391094i	$-0.127903\pi$
$653$	47.0370	1.84070	0.920351	+	0.391094i	$0.127903\pi$
$654$	12.3324	0.482236
$655$	−79.2180	−3.09530
$656$	22.4409	0.876169
$657$	11.1746	0.435964
$658$	−24.8543	−0.968923
$659$	30.7989	1.19975	0.599877	−	0.800092i	$-0.295216\pi$
$659$	30.7989	1.19975	0.599877	+	0.800092i	$0.295216\pi$
$660$	3.64364	0.141828
$661$	−43.7251	−1.70071	−0.850355	−	0.526210i	$-0.823613\pi$
$661$	−43.7251	−1.70071	−0.850355	+	0.526210i	$0.823613\pi$
$662$	−10.7610	−0.418239
$663$	4.16516	0.161762
$664$	29.0190	1.12616
$665$	−28.7525	−1.11497
$666$	17.0107	0.659150
$667$	−36.0345	−1.39526
$668$	−4.37212	−0.169162
$669$	−9.38079	−0.362682
$670$	18.4904	0.714348
$671$	−24.5111	−0.946241
$672$	−3.30242	−0.127394
$673$	−9.85859	−0.380021	−0.190010	−	0.981782i	$-0.560852\pi$
$673$	−9.85859	−0.380021	−0.190010	+	0.981782i	$0.560852\pi$
$674$	44.2566	1.70470
$675$	−9.71342	−0.373870
$676$	3.90112	0.150043
$677$	38.2887	1.47156	0.735778	−	0.677223i	$-0.236817\pi$
$677$	38.2887	1.47156	0.735778	+	0.677223i	$0.236817\pi$
$678$	3.91178	0.150231
$679$	15.2151	0.583903
$680$	−8.17361	−0.313444
$681$	1.81057	0.0693814
$682$	1.75484	0.0671962
$683$	−1.36803	−0.0523463	−0.0261732	−	0.999657i	$-0.508332\pi$
$683$	−1.36803	−0.0523463	−0.0261732	+	0.999657i	$0.508332\pi$
$684$	1.38162	0.0528276
$685$	−58.0385	−2.21754
$686$	29.4845	1.12572
$687$	17.5978	0.671399
$688$	27.4766	1.04753
$689$	−45.3411	−1.72736
$690$	37.2009	1.41621
$691$	8.08453	0.307550	0.153775	−	0.988106i	$-0.450857\pi$
$691$	8.08453	0.307550	0.153775	+	0.988106i	$0.450857\pi$
$692$	4.33395	0.164752
$693$	5.15358	0.195768
$694$	8.72651	0.331254
$695$	−56.4414	−2.14095
$696$	−14.4584	−0.548046
$697$	−4.12166	−0.156119
$698$	13.9170	0.526768
$699$	14.2539	0.539133
$700$	5.72600	0.216422
$701$	−16.8685	−0.637114	−0.318557	−	0.947904i	$-0.603198\pi$
$701$	−16.8685	−0.637114	−0.318557	+	0.947904i	$0.603198\pi$
$702$	−7.60632	−0.287082
$703$	−46.7135	−1.76183
$704$	18.1050	0.682359
$705$	34.9270	1.31543
$706$	−10.3570	−0.389789
$707$	−12.1657	−0.457538
$708$	−3.05160	−0.114686
$709$	33.0045	1.23951	0.619754	−	0.784796i	$-0.287232\pi$
$709$	33.0045	1.23951	0.619754	+	0.784796i	$0.287232\pi$
$710$	−34.3421	−1.28883
$711$	−14.4714	−0.542721
$712$	−44.0622	−1.65130
$713$	2.53509	0.0949397
$714$	2.28139	0.0853788
$715$	55.0861	2.06010
$716$	3.94021	0.147253
$717$	−7.17886	−0.268099
$718$	46.9609	1.75256
$719$	−9.53544	−0.355612	−0.177806	−	0.984066i	$-0.556900\pi$
$719$	−9.53544	−0.355612	−0.177806	+	0.984066i	$0.556900\pi$
$720$	17.4552	0.650518
