LMFDB - Embedded newform 4006.2.a.g.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4006,2,Mod(1,4006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4006, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4006 = 2 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4006.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:	$31.9880710497$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	4006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.535052 q^{3} +1.00000 q^{4} +2.84024 q^{5} +0.535052 q^{6} +2.46812 q^{7} -1.00000 q^{8} -2.71372 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.535052 q^{3} +1.00000 q^{4} +2.84024 q^{5} +0.535052 q^{6} +2.46812 q^{7} -1.00000 q^{8} -2.71372 q^{9} -2.84024 q^{10} +3.17739 q^{11} -0.535052 q^{12} -7.14791 q^{13} -2.46812 q^{14} -1.51968 q^{15} +1.00000 q^{16} +0.244682 q^{17} +2.71372 q^{18} -7.69456 q^{19} +2.84024 q^{20} -1.32057 q^{21} -3.17739 q^{22} +4.96361 q^{23} +0.535052 q^{24} +3.06699 q^{25} +7.14791 q^{26} +3.05714 q^{27} +2.46812 q^{28} +3.48771 q^{29} +1.51968 q^{30} -4.76087 q^{31} -1.00000 q^{32} -1.70007 q^{33} -0.244682 q^{34} +7.01006 q^{35} -2.71372 q^{36} -3.01634 q^{37} +7.69456 q^{38} +3.82450 q^{39} -2.84024 q^{40} +10.4380 q^{41} +1.32057 q^{42} -8.01689 q^{43} +3.17739 q^{44} -7.70763 q^{45} -4.96361 q^{46} -11.6638 q^{47} -0.535052 q^{48} -0.908392 q^{49} -3.06699 q^{50} -0.130918 q^{51} -7.14791 q^{52} -2.04870 q^{53} -3.05714 q^{54} +9.02456 q^{55} -2.46812 q^{56} +4.11699 q^{57} -3.48771 q^{58} -10.3363 q^{59} -1.51968 q^{60} -14.4000 q^{61} +4.76087 q^{62} -6.69778 q^{63} +1.00000 q^{64} -20.3018 q^{65} +1.70007 q^{66} -13.7795 q^{67} +0.244682 q^{68} -2.65579 q^{69} -7.01006 q^{70} -4.34345 q^{71} +2.71372 q^{72} +8.56207 q^{73} +3.01634 q^{74} -1.64100 q^{75} -7.69456 q^{76} +7.84217 q^{77} -3.82450 q^{78} -1.56339 q^{79} +2.84024 q^{80} +6.50543 q^{81} -10.4380 q^{82} +10.0964 q^{83} -1.32057 q^{84} +0.694957 q^{85} +8.01689 q^{86} -1.86611 q^{87} -3.17739 q^{88} +8.19194 q^{89} +7.70763 q^{90} -17.6419 q^{91} +4.96361 q^{92} +2.54731 q^{93} +11.6638 q^{94} -21.8544 q^{95} +0.535052 q^{96} +3.65276 q^{97} +0.908392 q^{98} -8.62255 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) $ 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9} + 23 q^{10} - 28 q^{11} - q^{12} - 12 q^{13} - 12 q^{14} - 14 q^{15} + 40 q^{16} - 10 q^{17} - 29 q^{18} + 3 q^{19} - 23 q^{20} - 40 q^{21} + 28 q^{22} - 10 q^{23} + q^{24} + 43 q^{25} + 12 q^{26} - 7 q^{27} + 12 q^{28} - 37 q^{29} + 14 q^{30} - 16 q^{31} - 40 q^{32} - 11 q^{33} + 10 q^{34} - 24 q^{35} + 29 q^{36} - 17 q^{37} - 3 q^{38} - 10 q^{39} + 23 q^{40} - 58 q^{41} + 40 q^{42} + 37 q^{43} - 28 q^{44} - 66 q^{45} + 10 q^{46} - 34 q^{47} - q^{48} + 28 q^{49} - 43 q^{50} - 7 q^{51} - 12 q^{52} - 43 q^{53} + 7 q^{54} + 28 q^{55} - 12 q^{56} - 25 q^{57} + 37 q^{58} - 92 q^{59} - 14 q^{60} - 37 q^{61} + 16 q^{62} + 14 q^{63} + 40 q^{64} - 54 q^{65} + 11 q^{66} - 10 q^{67} - 10 q^{68} - 49 q^{69} + 24 q^{70} - 87 q^{71} - 29 q^{72} + 12 q^{73} + 17 q^{74} - 31 q^{75} + 3 q^{76} - 53 q^{77} + 10 q^{78} + 14 q^{79} - 23 q^{80} - 4 q^{81} + 58 q^{82} - 42 q^{83} - 40 q^{84} - 24 q^{85} - 37 q^{86} + 24 q^{87} + 28 q^{88} - 118 q^{89} + 66 q^{90} - 35 q^{91} - 10 q^{92} - 22 q^{93} + 34 q^{94} - 18 q^{95} + q^{96} + 2 q^{97} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9 + 23 * q^10 - 28 * q^11 - q^12 - 12 * q^13 - 12 * q^14 - 14 * q^15 + 40 * q^16 - 10 * q^17 - 29 * q^18 + 3 * q^19 - 23 * q^20 - 40 * q^21 + 28 * q^22 - 10 * q^23 + q^24 + 43 * q^25 + 12 * q^26 - 7 * q^27 + 12 * q^28 - 37 * q^29 + 14 * q^30 - 16 * q^31 - 40 * q^32 - 11 * q^33 + 10 * q^34 - 24 * q^35 + 29 * q^36 - 17 * q^37 - 3 * q^38 - 10 * q^39 + 23 * q^40 - 58 * q^41 + 40 * q^42 + 37 * q^43 - 28 * q^44 - 66 * q^45 + 10 * q^46 - 34 * q^47 - q^48 + 28 * q^49 - 43 * q^50 - 7 * q^51 - 12 * q^52 - 43 * q^53 + 7 * q^54 + 28 * q^55 - 12 * q^56 - 25 * q^57 + 37 * q^58 - 92 * q^59 - 14 * q^60 - 37 * q^61 + 16 * q^62 + 14 * q^63 + 40 * q^64 - 54 * q^65 + 11 * q^66 - 10 * q^67 - 10 * q^68 - 49 * q^69 + 24 * q^70 - 87 * q^71 - 29 * q^72 + 12 * q^73 + 17 * q^74 - 31 * q^75 + 3 * q^76 - 53 * q^77 + 10 * q^78 + 14 * q^79 - 23 * q^80 - 4 * q^81 + 58 * q^82 - 42 * q^83 - 40 * q^84 - 24 * q^85 - 37 * q^86 + 24 * q^87 + 28 * q^88 - 118 * q^89 + 66 * q^90 - 35 * q^91 - 10 * q^92 - 22 * q^93 + 34 * q^94 - 18 * q^95 + q^96 + 2 * q^97 - 28 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.535052	−0.308912	−0.154456	−	0.988000i	$-0.549363\pi$
$3$	−0.535052	−0.308912	−0.154456	+	0.988000i	$0.549363\pi$
$4$	1.00000	0.500000
$5$	2.84024	1.27020	0.635098	−	0.772432i	$-0.280960\pi$
$5$	2.84024	1.27020	0.635098	+	0.772432i	$0.280960\pi$
$6$	0.535052	0.218434
$7$	2.46812	0.932861	0.466431	−	0.884558i	$-0.345540\pi$
$7$	2.46812	0.932861	0.466431	+	0.884558i	$0.345540\pi$
$8$	−1.00000	−0.353553
$9$	−2.71372	−0.904573
$10$	−2.84024	−0.898164
$11$	3.17739	0.958019	0.479010	−	0.877810i	$-0.340996\pi$
$11$	3.17739	0.958019	0.479010	+	0.877810i	$0.340996\pi$
$12$	−0.535052	−0.154456
$13$	−7.14791	−1.98247	−0.991237	−	0.132092i	$-0.957830\pi$
$13$	−7.14791	−1.98247	−0.991237	+	0.132092i	$0.957830\pi$
$14$	−2.46812	−0.659632
$15$	−1.51968	−0.392379
$16$	1.00000	0.250000
$17$	0.244682	0.0593442	0.0296721	−	0.999560i	$-0.490554\pi$
$17$	0.244682	0.0593442	0.0296721	+	0.999560i	$0.490554\pi$
$18$	2.71372	0.639630
$19$	−7.69456	−1.76525	−0.882626	−	0.470076i	$-0.844227\pi$
$19$	−7.69456	−1.76525	−0.882626	+	0.470076i	$0.844227\pi$
$20$	2.84024	0.635098
$21$	−1.32057	−0.288172
$22$	−3.17739	−0.677422
$23$	4.96361	1.03498	0.517492	−	0.855688i	$-0.326866\pi$
$23$	4.96361	1.03498	0.517492	+	0.855688i	$0.326866\pi$
$24$	0.535052	0.109217
$25$	3.06699	0.613398
$26$	7.14791	1.40182
$27$	3.05714	0.588346
$28$	2.46812	0.466431
$29$	3.48771	0.647652	0.323826	−	0.946117i	$-0.395031\pi$
$29$	3.48771	0.647652	0.323826	+	0.946117i	$0.395031\pi$
$30$	1.51968	0.277454
$31$	−4.76087	−0.855078	−0.427539	−	0.903997i	$-0.640619\pi$
$31$	−4.76087	−0.855078	−0.427539	+	0.903997i	$0.640619\pi$
