LMFDB - Embedded newform 1005.2.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1005,2,Mod(1,1005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1005, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("1005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1005 = 3 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1005.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:	$8.02496540314$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 6x^{5} + 15x^{4} + 14x^{3} - 15x^{2} - 6x + 4 $ x^7 - 3x^6 - 6x^5 + 15x^4 + 14x^3 - 15x^2 - 6x + 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.42013$ of defining polynomial
Character	$\chi$	$=$	1005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.42013 q^{2} +1.00000 q^{3} +0.0167760 q^{4} +1.00000 q^{5} -1.42013 q^{6} +3.66225 q^{7} +2.81644 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.42013 q^{2} +1.00000 q^{3} +0.0167760 q^{4} +1.00000 q^{5} -1.42013 q^{6} +3.66225 q^{7} +2.81644 q^{8} +1.00000 q^{9} -1.42013 q^{10} +3.26380 q^{11} +0.0167760 q^{12} -2.79966 q^{13} -5.20088 q^{14} +1.00000 q^{15} -4.03327 q^{16} +2.12064 q^{17} -1.42013 q^{18} +6.67086 q^{19} +0.0167760 q^{20} +3.66225 q^{21} -4.63502 q^{22} -1.64333 q^{23} +2.81644 q^{24} +1.00000 q^{25} +3.97589 q^{26} +1.00000 q^{27} +0.0614380 q^{28} +0.0189191 q^{29} -1.42013 q^{30} -10.5995 q^{31} +0.0948971 q^{32} +3.26380 q^{33} -3.01159 q^{34} +3.66225 q^{35} +0.0167760 q^{36} -1.71472 q^{37} -9.47350 q^{38} -2.79966 q^{39} +2.81644 q^{40} +1.81274 q^{41} -5.20088 q^{42} -9.11183 q^{43} +0.0547536 q^{44} +1.00000 q^{45} +2.33375 q^{46} +3.76947 q^{47} -4.03327 q^{48} +6.41206 q^{49} -1.42013 q^{50} +2.12064 q^{51} -0.0469673 q^{52} +11.3124 q^{53} -1.42013 q^{54} +3.26380 q^{55} +10.3145 q^{56} +6.67086 q^{57} -0.0268676 q^{58} +6.08164 q^{59} +0.0167760 q^{60} -7.18949 q^{61} +15.0527 q^{62} +3.66225 q^{63} +7.93177 q^{64} -2.79966 q^{65} -4.63502 q^{66} +1.00000 q^{67} +0.0355759 q^{68} -1.64333 q^{69} -5.20088 q^{70} -8.11351 q^{71} +2.81644 q^{72} +5.96747 q^{73} +2.43513 q^{74} +1.00000 q^{75} +0.111911 q^{76} +11.9528 q^{77} +3.97589 q^{78} -6.08780 q^{79} -4.03327 q^{80} +1.00000 q^{81} -2.57432 q^{82} -1.95253 q^{83} +0.0614380 q^{84} +2.12064 q^{85} +12.9400 q^{86} +0.0189191 q^{87} +9.19229 q^{88} +16.2631 q^{89} -1.42013 q^{90} -10.2531 q^{91} -0.0275686 q^{92} -10.5995 q^{93} -5.35315 q^{94} +6.67086 q^{95} +0.0948971 q^{96} +4.43089 q^{97} -9.10598 q^{98} +3.26380 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 4 q^{2} + 7 q^{3} + 8 q^{4} + 7 q^{5} + 4 q^{6} + 3 q^{7} + 9 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q + 4 * q^2 + 7 * q^3 + 8 * q^4 + 7 * q^5 + 4 * q^6 + 3 * q^7 + 9 * q^8 + 7 * q^9	\( 7 q + 4 q^{2} + 7 q^{3} + 8 q^{4} + 7 q^{5} + 4 q^{6} + 3 q^{7} + 9 q^{8} + 7 q^{9} + 4 q^{10} + 5 q^{11} + 8 q^{12} - q^{13} - 4 q^{14} + 7 q^{15} + 6 q^{16} + 11 q^{17} + 4 q^{18} + 8 q^{19} + 8 q^{20} + 3 q^{21} - 3 q^{22} + 11 q^{23} + 9 q^{24} + 7 q^{25} - 5 q^{26} + 7 q^{27} - 17 q^{28} + 4 q^{30} - 3 q^{31} + 22 q^{32} + 5 q^{33} + 4 q^{34} + 3 q^{35} + 8 q^{36} - 5 q^{37} - q^{39} + 9 q^{40} + q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 7 q^{45} - 12 q^{46} + 10 q^{47} + 6 q^{48} - 4 q^{49} + 4 q^{50} + 11 q^{51} - 6 q^{52} + 3 q^{53} + 4 q^{54} + 5 q^{55} - 12 q^{56} + 8 q^{57} - 24 q^{58} - 4 q^{59} + 8 q^{60} - 9 q^{61} + 20 q^{62} + 3 q^{63} - 3 q^{64} - q^{65} - 3 q^{66} + 7 q^{67} - 3 q^{68} + 11 q^{69} - 4 q^{70} + 6 q^{71} + 9 q^{72} - 9 q^{73} + 2 q^{74} + 7 q^{75} + 2 q^{76} + 17 q^{77} - 5 q^{78} - 11 q^{79} + 6 q^{80} + 7 q^{81} - 16 q^{82} + 30 q^{83} - 17 q^{84} + 11 q^{85} - 11 q^{86} - 25 q^{88} + 13 q^{89} + 4 q^{90} - 5 q^{91} + 10 q^{92} - 3 q^{93} - 25 q^{94} + 8 q^{95} + 22 q^{96} - 7 q^{97} - 10 q^{98} + 5 q^{99}+O(q^{100}) \) 7 * q + 4 * q^2 + 7 * q^3 + 8 * q^4 + 7 * q^5 + 4 * q^6 + 3 * q^7 + 9 * q^8 + 7 * q^9 + 4 * q^10 + 5 * q^11 + 8 * q^12 - q^13 - 4 * q^14 + 7 * q^15 + 6 * q^16 + 11 * q^17 + 4 * q^18 + 8 * q^19 + 8 * q^20 + 3 * q^21 - 3 * q^22 + 11 * q^23 + 9 * q^24 + 7 * q^25 - 5 * q^26 + 7 * q^27 - 17 * q^28 + 4 * q^30 - 3 * q^31 + 22 * q^32 + 5 * q^33 + 4 * q^34 + 3 * q^35 + 8 * q^36 - 5 * q^37 - q^39 + 9 * q^40 + q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 7 * q^45 - 12 * q^46 + 10 * q^47 + 6 * q^48 - 4 * q^49 + 4 * q^50 + 11 * q^51 - 6 * q^52 + 3 * q^53 + 4 * q^54 + 5 * q^55 - 12 * q^56 + 8 * q^57 - 24 * q^58 - 4 * q^59 + 8 * q^60 - 9 * q^61 + 20 * q^62 + 3 * q^63 - 3 * q^64 - q^65 - 3 * q^66 + 7 * q^67 - 3 * q^68 + 11 * q^69 - 4 * q^70 + 6 * q^71 + 9 * q^72 - 9 * q^73 + 2 * q^74 + 7 * q^75 + 2 * q^76 + 17 * q^77 - 5 * q^78 - 11 * q^79 + 6 * q^80 + 7 * q^81 - 16 * q^82 + 30 * q^83 - 17 * q^84 + 11 * q^85 - 11 * q^86 - 25 * q^88 + 13 * q^89 + 4 * q^90 - 5 * q^91 + 10 * q^92 - 3 * q^93 - 25 * q^94 + 8 * q^95 + 22 * q^96 - 7 * q^97 - 10 * q^98 + 5 * 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 $

$2$	−1.42013	−1.00419	−0.502093	−	0.864814i	$-0.667436\pi$
$2$	−1.42013	−1.00419	−0.502093	+	0.864814i	$0.667436\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.0167760	0.00838802
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.42013	−0.579767
$7$	3.66225	1.38420	0.692100	−	0.721802i	$-0.256686\pi$
$7$	3.66225	1.38420	0.692100	+	0.721802i	$0.256686\pi$
$8$	2.81644	0.995762
$9$	1.00000	0.333333
$10$	−1.42013	−0.449085
$11$	3.26380	0.984072	0.492036	−	0.870575i	$-0.336253\pi$
$11$	3.26380	0.984072	0.492036	+	0.870575i	$0.336253\pi$
$12$	0.0167760	0.00484282
$13$	−2.79966	−0.776487	−0.388244	−	0.921557i	$-0.626918\pi$
$13$	−2.79966	−0.776487	−0.388244	+	0.921557i	$0.626918\pi$
$14$	−5.20088	−1.38999
$15$	1.00000	0.258199
$16$	−4.03327	−1.00832
$17$	2.12064	0.514331	0.257165	−	0.966367i	$-0.417211\pi$
$17$	2.12064	0.514331	0.257165	+	0.966367i	$0.417211\pi$
$18$	−1.42013	−0.334728
$19$	6.67086	1.53040	0.765200	−	0.643793i	$-0.222640\pi$
$19$	6.67086	1.53040	0.765200	+	0.643793i	$0.222640\pi$
$20$	0.0167760	0.00375124
$21$	3.66225	0.799168
$22$	−4.63502	−0.988190
$23$	−1.64333	−0.342658	−0.171329	−	0.985214i	$-0.554806\pi$
$23$	−1.64333	−0.342658	−0.171329	+	0.985214i	$0.554806\pi$
$24$	2.81644	0.574904
$25$	1.00000	0.200000
$26$	3.97589	0.779737
$27$	1.00000	0.192450
$28$	0.0614380	0.0116107