$721$	7.32784	0.272903
$722$	2.18530	0.0813286
$723$	2.32260	0.0863783
$724$	−0.431738	−0.0160454
$725$	55.0855	2.04582
$726$	−4.11433	−0.152697
$727$	−30.1031	−1.11646	−0.558231	−	0.829686i	$-0.688520\pi$
$727$	−30.1031	−1.11646	−0.558231	+	0.829686i	$0.688520\pi$
$728$	−22.7218	−0.842126
$729$	1.00000	0.0370370
$730$	65.4235	2.42143
$731$	−5.04655	−0.186653
$732$	2.80371	0.103628
$733$	33.3631	1.23229	0.616147	−	0.787631i	$-0.288693\pi$
$733$	33.3631	1.23229	0.616147	+	0.787631i	$0.288693\pi$
$734$	−27.7769	−1.02527
$735$	−14.5829	−0.537897
$736$	−11.7336	−0.432506
$737$	9.10126	0.335249
$738$	7.52687	0.277068
$739$	−4.17360	−0.153528	−0.0767642	−	0.997049i	$-0.524459\pi$
$739$	−4.17360	−0.153528	−0.0767642	+	0.997049i	$0.524459\pi$
$740$	14.0916	0.518016
$741$	20.8879	0.767337
$742$	−24.8347	−0.911711
$743$	−33.4515	−1.22722	−0.613608	−	0.789611i	$-0.710282\pi$
$743$	−33.4515	−1.22722	−0.613608	+	0.789611i	$0.710282\pi$
$744$	1.01718	0.0372914
$745$	75.1498	2.75328
$746$	25.4020	0.930035
$747$	11.3822	0.416453
$748$	0.793925	0.0290288
$749$	28.0105	1.02348
$750$	−27.5954	−1.00764
$751$	28.6296	1.04471	0.522354	−	0.852729i	$-0.325054\pi$
$751$	28.6296	1.04471	0.522354	+	0.852729i	$0.325054\pi$
$752$	−41.4355	−1.51100
$753$	2.02091	0.0736460
$754$	43.1360	1.57092
$755$	62.4262	2.27192
$756$	−0.589494	−0.0214397
$757$	13.5596	0.492833	0.246416	−	0.969164i	$-0.420747\pi$
$757$	13.5596	0.492833	0.246416	+	0.969164i	$0.420747\pi$
$758$	−48.6199	−1.76595
$759$	18.3108	0.664640
$760$	−40.9900	−1.48686
$761$	−47.3421	−1.71615	−0.858074	−	0.513526i	$-0.828339\pi$
$761$	−47.3421	−1.71615	−0.858074	+	0.513526i	$0.828339\pi$
$762$	8.07406	0.292492
$763$	14.4497	0.523116
$764$	4.52304	0.163638
$765$	−3.20596	−0.115912
$766$	−14.2757	−0.515803
$767$	−46.1355	−1.66586
$768$	−7.70799	−0.278138
$769$	−6.45936	−0.232931	−0.116465	−	0.993195i	$-0.537156\pi$
$769$	−6.45936	−0.232931	−0.116465	+	0.993195i	$0.537156\pi$
$770$	30.1723	1.08734
$771$	−21.7673	−0.783929
$772$	1.77534	0.0638960
$773$	−30.0064	−1.07926	−0.539628	−	0.841904i	$-0.681435\pi$
$773$	−30.0064	−1.07926	−0.539628	+	0.841904i	$0.681435\pi$
$774$	9.21588	0.331258
$775$	−3.87535	−0.139207
$776$	21.6909	0.778657
$777$	19.9312	0.715026
$778$	−45.1241	−1.61778
$779$	−20.6698	−0.740571
$780$	−6.30105	−0.225614
$781$	−16.9036	−0.604860
$782$	8.10583	0.289864
$783$	−5.67107	−0.202668
$784$	17.3003	0.617869
$785$	16.7015	0.596102
$786$	31.5217	1.12434
$787$	−20.0135	−0.713405	−0.356703	−	0.934218i	$-0.616099\pi$