$32$	−1.00000	−0.176777
$33$	−1.70007	−0.295944
$34$	−0.244682	−0.0419627
$35$	7.01006	1.18492
$36$	−2.71372	−0.452287
$37$	−3.01634	−0.495883	−0.247941	−	0.968775i	$-0.579754\pi$
$37$	−3.01634	−0.495883	−0.247941	+	0.968775i	$0.579754\pi$
$38$	7.69456	1.24822
$39$	3.82450	0.612411
$40$	−2.84024	−0.449082
$41$	10.4380	1.63013	0.815067	−	0.579366i	$-0.196700\pi$
$41$	10.4380	1.63013	0.815067	+	0.579366i	$0.196700\pi$
$42$	1.32057	0.203768
$43$	−8.01689	−1.22256	−0.611282	−	0.791413i	$-0.709346\pi$
$43$	−8.01689	−1.22256	−0.611282	+	0.791413i	$0.709346\pi$
$44$	3.17739	0.479010
$45$	−7.70763	−1.14899
$46$	−4.96361	−0.731844
$47$	−11.6638	−1.70133	−0.850667	−	0.525705i	$-0.823801\pi$
$47$	−11.6638	−1.70133	−0.850667	+	0.525705i	$0.823801\pi$
$48$	−0.535052	−0.0772280
$49$	−0.908392	−0.129770
$50$	−3.06699	−0.433738
$51$	−0.130918	−0.0183321
$52$	−7.14791	−0.991237
$53$	−2.04870	−0.281410	−0.140705	−	0.990052i	$-0.544937\pi$
$53$	−2.04870	−0.281410	−0.140705	+	0.990052i	$0.544937\pi$
$54$	−3.05714	−0.416023
$55$	9.02456	1.21687
$56$	−2.46812	−0.329816
$57$	4.11699	0.545308
$58$	−3.48771	−0.457959
$59$	−10.3363	−1.34567	−0.672835	−	0.739792i	$-0.734924\pi$
$59$	−10.3363	−1.34567	−0.672835	+	0.739792i	$0.734924\pi$
$60$	−1.51968	−0.196190
$61$	−14.4000	−1.84373	−0.921866	−	0.387508i	$-0.873336\pi$
$61$	−14.4000	−1.84373	−0.921866	+	0.387508i	$0.873336\pi$
$62$	4.76087	0.604631
$63$	−6.69778	−0.843841
$64$	1.00000	0.125000
$65$	−20.3018	−2.51813
$66$	1.70007	0.209264
$67$	−13.7795	−1.68343	−0.841716	−	0.539920i	$-0.818454\pi$
$67$	−13.7795	−1.68343	−0.841716	+	0.539920i	$0.818454\pi$
$68$	0.244682	0.0296721
$69$	−2.65579	−0.319719
$70$	−7.01006	−0.837862
$71$	−4.34345	−0.515473	−0.257737	−	0.966215i	$-0.582977\pi$
$71$	−4.34345	−0.515473	−0.257737	+	0.966215i	$0.582977\pi$
$72$	2.71372	0.319815
$73$	8.56207	1.00211	0.501057	−	0.865414i	$-0.332945\pi$
$73$	8.56207	1.00211	0.501057	+	0.865414i	$0.332945\pi$
$74$	3.01634	0.350642
$75$	−1.64100	−0.189486
$76$	−7.69456	−0.882626
$77$	7.84217	0.893699
$78$	−3.82450	−0.433040
$79$	−1.56339	−0.175895	−0.0879473	−	0.996125i	$-0.528031\pi$
$79$	−1.56339	−0.175895	−0.0879473	+	0.996125i	$0.528031\pi$
$80$	2.84024	0.317549
$81$	6.50543	0.722826
$82$	−10.4380	−1.15268
$83$	10.0964	1.10822	0.554111	−	0.832443i	$-0.313058\pi$
$83$	10.0964	1.10822	0.554111	+	0.832443i	$0.313058\pi$
$84$	−1.32057	−0.144086
$85$	0.694957	0.0753787
$86$	8.01689	0.864483
$87$	−1.86611	−0.200068
$88$	−3.17739	−0.338711
$89$	8.19194	0.868344	0.434172	−	0.900830i	$-0.357041\pi$
$89$	8.19194	0.868344	0.434172	+	0.900830i	$0.357041\pi$
$90$	7.70763	0.812455
$91$	−17.6419	−1.84937
$92$	4.96361	0.517492
$93$	2.54731	0.264144
$94$	11.6638	1.20302
$95$	−21.8544	−2.24222
$96$	0.535052	0.0546085
$97$	3.65276	0.370881	0.185441	−	0.982655i	$-0.440629\pi$
$97$	3.65276	0.370881	0.185441	+	0.982655i	$0.440629\pi$
$98$	0.908392	0.0917615
$99$	−8.62255	−0.866598
$100$	3.06699	0.306699
$101$	−5.33264	−0.530618	−0.265309	−	0.964163i	$-0.585474\pi$
$101$	−5.33264	−0.530618	−0.265309	+	0.964163i	$0.585474\pi$
$102$	0.130918	0.0129628
$103$	6.12186	0.603205	0.301602	−	0.953434i	$-0.402478\pi$
$103$	6.12186	0.603205	0.301602	+	0.953434i	$0.402478\pi$
$104$	7.14791	0.700911
$105$	−3.75074	−0.366035
$106$	2.04870	0.198987
$107$	8.44585	0.816492	0.408246	−	0.912872i	$-0.366141\pi$
$107$	8.44585	0.816492	0.408246	+	0.912872i	$0.366141\pi$
$108$	3.05714	0.294173
$109$	−5.78322	−0.553932	−0.276966	−	0.960880i	$-0.589329\pi$
$109$	−5.78322	−0.553932	−0.276966	+	0.960880i	$0.589329\pi$
$110$	−9.02456	−0.860458
$111$	1.61390	0.153184
$112$	2.46812	0.233215
$113$	−8.59201	−0.808268	−0.404134	−	0.914700i	$-0.632427\pi$
$113$	−8.59201	−0.808268	−0.404134	+	0.914700i	$0.632427\pi$
$114$	−4.11699	−0.385591
$115$	14.0979	1.31463
$116$	3.48771	0.323826
$117$	19.3974	1.79329
$118$	10.3363	0.951533
$119$	0.603905	0.0553599
$120$	1.51968	0.138727
$121$	−0.904194	−0.0821995
$122$	14.4000	1.30372
$123$	−5.58484	−0.503568
$124$	−4.76087	−0.427539
$125$	−5.49022	−0.491060
$126$	6.69778	0.596686
$127$	18.1164	1.60757	0.803786	−	0.594919i	$-0.202816\pi$
$127$	18.1164	1.60757	0.803786	+	0.594919i	$0.202816\pi$
$128$	−1.00000	−0.0883883
$129$	4.28945	0.377665
$130$	20.3018	1.78059
$131$	11.1235	0.971869	0.485934	−	0.873995i	$-0.338479\pi$
$131$	11.1235	0.971869	0.485934	+	0.873995i	$0.338479\pi$
$132$	−1.70007	−0.147972
$133$	−18.9911	−1.64674
$134$	13.7795	1.19037
$135$	8.68301	0.747315
$136$	−0.244682	−0.0209813
$137$	−0.247378	−0.0211349	−0.0105674	−	0.999944i	$-0.503364\pi$
$137$	−0.247378	−0.0211349	−0.0105674	+	0.999944i	$0.503364\pi$
$138$	2.65579	0.226076
$139$	−4.73479	−0.401600	−0.200800	−	0.979632i	$-0.564354\pi$
$139$	−4.73479	−0.401600	−0.200800	+	0.979632i	$0.564354\pi$
$140$	7.01006	0.592458
$141$	6.24071	0.525563
$142$	4.34345	0.364495
$143$	−22.7117	−1.89925
$144$	−2.71372	−0.226143
$145$	9.90596	0.822645
$146$	−8.56207	−0.708602
$147$	0.486037	0.0400876
$148$	−3.01634	−0.247941
$149$	−13.2074	−1.08199	−0.540995	−	0.841026i	$-0.681952\pi$
$149$	−13.2074	−1.08199	−0.540995	+	0.841026i	$0.681952\pi$
$150$	1.64100	0.133987
$151$	−18.5776	−1.51182	−0.755912	−	0.654674i	$-0.772806\pi$
$151$	−18.5776	−1.51182	−0.755912	+	0.654674i	$0.772806\pi$
$152$	7.69456	0.624111
$153$	−0.663999	−0.0536811
$154$	−7.84217	−0.631940
$155$	−13.5220	−1.08612
$156$	3.82450	0.306205
$157$	5.00903	0.399764	0.199882	−	0.979820i	$-0.435944\pi$
$157$	5.00903	0.399764	0.199882	+	0.979820i	$0.435944\pi$
$158$	1.56339	0.124376
$159$	1.09616	0.0869311
$160$	−2.84024	−0.224541
$161$	12.2508	0.965496
$162$	−6.50543	−0.511115
$163$	−11.0324	−0.864121	−0.432060	−	0.901845i	$-0.642213\pi$
$163$	−11.0324	−0.864121	−0.432060	+	0.901845i	$0.642213\pi$
$164$	10.4380	0.815067
$165$	−4.82861	−0.375907
$166$	−10.0964	−0.783631
$167$	4.23271	0.327537	0.163769	−	0.986499i	$-0.447635\pi$
$167$	4.23271	0.327537	0.163769	+	0.986499i	$0.447635\pi$
$168$	1.32057	0.101884
$169$	38.0927	2.93021
$170$	−0.694957	−0.0533008
$171$	20.8809	1.59680
$172$	−8.01689	−0.611282
$173$	−6.77456	−0.515060	−0.257530	−	0.966270i	$-0.582909\pi$