$29$	0.0189191	0.00351319	0.00175660	−	0.999998i	$-0.499441\pi$
$29$	0.0189191	0.00351319	0.00175660	+	0.999998i	$0.499441\pi$
$30$	−1.42013	−0.259280
$31$	−10.5995	−1.90373	−0.951866	−	0.306516i	$-0.900837\pi$
$31$	−10.5995	−1.90373	−0.951866	+	0.306516i	$0.900837\pi$
$32$	0.0948971	0.0167756
$33$	3.26380	0.568154
$34$	−3.01159	−0.516483
$35$	3.66225	0.619033
$36$	0.0167760	0.00279601
$37$	−1.71472	−0.281898	−0.140949	−	0.990017i	$-0.545015\pi$
$37$	−1.71472	−0.281898	−0.140949	+	0.990017i	$0.545015\pi$
$38$	−9.47350	−1.53681
$39$	−2.79966	−0.448305
$40$	2.81644	0.445318
$41$	1.81274	0.283102	0.141551	−	0.989931i	$-0.454791\pi$
$41$	1.81274	0.283102	0.141551	+	0.989931i	$0.454791\pi$
$42$	−5.20088	−0.802513
$43$	−9.11183	−1.38954	−0.694770	−	0.719232i	$-0.744494\pi$
$43$	−9.11183	−1.38954	−0.694770	+	0.719232i	$0.744494\pi$
$44$	0.0547536	0.00825441
$45$	1.00000	0.149071
$46$	2.33375	0.344092
$47$	3.76947	0.549834	0.274917	−	0.961468i	$-0.411350\pi$
$47$	3.76947	0.549834	0.274917	+	0.961468i	$0.411350\pi$
$48$	−4.03327	−0.582152
$49$	6.41206	0.916009
$50$	−1.42013	−0.200837
$51$	2.12064	0.296949
$52$	−0.0469673	−0.00651319
$53$	11.3124	1.55387	0.776936	−	0.629579i	$-0.216773\pi$
$53$	11.3124	1.55387	0.776936	+	0.629579i	$0.216773\pi$
$54$	−1.42013	−0.193256
$55$	3.26380	0.440090
$56$	10.3145	1.37833
$57$	6.67086	0.883577
$58$	−0.0268676	−0.00352789
$59$	6.08164	0.791762	0.395881	−	0.918302i	$-0.370439\pi$
$59$	6.08164	0.791762	0.395881	+	0.918302i	$0.370439\pi$
$60$	0.0167760	0.00216578
$61$	−7.18949	−0.920519	−0.460260	−	0.887784i	$-0.652244\pi$
$61$	−7.18949	−0.920519	−0.460260	+	0.887784i	$0.652244\pi$
$62$	15.0527	1.91170
$63$	3.66225	0.461400
$64$	7.93177	0.991472
$65$	−2.79966	−0.347256
$66$	−4.63502	−0.570532
$67$	1.00000	0.122169
$67$	1.00000	0.122169
$68$	0.0355759	0.00431422
$69$	−1.64333	−0.197834
$70$	−5.20088	−0.621624
$71$	−8.11351	−0.962896	−0.481448	−	0.876475i	$-0.659889\pi$
$71$	−8.11351	−0.962896	−0.481448	+	0.876475i	$0.659889\pi$
$72$	2.81644	0.331921
$73$	5.96747	0.698440	0.349220	−	0.937041i	$-0.386447\pi$
$73$	5.96747	0.698440	0.349220	+	0.937041i	$0.386447\pi$
$74$	2.43513	0.283078
$75$	1.00000	0.115470
$76$	0.111911	0.0128370
$77$	11.9528	1.36215
$78$	3.97589	0.450181
$79$	−6.08780	−0.684932	−0.342466	−	0.939530i	$-0.611262\pi$
$79$	−6.08780	−0.684932	−0.342466	+	0.939530i	$0.611262\pi$
$80$	−4.03327	−0.450933
$81$	1.00000	0.111111
$82$	−2.57432	−0.284287
$83$	−1.95253	−0.214318	−0.107159	−	0.994242i	$-0.534175\pi$
$83$	−1.95253	−0.214318	−0.107159	+	0.994242i	$0.534175\pi$
$84$	0.0614380	0.00670344
$85$	2.12064	0.230016
$86$	12.9400	1.39536
$87$	0.0189191	0.00202834
$88$	9.19229	0.979902
$89$	16.2631	1.72388	0.861942	−	0.507007i	$-0.169248\pi$
$89$	16.2631	1.72388	0.861942	+	0.507007i	$0.169248\pi$
$90$	−1.42013	−0.149695
$91$	−10.2531	−1.07481
$92$	−0.0275686	−0.00287422
$93$	−10.5995	−1.09912
$94$	−5.35315	−0.552135
$95$	6.67086	0.684416
$96$	0.0948971	0.00968539
$97$	4.43089	0.449888	0.224944	−	0.974372i	$-0.427780\pi$
$97$	4.43089	0.449888	0.224944	+	0.974372i	$0.427780\pi$
$98$	−9.10598	−0.919843
$99$	3.26380	0.328024
$100$	0.0167760	0.00167760
$101$	−15.6077	−1.55302	−0.776510	−	0.630105i	$-0.783012\pi$
$101$	−15.6077	−1.55302	−0.776510	+	0.630105i	$0.783012\pi$
$102$	−3.01159	−0.298192
$103$	−1.97784	−0.194882	−0.0974411	−	0.995241i	$-0.531066\pi$
$103$	−1.97784	−0.194882	−0.0974411	+	0.995241i	$0.531066\pi$
$104$	−7.88509	−0.773197
$105$	3.66225	0.357399
$106$	−16.0651	−1.56038
$107$	14.1608	1.36898	0.684488	−	0.729024i	$-0.260026\pi$
$107$	14.1608	1.36898	0.684488	+	0.729024i	$0.260026\pi$
$108$	0.0167760	0.00161427
$109$	7.47058	0.715552	0.357776	−	0.933807i	$-0.383535\pi$
$109$	7.47058	0.715552	0.357776	+	0.933807i	$0.383535\pi$
$110$	−4.63502	−0.441932
$111$	−1.71472	−0.162754
$112$	−14.7708	−1.39571
$113$	9.85628	0.927200	0.463600	−	0.886044i	$-0.346557\pi$
$113$	9.85628	0.927200	0.463600	+	0.886044i	$0.346557\pi$
$114$	−9.47350	−0.887275
$115$	−1.64333	−0.153241
$116$	0.000317388 0	2.94687e−5 0
$117$	−2.79966	−0.258829
$118$	−8.63674	−0.795076
$119$	7.76631	0.711937
$120$	2.81644	0.257105
$121$	−0.347627	−0.0316025
$122$	10.2100	0.924372
$123$	1.81274	0.163449
$124$	−0.177818	−0.0159685
$125$	1.00000	0.0894427
$126$	−5.20088	−0.463331
$127$	2.58185	0.229102	0.114551	−	0.993417i	$-0.463457\pi$
$127$	2.58185	0.229102	0.114551	+	0.993417i	$0.463457\pi$
$128$	−11.4540	−1.01240
$129$	−9.11183	−0.802252
$130$	3.97589	0.348709
$131$	−6.97007	−0.608978	−0.304489	−	0.952516i	$-0.598486\pi$
$131$	−6.97007	−0.608978	−0.304489	+	0.952516i	$0.598486\pi$
$132$	0.0547536	0.00476569
$133$	24.4303	2.11838
$134$	−1.42013	−0.122681
$135$	1.00000	0.0860663
$136$	5.97266	0.512151
$137$	11.0644	0.945295	0.472648	−	0.881251i	$-0.343298\pi$
$137$	11.0644	0.945295	0.472648	+	0.881251i	$0.343298\pi$
$138$	2.33375	0.198662
$139$	−3.51297	−0.297966	−0.148983	−	0.988840i	$-0.547600\pi$
$139$	−3.51297	−0.297966	−0.148983	+	0.988840i	$0.547600\pi$
$140$	0.0614380	0.00519246
$141$	3.76947	0.317447
$142$	11.5223	0.966926
$143$	−9.13754	−0.764119
$144$	−4.03327	−0.336106
$145$	0.0189191	0.00157115
$146$	−8.47460	−0.701363
$147$	6.41206	0.528858
$148$	−0.0287662	−0.00236457
$149$	−7.82118	−0.640736	−0.320368	−	0.947293i	$-0.603807\pi$
$149$	−7.82118	−0.640736	−0.320368	+	0.947293i	$0.603807\pi$
$150$	−1.42013	−0.115953
$151$	−8.04607	−0.654780	−0.327390	−	0.944889i	$-0.606169\pi$
$151$	−8.04607	−0.654780	−0.327390	+	0.944889i	$0.606169\pi$
$152$	18.7881	1.52391
$153$	2.12064	0.171444
$154$	−16.9746	−1.36785
$155$	−10.5995	−0.851375
$156$	−0.0469673	−0.00376039
$157$	−2.78927	−0.222608	−0.111304	−	0.993786i	$-0.535503\pi$
$157$	−2.78927	−0.222608	−0.111304	+	0.993786i	$0.535503\pi$
$158$	8.64549	0.687798
$159$	11.3124	0.897129
$160$	0.0948971	0.00750227
$161$	−6.01828	−0.474307
$162$	−1.42013	−0.111576
$163$	21.6024	1.69203	0.846016	−	0.533158i	$-0.178995\pi$
$163$	21.6024	1.69203	0.846016	+	0.533158i	$0.178995\pi$
$164$	0.0304105	0.00237466
$165$	3.26380	0.254086
$166$	2.77285	0.215215
$167$	18.3413	1.41930	0.709648	−	0.704557i	$-0.248854\pi$
$167$	18.3413	1.41930	0.709648	+	0.704557i	$0.248854\pi$
$168$	10.3145	0.795781
$169$	−5.16188	−0.397068
$170$	−3.01159	−0.230978
$171$	6.67086	0.510133