$787$	−20.0135	−0.713405	−0.356703	+	0.934218i	$0.616099\pi$
$788$	5.44701	0.194042
$789$	−15.9607	−0.568218
$790$	−84.7251	−3.01438
$791$	4.58338	0.162966
$792$	7.34701	0.261065
$793$	42.3878	1.50523
$794$	3.74783	0.133006
$795$	34.8994	1.23775
$796$	4.73530	0.167838
$797$	4.72399	0.167332	0.0836661	−	0.996494i	$-0.473337\pi$
$797$	4.72399	0.167332	0.0836661	+	0.996494i	$0.473337\pi$
$798$	11.4410	0.405005
$799$	7.61036	0.269235
$800$	17.9370	0.634169
$801$	−17.2826	−0.610652
$802$	−20.6109	−0.727795
$803$	32.2024	1.13640
$804$	−1.04105	−0.0367150
$805$	43.5878	1.53627
$806$	−3.03469	−0.106892
$807$	26.6937	0.939663
$808$	−17.3436	−0.610145
$809$	−10.2590	−0.360689	−0.180344	−	0.983604i	$-0.557721\pi$
$809$	−10.2590	−0.360689	−0.180344	+	0.983604i	$0.557721\pi$
$810$	5.85464	0.205711
$811$	54.7186	1.92143	0.960715	−	0.277538i	$-0.0895184\pi$
$811$	54.7186	1.92143	0.960715	+	0.277538i	$0.0895184\pi$
$812$	3.34306	0.117318
$813$	2.98310	0.104622
$814$	49.0202	1.71816
$815$	−29.5845	−1.03630
$816$	3.80338	0.133145
$817$	−25.3080	−0.885415
$818$	−5.29385	−0.185095
$819$	−8.91222	−0.311418
$820$	6.23523	0.217744
$821$	31.9214	1.11406	0.557032	−	0.830491i	$-0.311940\pi$
$821$	31.9214	1.11406	0.557032	+	0.830491i	$0.311940\pi$
$822$	23.0942	0.805503
$823$	17.2329	0.600701	0.300351	−	0.953829i	$-0.402896\pi$
$823$	17.2329	0.600701	0.300351	+	0.953829i	$0.402896\pi$
$824$	10.4467	0.363927
$825$	−27.9915	−0.974539
$826$	−25.2698	−0.879249
$827$	−4.27165	−0.148540	−0.0742698	−	0.997238i	$-0.523663\pi$
$827$	−4.27165	−0.148540	−0.0742698	+	0.997238i	$0.523663\pi$
$828$	−2.09449	−0.0727885
$829$	2.86706	0.0995771	0.0497885	−	0.998760i	$-0.484145\pi$
$829$	2.86706	0.0995771	0.0497885	+	0.998760i	$0.484145\pi$
$830$	66.6387	2.31306
$831$	18.5206	0.642472
$832$	−31.3095	−1.08546
$833$	−3.17751	−0.110094
$834$	22.4587	0.777681
$835$	50.8773	1.76068
$836$	3.98146	0.137702
$837$	0.398969	0.0137904
$838$	3.80992	0.131611
$839$	7.33246	0.253144	0.126572	−	0.991957i	$-0.459602\pi$
$839$	7.33246	0.253144	0.126572	+	0.991957i	$0.459602\pi$
$840$	17.4891	0.603432
$841$	3.16104	0.109001
$842$	2.52127	0.0868885
$843$	18.7561	0.645995
$844$	−3.44111	−0.118448
$845$	−45.3964	−1.56169
$846$	−13.8978	−0.477818
$847$	−4.82070	−0.165641
$848$	−41.4028	−1.42178
$849$	17.0995	0.586854
$850$	−12.3913	−0.425017
$851$	70.8160	2.42754
$852$	1.93353	0.0662416
$853$	−4.17337	−0.142894	−0.0714468	−	0.997444i	$-0.522762\pi$
$853$	−4.17337	−0.142894	−0.0714468	+	0.997444i	$0.522762\pi$
$854$	23.2171	0.794471
$855$	−16.0776	−0.549842
$856$	39.9321	1.36485