$173$	−6.77456	−0.515060	−0.257530	+	0.966270i	$0.582909\pi$
$174$	1.86611	0.141469
$175$	7.56969	0.572215
$176$	3.17739	0.239505
$177$	5.53045	0.415694
$178$	−8.19194	−0.614012
$179$	0.473280	0.0353746	0.0176873	−	0.999844i	$-0.494370\pi$
$179$	0.473280	0.0353746	0.0176873	+	0.999844i	$0.494370\pi$
$180$	−7.70763	−0.574493
$181$	−11.1549	−0.829139	−0.414569	−	0.910018i	$-0.636068\pi$
$181$	−11.1549	−0.829139	−0.414569	+	0.910018i	$0.636068\pi$
$182$	17.6419	1.30770
$183$	7.70475	0.569551
$184$	−4.96361	−0.365922
$185$	−8.56713	−0.629868
$186$	−2.54731	−0.186778
$187$	0.777451	0.0568528
$188$	−11.6638	−0.850667
$189$	7.54537	0.548845
$190$	21.8544	1.58549
$191$	14.5246	1.05096	0.525481	−	0.850805i	$-0.323885\pi$
$191$	14.5246	1.05096	0.525481	+	0.850805i	$0.323885\pi$
$192$	−0.535052	−0.0386140
$193$	−15.2728	−1.09936	−0.549680	−	0.835375i	$-0.685250\pi$
$193$	−15.2728	−1.09936	−0.549680	+	0.835375i	$0.685250\pi$
$194$	−3.65276	−0.262253
$195$	10.8625	0.777882
$196$	−0.908392	−0.0648852
$197$	−8.80473	−0.627311	−0.313656	−	0.949537i	$-0.601554\pi$
$197$	−8.80473	−0.627311	−0.313656	+	0.949537i	$0.601554\pi$
$198$	8.62255	0.612778
$199$	19.3037	1.36840	0.684202	−	0.729292i	$-0.260151\pi$
$199$	19.3037	1.36840	0.684202	+	0.729292i	$0.260151\pi$
$200$	−3.06699	−0.216869
$201$	7.37274	0.520033
$202$	5.33264	0.375203
$203$	8.60809	0.604169
$204$	−0.130918	−0.00916607
$205$	29.6463	2.07059
$206$	−6.12186	−0.426530
$207$	−13.4698	−0.936219
$208$	−7.14791	−0.495619
$209$	−24.4486	−1.69115
$210$	3.75074	0.258826
$211$	4.05547	0.279190	0.139595	−	0.990209i	$-0.455420\pi$
$211$	4.05547	0.279190	0.139595	+	0.990209i	$0.455420\pi$
$212$	−2.04870	−0.140705
$213$	2.32397	0.159236
$214$	−8.44585	−0.577347
$215$	−22.7699	−1.55290
$216$	−3.05714	−0.208012
$217$	−11.7504	−0.797669
$218$	5.78322	0.391689
$219$	−4.58115	−0.309565
$220$	9.02456	0.608436
$221$	−1.74897	−0.117648
$222$	−1.61390	−0.108318
$223$	10.0228	0.671178	0.335589	−	0.942008i	$-0.391065\pi$
$223$	10.0228	0.671178	0.335589	+	0.942008i	$0.391065\pi$
$224$	−2.46812	−0.164908
$225$	−8.32295	−0.554863
$226$	8.59201	0.571532
$227$	4.14121	0.274862	0.137431	−	0.990511i	$-0.456116\pi$
$227$	4.14121	0.274862	0.137431	+	0.990511i	$0.456116\pi$
$228$	4.11699	0.272654
$229$	6.73526	0.445079	0.222539	−	0.974924i	$-0.428565\pi$
$229$	6.73526	0.445079	0.222539	+	0.974924i	$0.428565\pi$
$230$	−14.0979	−0.929585
$231$	−4.19597	−0.276074
$232$	−3.48771	−0.228980
$233$	2.49761	0.163624	0.0818121	−	0.996648i	$-0.473929\pi$
$233$	2.49761	0.163624	0.0818121	+	0.996648i	$0.473929\pi$
$234$	−19.3974	−1.26805
$235$	−33.1279	−2.16103
$236$	−10.3363	−0.672835
$237$	0.836492	0.0543360
$238$	−0.603905	−0.0391453
$239$	−1.31372	−0.0849776	−0.0424888	−	0.999097i	$-0.513529\pi$
$239$	−1.31372	−0.0849776	−0.0424888	+	0.999097i	$0.513529\pi$
$240$	−1.51968	−0.0980948
$241$	−29.9918	−1.93194	−0.965970	−	0.258656i	$-0.916720\pi$
$241$	−29.9918	−1.93194	−0.965970	+	0.258656i	$0.916720\pi$
$242$	0.904194	0.0581238
$243$	−12.6521	−0.811636
$244$	−14.4000	−0.921866
$245$	−2.58006	−0.164834
$246$	5.58484	0.356077
$247$	55.0000	3.49957
$248$	4.76087	0.302316
$249$	−5.40208	−0.342343
$250$	5.49022	0.347232
$251$	−18.0047	−1.13645	−0.568224	−	0.822874i	$-0.692369\pi$
$251$	−18.0047	−1.13645	−0.568224	+	0.822874i	$0.692369\pi$
$252$	−6.69778	−0.421921
$253$	15.7713	0.991534
$254$	−18.1164	−1.13672
$255$	−0.371838	−0.0232854
$256$	1.00000	0.0625000
$257$	7.64688	0.476999	0.238500	−	0.971143i	$-0.423344\pi$
$257$	7.64688	0.476999	0.238500	+	0.971143i	$0.423344\pi$
$258$	−4.28945	−0.267049
$259$	−7.44467	−0.462590
$260$	−20.3018	−1.25907
$261$	−9.46468	−0.585849
$262$	−11.1235	−0.687215
$263$	−28.0698	−1.73086	−0.865428	−	0.501033i	$-0.832954\pi$
$263$	−28.0698	−1.73086	−0.865428	+	0.501033i	$0.832954\pi$
$264$	1.70007	0.104632
$265$	−5.81880	−0.357446
$266$	18.9911	1.16442
$267$	−4.38311	−0.268242
$268$	−13.7795	−0.841716
$269$	4.13235	0.251954	0.125977	−	0.992033i	$-0.459793\pi$
$269$	4.13235	0.251954	0.125977	+	0.992033i	$0.459793\pi$
$270$	−8.68301	−0.528431
$271$	10.4250	0.633272	0.316636	−	0.948547i	$-0.397447\pi$
$271$	10.4250	0.633272	0.316636	+	0.948547i	$0.397447\pi$
$272$	0.244682	0.0148360
$273$	9.43933	0.571294
$274$	0.247378	0.0149446
$275$	9.74502	0.587647
$276$	−2.65579	−0.159860
$277$	−7.58992	−0.456034	−0.228017	−	0.973657i	$-0.573224\pi$
$277$	−7.58992	−0.456034	−0.228017	+	0.973657i	$0.573224\pi$
$278$	4.73479	0.283974
$279$	12.9197	0.773480
$280$	−7.01006	−0.418931
$281$	23.5833	1.40686	0.703432	−	0.710762i	$-0.251650\pi$
$281$	23.5833	1.40686	0.703432	+	0.710762i	$0.251650\pi$
$282$	−6.24071	−0.371629
$283$	26.0471	1.54834	0.774170	−	0.632978i	$-0.218168\pi$
$283$	26.0471	1.54834	0.774170	+	0.632978i	$0.218168\pi$
$284$	−4.34345	−0.257737
$285$	11.6932	0.692648
$286$	22.7117	1.34297
$287$	25.7621	1.52069
$288$	2.71372	0.159907
$289$	−16.9401	−0.996478
$290$	−9.90596	−0.581698
$291$	−1.95441	−0.114570
$292$	8.56207	0.501057
$293$	−14.6448	−0.855561	−0.427780	−	0.903883i	$-0.640704\pi$
$293$	−14.6448	−0.855561	−0.427780	+	0.903883i	$0.640704\pi$
$294$	−0.486037	−0.0283462
$295$	−29.3576	−1.70927
$296$	3.01634	0.175321
$297$	9.71371	0.563647
$298$	13.2074	0.765083
$299$	−35.4794	−2.05183
$300$	−1.64100	−0.0947430
$301$	−19.7866	−1.14048
$302$	18.5776	1.06902
$303$	2.85324	0.163914
$304$	−7.69456	−0.441313
$305$	−40.8995	−2.34190
$306$	0.663999	0.0379583
$307$	−3.84873	−0.219659	−0.109829	−	0.993950i	$-0.535030\pi$
$307$	−3.84873	−0.219659	−0.109829	+	0.993950i	$0.535030\pi$
$308$	7.84217	0.446849
$309$	−3.27551	−0.186337
$310$	13.5220	0.768000
$311$	8.00308	0.453813	0.226906	−	0.973917i	$-0.427139\pi$
$311$	8.00308	0.453813	0.226906	+	0.973917i	$0.427139\pi$
$312$	−3.82450	−0.216520
$313$	31.6279	1.78772	0.893859	−	0.448349i	$-0.147988\pi$
$313$	31.6279	1.78772	0.893859	+	0.448349i	$0.147988\pi$
$314$	−5.00903	−0.282676
$315$	−19.0233	−1.07184
$316$	−1.56339	−0.0879473
$317$	−16.9172	−0.950166	−0.475083	−	0.879941i	$-0.657582\pi$
$317$	−16.9172	−0.950166	−0.475083	+	0.879941i	$0.657582\pi$
$318$	−1.09616	−0.0614696
$319$	11.0818	0.620463