$172$	−0.152860	−0.0116555
$173$	−21.7221	−1.65150	−0.825751	−	0.564035i	$-0.809248\pi$
$173$	−21.7221	−1.65150	−0.825751	+	0.564035i	$0.809248\pi$
$174$	−0.0268676	−0.00203683
$175$	3.66225	0.276840
$176$	−13.1638	−0.992257
$177$	6.08164	0.457124
$178$	−23.0957	−1.73110
$179$	−16.1880	−1.20995	−0.604973	−	0.796246i	$-0.706816\pi$
$179$	−16.1880	−1.20995	−0.604973	+	0.796246i	$0.706816\pi$
$180$	0.0167760	0.00125041
$181$	−0.670680	−0.0498513	−0.0249256	−	0.999689i	$-0.507935\pi$
$181$	−0.670680	−0.0498513	−0.0249256	+	0.999689i	$0.507935\pi$
$182$	14.5607	1.07931
$183$	−7.18949	−0.531462
$184$	−4.62834	−0.341206
$185$	−1.71472	−0.126069
$186$	15.0527	1.10372
$187$	6.92134	0.506138
$188$	0.0632368	0.00461202
$189$	3.66225	0.266389
$190$	−9.47350	−0.687280
$191$	10.6974	0.774036	0.387018	−	0.922072i	$-0.373505\pi$
$191$	10.6974	0.774036	0.387018	+	0.922072i	$0.373505\pi$
$192$	7.93177	0.572427
$193$	−7.09859	−0.510968	−0.255484	−	0.966813i	$-0.582235\pi$
$193$	−7.09859	−0.510968	−0.255484	+	0.966813i	$0.582235\pi$
$194$	−6.29244	−0.451771
$195$	−2.79966	−0.200488
$196$	0.107569	0.00768350
$197$	−13.9254	−0.992147	−0.496074	−	0.868281i	$-0.665225\pi$
$197$	−13.9254	−0.992147	−0.496074	+	0.868281i	$0.665225\pi$
$198$	−4.63502	−0.329397
$199$	−23.9299	−1.69635	−0.848173	−	0.529719i	$-0.822297\pi$
$199$	−23.9299	−1.69635	−0.848173	+	0.529719i	$0.822297\pi$
$200$	2.81644	0.199152
$201$	1.00000	0.0705346
$202$	22.1649	1.55952
$203$	0.0692865	0.00486296
$204$	0.0355759	0.00249081
$205$	1.81274	0.126607
$206$	2.80879	0.195698
$207$	−1.64333	−0.114219
$208$	11.2918	0.782946
$209$	21.7723	1.50602
$210$	−5.20088	−0.358895
$211$	−18.8988	−1.30105	−0.650524	−	0.759485i	$-0.725451\pi$
$211$	−18.8988	−1.30105	−0.650524	+	0.759485i	$0.725451\pi$
$212$	0.189777	0.0130339
$213$	−8.11351	−0.555928
$214$	−20.1102	−1.37471
$215$	−9.11183	−0.621422
$216$	2.81644	0.191635
$217$	−38.8181	−2.63514
$218$	−10.6092	−0.718547
$219$	5.96747	0.403244
$220$	0.0547536	0.00369149
$221$	−5.93708	−0.399371
$222$	2.43513	0.163435
$223$	3.78003	0.253129	0.126565	−	0.991958i	$-0.459605\pi$
$223$	3.78003	0.253129	0.126565	+	0.991958i	$0.459605\pi$
$224$	0.347537	0.0232208
$225$	1.00000	0.0666667
$226$	−13.9972	−0.931081
$227$	4.02424	0.267098	0.133549	−	0.991042i	$-0.457363\pi$
$227$	4.02424	0.267098	0.133549	+	0.991042i	$0.457363\pi$
$228$	0.111911	0.00741146
$229$	−15.3718	−1.01580	−0.507899	−	0.861416i	$-0.669578\pi$
$229$	−15.3718	−1.01580	−0.507899	+	0.861416i	$0.669578\pi$
$230$	2.33375	0.153883
$231$	11.9528	0.786439
$232$	0.0532845	0.00349830
$233$	−16.8263	−1.10233	−0.551164	−	0.834397i	$-0.685816\pi$
$233$	−16.8263	−1.10233	−0.551164	+	0.834397i	$0.685816\pi$
$234$	3.97589	0.259912
$235$	3.76947	0.245893
$236$	0.102026	0.00664132
$237$	−6.08780	−0.395445
$238$	−11.0292	−0.714916
$239$	18.1984	1.17715	0.588577	−	0.808441i	$-0.299688\pi$
$239$	18.1984	1.17715	0.588577	+	0.808441i	$0.299688\pi$
$240$	−4.03327	−0.260347
$241$	9.42628	0.607200	0.303600	−	0.952800i	$-0.401811\pi$
$241$	9.42628	0.607200	0.303600	+	0.952800i	$0.401811\pi$
$242$	0.493677	0.0317347
$243$	1.00000	0.0641500
$244$	−0.120611	−0.00772133
$245$	6.41206	0.409652
$246$	−2.57432	−0.164133
$247$	−18.6762	−1.18834
$248$	−29.8529	−1.89566
$249$	−1.95253	−0.123737
$250$	−1.42013	−0.0898171
$251$	5.65618	0.357015	0.178507	−	0.983939i	$-0.442873\pi$
$251$	5.65618	0.357015	0.178507	+	0.983939i	$0.442873\pi$
$252$	0.0614380	0.00387023
$253$	−5.36349	−0.337200
$254$	−3.66657	−0.230061
$255$	2.12064	0.132800
$256$	0.402597	0.0251623
$257$	−19.5519	−1.21961	−0.609806	−	0.792551i	$-0.708753\pi$
$257$	−19.5519	−1.21961	−0.609806	+	0.792551i	$0.708753\pi$
$258$	12.9400	0.805609
$259$	−6.27973	−0.390203
$260$	−0.0469673	−0.00291279
$261$	0.0189191	0.00117106
$262$	9.89842	0.611526
$263$	−2.84131	−0.175203	−0.0876013	−	0.996156i	$-0.527920\pi$
$263$	−2.84131	−0.175203	−0.0876013	+	0.996156i	$0.527920\pi$
$264$	9.19229	0.565746
$265$	11.3124	0.694913
$266$	−34.6943	−2.12725
$267$	16.2631	0.995284
$268$	0.0167760	0.00102476
$269$	−18.4970	−1.12778	−0.563890	−	0.825850i	$-0.690696\pi$
$269$	−18.4970	−1.12778	−0.563890	+	0.825850i	$0.690696\pi$
$270$	−1.42013	−0.0864265
$271$	5.41652	0.329030	0.164515	−	0.986375i	$-0.447394\pi$
$271$	5.41652	0.329030	0.164515	+	0.986375i	$0.447394\pi$
$272$	−8.55311	−0.518609
$273$	−10.2531	−0.620544
$274$	−15.7129	−0.949252
$275$	3.26380	0.196814
$276$	−0.0275686	−0.00165943
$277$	31.1357	1.87076	0.935381	−	0.353643i	$-0.115057\pi$
$277$	31.1357	1.87076	0.935381	+	0.353643i	$0.115057\pi$
$278$	4.98888	0.299213
$279$	−10.5995	−0.634577
$280$	10.3145	0.616410
$281$	0.812247	0.0484546	0.0242273	−	0.999706i	$-0.492287\pi$
$281$	0.812247	0.0484546	0.0242273	+	0.999706i	$0.492287\pi$
$282$	−5.35315	−0.318776
$283$	−7.04330	−0.418681	−0.209340	−	0.977843i	$-0.567132\pi$
$283$	−7.04330	−0.418681	−0.209340	+	0.977843i	$0.567132\pi$
$284$	−0.136113	−0.00807679
$285$	6.67086	0.395148
$286$	12.9765	0.767317
$287$	6.63869	0.391869
$288$	0.0948971	0.00559186
$289$	−12.5029	−0.735464
$290$	−0.0268676	−0.00157772
$291$	4.43089	0.259743
$292$	0.100110	0.00585852
$293$	13.0361	0.761578	0.380789	−	0.924662i	$-0.375652\pi$
$293$	13.0361	0.761578	0.380789	+	0.924662i	$0.375652\pi$
$294$	−9.10598	−0.531072
$295$	6.08164	0.354087
$296$	−4.82941	−0.280704
$297$	3.26380	0.189385
$298$	11.1071	0.643418
$299$	4.60077	0.266069
$300$	0.0167760	0.000968565 0
$301$	−33.3698	−1.92340
$302$	11.4265	0.657520
$303$	−15.6077	−0.896637
$304$	−26.9054	−1.54313
$305$	−7.18949	−0.411669
$306$	−3.01159	−0.172161
$307$	18.9833	1.08343	0.541716	−	0.840562i	$-0.317775\pi$
$307$	18.9833	1.08343	0.541716	+	0.840562i	$0.317775\pi$
$308$	0.200521	0.0114258
$309$	−1.97784	−0.112515
$310$	15.0527	0.854938
$311$	−1.11836	−0.0634166	−0.0317083	−	0.999497i	$-0.510095\pi$
$311$	−1.11836	−0.0634166	−0.0317083	+	0.999497i	$0.510095\pi$
$312$	−7.88509	−0.446405
$313$	−26.5721	−1.50194	−0.750972	−	0.660334i	$-0.770415\pi$
$313$	−26.5721	−1.50194	−0.750972	+	0.660334i	$0.770415\pi$
$314$	3.96113	0.223540
$315$	3.66225	0.206344
$316$	−0.102129	−0.00574522
$317$	−10.2185	−0.573930	−0.286965	−	0.957941i	$-0.592646\pi$
$317$	−10.2185	−0.573930	−0.286965	+	0.957941i	$0.592646\pi$
$318$	−16.0651	−0.900883