$857$	−23.1697	−0.791463	−0.395732	−	0.918366i	$-0.629509\pi$
$857$	−23.1697	−0.791463	−0.395732	+	0.918366i	$0.629509\pi$
$858$	−21.9194	−0.748316
$859$	20.2736	0.691726	0.345863	−	0.938285i	$-0.387586\pi$
$859$	20.2736	0.691726	0.345863	+	0.938285i	$0.387586\pi$
$860$	7.63440	0.260331
$861$	8.81913	0.300555
$862$	−2.30501	−0.0785090
$863$	29.7724	1.01346	0.506732	−	0.862104i	$-0.330853\pi$
$863$	29.7724	1.01346	0.506732	+	0.862104i	$0.330853\pi$
$864$	−1.84662	−0.0628233
$865$	−50.4331	−1.71478
$866$	23.7127	0.805791
$867$	16.3014	0.553626
$868$	−0.235190	−0.00798286
$869$	−41.7029	−1.41467
$870$	−33.2021	−1.12566
$871$	−15.7391	−0.533298
$872$	20.5997	0.697595
$873$	8.50787	0.287948
$874$	40.6500	1.37501
$875$	−32.3331	−1.09306
$876$	−3.68348	−0.124453
$877$	−24.8787	−0.840094	−0.420047	−	0.907502i	$-0.637986\pi$
$877$	−24.8787	−0.840094	−0.420047	+	0.907502i	$0.637986\pi$
$878$	38.7670	1.30832
$879$	24.1211	0.813585
$880$	50.3014	1.69566
$881$	−5.60415	−0.188809	−0.0944043	−	0.995534i	$-0.530095\pi$
$881$	−5.60415	−0.188809	−0.0944043	+	0.995534i	$0.530095\pi$
$882$	5.80269	0.195387
$883$	−5.88876	−0.198173	−0.0990863	−	0.995079i	$-0.531592\pi$
$883$	−5.88876	−0.198173	−0.0990863	+	0.995079i	$0.531592\pi$
$884$	−1.37296	−0.0461775
$885$	35.5108	1.19368
$886$	20.7896	0.698440
$887$	−47.2965	−1.58806	−0.794031	−	0.607878i	$-0.792021\pi$
$887$	−47.2965	−1.58806	−0.794031	+	0.607878i	$0.792021\pi$
$888$	28.4141	0.953515
$889$	9.46027	0.317287
$890$	−101.184	−3.39168
$891$	2.88174	0.0965418
$892$	3.09217	0.103534
$893$	38.1653	1.27715
$894$	−29.9030	−1.00010
$895$	−45.8513	−1.53264
$896$	−23.7540	−0.793566
$897$	−31.6654	−1.05728
$898$	52.4779	1.75121
$899$	−2.26258	−0.0754613
$900$	3.20182	0.106727
$901$	7.60435	0.253338
$902$	21.6905	0.722213
$903$	10.7981	0.359339
$904$	6.53413	0.217322
$905$	5.02404	0.167005
$906$	−24.8401	−0.825257
$907$	−34.0530	−1.13071	−0.565356	−	0.824847i	$-0.691261\pi$
$907$	−34.0530	−1.13071	−0.565356	+	0.824847i	$0.691261\pi$
$908$	−0.596816	−0.0198061
$909$	−6.80272	−0.225632
$910$	−52.1779	−1.72968
$911$	−50.0174	−1.65715	−0.828575	−	0.559878i	$-0.810848\pi$
$911$	−50.0174	−1.65715	−0.828575	+	0.559878i	$0.810848\pi$
$912$	19.0736	0.631591
$913$	32.8005	1.08554
$914$	53.7710	1.77859
$915$	−32.6262	−1.07859
$916$	−5.80074	−0.191662
$917$	36.9336	1.21965
$918$	1.27569	0.0421039
$919$	1.69767	0.0560009	0.0280005	−	0.999608i	$-0.491086\pi$
$919$	1.69767	0.0560009	0.0280005	+	0.999608i	$0.491086\pi$
$920$	62.1393	2.04867
$921$	−17.7188	−0.583856
$922$	18.3926	0.605729