$320$	2.84024	0.158774
$321$	−4.51897	−0.252224
$322$	−12.2508	−0.682709
$323$	−1.88272	−0.104757
$324$	6.50543	0.361413
$325$	−21.9226	−1.21605
$326$	11.0324	0.611026
$327$	3.09432	0.171116
$328$	−10.4380	−0.576340
$329$	−28.7875	−1.58711
$330$	4.82861	0.265806
$331$	25.2684	1.38887	0.694437	−	0.719553i	$-0.255653\pi$
$331$	25.2684	1.38887	0.694437	+	0.719553i	$0.255653\pi$
$332$	10.0964	0.554111
$333$	8.18549	0.448562
$334$	−4.23271	−0.231604
$335$	−39.1371	−2.13829
$336$	−1.32057	−0.0720430
$337$	12.5215	0.682092	0.341046	−	0.940047i	$-0.389219\pi$
$337$	12.5215	0.682092	0.341046	+	0.940047i	$0.389219\pi$
$338$	−38.0927	−2.07197
$339$	4.59717	0.249684
$340$	0.694957	0.0376894
$341$	−15.1271	−0.819181
$342$	−20.8809	−1.12911
$343$	−19.5188	−1.05392
$344$	8.01689	0.432242
$345$	−7.54308	−0.406106
$346$	6.77456	0.364203
$347$	31.1396	1.67166	0.835830	−	0.548988i	$-0.184987\pi$
$347$	31.1396	1.67166	0.835830	+	0.548988i	$0.184987\pi$
$348$	−1.86611	−0.100034
$349$	−8.89742	−0.476268	−0.238134	−	0.971232i	$-0.576536\pi$
$349$	−8.89742	−0.476268	−0.238134	+	0.971232i	$0.576536\pi$
$350$	−7.56969	−0.404617
$351$	−21.8521	−1.16638
$352$	−3.17739	−0.169355
$353$	−1.90600	−0.101446	−0.0507231	−	0.998713i	$-0.516153\pi$
$353$	−1.90600	−0.101446	−0.0507231	+	0.998713i	$0.516153\pi$
$354$	−5.53045	−0.293940
$355$	−12.3365	−0.654752
$356$	8.19194	0.434172
$357$	−0.323120	−0.0171013
$358$	−0.473280	−0.0250136
$359$	8.14581	0.429919	0.214960	−	0.976623i	$-0.431038\pi$
$359$	8.14581	0.429919	0.214960	+	0.976623i	$0.431038\pi$
$360$	7.70763	0.406228
$361$	40.2062	2.11612
$362$	11.1549	0.586290
$363$	0.483791	0.0253924
$364$	−17.6419	−0.924687
$365$	24.3184	1.27288
$366$	−7.70475	−0.402734
$367$	−0.469826	−0.0245247	−0.0122624	−	0.999925i	$-0.503903\pi$
$367$	−0.469826	−0.0245247	−0.0122624	+	0.999925i	$0.503903\pi$
$368$	4.96361	0.258746
$369$	−28.3257	−1.47458
$370$	8.56713	0.445384
$371$	−5.05643	−0.262517
$372$	2.54731	0.132072
$373$	−6.01461	−0.311425	−0.155712	−	0.987802i	$-0.549767\pi$
$373$	−6.01461	−0.311425	−0.155712	+	0.987802i	$0.549767\pi$
$374$	−0.777451	−0.0402010
$375$	2.93755	0.151695
$376$	11.6638	0.601512
$377$	−24.9299	−1.28395
$378$	−7.54537	−0.388092
$379$	−28.2641	−1.45183	−0.725914	−	0.687786i	$-0.758583\pi$
$379$	−28.2641	−1.45183	−0.725914	+	0.687786i	$0.758583\pi$
$380$	−21.8544	−1.12111
$381$	−9.69322	−0.496599
$382$	−14.5246	−0.743143
$383$	−20.2284	−1.03362	−0.516811	−	0.856100i	$-0.672881\pi$
$383$	−20.2284	−1.03362	−0.516811	+	0.856100i	$0.672881\pi$
$384$	0.535052	0.0273042
$385$	22.2737	1.13517
$386$	15.2728	0.777365
$387$	21.7556	1.10590
$388$	3.65276	0.185441
$389$	26.8697	1.36235	0.681174	−	0.732122i	$-0.261470\pi$
$389$	26.8697	1.36235	0.681174	+	0.732122i	$0.261470\pi$
$390$	−10.8625	−0.550045
$391$	1.21451	0.0614202
$392$	0.908392	0.0458807
$393$	−5.95167	−0.300222
$394$	8.80473	0.443576
$395$	−4.44040	−0.223421
$396$	−8.62255	−0.433299
$397$	−1.98115	−0.0994313	−0.0497156	−	0.998763i	$-0.515832\pi$
$397$	−1.98115	−0.0994313	−0.0497156	+	0.998763i	$0.515832\pi$
$398$	−19.3037	−0.967608
$399$	10.1612	0.508697
$400$	3.06699	0.153349
$401$	9.52766	0.475789	0.237894	−	0.971291i	$-0.423543\pi$
$401$	9.52766	0.475789	0.237894	+	0.971291i	$0.423543\pi$
$402$	−7.37274	−0.367719
$403$	34.0303	1.69517
$404$	−5.33264	−0.265309
$405$	18.4770	0.918131
$406$	−8.60809	−0.427212
$407$	−9.58408	−0.475065
$408$	0.130918	0.00648139
$409$	−31.4732	−1.55625	−0.778126	−	0.628108i	$-0.783830\pi$
$409$	−31.4732	−1.55625	−0.778126	+	0.628108i	$0.783830\pi$
$410$	−29.6463	−1.46413
$411$	0.132360	0.00652882
$412$	6.12186	0.301602
$413$	−25.5112	−1.25532
$414$	13.4698	0.662007
$415$	28.6762	1.40766
$416$	7.14791	0.350455
$417$	2.53336	0.124059
$418$	24.4486	1.19582
$419$	−22.7639	−1.11209	−0.556044	−	0.831153i	$-0.687681\pi$
$419$	−22.7639	−1.11209	−0.556044	+	0.831153i	$0.687681\pi$
$420$	−3.75074	−0.183018
$421$	−15.8516	−0.772558	−0.386279	−	0.922382i	$-0.626240\pi$
$421$	−15.8516	−0.772558	−0.386279	+	0.922382i	$0.626240\pi$
$422$	−4.05547	−0.197417
$423$	31.6522	1.53898
$424$	2.04870	0.0994936
$425$	0.750438	0.0364016
$426$	−2.32397	−0.112597
$427$	−35.5409	−1.71995
$428$	8.44585	0.408246
$429$	12.1519	0.586701
$430$	22.7699	1.09806
$431$	25.9137	1.24822	0.624109	−	0.781337i	$-0.285462\pi$
$431$	25.9137	1.24822	0.624109	+	0.781337i	$0.285462\pi$
$432$	3.05714	0.147086
$433$	−27.1746	−1.30593	−0.652964	−	0.757389i	$-0.726475\pi$
$433$	−27.1746	−1.30593	−0.652964	+	0.757389i	$0.726475\pi$
$434$	11.7504	0.564037
$435$	−5.30020	−0.254125
$436$	−5.78322	−0.276966
$437$	−38.1928	−1.82701
$438$	4.58115	0.218896
$439$	−20.2089	−0.964518	−0.482259	−	0.876029i	$-0.660184\pi$
$439$	−20.2089	−0.964518	−0.482259	+	0.876029i	$0.660184\pi$
$440$	−9.02456	−0.430229
$441$	2.46512	0.117387
$442$	1.74897	0.0831899
$443$	−10.5329	−0.500432	−0.250216	−	0.968190i	$-0.580502\pi$
$443$	−10.5329	−0.500432	−0.250216	+	0.968190i	$0.580502\pi$
$444$	1.61390	0.0765921
$445$	23.2671	1.10297
$446$	−10.0228	−0.474595
$447$	7.06663	0.334240
$448$	2.46812	0.116608
$449$	−26.5774	−1.25427	−0.627133	−	0.778912i	$-0.715772\pi$
$449$	−26.5774	−1.25427	−0.627133	+	0.778912i	$0.715772\pi$
$450$	8.32295	0.392348
$451$	33.1654	1.56170
$452$	−8.59201	−0.404134
$453$	9.93997	0.467021
$454$	−4.14121	−0.194357
$455$	−50.1073	−2.34907
$456$	−4.11699	−0.192795
$457$	5.28293	0.247125	0.123563	−	0.992337i	$-0.460568\pi$
$457$	5.28293	0.247125	0.123563	+	0.992337i	$0.460568\pi$
$458$	−6.73526	−0.314718
$459$	0.748027	0.0349149
$460$	14.0979	0.657316
$461$	−17.6090	−0.820132	−0.410066	−	0.912056i	$-0.634494\pi$
$461$	−17.6090	−0.820132	−0.410066	+	0.912056i	$0.634494\pi$
$462$	4.19597	0.195214
$463$	−6.25917	−0.290888	−0.145444	−	0.989366i	$-0.546461\pi$
$463$	−6.25917	−0.290888	−0.145444	+	0.989366i	$0.546461\pi$
$464$	3.48771	0.161913
$465$	7.23499	0.335515
$466$	−2.49761	−0.115700
$467$	33.3466	1.54310	0.771549	−	0.636170i	$-0.219482\pi$
$467$	33.3466	1.54310	0.771549	+	0.636170i	$0.219482\pi$
$468$	19.3974	0.896647
$469$	−34.0094	−1.57041
$470$	33.1279	1.52808
$471$	−2.68009	−0.123492