$319$	0.0617481	0.00345723
$320$	7.93177	0.443400
$321$	14.1608	0.790379
$322$	8.54676	0.476292
$323$	14.1465	0.787132
$324$	0.0167760	0.000932002 0
$325$	−2.79966	−0.155297
$326$	−30.6783	−1.69911
$327$	7.47058	0.413124
$328$	5.10546	0.281902
$329$	13.8047	0.761080
$330$	−4.63502	−0.255150
$331$	−3.73565	−0.205330	−0.102665	−	0.994716i	$-0.532737\pi$
$331$	−3.73565	−0.205330	−0.102665	+	0.994716i	$0.532737\pi$
$332$	−0.0327557	−0.00179771
$333$	−1.71472	−0.0939661
$334$	−26.0471	−1.42524
$335$	1.00000	0.0546358
$336$	−14.7708	−0.805815
$337$	−34.0269	−1.85356	−0.926782	−	0.375599i	$-0.877437\pi$
$337$	−34.0269	−1.85356	−0.926782	+	0.375599i	$0.877437\pi$
$338$	7.33055	0.398729
$339$	9.85628	0.535319
$340$	0.0355759	0.00192938
$341$	−34.5947	−1.87341
$342$	−9.47350	−0.512268
$343$	−2.15317	−0.116260
$344$	−25.6629	−1.38365
$345$	−1.64333	−0.0884739
$346$	30.8483	1.65841
$347$	−29.2097	−1.56806	−0.784031	−	0.620722i	$-0.786840\pi$
$347$	−29.2097	−1.56806	−0.784031	+	0.620722i	$0.786840\pi$
$348$	0.000317388 0	1.70138e−5 0
$349$	21.3114	1.14077	0.570386	−	0.821377i	$-0.306794\pi$
$349$	21.3114	1.14077	0.570386	+	0.821377i	$0.306794\pi$
$350$	−5.20088	−0.277999
$351$	−2.79966	−0.149435
$352$	0.309725	0.0165084
$353$	−6.32580	−0.336688	−0.168344	−	0.985728i	$-0.553842\pi$
$353$	−6.32580	−0.336688	−0.168344	+	0.985728i	$0.553842\pi$
$354$	−8.63674	−0.459037
$355$	−8.11351	−0.430620
$356$	0.272830	0.0144600
$357$	7.76631	0.411037
$358$	22.9891	1.21501
$359$	−14.7835	−0.780245	−0.390123	−	0.920763i	$-0.627567\pi$
$359$	−14.7835	−0.780245	−0.390123	+	0.920763i	$0.627567\pi$
$360$	2.81644	0.148439
$361$	25.5004	1.34212
$362$	0.952454	0.0500599
$363$	−0.347627	−0.0182457
$364$	−0.172006	−0.00901555
$365$	5.96747	0.312352
$366$	10.2100	0.533686
$367$	22.8315	1.19180	0.595898	−	0.803060i	$-0.296796\pi$
$367$	22.8315	1.19180	0.595898	+	0.803060i	$0.296796\pi$
$368$	6.62799	0.345508
$369$	1.81274	0.0943672
$370$	2.43513	0.126596
$371$	41.4287	2.15087
$372$	−0.177818	−0.00921944
$373$	29.0985	1.50666	0.753332	−	0.657640i	$-0.228445\pi$
$373$	29.0985	1.50666	0.753332	+	0.657640i	$0.228445\pi$
$374$	−9.82922	−0.508257
$375$	1.00000	0.0516398
$376$	10.6165	0.547504
$377$	−0.0529672	−0.00272795
$378$	−5.20088	−0.267504
$379$	16.6978	0.857708	0.428854	−	0.903374i	$-0.358917\pi$
$379$	16.6978	0.857708	0.428854	+	0.903374i	$0.358917\pi$
$380$	0.111911	0.00574089
$381$	2.58185	0.132272
$382$	−15.1917	−0.777275
$383$	24.5499	1.25444	0.627220	−	0.778842i	$-0.284193\pi$
$383$	24.5499	1.25444	0.627220	+	0.778842i	$0.284193\pi$
$384$	−11.4540	−0.584508
$385$	11.9528	0.609173
$386$	10.0809	0.513106
$387$	−9.11183	−0.463180
$388$	0.0743327	0.00377367
$389$	−35.1081	−1.78005	−0.890025	−	0.455912i	$-0.849313\pi$
$389$	−35.1081	−1.78005	−0.890025	+	0.455912i	$0.849313\pi$
$390$	3.97589	0.201327
$391$	−3.48491	−0.176239
$392$	18.0592	0.912127
$393$	−6.97007	−0.351593
$394$	19.7760	0.996299
$395$	−6.08780	−0.306311
$396$	0.0547536	0.00275147
$397$	−17.8265	−0.894686	−0.447343	−	0.894363i	$-0.647630\pi$
$397$	−17.8265	−0.894686	−0.447343	+	0.894363i	$0.647630\pi$
$398$	33.9836	1.70345
$399$	24.4303	1.22305
$400$	−4.03327	−0.201664
$401$	3.97752	0.198628	0.0993140	−	0.995056i	$-0.468335\pi$
$401$	3.97752	0.198628	0.0993140	+	0.995056i	$0.468335\pi$
$402$	−1.42013	−0.0708298
$403$	29.6751	1.47822
$404$	−0.261835	−0.0130268
$405$	1.00000	0.0496904
$406$	−0.0983960	−0.00488331
$407$	−5.59650	−0.277408
$408$	5.97266	0.295691
$409$	35.9212	1.77619	0.888094	−	0.459661i	$-0.152029\pi$
$409$	35.9212	1.77619	0.888094	+	0.459661i	$0.152029\pi$
$410$	−2.57432	−0.127137
$411$	11.0644	0.545767
$412$	−0.0331803	−0.00163468
$413$	22.2725	1.09596
$414$	2.33375	0.114697
$415$	−1.95253	−0.0958460
$416$	−0.265680	−0.0130260
$417$	−3.51297	−0.172031
$418$	−30.9196	−1.51233
$419$	−13.8740	−0.677789	−0.338895	−	0.940824i	$-0.610053\pi$
$419$	−13.8740	−0.677789	−0.338895	+	0.940824i	$0.610053\pi$
$420$	0.0614380	0.00299787
$421$	40.5473	1.97616	0.988078	−	0.153952i	$-0.0492000\pi$
$421$	40.5473	1.97616	0.988078	+	0.153952i	$0.0492000\pi$
$422$	26.8388	1.30649
$423$	3.76947	0.183278
$424$	31.8606	1.54729
$425$	2.12064	0.102866
$426$	11.5223	0.558255
$427$	−26.3297	−1.27418
$428$	0.237562	0.0114830
$429$	−9.13754	−0.441164
$430$	12.9400	0.624022
$431$	−9.79550	−0.471833	−0.235916	−	0.971773i	$-0.575809\pi$
$431$	−9.79550	−0.471833	−0.235916	+	0.971773i	$0.575809\pi$
$432$	−4.03327	−0.194051
$433$	−19.1370	−0.919667	−0.459833	−	0.888005i	$-0.652091\pi$
$433$	−19.1370	−0.919667	−0.459833	+	0.888005i	$0.652091\pi$
$434$	55.1268	2.64617
$435$	0.0189191	0.000907102 0
$436$	0.125327	0.00600206
$437$	−10.9624	−0.524404
$438$	−8.47460	−0.404932
$439$	8.03843	0.383653	0.191827	−	0.981429i	$-0.438559\pi$
$439$	8.03843	0.383653	0.191827	+	0.981429i	$0.438559\pi$
$440$	9.19229	0.438225
$441$	6.41206	0.305336
$442$	8.43144	0.401043
$443$	−13.0740	−0.621162	−0.310581	−	0.950547i	$-0.600524\pi$
$443$	−13.0740	−0.621162	−0.310581	+	0.950547i	$0.600524\pi$
$444$	−0.0287662	−0.00136518
$445$	16.2631	0.770944
$446$	−5.36814	−0.254189
$447$	−7.82118	−0.369929
$448$	29.0481	1.37240
$449$	−25.1929	−1.18892	−0.594462	−	0.804124i	$-0.702635\pi$
$449$	−25.1929	−1.18892	−0.594462	+	0.804124i	$0.702635\pi$
$450$	−1.42013	−0.0669457
$451$	5.91640	0.278592
$452$	0.165349	0.00777737
$453$	−8.04607	−0.378037
$454$	−5.71495	−0.268216
$455$	−10.2531	−0.480671
$456$	18.7881	0.879832
$457$	4.80210	0.224633	0.112316	−	0.993672i	$-0.464173\pi$
$457$	4.80210	0.224633	0.112316	+	0.993672i	$0.464173\pi$
$458$	21.8300	1.02005
$459$	2.12064	0.0989830
$460$	−0.0275686	−0.00128539
$461$	−6.82376	−0.317814	−0.158907	−	0.987294i	$-0.550797\pi$
$461$	−6.82376	−0.317814	−0.158907	+	0.987294i	$0.550797\pi$
$462$	−16.9746	−0.789730
$463$	−6.34009	−0.294649	−0.147324	−	0.989088i	$-0.547066\pi$
$463$	−6.34009	−0.294649	−0.147324	+	0.989088i	$0.547066\pi$
$464$	−0.0763059	−0.00354241
$465$	−10.5995	−0.491541
$466$	23.8956	1.10694
$467$	−13.1557	−0.608774	−0.304387	−	0.952549i	$-0.598452\pi$
$467$	−13.1557	−0.608774	−0.304387	+	0.952549i	$0.598452\pi$
$468$	−0.0469673	−0.00217106
$469$	3.66225	0.169107
$470$	−5.35315	−0.246922
$471$	−2.78927	−0.128523
$472$	17.1286	0.788407
$473$	−29.7392	−1.36741
$474$	8.64549	0.397100