$923$	29.2319	0.962181
$924$	−1.69877	−0.0558853
$925$	−108.255	−3.55942
$926$	−56.5730	−1.85910
$927$	4.09752	0.134580
$928$	10.4723	0.343771
$929$	−25.7928	−0.846236	−0.423118	−	0.906075i	$-0.639064\pi$
$929$	−25.7928	−0.846236	−0.423118	+	0.906075i	$0.639064\pi$
$930$	2.33582	0.0765946
$931$	−15.9349	−0.522246
$932$	−4.69850	−0.153905
$933$	20.9912	0.687220
$934$	11.0557	0.361754
$935$	−9.23872	−0.302138
$936$	−12.7054	−0.415288
$937$	−8.52494	−0.278498	−0.139249	−	0.990257i	$-0.544469\pi$
$937$	−8.52494	−0.278498	−0.139249	+	0.990257i	$0.544469\pi$
$938$	−8.62076	−0.281478
$939$	−9.51265	−0.310434
$940$	−11.5129	−0.375510
$941$	23.6191	0.769959	0.384980	−	0.922925i	$-0.374208\pi$
$941$	23.6191	0.769959	0.384980	+	0.922925i	$0.374208\pi$
$942$	−6.64571	−0.216529
$943$	31.3346	1.02040
$944$	−42.1282	−1.37116
$945$	6.85980	0.223149
$946$	26.5577	0.863466
$947$	−6.17085	−0.200526	−0.100263	−	0.994961i	$-0.531968\pi$
$947$	−6.17085	−0.200526	−0.100263	+	0.994961i	$0.531968\pi$
$948$	4.77020	0.154929
$949$	−55.6884	−1.80772
$950$	−62.1412	−2.01613
$951$	8.33184	0.270179
$952$	3.81076	0.123508
$953$	−5.81878	−0.188489	−0.0942444	−	0.995549i	$-0.530044\pi$
$953$	−5.81878	−0.188489	−0.0942444	+	0.995549i	$0.530044\pi$
$954$	−13.8869	−0.449604
$955$	−52.6336	−1.70318
$956$	2.36636	0.0765334
$957$	−16.3425	−0.528279
$958$	−57.3578	−1.85315
$959$	27.0592	0.873786
$960$	24.0992	0.777797
$961$	−30.8408	−0.994865
$962$	−84.7720	−2.73316
$963$	15.6627	0.504723
$964$	−0.765594	−0.0246581
$965$	−20.6592	−0.665045
$966$	−17.3441	−0.558037
$967$	−25.7332	−0.827524	−0.413762	−	0.910385i	$-0.635785\pi$
$967$	−25.7332	−0.827524	−0.413762	+	0.910385i	$0.635785\pi$
$968$	−6.87246	−0.220889
$969$	−3.50320	−0.112539
$970$	49.8105	1.59932
$971$	14.1598	0.454410	0.227205	−	0.973847i	$-0.427041\pi$
$971$	14.1598	0.454410	0.227205	+	0.973847i	$0.427041\pi$
$972$	−0.329628	−0.0105728
$973$	26.3145	0.843606
$974$	−21.6580	−0.693968
$975$	48.4065	1.55025
$976$	38.7060	1.23895
$977$	−57.7419	−1.84733	−0.923663	−	0.383205i	$-0.874820\pi$
$977$	−57.7419	−1.84733	−0.923663	+	0.383205i	$0.874820\pi$
$978$	11.7720	0.376427
$979$	−49.8040	−1.59174
$980$	4.80692	0.153552
$981$	8.07989	0.257971
$982$	−29.8510	−0.952585
$983$	−6.77040	−0.215942	−0.107971	−	0.994154i	$-0.534435\pi$
$983$	−6.77040	−0.215942	−0.107971	+	0.994154i	$0.534435\pi$
$984$	12.5727	0.400802
$985$	−63.3856	−2.01963
$986$	−7.23451	−0.230394
$987$	−16.2839	−0.518323
$988$	−6.88525	−0.219049
$989$	38.3660	1.21997
$990$	16.8715	0.536212