$472$	10.3363	0.475766
$473$	−25.4728	−1.17124
$474$	−0.836492	−0.0384213
$475$	−23.5991	−1.08280
$476$	0.603905	0.0276799
$477$	5.55959	0.254556
$478$	1.31372	0.0600882
$479$	−27.0053	−1.23391	−0.616953	−	0.787000i	$-0.711633\pi$
$479$	−27.0053	−1.23391	−0.616953	+	0.787000i	$0.711633\pi$
$480$	1.51968	0.0693635
$481$	21.5605	0.983075
$482$	29.9918	1.36609
$483$	−6.55480	−0.298254
$484$	−0.904194	−0.0410997
$485$	10.3747	0.471092
$486$	12.6521	0.573913
$487$	−8.12994	−0.368403	−0.184201	−	0.982889i	$-0.558970\pi$
$487$	−8.12994	−0.368403	−0.184201	+	0.982889i	$0.558970\pi$
$488$	14.4000	0.651858
$489$	5.90288	0.266937
$490$	2.58006	0.116555
$491$	33.7450	1.52289	0.761446	−	0.648228i	$-0.224490\pi$
$491$	33.7450	1.52289	0.761446	+	0.648228i	$0.224490\pi$
$492$	−5.58484	−0.251784
$493$	0.853382	0.0384344
$494$	−55.0000	−2.47457
$495$	−24.4901	−1.10075
$496$	−4.76087	−0.213769
$497$	−10.7202	−0.480865
$498$	5.40208	0.242073
$499$	−15.9315	−0.713192	−0.356596	−	0.934259i	$-0.616063\pi$
$499$	−15.9315	−0.713192	−0.356596	+	0.934259i	$0.616063\pi$
$500$	−5.49022	−0.245530
$501$	−2.26472	−0.101180
$502$	18.0047	0.803589
$503$	9.15376	0.408146	0.204073	−	0.978956i	$-0.434582\pi$
$503$	9.15376	0.408146	0.204073	+	0.978956i	$0.434582\pi$
$504$	6.69778	0.298343
$505$	−15.1460	−0.673988
$506$	−15.7713	−0.701121
$507$	−20.3816	−0.905177
$508$	18.1164	0.803786
$509$	−19.7803	−0.876746	−0.438373	−	0.898793i	$-0.644445\pi$
$509$	−19.7803	−0.876746	−0.438373	+	0.898793i	$0.644445\pi$
$510$	0.371838	0.0164653
$511$	21.1322	0.934833
$512$	−1.00000	−0.0441942
$513$	−23.5233	−1.03858
$514$	−7.64688	−0.337290
$515$	17.3876	0.766189
$516$	4.28945	0.188832
$517$	−37.0603	−1.62991
$518$	7.44467	0.327100
$519$	3.62474	0.159108
$520$	20.3018	0.890294
$521$	−14.5791	−0.638721	−0.319361	−	0.947633i	$-0.603468\pi$
$521$	−14.5791	−0.638721	−0.319361	+	0.947633i	$0.603468\pi$
$522$	9.46468	0.414258
$523$	−37.6334	−1.64560	−0.822798	−	0.568335i	$-0.807588\pi$
$523$	−37.6334	−1.64560	−0.822798	+	0.568335i	$0.807588\pi$
$524$	11.1235	0.485934
$525$	−4.05018	−0.176764
$526$	28.0698	1.22390
$527$	−1.16490	−0.0507439
$528$	−1.70007	−0.0739859
$529$	1.63741	0.0711917
$530$	5.81880	0.252753
$531$	28.0498	1.21726
$532$	−18.9911	−0.823368
$533$	−74.6096	−3.23170
$534$	4.38311	0.189676
$535$	23.9883	1.03710
$536$	13.7795	0.595183
$537$	−0.253229	−0.0109277
$538$	−4.13235	−0.178158
$539$	−2.88632	−0.124322
$540$	8.68301	0.373657
$541$	−20.4824	−0.880608	−0.440304	−	0.897849i	$-0.645129\pi$
$541$	−20.4824	−0.880608	−0.440304	+	0.897849i	$0.645129\pi$
$542$	−10.4250	−0.447791
$543$	5.96846	0.256131
$544$	−0.244682	−0.0104907
$545$	−16.4258	−0.703603
$546$	−9.43933	−0.403966
$547$	14.6175	0.625000	0.312500	−	0.949918i	$-0.398834\pi$
$547$	14.6175	0.625000	0.312500	+	0.949918i	$0.398834\pi$
$548$	−0.247378	−0.0105674
$549$	39.0776	1.66779
$550$	−9.74502	−0.415529
$551$	−26.8364	−1.14327
$552$	2.65579	0.113038
$553$	−3.85862	−0.164085
$554$	7.58992	0.322465
$555$	4.58386	0.194574
$556$	−4.73479	−0.200800
$557$	7.55027	0.319915	0.159958	−	0.987124i	$-0.448864\pi$
$557$	7.55027	0.319915	0.159958	+	0.987124i	$0.448864\pi$
$558$	−12.9197	−0.546933
$559$	57.3040	2.42370
$560$	7.01006	0.296229
$561$	−0.415976	−0.0175625
$562$	−23.5833	−0.994803
$563$	−38.3467	−1.61612	−0.808061	−	0.589099i	$-0.799483\pi$
$563$	−38.3467	−1.61612	−0.808061	+	0.589099i	$0.799483\pi$
$564$	6.24071	0.262781
$565$	−24.4034	−1.02666
$566$	−26.0471	−1.09484
$567$	16.0562	0.674296
$568$	4.34345	0.182247
$569$	24.4808	1.02629	0.513144	−	0.858302i	$-0.328480\pi$
$569$	24.4808	1.02629	0.513144	+	0.858302i	$0.328480\pi$
$570$	−11.6932	−0.489776
$571$	31.4249	1.31509	0.657546	−	0.753414i	$-0.271594\pi$
$571$	31.4249	1.31509	0.657546	+	0.753414i	$0.271594\pi$
$572$	−22.7117	−0.949624
$573$	−7.77141	−0.324655
$574$	−25.7621	−1.07529
$575$	15.2233	0.634857
$576$	−2.71372	−0.113072
$577$	−31.2796	−1.30219	−0.651094	−	0.758997i	$-0.725690\pi$
$577$	−31.2796	−1.30219	−0.651094	+	0.758997i	$0.725690\pi$
$578$	16.9401	0.704617
$579$	8.17173	0.339606
$580$	9.90596	0.411323
$581$	24.9190	1.03382
$582$	1.95441	0.0810131
$583$	−6.50951	−0.269596
$584$	−8.56207	−0.354301
$585$	55.0935	2.27783
$586$	14.6448	0.604973
$587$	34.8648	1.43902	0.719511	−	0.694481i	$-0.244366\pi$
$587$	34.8648	1.43902	0.719511	+	0.694481i	$0.244366\pi$
$588$	0.486037	0.0200438
$589$	36.6328	1.50943
$590$	29.3576	1.20863
$591$	4.71099	0.193784
$592$	−3.01634	−0.123971
$593$	14.3276	0.588365	0.294183	−	0.955749i	$-0.404953\pi$
$593$	14.3276	0.588365	0.294183	+	0.955749i	$0.404953\pi$
$594$	−9.71371	−0.398558
$595$	1.71524	0.0703179
$596$	−13.2074	−0.540995
$597$	−10.3285	−0.422717
$598$	35.4794	1.45086
$599$	24.0966	0.984560	0.492280	−	0.870437i	$-0.336164\pi$
$599$	24.0966	0.984560	0.492280	+	0.870437i	$0.336164\pi$
$600$	1.64100	0.0669934
$601$	−3.60215	−0.146935	−0.0734674	−	0.997298i	$-0.523406\pi$
$601$	−3.60215	−0.146935	−0.0734674	+	0.997298i	$0.523406\pi$
$602$	19.7866	0.806443
$603$	37.3937	1.52279
$604$	−18.5776	−0.755912
$605$	−2.56813	−0.104409
$606$	−2.85324	−0.115905
$607$	26.6291	1.08084	0.540422	−	0.841394i	$-0.318265\pi$
$607$	26.6291	1.08084	0.540422	+	0.841394i	$0.318265\pi$
$608$	7.69456	0.312055
$609$	−4.60577	−0.186635
$610$	40.8995	1.65597
$611$	83.3715	3.37285
$612$	−0.663999	−0.0268406
$613$	−6.97460	−0.281701	−0.140851	−	0.990031i	$-0.544984\pi$
$613$	−6.97460	−0.281701	−0.140851	+	0.990031i	$0.544984\pi$
$614$	3.84873	0.155322
$615$	−15.8623	−0.639631
$616$	−7.84217	−0.315970
$617$	20.3877	0.820778	0.410389	−	0.911911i	$-0.365393\pi$
$617$	20.3877	0.820778	0.410389	+	0.911911i	$0.365393\pi$
$618$	3.27551	0.131760
$619$	10.6780	0.429186	0.214593	−	0.976704i	$-0.431157\pi$
$619$	10.6780	0.429186	0.214593	+	0.976704i	$0.431157\pi$
$620$	−13.5220	−0.543058
$621$	15.1744	0.608929
$622$	−8.00308	−0.320894
$623$	20.2187	0.810044
$624$	3.82450	0.153103
$625$	−30.9285	−1.23714
$626$	−31.6279	−1.26411
$627$	13.0813	0.522415
$628$	5.00903	0.199882
$629$	−0.738044	−0.0294277
$630$	19.0233	0.757908
$631$	−17.2178	−0.685431	−0.342716	−	0.939439i	$-0.611347\pi$