$475$	6.67086	0.306080
$476$	0.130288	0.00597174
$477$	11.3124	0.517957
$478$	−25.8441	−1.18208
$479$	−34.9990	−1.59915	−0.799574	−	0.600568i	$-0.794941\pi$
$479$	−34.9990	−1.59915	−0.799574	+	0.600568i	$0.794941\pi$
$480$	0.0948971	0.00433144
$481$	4.80064	0.218890
$482$	−13.3866	−0.609741
$483$	−6.01828	−0.273841
$484$	−0.00583181	−0.000265082 0
$485$	4.43089	0.201196
$486$	−1.42013	−0.0644185
$487$	−35.5178	−1.60946	−0.804732	−	0.593639i	$-0.797691\pi$
$487$	−35.5178	−1.60946	−0.804732	+	0.593639i	$0.797691\pi$
$488$	−20.2488	−0.916618
$489$	21.6024	0.976895
$490$	−9.10598	−0.411366
$491$	25.2985	1.14171	0.570853	−	0.821052i	$-0.306613\pi$
$491$	25.2985	1.14171	0.570853	+	0.821052i	$0.306613\pi$
$492$	0.0304105	0.00137101
$493$	0.0401206	0.00180694
$494$	26.5226	1.19331
$495$	3.26380	0.146697
$496$	42.7508	1.91957
$497$	−29.7137	−1.33284
$498$	2.77285	0.124255
$499$	−6.05417	−0.271022	−0.135511	−	0.990776i	$-0.543268\pi$
$499$	−6.05417	−0.271022	−0.135511	+	0.990776i	$0.543268\pi$
$500$	0.0167760	0.000750247 0
$501$	18.3413	0.819430
$502$	−8.03252	−0.358509
$503$	17.6401	0.786533	0.393266	−	0.919425i	$-0.371345\pi$
$503$	17.6401	0.786533	0.393266	+	0.919425i	$0.371345\pi$
$504$	10.3145	0.459445
$505$	−15.6077	−0.694532
$506$	7.61687	0.338611
$507$	−5.16188	−0.229247
$508$	0.0433132	0.00192171
$509$	38.6106	1.71138	0.855692	−	0.517486i	$-0.173132\pi$
$509$	38.6106	1.71138	0.855692	+	0.517486i	$0.173132\pi$
$510$	−3.01159	−0.133355
$511$	21.8544	0.966780
$512$	22.3362	0.987129
$513$	6.67086	0.294526
$514$	27.7662	1.22472
$515$	−1.97784	−0.0871540
$516$	−0.152860	−0.00672930
$517$	12.3028	0.541076
$518$	8.91805	0.391837
$519$	−21.7221	−0.953495
$520$	−7.88509	−0.345784
$521$	0.934016	0.0409200	0.0204600	−	0.999791i	$-0.493487\pi$
$521$	0.934016	0.0409200	0.0204600	+	0.999791i	$0.493487\pi$
$522$	−0.0268676	−0.00117596
$523$	44.0708	1.92708	0.963542	−	0.267558i	$-0.0862168\pi$
$523$	44.0708	1.92708	0.963542	+	0.267558i	$0.0862168\pi$
$524$	−0.116930	−0.00510812
$525$	3.66225	0.159834
$526$	4.03503	0.175936
$527$	−22.4778	−0.979148
$528$	−13.1638	−0.572880
$529$	−20.2995	−0.882586
$530$	−16.0651	−0.697821
$531$	6.08164	0.263921
$532$	0.409844	0.0177690
$533$	−5.07505	−0.219825
$534$	−23.0957	−0.999450
$535$	14.1608	0.612225
$536$	2.81644	0.121652
$537$	−16.1880	−0.698562
$538$	26.2681	1.13250
$539$	20.9277	0.901419
$540$	0.0167760	0.000721926 0
$541$	−23.5988	−1.01459	−0.507295	−	0.861772i	$-0.669355\pi$
$541$	−23.5988	−1.01459	−0.507295	+	0.861772i	$0.669355\pi$
$542$	−7.69218	−0.330407
$543$	−0.670680	−0.0287816
$544$	0.201243	0.00862820
$545$	7.47058	0.320005
$546$	14.5607	0.623141
$547$	25.0627	1.07160	0.535801	−	0.844344i	$-0.320010\pi$
$547$	25.0627	1.07160	0.535801	+	0.844344i	$0.320010\pi$
$548$	0.185617	0.00792915
$549$	−7.18949	−0.306840
$550$	−4.63502	−0.197638
$551$	0.126207	0.00537659
$552$	−4.62834	−0.196995
$553$	−22.2951	−0.948082
$554$	−44.2168	−1.87859
$555$	−1.71472	−0.0727858
$556$	−0.0589337	−0.00249934
$557$	34.0542	1.44292	0.721461	−	0.692456i	$-0.243471\pi$
$557$	34.0542	1.44292	0.721461	+	0.692456i	$0.243471\pi$
$558$	15.0527	0.637233
$559$	25.5101	1.07896
$560$	−14.7708	−0.624182
$561$	6.92134	0.292219
$562$	−1.15350	−0.0486574
$563$	−12.2856	−0.517777	−0.258889	−	0.965907i	$-0.583356\pi$
$563$	−12.2856	−0.517777	−0.258889	+	0.965907i	$0.583356\pi$
$564$	0.0632368	0.00266275
$565$	9.85628	0.414657
$566$	10.0024	0.420433
$567$	3.66225	0.153800
$568$	−22.8512	−0.958816
$569$	28.8290	1.20858	0.604288	−	0.796766i	$-0.293458\pi$
$569$	28.8290	1.20858	0.604288	+	0.796766i	$0.293458\pi$
$570$	−9.47350	−0.396801
$571$	−2.57238	−0.107651	−0.0538253	−	0.998550i	$-0.517141\pi$
$571$	−2.57238	−0.107651	−0.0538253	+	0.998550i	$0.517141\pi$
$572$	−0.153292	−0.00640945
$573$	10.6974	0.446890
$574$	−9.42782	−0.393509
$575$	−1.64333	−0.0685316
$576$	7.93177	0.330491
$577$	−22.9339	−0.954752	−0.477376	−	0.878699i	$-0.658412\pi$
$577$	−22.9339	−0.954752	−0.477376	+	0.878699i	$0.658412\pi$
$578$	17.7558	0.738542
$579$	−7.09859	−0.295007
$580$	0.000317388 0	1.31788e−5 0
$581$	−7.15066	−0.296659
$582$	−6.29244	−0.260830
$583$	36.9213	1.52912
$584$	16.8070	0.695480
$585$	−2.79966	−0.115752
$586$	−18.5130	−0.764765
$587$	28.1157	1.16046	0.580229	−	0.814453i	$-0.302963\pi$
$587$	28.1157	1.16046	0.580229	+	0.814453i	$0.302963\pi$
$588$	0.107569	0.00443607
$589$	−70.7079	−2.91347
$590$	−8.63674	−0.355569
$591$	−13.9254	−0.572816
$592$	6.91593	0.284243
$593$	−17.2239	−0.707301	−0.353650	−	0.935378i	$-0.615060\pi$
$593$	−17.2239	−0.707301	−0.353650	+	0.935378i	$0.615060\pi$
$594$	−4.63502	−0.190177
$595$	7.76631	0.318388
$596$	−0.131208	−0.00537451
$597$	−23.9299	−0.979386
$598$	−6.53370	−0.267183
$599$	−27.8806	−1.13917	−0.569585	−	0.821933i	$-0.692896\pi$
$599$	−27.8806	−1.13917	−0.569585	+	0.821933i	$0.692896\pi$
$600$	2.81644	0.114981
$601$	−8.48766	−0.346219	−0.173109	−	0.984903i	$-0.555381\pi$
$601$	−8.48766	−0.346219	−0.173109	+	0.984903i	$0.555381\pi$
$602$	47.3895	1.93145
$603$	1.00000	0.0407231
$604$	−0.134981	−0.00549230
$605$	−0.347627	−0.0141331
$606$	22.1649	0.900389
$607$	44.8744	1.82140	0.910698	−	0.413074i	$-0.135545\pi$
$607$	44.8744	1.82140	0.910698	+	0.413074i	$0.135545\pi$
$608$	0.633045	0.0256734
$609$	0.0692865	0.00280763
$610$	10.2100	0.413392
$611$	−10.5533	−0.426939
$612$	0.0355759	0.00143807
$613$	−10.6398	−0.429738	−0.214869	−	0.976643i	$-0.568932\pi$
$613$	−10.6398	−0.429738	−0.214869	+	0.976643i	$0.568932\pi$
$614$	−26.9587	−1.08797
$615$	1.81274	0.0730966
$616$	33.6645	1.35638
$617$	36.3155	1.46201	0.731003	−	0.682374i	$-0.239052\pi$
$617$	36.3155	1.46201	0.731003	+	0.682374i	$0.239052\pi$
$618$	2.80879	0.112986
$619$	−26.4333	−1.06244	−0.531221	−	0.847233i	$-0.678267\pi$
$619$	−26.4333	−1.06244	−0.531221	+	0.847233i	$0.678267\pi$
$620$	−0.177818	−0.00714134
$621$	−1.64333	−0.0659445
$622$	1.58823	0.0636821
$623$	59.5595	2.38620
$624$	11.2918	0.452034
$625$	1.00000	0.0400000
$626$	37.7359	1.50823
$627$	21.7723	0.869503
$628$	−0.0467929	−0.00186724
$629$	−3.63630	−0.144989
$630$	−5.20088	−0.207208
$631$	25.0074	0.995529	0.497765	−	0.867312i	$-0.334154\pi$
$631$	25.0074	0.995529	0.497765	+	0.867312i	$0.334154\pi$
$632$	−17.1459	−0.682029
$633$	−18.8988	−0.751161
$634$	14.5117	0.576332