$991$	12.0557	0.382962	0.191481	−	0.981496i	$-0.438671\pi$
$991$	12.0557	0.382962	0.191481	+	0.981496i	$0.438671\pi$
$992$	−0.736745	−0.0233917
$993$	−7.05034	−0.223736
$994$	16.0112	0.507845
$995$	−55.1036	−1.74690
$996$	−3.75190	−0.118883
$997$	−1.26161	−0.0399557	−0.0199778	−	0.999800i	$-0.506360\pi$
$997$	−1.26161	−0.0399557	−0.0199778	+	0.999800i	$0.506360\pi$
$998$	37.3232	1.18144
$999$	11.1449	0.352610

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6009.2.a.b.1.20	✓	74

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6009.2.a.b.1.20	✓	74	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:	\( N \)	\(=\)	\( 6009 = 3 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6009.a (trivial)

\(f(q)\)	\(=\)	\(q-1.52631 q^{2} -1.00000 q^{3} +0.329628 q^{4} -3.83581 q^{5} +1.52631 q^{6} +1.78836 q^{7} +2.54951 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.52631 q^{2} -1.00000 q^{3} +0.329628 q^{4} -3.83581 q^{5} +1.52631 q^{6} +1.78836 q^{7} +2.54951 q^{8} +1.00000 q^{9} +5.85464 q^{10} +2.88174 q^{11} -0.329628 q^{12} -4.98346 q^{13} -2.72959 q^{14} +3.83581 q^{15} -4.55060 q^{16} +0.835797 q^{17} -1.52631 q^{18} +4.19145 q^{19} -1.26439 q^{20} -1.78836 q^{21} -4.39843 q^{22} -6.35409 q^{23} -2.54951 q^{24} +9.71342 q^{25} +7.60632 q^{26} -1.00000 q^{27} +0.589494 q^{28} +5.67107 q^{29} -5.85464 q^{30} -0.398969 q^{31} +1.84662 q^{32} -2.88174 q^{33} -1.27569 q^{34} -6.85980 q^{35} +0.329628 q^{36} -11.1449 q^{37} -6.39746 q^{38} +4.98346 q^{39} -9.77942 q^{40} -4.93141 q^{41} +2.72959 q^{42} -6.03801 q^{43} +0.949901 q^{44} -3.83581 q^{45} +9.69833 q^{46} +9.10551 q^{47} +4.55060 q^{48} -3.80177 q^{49} -14.8257 q^{50} -0.835797 q^{51} -1.64269 q^{52} +9.09832 q^{53} +1.52631 q^{54} -11.0538 q^{55} +4.55944 q^{56} -4.19145 q^{57} -8.65582 q^{58} +9.25771 q^{59} +1.26439 q^{60} -8.50568 q^{61} +0.608951 q^{62} +1.78836 q^{63} +6.28268 q^{64} +19.1156 q^{65} +4.39843 q^{66} +3.15826 q^{67} +0.275502 q^{68} +6.35409 q^{69} +10.4702 q^{70} -5.86579 q^{71} +2.54951 q^{72} +11.1746 q^{73} +17.0107 q^{74} -9.71342 q^{75} +1.38162 q^{76} +5.15358 q^{77} -7.60632 q^{78} -14.4714 q^{79} +17.4552 q^{80} +1.00000 q^{81} +7.52687 q^{82} +11.3822 q^{83} -0.589494 q^{84} -3.20596 q^{85} +9.21588 q^{86} -5.67107 q^{87} +7.34701 q^{88} -17.2826 q^{89} +5.85464 q^{90} -8.91222 q^{91} -2.09449 q^{92} +0.398969 q^{93} -13.8978 q^{94} -16.0776 q^{95} -1.84662 q^{96} +8.50787 q^{97} +5.80269 q^{98} +2.88174 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 74 q - 3 q^{2} - 74 q^{3} + 57 q^{4} + 