$631$	−17.2178	−0.685431	−0.342716	+	0.939439i	$0.611347\pi$
$632$	1.56339	0.0621881
$633$	−2.16989	−0.0862453
$634$	16.9172	0.671869
$635$	51.4551	2.04193
$636$	1.09616	0.0434655
$637$	6.49311	0.257266
$638$	−11.0818	−0.438734
$639$	11.7869	0.466283
$640$	−2.84024	−0.112271
$641$	−24.7289	−0.976732	−0.488366	−	0.872639i	$-0.662407\pi$
$641$	−24.7289	−0.976732	−0.488366	+	0.872639i	$0.662407\pi$
$642$	4.51897	0.178349
$643$	−44.9752	−1.77365	−0.886824	−	0.462107i	$-0.847093\pi$
$643$	−44.9752	−1.77365	−0.886824	+	0.462107i	$0.847093\pi$
$644$	12.2508	0.482748
$645$	12.1831	0.479709
$646$	1.88272	0.0740747
$647$	31.7453	1.24804	0.624018	−	0.781410i	$-0.285499\pi$
$647$	31.7453	1.24804	0.624018	+	0.781410i	$0.285499\pi$
$648$	−6.50543	−0.255558
$649$	−32.8424	−1.28918
$650$	21.9226	0.859874
$651$	6.28707	0.246410
$652$	−11.0324	−0.432060
$653$	10.0872	0.394741	0.197371	−	0.980329i	$-0.436760\pi$
$653$	10.0872	0.394741	0.197371	+	0.980329i	$0.436760\pi$
$654$	−3.09432	−0.120998
$655$	31.5936	1.23446
$656$	10.4380	0.407534
$657$	−23.2350	−0.906486
$658$	28.7875	1.12225
$659$	27.6259	1.07615	0.538077	−	0.842896i	$-0.319151\pi$
$659$	27.6259	1.07615	0.538077	+	0.842896i	$0.319151\pi$
$660$	−4.82861	−0.187953
$661$	−26.9595	−1.04860	−0.524301	−	0.851533i	$-0.675674\pi$
$661$	−26.9595	−1.04860	−0.524301	+	0.851533i	$0.675674\pi$
$662$	−25.2684	−0.982083
$663$	0.935788	0.0363430
$664$	−10.0964	−0.391815
$665$	−53.9393	−2.09168
$666$	−8.18549	−0.317181
$667$	17.3116	0.670310
$668$	4.23271	0.163769
$669$	−5.36273	−0.207335
$670$	39.1371	1.51200
$671$	−45.7544	−1.76633
$672$	1.32057	0.0509421
$673$	14.3848	0.554494	0.277247	−	0.960799i	$-0.410578\pi$
$673$	14.3848	0.554494	0.277247	+	0.960799i	$0.410578\pi$
$674$	−12.5215	−0.482312
$675$	9.37620	0.360890
$676$	38.0927	1.46510
$677$	45.3629	1.74344	0.871719	−	0.490006i	$-0.163006\pi$
$677$	45.3629	1.74344	0.871719	+	0.490006i	$0.163006\pi$
$678$	−4.59717	−0.176553
$679$	9.01544	0.345981
$680$	−0.694957	−0.0266504
$681$	−2.21576	−0.0849081
$682$	15.1271	0.579248
$683$	−16.8562	−0.644983	−0.322492	−	0.946572i	$-0.604520\pi$
$683$	−16.8562	−0.644983	−0.322492	+	0.946572i	$0.604520\pi$
$684$	20.8809	0.798400
$685$	−0.702613	−0.0268455
$686$	19.5188	0.745233
$687$	−3.60371	−0.137490
$688$	−8.01689	−0.305641
$689$	14.6439	0.557889
$690$	7.54308	0.287160
$691$	−7.84206	−0.298326	−0.149163	−	0.988813i	$-0.547658\pi$
$691$	−7.84206	−0.298326	−0.149163	+	0.988813i	$0.547658\pi$
$692$	−6.77456	−0.257530
$693$	−21.2815	−0.808416
$694$	−31.1396	−1.18204
$695$	−13.4480	−0.510110
$696$	1.86611	0.0707346
$697$	2.55398	0.0967389
$698$	8.89742	0.336772
$699$	−1.33635	−0.0505455
$700$	7.56969	0.286107
$701$	32.4126	1.22421	0.612103	−	0.790778i	$-0.290324\pi$
$701$	32.4126	1.22421	0.612103	+	0.790778i	$0.290324\pi$
$702$	21.8521	0.824756
$703$	23.2094	0.875358
$704$	3.17739	0.119752
$705$	17.7251	0.667568
$706$	1.90600	0.0717334
$707$	−13.1616	−0.494992
$708$	5.53045	0.207847
$709$	10.5685	0.396909	0.198455	−	0.980110i	$-0.436408\pi$
$709$	10.5685	0.396909	0.198455	+	0.980110i	$0.436408\pi$
$710$	12.3365	0.462979
$711$	4.24259	0.159110
$712$	−8.19194	−0.307006
$713$	−23.6311	−0.884992
$714$	0.323120	0.0120925
$715$	−64.5068	−2.41242
$716$	0.473280	0.0176873
$717$	0.702909	0.0262506
$718$	−8.14581	−0.303999
$719$	20.5110	0.764932	0.382466	−	0.923969i	$-0.375075\pi$
$719$	20.5110	0.764932	0.382466	+	0.923969i	$0.375075\pi$
$720$	−7.70763	−0.287246
$721$	15.1095	0.562706
$722$	−40.2062	−1.49632
$723$	16.0471	0.596800
$724$	−11.1549	−0.414569
$725$	10.6968	0.397268
$726$	−0.483791	−0.0179552
$727$	43.7025	1.62083	0.810417	−	0.585853i	$-0.199240\pi$
$727$	43.7025	1.62083	0.810417	+	0.585853i	$0.199240\pi$
$728$	17.6419	0.653852
$729$	−12.7468	−0.472102
$730$	−24.3184	−0.900063
$731$	−1.96159	−0.0725520
$732$	7.70475	0.284776
$733$	−3.01984	−0.111540	−0.0557701	−	0.998444i	$-0.517761\pi$
$733$	−3.01984	−0.111540	−0.0557701	+	0.998444i	$0.517761\pi$
$734$	0.469826	0.0173416
$735$	1.38046	0.0509192
$736$	−4.96361	−0.182961
$737$	−43.7828	−1.61276
$738$	28.3257	1.04268
$739$	−5.34037	−0.196449	−0.0982244	−	0.995164i	$-0.531316\pi$
$739$	−5.34037	−0.196449	−0.0982244	+	0.995164i	$0.531316\pi$
$740$	−8.56713	−0.314934
$741$	−29.4279	−1.08106
$742$	5.05643	0.185627
$743$	5.18726	0.190302	0.0951511	−	0.995463i	$-0.469667\pi$
$743$	5.18726	0.190302	0.0951511	+	0.995463i	$0.469667\pi$
$744$	−2.54731	−0.0933890
$745$	−37.5122	−1.37434
$746$	6.01461	0.220210
$747$	−27.3987	−1.00247
$748$	0.777451	0.0284264
$749$	20.8454	0.761673
$750$	−2.93755	−0.107264
$751$	−47.2946	−1.72580	−0.862902	−	0.505371i	$-0.831356\pi$
$751$	−47.2946	−1.72580	−0.862902	+	0.505371i	$0.831356\pi$
$752$	−11.6638	−0.425333
$753$	9.63345	0.351062
$754$	24.9299	0.907893
$755$	−52.7649	−1.92031
$756$	7.54537	0.274422
$757$	−5.19299	−0.188742	−0.0943712	−	0.995537i	$-0.530084\pi$
$757$	−5.19299	−0.188742	−0.0943712	+	0.995537i	$0.530084\pi$
$758$	28.2641	1.02660
$759$	−8.43847	−0.306297
$760$	21.8544	0.792743
$761$	17.8016	0.645309	0.322654	−	0.946517i	$-0.395425\pi$
$761$	17.8016	0.645309	0.322654	+	0.946517i	$0.395425\pi$
$762$	9.69322	0.351148
$763$	−14.2737	−0.516742
$764$	14.5246	0.525481
$765$	−1.88592	−0.0681856
$766$	20.2284	0.730881
$767$	73.8829	2.66776
$768$	−0.535052	−0.0193070
$769$	−21.7271	−0.783500	−0.391750	−	0.920072i	$-0.628130\pi$
$769$	−21.7271	−0.783500	−0.391750	+	0.920072i	$0.628130\pi$
$770$	−22.2737	−0.802688
$771$	−4.09148	−0.147351
$772$	−15.2728	−0.549680
$773$	−34.9859	−1.25836	−0.629178	−	0.777261i	$-0.716608\pi$
$773$	−34.9859	−1.25836	−0.629178	+	0.777261i	$0.716608\pi$
$774$	−21.7556	−0.781989
$775$	−14.6015	−0.524503
$776$	−3.65276	−0.131126
$777$	3.98329	0.142900
$778$	−26.8697	−0.963325
$779$	−80.3154	−2.87760
$780$	10.8625	0.388941
$781$	−13.8008	−0.493833
$782$	−1.21451	−0.0434307
$783$	10.6624	0.381044
$784$	−0.908392	−0.0324426
$785$	14.2269	0.507778
$786$	5.95167	0.212289
$787$	26.4416	0.942543	0.471271	−	0.881988i	$-0.343795\pi$
$787$	26.4416	0.942543	0.471271	+	0.881988i	$0.343795\pi$
$788$	−8.80473	−0.313656
$789$	15.0188	0.534683