$635$	2.58185	0.102458
$636$	0.189777	0.00752513
$637$	−17.9516	−0.711269
$638$	−0.0876905	−0.00347170
$639$	−8.11351	−0.320965
$640$	−11.4540	−0.452758
$641$	−42.6060	−1.68283	−0.841417	−	0.540386i	$-0.818278\pi$
$641$	−42.6060	−1.68283	−0.841417	+	0.540386i	$0.818278\pi$
$642$	−20.1102	−0.793687
$643$	−20.6664	−0.815003	−0.407502	−	0.913205i	$-0.633600\pi$
$643$	−20.6664	−0.815003	−0.407502	+	0.913205i	$0.633600\pi$
$644$	−0.100963	−0.00397850
$645$	−9.11183	−0.358778
$646$	−20.0899	−0.790426
$647$	39.4826	1.55222	0.776111	−	0.630596i	$-0.217190\pi$
$647$	39.4826	1.55222	0.776111	+	0.630596i	$0.217190\pi$
$648$	2.81644	0.110640
$649$	19.8492	0.779151
$650$	3.97589	0.155947
$651$	−38.8181	−1.52140
$652$	0.362403	0.0141928
$653$	−9.79998	−0.383503	−0.191751	−	0.981444i	$-0.561417\pi$
$653$	−9.79998	−0.383503	−0.191751	+	0.981444i	$0.561417\pi$
$654$	−10.6092	−0.414853
$655$	−6.97007	−0.272343
$656$	−7.31125	−0.285456
$657$	5.96747	0.232813
$658$	−19.6046	−0.764266
$659$	2.40593	0.0937218	0.0468609	−	0.998901i	$-0.485078\pi$
$659$	2.40593	0.0937218	0.0468609	+	0.998901i	$0.485078\pi$
$660$	0.0547536	0.00213128
$661$	18.3264	0.712813	0.356407	−	0.934331i	$-0.384002\pi$
$661$	18.3264	0.712813	0.356407	+	0.934331i	$0.384002\pi$
$662$	5.30511	0.206189
$663$	−5.93708	−0.230577
$664$	−5.49919	−0.213410
$665$	24.4303	0.947368
$666$	2.43513	0.0943593
$667$	−0.0310903	−0.00120382
$668$	0.307695	0.0119051
$669$	3.78003	0.146144
$670$	−1.42013	−0.0548645
$671$	−23.4650	−0.905857
$672$	0.347537	0.0134065
$673$	−18.7300	−0.721988	−0.360994	−	0.932568i	$-0.617563\pi$
$673$	−18.7300	−0.721988	−0.360994	+	0.932568i	$0.617563\pi$
$674$	48.3227	1.86132
$675$	1.00000	0.0384900
$676$	−0.0865959	−0.00333061
$677$	38.8504	1.49314	0.746570	−	0.665307i	$-0.231699\pi$
$677$	38.8504	1.49314	0.746570	+	0.665307i	$0.231699\pi$
$678$	−13.9972	−0.537560
$679$	16.2270	0.622735
$680$	5.97266	0.229041
$681$	4.02424	0.154209
$682$	49.1291	1.88125
$683$	21.5365	0.824070	0.412035	−	0.911168i	$-0.364818\pi$
$683$	21.5365	0.824070	0.412035	+	0.911168i	$0.364818\pi$
$684$	0.111911	0.00427901
$685$	11.0644	0.422749
$686$	3.05778	0.116747
$687$	−15.3718	−0.586472
$688$	36.7505	1.40110
$689$	−31.6708	−1.20656
$690$	2.33375	0.0888442
$691$	−35.4334	−1.34795	−0.673974	−	0.738755i	$-0.735414\pi$
$691$	−35.4334	−1.34795	−0.673974	+	0.738755i	$0.735414\pi$
$692$	−0.364411	−0.0138528
$693$	11.9528	0.454051
$694$	41.4817	1.57462
$695$	−3.51297	−0.133254
$696$	0.0532845	0.00201975
$697$	3.84416	0.145608
$698$	−30.2650	−1.14555
$699$	−16.8263	−0.636429
$700$	0.0614380	0.00232214
$701$	48.8588	1.84537	0.922686	−	0.385551i	$-0.125989\pi$
$701$	48.8588	1.84537	0.922686	+	0.385551i	$0.125989\pi$
$702$	3.97589	0.150060
$703$	−11.4387	−0.431417
$704$	25.8877	0.975680
$705$	3.76947	0.141967
$706$	8.98348	0.338098
$707$	−57.1591	−2.14969
$708$	0.102026	0.00383437
$709$	−24.4737	−0.919128	−0.459564	−	0.888145i	$-0.651994\pi$
$709$	−24.4737	−0.919128	−0.459564	+	0.888145i	$0.651994\pi$
$710$	11.5223	0.432423
$711$	−6.08780	−0.228311
$712$	45.8040	1.71658
$713$	17.4185	0.652329
$714$	−11.0292	−0.412757
$715$	−9.13754	−0.341725
$716$	−0.271570	−0.0101490
$717$	18.1984	0.679630
$718$	20.9946	0.783511
$719$	−6.98045	−0.260327	−0.130163	−	0.991493i	$-0.541550\pi$
$719$	−6.98045	−0.260327	−0.130163	+	0.991493i	$0.541550\pi$
$720$	−4.03327	−0.150311
$721$	−7.24334	−0.269756
$722$	−36.2139	−1.34774
$723$	9.42628	0.350567
$724$	−0.0112514	−0.000418153 0
$725$	0.0189191	0.000702638 0
$726$	0.493677	0.0183221
$727$	−23.9628	−0.888731	−0.444366	−	0.895846i	$-0.646571\pi$
$727$	−23.9628	−0.888731	−0.444366	+	0.895846i	$0.646571\pi$
$728$	−28.8772	−1.07026
$729$	1.00000	0.0370370
$730$	−8.47460	−0.313659
$731$	−19.3229	−0.714684
$732$	−0.120611	−0.00445791
$733$	−23.1099	−0.853582	−0.426791	−	0.904350i	$-0.640356\pi$
$733$	−23.1099	−0.853582	−0.426791	+	0.904350i	$0.640356\pi$
$734$	−32.4238	−1.19678
$735$	6.41206	0.236513
$736$	−0.155947	−0.00574829
$737$	3.26380	0.120224
$738$	−2.57432	−0.0947622
$739$	33.9813	1.25002	0.625011	−	0.780616i	$-0.285095\pi$
$739$	33.9813	1.25002	0.625011	+	0.780616i	$0.285095\pi$
$740$	−0.0287662	−0.00105747
$741$	−18.6762	−0.686086
$742$	−58.8342	−2.15987
$743$	−48.0961	−1.76447	−0.882237	−	0.470805i	$-0.843964\pi$
$743$	−48.0961	−1.76447	−0.882237	+	0.470805i	$0.843964\pi$
$744$	−29.8529	−1.09446
$745$	−7.82118	−0.286546
$746$	−41.3238	−1.51297
$747$	−1.95253	−0.0714394
$748$	0.116113	0.00424550
$749$	51.8604	1.89494
$750$	−1.42013	−0.0518559
$751$	−54.3642	−1.98378	−0.991888	−	0.127113i	$-0.959429\pi$
$751$	−54.3642	−1.98378	−0.991888	+	0.127113i	$0.959429\pi$
$752$	−15.2033	−0.554408
$753$	5.65618	0.206123
$754$	0.0752204	0.00273936
$755$	−8.04607	−0.292826
$756$	0.0614380	0.00223448
$757$	−33.9263	−1.23307	−0.616537	−	0.787326i	$-0.711465\pi$
$757$	−33.9263	−1.23307	−0.616537	+	0.787326i	$0.711465\pi$
$758$	−23.7131	−0.861298
$759$	−5.36349	−0.194683
$760$	18.7881	0.681515
$761$	−35.4554	−1.28526	−0.642628	−	0.766178i	$-0.722156\pi$
$761$	−35.4554	−1.28526	−0.642628	+	0.766178i	$0.722156\pi$
$762$	−3.66657	−0.132826
$763$	27.3591	0.990467
$764$	0.179460	0.00649262
$765$	2.12064	0.0766719
$766$	−34.8641	−1.25969
$767$	−17.0266	−0.614793
$768$	0.402597	0.0145275
$769$	−31.2069	−1.12535	−0.562675	−	0.826678i	$-0.690228\pi$
$769$	−31.2069	−1.12535	−0.562675	+	0.826678i	$0.690228\pi$
$770$	−16.9746	−0.611723
$771$	−19.5519	−0.704143
$772$	−0.119086	−0.00428601
$773$	27.8700	1.00241	0.501207	−	0.865328i	$-0.332890\pi$
$773$	27.8700	1.00241	0.501207	+	0.865328i	$0.332890\pi$
$774$	12.9400	0.465119
$775$	−10.5995	−0.380746
$776$	12.4793	0.447982
$777$	−6.27973	−0.225284
$778$	49.8581	1.78750
$779$	12.0925	0.433259
$780$	−0.0469673	−0.00168170
$781$	−26.4808	−0.947559
$782$	4.94903	0.176977
$783$	0.0189191	0.000676114 0
$784$	−25.8616	−0.923628
$785$	−2.78927	−0.0995533
$786$	9.89842	0.353065
$787$	−30.5100	−1.08756	−0.543782	−	0.839227i	$-0.683008\pi$
$787$	−30.5100	−1.08756	−0.543782	+	0.839227i	$0.683008\pi$
$788$	−0.233614	−0.00832215
$789$	−2.84131	−0.101153
$790$	8.64549	0.307593
$791$	36.0961	1.28343
$792$	9.19229	0.326634
$793$	20.1282	0.714772
$794$	25.3160	0.898430
$795$	11.3124	0.401208
$796$	−0.401449	−0.0142290
$797$	5.47315	0.193869	0.0969345	−	0.995291i	$-0.469096\pi$