14 q^{5} + 3 q^{6} - 26 q^{7} - 9 q^{8} + 74 q^{9}+O(q^{10}) \) 74 * q - 3 * q^2 - 74 * q^3 + 57 * q^4 + 14 * q^5 + 3 * q^6 - 26 * q^7 - 9 * q^8 + 74 * q^9	\( 74 q - 3 q^{2} - 74 q^{3} + 57 q^{4} + 14 q^{5} + 3 q^{6} - 26 q^{7} - 9 q^{8} + 74 q^{9} - 21 q^{10} - 16 q^{11} - 57 q^{12} - 16 q^{13} - 17 q^{14} - 14 q^{15} + 15 q^{16} + 33 q^{17} - 3 q^{18} - 46 q^{19} + 17 q^{20} + 26 q^{21} - 28 q^{22} - 31 q^{23} + 9 q^{24} + 42 q^{25} - 8 q^{26} - 74 q^{27} - 46 q^{28} - 7 q^{29} + 21 q^{30} - 60 q^{31} - 16 q^{32} + 16 q^{33} - 42 q^{34} - 46 q^{35} + 57 q^{36} - 22 q^{37} + 10 q^{38} + 16 q^{39} - 67 q^{40} - 11 q^{41} + 17 q^{42} - 56 q^{43} - 25 q^{44} + 14 q^{45} - 59 q^{46} - q^{47} - 15 q^{48} + 12 q^{49} - 24 q^{50} - 33 q^{51} - 37 q^{52} + 25 q^{53} + 3 q^{54} - 90 q^{55} - 46 q^{56} + 46 q^{57} - 20 q^{58} - 60 q^{59} - 17 q^{60} - 55 q^{61} + 40 q^{62} - 26 q^{63} - 55 q^{64} - 12 q^{65} + 28 q^{66} - 64 q^{67} + 75 q^{68} + 31 q^{69} - 23 q^{70} - 128 q^{71} - 9 q^{72} - 31 q^{73} - 51 q^{74} - 42 q^{75} - 109 q^{76} + 70 q^{77} + 8 q^{78} - 193 q^{79} + 39 q^{80} + 74 q^{81} - 26 q^{82} - 5 q^{83} + 46 q^{84} - 60 q^{85} - 36 q^{86} + 7 q^{87} - 56 q^{88} - 21 q^{90} - 99 q^{91} - 54 q^{92} + 60 q^{93} - 66 q^{94} - 101 q^{95} + 16 q^{96} - 36 q^{97} - 21 q^{98} - 16 q^{99}+O(q^{100}) \) 74 * q - 3 * q^2 - 74 * q^3 + 57 * q^4 + 14 * q^5 + 3 * q^6 - 26 * q^7 - 9 * q^8 + 74 * q^9 - 21 * q^10 - 16 * q^11 - 57 * q^12 - 16 * q^13 - 17 * q^14 - 14 * q^15 + 15 * q^16 + 33 * q^17 - 3 * q^18 - 46 * q^19 + 17 * q^20 + 26 * q^21 - 28 * q^22 - 31 * q^23 + 9 * q^24 + 42 * q^25 - 8 * q^26 - 74 * q^27 - 46 * q^28 - 7 * q^29 + 21 * q^30 - 60 * q^31 - 16 * q^32 + 16 * q^33 - 42 * q^34 - 46 * q^35 + 57 * q^36 - 22 * q^37 + 10 * q^38 + 16 * q^39 - 67 * q^40 - 11 * q^41 + 17 * q^42 - 56 * q^43 - 25 * q^44 + 14 * q^45 - 59 * q^46 - q^47 - 15 * q^48 + 12 * q^49 - 24 * q^50 - 33 * q^51 - 37 * q^52 + 25 * q^53 + 3 * q^54 - 90 * q^55 - 46 * q^56 + 46 * q^57 - 20 * q^58 - 60 * q^59 - 17 * q^60 - 55 * q^61 + 40 * q^62 - 26 * q^63 - 55 * q^64 - 12 * q^65 + 28 * q^66 - 64 * q^67 + 75 * q^68 + 31 * q^69 - 23 * q^70 - 128 * q^71 - 9 * q^72 - 31 * q^73 - 51 * q^74 - 42 * q^75 - 109 * q^76 + 70 * q^77 + 8 * q^78 - 193 * q^79 + 39 * q^80 + 74 * q^81 - 26 * q^82 - 5 * q^83 + 46 * q^84 - 60 * q^85 - 36 * q^86 + 7 * q^87 - 56 * q^88 - 21 * q^90 - 99 * q^91 - 54 * q^92 + 60 * q^93 - 66 * q^94 - 101 * q^95 + 16 * q^96 - 36 * q^97 - 21 * q^98 - 16 * q^99

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