$790$	4.44040	0.157982
$791$	−21.2061	−0.754002
$792$	8.62255	0.306389
$793$	102.930	3.65515
$794$	1.98115	0.0703085
$795$	3.11336	0.110420
$796$	19.3037	0.684202
$797$	−20.1583	−0.714042	−0.357021	−	0.934096i	$-0.616208\pi$
$797$	−20.1583	−0.714042	−0.357021	+	0.934096i	$0.616208\pi$
$798$	−10.1612	−0.359703
$799$	−2.85391	−0.100964
$800$	−3.06699	−0.108434
$801$	−22.2306	−0.785480
$802$	−9.52766	−0.336433
$803$	27.2050	0.960044
$804$	7.37274	0.260016
$805$	34.7952	1.22637
$806$	−34.0303	−1.19867
$807$	−2.21102	−0.0778317
$808$	5.33264	0.187602
$809$	4.97927	0.175062	0.0875310	−	0.996162i	$-0.472102\pi$
$809$	4.97927	0.175062	0.0875310	+	0.996162i	$0.472102\pi$
$810$	−18.4770	−0.649216
$811$	−43.3426	−1.52197	−0.760983	−	0.648772i	$-0.775283\pi$
$811$	−43.3426	−1.52197	−0.760983	+	0.648772i	$0.775283\pi$
$812$	8.60809	0.302085
$813$	−5.57790	−0.195626
$814$	9.58408	0.335922
$815$	−31.3346	−1.09760
$816$	−0.130918	−0.00458303
$817$	61.6864	2.15813
$818$	31.4732	1.10044
$819$	47.8752	1.67289
$820$	29.6463	1.03530
$821$	18.5870	0.648691	0.324346	−	0.945939i	$-0.394856\pi$
$821$	18.5870	0.648691	0.324346	+	0.945939i	$0.394856\pi$
$822$	−0.132360	−0.00461658
$823$	−1.06540	−0.0371376	−0.0185688	−	0.999828i	$-0.505911\pi$
$823$	−1.06540	−0.0371376	−0.0185688	+	0.999828i	$0.505911\pi$
$824$	−6.12186	−0.213265
$825$	−5.21409	−0.181531
$826$	25.5112	0.887648
$827$	16.2334	0.564489	0.282245	−	0.959342i	$-0.408921\pi$
$827$	16.2334	0.564489	0.282245	+	0.959342i	$0.408921\pi$
$828$	−13.4698	−0.468109
$829$	12.7407	0.442504	0.221252	−	0.975217i	$-0.428986\pi$
$829$	12.7407	0.442504	0.221252	+	0.975217i	$0.428986\pi$
$830$	−28.6762	−0.995365
$831$	4.06100	0.140875
$832$	−7.14791	−0.247809
$833$	−0.222267	−0.00770111
$834$	−2.53336	−0.0877230
$835$	12.0219	0.416036
$836$	−24.4486	−0.845573
$837$	−14.5546	−0.503081
$838$	22.7639	0.786365
$839$	−28.9520	−0.999535	−0.499768	−	0.866160i	$-0.666581\pi$
$839$	−28.9520	−0.999535	−0.499768	+	0.866160i	$0.666581\pi$
$840$	3.75074	0.129413
$841$	−16.8359	−0.580547
$842$	15.8516	0.546281
$843$	−12.6183	−0.434598
$844$	4.05547	0.139595
$845$	108.193	3.72194
$846$	−31.6522	−1.08822
$847$	−2.23166	−0.0766807
$848$	−2.04870	−0.0703526
$849$	−13.9365	−0.478301
$850$	−0.750438	−0.0257398
$851$	−14.9719	−0.513231
$852$	2.32397	0.0796180
$853$	23.1007	0.790953	0.395476	−	0.918476i	$-0.370579\pi$
$853$	23.1007	0.790953	0.395476	+	0.918476i	$0.370579\pi$
$854$	35.5409	1.21619
$855$	59.3068	2.02825
$856$	−8.44585	−0.288673
$857$	−31.9681	−1.09201	−0.546005	−	0.837782i	$-0.683852\pi$
$857$	−31.9681	−1.09201	−0.546005	+	0.837782i	$0.683852\pi$
$858$	−12.1519	−0.414860
$859$	21.1719	0.722377	0.361188	−	0.932493i	$-0.382371\pi$
$859$	21.1719	0.722377	0.361188	+	0.932493i	$0.382371\pi$
$860$	−22.7699	−0.776448
$861$	−13.7841	−0.469759
$862$	−25.9137	−0.882624
$863$	18.7336	0.637700	0.318850	−	0.947805i	$-0.396703\pi$
$863$	18.7336	0.637700	0.318850	+	0.947805i	$0.396703\pi$
$864$	−3.05714	−0.104006
$865$	−19.2414	−0.654227
$866$	27.1746	0.923431
$867$	9.06384	0.307824
$868$	−11.7504	−0.398834
$869$	−4.96748	−0.168510
$870$	5.30020	0.179694
$871$	98.4946	3.33736
$872$	5.78322	0.195845
$873$	−9.91256	−0.335489
$874$	38.1928	1.29189
$875$	−13.5505	−0.458091
$876$	−4.58115	−0.154783
$877$	51.1590	1.72752	0.863758	−	0.503908i	$-0.168105\pi$
$877$	51.1590	1.72752	0.863758	+	0.503908i	$0.168105\pi$
$878$	20.2089	0.682017
$879$	7.83575	0.264293
$880$	9.02456	0.304218
$881$	−51.9475	−1.75016	−0.875078	−	0.483982i	$-0.839190\pi$
$881$	−51.9475	−1.75016	−0.875078	+	0.483982i	$0.839190\pi$
$882$	−2.46512	−0.0830050
$883$	31.3160	1.05387	0.526934	−	0.849906i	$-0.323341\pi$
$883$	31.3160	1.05387	0.526934	+	0.849906i	$0.323341\pi$
$884$	−1.74897	−0.0588242
$885$	15.7078	0.528013
$886$	10.5329	0.353859
$887$	26.1116	0.876742	0.438371	−	0.898794i	$-0.355556\pi$
$887$	26.1116	0.876742	0.438371	+	0.898794i	$0.355556\pi$
$888$	−1.61390	−0.0541588
$889$	44.7135	1.49964
$890$	−23.2671	−0.779915
$891$	20.6703	0.692481
$892$	10.0228	0.335589
$893$	89.7474	3.00328
$894$	−7.06663	−0.236343
$895$	1.34423	0.0449327
$896$	−2.46812	−0.0824540
$897$	18.9833	0.633835
$898$	26.5774	0.886900
$899$	−16.6046	−0.553793
$900$	−8.32295	−0.277432
$901$	−0.501280	−0.0167001
$902$	−33.1654	−1.10429
$903$	10.5869	0.352309
$904$	8.59201	0.285766
$905$	−31.6827	−1.05317
$906$	−9.93997	−0.330233
$907$	35.6314	1.18312	0.591561	−	0.806260i	$-0.298512\pi$
$907$	35.6314	1.18312	0.591561	+	0.806260i	$0.298512\pi$
$908$	4.14121	0.137431
$909$	14.4713	0.479983
$910$	50.1073	1.66104
$911$	30.3967	1.00709	0.503545	−	0.863969i	$-0.332029\pi$
$911$	30.3967	1.00709	0.503545	+	0.863969i	$0.332029\pi$
$912$	4.11699	0.136327
$913$	32.0801	1.06170
$914$	−5.28293	−0.174744
$915$	21.8834	0.723442
$916$	6.73526	0.222539
$917$	27.4542	0.906619
$918$	−0.748027	−0.0246886
$919$	−49.8472	−1.64431	−0.822153	−	0.569267i	$-0.807227\pi$
$919$	−49.8472	−1.64431	−0.822153	+	0.569267i	$0.807227\pi$
$920$	−14.0979	−0.464793
$921$	2.05927	0.0678552
$922$	17.6090	0.579921
$923$	31.0466	1.02191
$924$	−4.19597	−0.138037
$925$	−9.25107	−0.304173
$926$	6.25917	0.205689
$927$	−16.6130	−0.545643
$928$	−3.48771	−0.114490
$929$	−53.2949	−1.74855	−0.874274	−	0.485433i	$-0.838662\pi$
$929$	−53.2949	−1.74855	−0.874274	+	0.485433i	$0.838662\pi$
$930$	−7.23499	−0.237245
$931$	6.98968	0.229077
$932$	2.49761	0.0818121
$933$	−4.28206	−0.140188
$934$	−33.3466	−1.09113
$935$	2.20815	0.0722142
$936$	−19.3974	−0.634025
$937$	11.5583	0.377592	0.188796	−	0.982016i	$-0.439541\pi$
$937$	11.5583	0.377592	0.188796	+	0.982016i	$0.439541\pi$
$938$	34.0094	1.11045
$939$	−16.9226	−0.552248
$940$	−33.1279	−1.08051
$941$	−6.54093	−0.213228	−0.106614	−	0.994300i	$-0.534001\pi$
$941$	−6.54093	−0.213228	−0.106614	+	0.994300i	$0.534001\pi$
$942$	2.68009	0.0873220
$943$	51.8099	1.68716
$944$	−10.3363	−0.336418
$945$	21.4307	0.697141
$946$	25.4728	0.828192
$947$	−34.4635	−1.11991	−0.559956	−	0.828522i	$-0.689182\pi$
$947$	−34.4635	−1.11991	−0.559956	+	0.828522i	$0.689182\pi$
$948$	0.836492	0.0271680
$949$	−61.2009	−1.98667
$950$	23.5991	0.765657
$951$	9.05159	0.293518