$797$	5.47315	0.193869	0.0969345	+	0.995291i	$0.469096\pi$
$798$	−34.6943	−1.22817
$799$	7.99370	0.282797
$800$	0.0948971	0.00335512
$801$	16.2631	0.574628
$802$	−5.64861	−0.199459
$803$	19.4766	0.687315
$804$	0.0167760	0.000591645 0
$805$	−6.01828	−0.212117
$806$	−42.1426	−1.48441
$807$	−18.4970	−0.651124
$808$	−43.9580	−1.54644
$809$	−2.36549	−0.0831661	−0.0415830	−	0.999135i	$-0.513240\pi$
$809$	−2.36549	−0.0831661	−0.0415830	+	0.999135i	$0.513240\pi$
$810$	−1.42013	−0.0498984
$811$	−21.2573	−0.746443	−0.373222	−	0.927742i	$-0.621747\pi$
$811$	−21.2573	−0.746443	−0.373222	+	0.927742i	$0.621747\pi$
$812$	0.00116235	4.07906e−5 0
$813$	5.41652	0.189966
$814$	7.94777	0.278569
$815$	21.6024	0.756700
$816$	−8.55311	−0.299419
$817$	−60.7837	−2.12655
$818$	−51.0129	−1.78362
$819$	−10.2531	−0.358271
$820$	0.0304105	0.00106198
$821$	−27.6538	−0.965124	−0.482562	−	0.875862i	$-0.660294\pi$
$821$	−27.6538	−0.965124	−0.482562	+	0.875862i	$0.660294\pi$
$822$	−15.7129	−0.548051
$823$	−1.58378	−0.0552070	−0.0276035	−	0.999619i	$-0.508788\pi$
$823$	−1.58378	−0.0552070	−0.0276035	+	0.999619i	$0.508788\pi$
$824$	−5.57047	−0.194056
$825$	3.26380	0.113631
$826$	−31.6299	−1.10054
$827$	13.1210	0.456261	0.228130	−	0.973631i	$-0.426739\pi$
$827$	13.1210	0.456261	0.228130	+	0.973631i	$0.426739\pi$
$828$	−0.0275686	−0.000958073 0
$829$	5.81240	0.201873	0.100937	−	0.994893i	$-0.467816\pi$
$829$	5.81240	0.201873	0.100937	+	0.994893i	$0.467816\pi$
$830$	2.77285	0.0962472
$831$	31.1357	1.08008
$832$	−22.2063	−0.769865
$833$	13.5977	0.471132
$834$	4.98888	0.172751
$835$	18.3413	0.634728
$836$	0.365253	0.0126326
$837$	−10.5995	−0.366373
$838$	19.7029	0.680626
$839$	15.3259	0.529108	0.264554	−	0.964371i	$-0.414775\pi$
$839$	15.3259	0.529108	0.264554	+	0.964371i	$0.414775\pi$
$840$	10.3145	0.355884
$841$	−28.9996	−0.999988
$842$	−57.5826	−1.98443
$843$	0.812247	0.0279753
$844$	−0.317047	−0.0109132
$845$	−5.16188	−0.177574
$846$	−5.35315	−0.184045
$847$	−1.27310	−0.0437441
$848$	−45.6258	−1.56680
$849$	−7.04330	−0.241725
$850$	−3.01159	−0.103297
$851$	2.81785	0.0965946
$852$	−0.136113	−0.00466314
$853$	5.98528	0.204932	0.102466	−	0.994737i	$-0.467327\pi$
$853$	5.98528	0.204932	0.102466	+	0.994737i	$0.467327\pi$
$854$	37.3916	1.27952
$855$	6.67086	0.228139
$856$	39.8831	1.36318
$857$	−31.0336	−1.06009	−0.530044	−	0.847970i	$-0.677825\pi$
$857$	−31.0336	−1.06009	−0.530044	+	0.847970i	$0.677825\pi$
$858$	12.9765	0.443011
$859$	26.3730	0.899834	0.449917	−	0.893070i	$-0.351454\pi$
$859$	26.3730	0.899834	0.449917	+	0.893070i	$0.351454\pi$
$860$	−0.152860	−0.00521250
$861$	6.63869	0.226246
$862$	13.9109	0.473807
$863$	−20.2885	−0.690630	−0.345315	−	0.938487i	$-0.612228\pi$
$863$	−20.2885	−0.690630	−0.345315	+	0.938487i	$0.612228\pi$
$864$	0.0948971	0.00322846
$865$	−21.7221	−0.738574
$866$	27.1771	0.923516
$867$	−12.5029	−0.424620
$868$	−0.651214	−0.0221036
$869$	−19.8694	−0.674022
$870$	−0.0268676	−0.000910898 0
$871$	−2.79966	−0.0948630
$872$	21.0405	0.712520
$873$	4.43089	0.149963
$874$	15.5681	0.526598
$875$	3.66225	0.123807
$876$	0.100110	0.00338242
$877$	−45.1636	−1.52507	−0.762533	−	0.646949i	$-0.776045\pi$
$877$	−45.1636	−1.52507	−0.762533	+	0.646949i	$0.776045\pi$
$878$	−11.4156	−0.385259
$879$	13.0361	0.439697
$880$	−13.1638	−0.443751
$881$	−12.0663	−0.406524	−0.203262	−	0.979124i	$-0.565154\pi$
$881$	−12.0663	−0.406524	−0.203262	+	0.979124i	$0.565154\pi$
$882$	−9.10598	−0.306614
$883$	−7.10948	−0.239253	−0.119627	−	0.992819i	$-0.538170\pi$
$883$	−7.10948	−0.239253	−0.119627	+	0.992819i	$0.538170\pi$
$884$	−0.0996007	−0.00334993
$885$	6.08164	0.204432
$886$	18.5667	0.623762
$887$	−14.8013	−0.496980	−0.248490	−	0.968634i	$-0.579934\pi$
$887$	−14.8013	−0.496980	−0.248490	+	0.968634i	$0.579934\pi$
$888$	−4.82941	−0.162064
$889$	9.45538	0.317123
$890$	−23.0957	−0.774171
$891$	3.26380	0.109341
$892$	0.0634139	0.00212325
$893$	25.1456	0.841466
$894$	11.1071	0.371477
$895$	−16.1880	−0.541104
$896$	−41.9473	−1.40136
$897$	4.60077	0.153615
$898$	35.7772	1.19390
$899$	−0.200534	−0.00668817
$900$	0.0167760	0.000559201 0
$901$	23.9894	0.799204
$902$	−8.40207	−0.279758
$903$	−33.3698	−1.11048
$904$	27.7596	0.923271
$905$	−0.670680	−0.0222942
$906$	11.4265	0.379619
$907$	37.2992	1.23850	0.619250	−	0.785194i	$-0.287437\pi$
$907$	37.2992	1.23850	0.619250	+	0.785194i	$0.287437\pi$
$908$	0.0675108	0.00224042
$909$	−15.6077	−0.517673
$910$	14.5607	0.482683
$911$	22.6810	0.751455	0.375728	−	0.926730i	$-0.377393\pi$
$911$	22.6810	0.751455	0.375728	+	0.926730i	$0.377393\pi$
$912$	−26.9054	−0.890926
$913$	−6.37267	−0.210905
$914$	−6.81962	−0.225573
$915$	−7.18949	−0.237677
$916$	−0.257878	−0.00852054
$917$	−25.5261	−0.842947
$918$	−3.01159	−0.0993973
$919$	−18.0709	−0.596103	−0.298052	−	0.954550i	$-0.596337\pi$
$919$	−18.0709	−0.596103	−0.298052	+	0.954550i	$0.596337\pi$
$920$	−4.62834	−0.152592
$921$	18.9833	0.625520
$922$	9.69064	0.319144
$923$	22.7151	0.747677
$924$	0.200521	0.00659666
$925$	−1.71472	−0.0563796
$926$	9.00376	0.295882
$927$	−1.97784	−0.0649608
$928$	0.00179537	5.89359e−5 0
$929$	7.79262	0.255667	0.127834	−	0.991796i	$-0.459198\pi$
$929$	7.79262	0.255667	0.127834	+	0.991796i	$0.459198\pi$
$930$	15.0527	0.493599
$931$	42.7740	1.40186
$932$	−0.282279	−0.00924635
$933$	−1.11836	−0.0366136
$934$	18.6828	0.611321
$935$	6.92134	0.226352
$936$	−7.88509	−0.257732
$937$	−10.5694	−0.345289	−0.172644	−	0.984984i	$-0.555231\pi$
$937$	−10.5694	−0.345289	−0.172644	+	0.984984i	$0.555231\pi$
$938$	−5.20088	−0.169815
$939$	−26.5721	−0.867148
$940$	0.0632368	0.00206256
$941$	−28.2843	−0.922040	−0.461020	−	0.887390i	$-0.652516\pi$
$941$	−28.2843	−0.922040	−0.461020	+	0.887390i	$0.652516\pi$
$942$	3.96113	0.129061
$943$	−2.97892	−0.0970070
$944$	−24.5289	−0.798348
$945$	3.66225	0.119133
$946$	42.2335	1.37313
$947$	36.7152	1.19308	0.596541	−	0.802582i	$-0.296541\pi$
$947$	36.7152	1.19308	0.596541	+	0.802582i	$0.296541\pi$
$948$	−0.102129	−0.00331700
$949$	−16.7069	−0.542329
$950$	−9.47350	−0.307361
$951$	−10.2185	−0.331359
$952$	21.8734	0.708919
$953$	1.66770	0.0540220	0.0270110	−	0.999635i	$-0.491401\pi$
$953$	1.66770	0.0540220	0.0270110	+	0.999635i	$0.491401\pi$
$954$	−16.0651	−0.520125
$955$	10.6974	0.346159
$956$	0.305296	0.00987398