$952$	−0.603905	−0.0195727
$953$	−45.1326	−1.46199	−0.730995	−	0.682383i	$-0.760944\pi$
$953$	−45.1326	−1.46199	−0.730995	+	0.682383i	$0.760944\pi$
$954$	−5.55959	−0.179998
$955$	41.2534	1.33493
$956$	−1.31372	−0.0424888
$957$	−5.92935	−0.191669
$958$	27.0053	0.872503
$959$	−0.610557	−0.0197159
$960$	−1.51968	−0.0490474
$961$	−8.33411	−0.268842
$962$	−21.5605	−0.695139
$963$	−22.9197	−0.738576
$964$	−29.9918	−0.965970
$965$	−43.3785	−1.39640
$966$	6.55480	0.210897
$967$	54.1158	1.74025	0.870123	−	0.492834i	$-0.164039\pi$
$967$	54.1158	1.74025	0.870123	+	0.492834i	$0.164039\pi$
$968$	0.904194	0.0290619
$969$	1.00735	0.0323608
$970$	−10.3747	−0.333112
$971$	22.6846	0.727983	0.363992	−	0.931402i	$-0.381414\pi$
$971$	22.6846	0.727983	0.363992	+	0.931402i	$0.381414\pi$
$972$	−12.6521	−0.405818
$973$	−11.6860	−0.374637
$974$	8.12994	0.260500
$975$	11.7297	0.375651
$976$	−14.4000	−0.460933
$977$	20.3349	0.650573	0.325286	−	0.945616i	$-0.394539\pi$
$977$	20.3349	0.650573	0.325286	+	0.945616i	$0.394539\pi$
$978$	−5.90288	−0.188753
$979$	26.0290	0.831890
$980$	−2.58006	−0.0824169
$981$	15.6941	0.501073
$982$	−33.7450	−1.07685
$983$	−9.24115	−0.294747	−0.147373	−	0.989081i	$-0.547082\pi$
$983$	−9.24115	−0.294747	−0.147373	+	0.989081i	$0.547082\pi$
$984$	5.58484	0.178038
$985$	−25.0076	−0.796808
$986$	−0.853382	−0.0271772
$987$	15.4028	0.490277
$988$	55.0000	1.74978
$989$	−39.7927	−1.26533
$990$	24.4901	0.778348
$991$	−20.1435	−0.639878	−0.319939	−	0.947438i	$-0.603662\pi$
$991$	−20.1435	−0.639878	−0.319939	+	0.947438i	$0.603662\pi$
$992$	4.76087	0.151158
$993$	−13.5199	−0.429040
$994$	10.7202	0.340023
$995$	54.8273	1.73814
$996$	−5.40208	−0.171172
$997$	−3.82037	−0.120992	−0.0604961	−	0.998168i	$-0.519268\pi$
$997$	−3.82037	−0.120992	−0.0604961	+	0.998168i	$0.519268\pi$
$998$	15.9315	0.504303
$999$	−9.22135	−0.291751

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.g.1.19	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.g.1.19	✓	40	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:	\( N \)	\(=\)	\( 4006 = 2 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.535052 q^{3} +1.00000 q^{4} +2.84024 q^{5} +0.535052 q^{6} +2.46812 q^{7} -1.00000 q^{8} -2.71372 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.535052 q^{3} +1.00000 q^{4} +2.84024 q^{5} +0.535052 q^{6} +2.46812 q^{7} -1.00000 q^{8} -2.71372 q^{9} -2.84024 q^{10} +3.17739 q^{11} -0.535052 q^{12} -7.14791 q^{13} -2.46812 q^{14} -1.51968 q^{15} +1.00000 q^{16} +0.244682 q^{17} +2.71372 q^{18} -7.69456 q^{19} +2.84024 q^{20} -1.32057 q^{21} -3.17739 q^{22} +4.96361 q^{23} +0.535052 q^{24} +3.06699 q^{25} +7.14791 q^{26} +3.05714 q^{27} +2.46812 q^{28} +3.48771 q^{29} +1.51968 q^{30} -4.76087 q^{31} -1.00000 q^{32} -1.70007 q^{33} -0.244682 q^{34} +7.01006 q^{35} -2.71372 q^{36} -3.01634 q^{37} +7.69456 q^{38} +3.82450 q^{39} -2.84024 q^{40} +10.4380 q^{41} +1.32057 q^{42} -8.01689 q^{43} +3.17739 q^{44} -7.70763 q^{45} -4.96361 q^{46} -11.6638 q^{47} -0.535052 q^{48} -0.908392 q^{49} -3.06699 q^{50} -0.130918 q^{51} -7.14791 q^{52} -2.04870 q^{53} -3.05714 q^{54} +9.02456 q^{55} -2.46812 q^{56} +4.11699 q^{57} -3.48771 q^{58} -10.3363 q^{59} -1.51968 q^{60} -14.4000 q^{61} +4.76087 q^{62} -6.69778 q^{63} +1.00000 q^{64} -20.3018 q^{65} +1.70007 q^{66} -13.7795 q^{67} +0.244682 q^{68} -2.65579 q^{69} -7.01006 q^{70} -4.34345 q^{71} +2.71372 q^{72} +8.56207 q^{73} +3.01634 q^{74} -1.64100 q^{75} -7.69456 q^{76} +7.84217 q^{77} -3.82450 q^{78} -1.56339 q^{79} +2.84024 q^{80} +6.50543 q^{81} -10.4380 q^{82} +10.0964 q^{83} -1.32057 q^{84} +0.694957 q^{85} +8.01689 q^{86} -1.86611 q^{87} -3.17739 q^{88} +8.19194 q^{89} +7.70763 q^{90} -17.6419 q^{91} +4.96361 q^{92} +2.54731 q^{93} +11.6638 q^{94} -21.8544 q^{95} +0.535052 q^{96} +3.65276 q^{97} +0.908392 q^{98} -8.62255 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9} + 23 q^{10} - 28 q^{11} - q^{12} - 12 q^{13} - 12 q^{14} - 14 q^{15} + 40 q^{16} - 10 q^{17} - 29 q^{18} + 3 q^{19} - 23 q^{20} - 40 q^{21} + 28 q^{22} - 10 q^{23} + q^{24} + 43 q^{25} + 12 q^{26} - 7 q^{27} + 12 q^{28} - 37 q^{29} + 14 q^{30} - 16 q^{31} - 40 q^{32} - 11 q^{33} + 10 q^{34} - 24 q^{35} + 29 q^{36} - 17 q^{37} - 3 q^{38} - 10 q^{39} + 23 q^{40} - 58 q^{41} + 40 q^{42} + 37 q^{43} - 28 q^{44} - 66 q^{45} + 10 q^{46} - 34 q^{47} - q^{48} + 28 q^{49} - 43 q^{50} - 7 q^{51} - 12 q^{52} - 43 q^{53} + 7 q^{54} + 28 q^{55} - 12 q^{56} - 25 q^{57} + 37 q^{58} - 92 q^{59} - 14 q^{60} - 37 q^{61} + 16 q^{62} + 14 q^{63} + 40 q^{64} - 54 q^{65} + 11 q^{66} - 10 q^{67} - 10 q^{68} - 49 q^{69} + 24 q^{70} - 87 q^{71} - 29 q^{72} + 12 q^{73} + 17 q^{74} - 31 q^{75} + 3 q^{76} - 53 q^{77} + 10 q^{78} + 14 q^{79} - 23 q^{80} - 4 q^{81} + 58 q^{82} - 42 q^{83} - 40 q^{84} - 24 q^{85} - 37 q^{86} + 24 q^{87} + 28 q^{88} - 118 q^{89} + 66 q^{90} - 35 q^{91} - 10 q^{92} - 22 q^{93} + 34 q^{94} - 18 q^{95} + q^{96} + 2 q^{97} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9 + 23 * q^10 - 28 * q^11 - q^12 - 12 * q^13 - 12 * q^14 - 14 * q^15 + 40 * q^16 - 10 * q^17 - 29 * q^18 + 3 * q^19 - 23 * q^20 - 40 * q^21 + 28 * q^22 - 10 * q^23 + q^24 + 43 * q^25 + 12 * q^26 - 7 * q^27 + 12 * q^28 - 37 * q^29 + 14 * q^30 - 16 * q^31 - 40 * q^32 - 11 * q^33 + 10 * q^34 - 24 * q^35 + 29 * q^36 - 17 * q^37 - 3 * q^38 - 10 * q^39 + 23 * q^40 - 58 * q^41 + 40 * q^42 + 37 * q^43 - 28 * q^44 - 66 * q^45 + 10 * q^46 - 34 * q^47 - q^48 + 28 * q^49 - 43 * q^50 - 7 * q^51 - 12 * q^52 - 43 * q^53 + 7 * q^54 + 28 * q^55 - 12 * q^56 - 25 * q^57 + 37 * q^58 - 92 * q^59 - 14 * q^60 - 37 * q^61 + 16 * q^62 + 14 * q^63 + 40 * q^64 - 54 * q^65 + 11 * q^66 - 10 * q^67 - 10 * q^68 - 49 * q^69 + 24 * q^70 - 87 * q^71 - 29 * q^72 + 12 * q^73 + 17 * q^74 - 31 * q^75 + 3 * q^76 - 53 * q^77 + 10 * q^78 + 14 * q^79 - 23 * q^80 - 4 * q^81 + 58 * q^82 - 42 * q^83 - 40 * q^84 - 24 * q^85 - 37 * q^86 + 24 * q^87 + 28 * q^88 - 118 * q^89 + 66 * q^90 - 35 * q^91 - 10 * q^92 - 22 * q^93 + 34 * q^94 - 18 * q^95 + q^96 + 2 * q^97 - 28 * q^98 - 48 * q^99

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