$957$	0.0617481	0.00199603
$958$	49.7033	1.60584
$959$	40.5206	1.30848
$960$	7.93177	0.255997
$961$	81.3500	2.62419
$962$	−6.81754	−0.219806
$963$	14.1608	0.456326
$964$	0.158136	0.00509320
$965$	−7.09859	−0.228512
$966$	8.54676	0.274987
$967$	−4.98539	−0.160319	−0.0801597	−	0.996782i	$-0.525543\pi$
$967$	−4.98539	−0.160319	−0.0801597	+	0.996782i	$0.525543\pi$
$968$	−0.979071	−0.0314685
$969$	14.1465	0.454451
$970$	−6.29244	−0.202038
$971$	−40.0306	−1.28464	−0.642321	−	0.766436i	$-0.722028\pi$
$971$	−40.0306	−1.28464	−0.642321	+	0.766436i	$0.722028\pi$
$972$	0.0167760	0.000538092 0
$973$	−12.8654	−0.412445
$974$	50.4399	1.61620
$975$	−2.79966	−0.0896610
$976$	28.9971	0.928176
$977$	58.9565	1.88619	0.943094	−	0.332527i	$-0.107901\pi$
$977$	58.9565	1.88619	0.943094	+	0.332527i	$0.107901\pi$
$978$	−30.6783	−0.980983
$979$	53.0794	1.69643
$980$	0.107569	0.00343617
$981$	7.47058	0.238517
$982$	−35.9272	−1.14648
$983$	−23.1568	−0.738587	−0.369293	−	0.929313i	$-0.620400\pi$
$983$	−23.1568	−0.738587	−0.369293	+	0.929313i	$0.620400\pi$
$984$	5.10546	0.162756
$985$	−13.9254	−0.443702
$986$	−0.0569766	−0.00181450
$987$	13.8047	0.439410
$988$	−0.313312	−0.00996778
$989$	14.9737	0.476137
$990$	−4.63502	−0.147311
$991$	−23.9504	−0.760810	−0.380405	−	0.924820i	$-0.624215\pi$
$991$	−23.9504	−0.760810	−0.380405	+	0.924820i	$0.624215\pi$
$992$	−1.00586	−0.0319362
$993$	−3.73565	−0.118547
$994$	42.1974	1.33842
$995$	−23.9299	−0.758629
$996$	−0.0327557	−0.00103791
$997$	−46.4764	−1.47192	−0.735961	−	0.677024i	$-0.763269\pi$
$997$	−46.4764	−1.47192	−0.735961	+	0.677024i	$0.763269\pi$
$998$	8.59773	0.272156
$999$	−1.71472	−0.0542513

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1005.2.a.i.1.2	✓	7
3.2	odd	2		3015.2.a.l.1.6		7
5.4	even	2		5025.2.a.bb.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1005.2.a.i.1.2	✓	7	1.1	even	1	trivial
3015.2.a.l.1.6		7	3.2	odd	2
5025.2.a.bb.1.6		7	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1005 = 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1005.a (trivial)

\(f(q)\)	\(=\)	\(q-1.42013 q^{2} +1.00000 q^{3} +0.0167760 q^{4} +1.00000 q^{5} -1.42013 q^{6} +3.66225 q^{7} +2.81644 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.42013 q^{2} +1.00000 q^{3} +0.0167760 q^{4} +1.00000 q^{5} -1.42013 q^{6} +3.66225 q^{7} +2.81644 q^{8} +1.00000 q^{9} -1.42013 q^{10} +3.26380 q^{11} +0.0167760 q^{12} -2.79966 q^{13} -5.20088 q^{14} +1.00000 q^{15} -4.03327 q^{16} +2.12064 q^{17} -1.42013 q^{18} +6.67086 q^{19} +0.0167760 q^{20} +3.66225 q^{21} -4.63502 q^{22} -1.64333 q^{23} +2.81644 q^{24} +1.00000 q^{25} +3.97589 q^{26} +1.00000 q^{27} +0.0614380 q^{28} +0.0189191 q^{29} -1.42013 q^{30} -10.5995 q^{31} +0.0948971 q^{32} +3.26380 q^{33} -3.01159 q^{34} +3.66225 q^{35} +0.0167760 q^{36} -1.71472 q^{37} -9.47350 q^{38} -2.79966 q^{39} +2.81644 q^{40} +1.81274 q^{41} -5.20088 q^{42} -9.11183 q^{43} +0.0547536 q^{44} +1.00000 q^{45} +2.33375 q^{46} +3.76947 q^{47} -4.03327 q^{48} +6.41206 q^{49} -1.42013 q^{50} +2.12064 q^{51} -0.0469673 q^{52} +11.3124 q^{53} -1.42013 q^{54} +3.26380 q^{55} +10.3145 q^{56} +6.67086 q^{57} -0.0268676 q^{58} +6.08164 q^{59} +0.0167760 q^{60} -7.18949 q^{61} +15.0527 q^{62} +3.66225 q^{63} +7.93177 q^{64} -2.79966 q^{65} -4.63502 q^{66} +1.00000 q^{67} +0.0355759 q^{68} -1.64333 q^{69} -5.20088 q^{70} -8.11351 q^{71} +2.81644 q^{72} +5.96747 q^{73} +2.43513 q^{74} +1.00000 q^{75} +0.111911 q^{76} +11.9528 q^{77} +3.97589 q^{78} -6.08780 q^{79} -4.03327 q^{80} +1.00000 q^{81} -2.57432 q^{82} -1.95253 q^{83} +0.0614380 q^{84} +2.12064 q^{85} +12.9400 q^{86} +0.0189191 q^{87} +9.19229 q^{88} +16.2631 q^{89} -1.42013 q^{90} -10.2531 q^{91} -0.0275686 q^{92} -10.5995 q^{93} -5.35315 q^{94} +6.67086 q^{95} +0.0948971 q^{96} +4.43089 q^{97} -9.10598 q^{98} +3.26380 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 4 q^{2} + 7 q^{3} + 8 q^{4} + 7 q^{5} + 4 q^{6} + 3 q^{7} + 9 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q + 4 * q^2 + 7 * q^3 + 8 * q^4 + 7 * q^5 + 4 * q^6 + 3 * q^7 + 9 * q^8 + 7 * q^9	\( 7 q + 4 q^{2} + 7 q^{3} + 8 q^{4} + 7 q^{5} + 4 q^{6} + 3 q^{7} + 9 q^{8} + 7 q^{9} + 4 q^{10} + 5 q^{11} + 8 q^{12} - q^{13} - 4 q^{14} + 7 q^{15} + 6 q^{16} + 11 q^{17} + 4 q^{18} + 8 q^{19} + 8 q^{20} + 3 q^{21} - 3 q^{22} + 11 q^{23} + 9 q^{24} + 7 q^{25} - 5 q^{26} + 7 q^{27} - 17 q^{28} + 4 q^{30} - 3 q^{31} + 22 q^{32} + 5 q^{33} + 4 q^{34} + 3 q^{35} + 8 q^{36} - 5 q^{37} - q^{39} + 9 q^{40} + q^{41} - 4 q^{42} - 3 q^{43} - 9 q^{44} + 7 q^{45} - 12 q^{46} + 10 q^{47} + 6 q^{48} - 4 q^{49} + 4 q^{50} + 11 q^{51} - 6 q^{52} + 3 q^{53} + 4 q^{54} + 5 q^{55} - 12 q^{56} + 8 q^{57} - 24 q^{58} - 4 q^{59} + 8 q^{60} - 9 q^{61} + 20 q^{62} + 3 q^{63} - 3 q^{64} - q^{65} - 3 q^{66} + 7 q^{67} - 3 q^{68} + 11 q^{69} - 4 q^{70} + 6 q^{71} + 9 q^{72} - 9 q^{73} + 2 q^{74} + 7 q^{75} + 2 q^{76} + 17 q^{77} - 5 q^{78} - 11 q^{79} + 6 q^{80} + 7 q^{81} - 16 q^{82} + 30 q^{83} - 17 q^{84} + 11 q^{85} - 11 q^{86} - 25 q^{88} + 13 q^{89} + 4 q^{90} - 5 q^{91} + 10 q^{92} - 3 q^{93} - 25 q^{94} + 8 q^{95} + 22 q^{96} - 7 q^{97} - 10 q^{98} + 5 q^{99}+O(q^{100}) \) 7 * q + 4 * q^2 + 7 * q^3 + 8 * q^4 + 7 * q^5 + 4 * q^6 + 3 * q^7 + 9 * q^8 + 7 * q^9 + 4 * q^10 + 5 * q^11 + 8 * q^12 - q^13 - 4 * q^14 + 7 * q^15 + 6 * q^16 + 11 * q^17 + 4 * q^18 + 8 * q^19 + 8 * q^20 + 3 * q^21 - 3 * q^22 + 11 * q^23 + 9 * q^24 + 7 * q^25 - 5 * q^26 + 7 * q^27 - 17 * q^28 + 4 * q^30 - 3 * q^31 + 22 * q^32 + 5 * q^33 + 4 * q^34 + 3 * q^35 + 8 * q^36 - 5 * q^37 - q^39 + 9 * q^40 + q^41 - 4 * q^42 - 3 * q^43 - 9 * q^44 + 7 * q^45 - 12 * q^46 + 10 * q^47 + 6 * q^48 - 4 * q^49 + 4 * q^50 + 11 * q^51 - 6 * q^52 + 3 * q^53 + 4 * q^54 + 5 * q^55 - 12 * q^56 + 8 * q^57 - 24 * q^58 - 4 * q^59 + 8 * q^60 - 9 * q^61 + 20 * q^62 + 3 * q^63 - 3 * q^64 - q^65 - 3 * q^66 + 7 * q^67 - 3 * q^68 + 11 * q^69 - 4 * q^70 + 6 * q^71 + 9 * q^72 - 9 * q^73 + 2 * q^74 + 7 * q^75 + 2 * q^76 + 17 * q^77 - 5 * q^78 - 11 * q^79 + 6 * q^80 + 7 * q^81 - 16 * q^82 + 30 * q^83 - 17 * q^84 + 11 * q^85 - 11 * q^86 - 25 * q^88 + 13 * q^89 + 4 * q^90 - 5 * q^91 + 10 * q^92 - 3 * q^93 - 25 * q^94 + 8 * q^95 + 22 * q^96 - 7 * q^97 - 10 * q^98 + 5 * q^99

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