LMFDB - Embedded newform 6041.2.a.f.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$0$
Dimension:	$132$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.71866 q^{2} -0.898623 q^{3} +5.39111 q^{4} +3.58669 q^{5} +2.44305 q^{6} +1.00000 q^{7} -9.21926 q^{8} -2.19248 q^{9} +O(q^{10})$	\(q-2.71866 q^{2} -0.898623 q^{3} +5.39111 q^{4} +3.58669 q^{5} +2.44305 q^{6} +1.00000 q^{7} -9.21926 q^{8} -2.19248 q^{9} -9.75100 q^{10} -6.15231 q^{11} -4.84457 q^{12} +0.437075 q^{13} -2.71866 q^{14} -3.22309 q^{15} +14.2818 q^{16} -4.15017 q^{17} +5.96060 q^{18} -2.98619 q^{19} +19.3362 q^{20} -0.898623 q^{21} +16.7260 q^{22} +3.64443 q^{23} +8.28464 q^{24} +7.86437 q^{25} -1.18826 q^{26} +4.66608 q^{27} +5.39111 q^{28} -7.47833 q^{29} +8.76247 q^{30} -0.0845463 q^{31} -20.3889 q^{32} +5.52861 q^{33} +11.2829 q^{34} +3.58669 q^{35} -11.8199 q^{36} +4.52200 q^{37} +8.11843 q^{38} -0.392766 q^{39} -33.0667 q^{40} +5.05744 q^{41} +2.44305 q^{42} +11.2055 q^{43} -33.1678 q^{44} -7.86374 q^{45} -9.90795 q^{46} -6.30676 q^{47} -12.8340 q^{48} +1.00000 q^{49} -21.3805 q^{50} +3.72943 q^{51} +2.35632 q^{52} -10.0023 q^{53} -12.6855 q^{54} -22.0665 q^{55} -9.21926 q^{56} +2.68346 q^{57} +20.3310 q^{58} +1.07947 q^{59} -17.3760 q^{60} -5.39020 q^{61} +0.229853 q^{62} -2.19248 q^{63} +26.8667 q^{64} +1.56766 q^{65} -15.0304 q^{66} +0.429232 q^{67} -22.3740 q^{68} -3.27497 q^{69} -9.75100 q^{70} +13.6946 q^{71} +20.2130 q^{72} -13.2913 q^{73} -12.2938 q^{74} -7.06710 q^{75} -16.0989 q^{76} -6.15231 q^{77} +1.06780 q^{78} +4.10176 q^{79} +51.2245 q^{80} +2.38438 q^{81} -13.7494 q^{82} -1.17732 q^{83} -4.84457 q^{84} -14.8854 q^{85} -30.4639 q^{86} +6.72020 q^{87} +56.7198 q^{88} -14.0167 q^{89} +21.3788 q^{90} +0.437075 q^{91} +19.6475 q^{92} +0.0759753 q^{93} +17.1459 q^{94} -10.7105 q^{95} +18.3219 q^{96} +2.83308 q^{97} -2.71866 q^{98} +13.4888 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9}+O(q^{10}) $ 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9} + 22 q^{10} + 32 q^{11} + 30 q^{12} + 16 q^{13} + 8 q^{14} + 59 q^{15} + 254 q^{16} + 11 q^{17} + 33 q^{18} + 40 q^{19} + 4 q^{20} + 10 q^{21} + 66 q^{22} + 62 q^{23} + 36 q^{24} + 235 q^{25} + 25 q^{26} + 37 q^{27} + 174 q^{28} + 28 q^{29} + 45 q^{30} + 121 q^{31} + 53 q^{32} - 13 q^{33} + 44 q^{34} + 11 q^{35} + 274 q^{36} + 61 q^{37} - 28 q^{38} + 114 q^{39} + 32 q^{40} - q^{41} + 16 q^{42} + 105 q^{43} + 54 q^{44} + 29 q^{45} + 104 q^{46} + 33 q^{47} + 16 q^{48} + 132 q^{49} - 14 q^{50} + 53 q^{51} - 11 q^{52} + 48 q^{53} + 11 q^{54} + 118 q^{55} + 30 q^{56} + 93 q^{57} + 87 q^{58} + 12 q^{59} + 41 q^{60} + 54 q^{61} - 28 q^{62} + 178 q^{63} + 376 q^{64} + 22 q^{65} + 6 q^{66} + 123 q^{67} - 47 q^{68} + 58 q^{69} + 22 q^{70} + 108 q^{71} + 97 q^{72} + q^{73} - 10 q^{74} + 23 q^{75} + 71 q^{76} + 32 q^{77} + 5 q^{78} + 204 q^{79} - 10 q^{80} + 296 q^{81} + 80 q^{82} - 10 q^{83} + 30 q^{84} + 94 q^{85} + 48 q^{86} + 4 q^{87} + 155 q^{88} + q^{89} - 66 q^{90} + 16 q^{91} + 49 q^{92} + 90 q^{93} + 79 q^{94} + 100 q^{95} + q^{96} + 18 q^{97} + 8 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9 + 22 * q^10 + 32 * q^11 + 30 * q^12 + 16 * q^13 + 8 * q^14 + 59 * q^15 + 254 * q^16 + 11 * q^17 + 33 * q^18 + 40 * q^19 + 4 * q^20 + 10 * q^21 + 66 * q^22 + 62 * q^23 + 36 * q^24 + 235 * q^25 + 25 * q^26 + 37 * q^27 + 174 * q^28 + 28 * q^29 + 45 * q^30 + 121 * q^31 + 53 * q^32 - 13 * q^33 + 44 * q^34 + 11 * q^35 + 274 * q^36 + 61 * q^37 - 28 * q^38 + 114 * q^39 + 32 * q^40 - q^41 + 16 * q^42 + 105 * q^43 + 54 * q^44 + 29 * q^45 + 104 * q^46 + 33 * q^47 + 16 * q^48 + 132 * q^49 - 14 * q^50 + 53 * q^51 - 11 * q^52 + 48 * q^53 + 11 * q^54 + 118 * q^55 + 30 * q^56 + 93 * q^57 + 87 * q^58 + 12 * q^59 + 41 * q^60 + 54 * q^61 - 28 * q^62 + 178 * q^63 + 376 * q^64 + 22 * q^65 + 6 * q^66 + 123 * q^67 - 47 * q^68 + 58 * q^69 + 22 * q^70 + 108 * q^71 + 97 * q^72 + q^73 - 10 * q^74 + 23 * q^75 + 71 * q^76 + 32 * q^77 + 5 * q^78 + 204 * q^79 - 10 * q^80 + 296 * q^81 + 80 * q^82 - 10 * q^83 + 30 * q^84 + 94 * q^85 + 48 * q^86 + 4 * q^87 + 155 * q^88 + q^89 - 66 * q^90 + 16 * q^91 + 49 * q^92 + 90 * q^93 + 79 * q^94 + 100 * q^95 + q^96 + 18 * q^97 + 8 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.71866	−1.92238	−0.961191	−	0.275884i	$-0.911030\pi$
$2$	−2.71866	−1.92238	−0.961191	+	0.275884i	$0.911030\pi$
$3$	−0.898623	−0.518820	−0.259410	−	0.965767i	$-0.583528\pi$
$3$	−0.898623	−0.518820	−0.259410	+	0.965767i	$0.583528\pi$
$4$	5.39111	2.69555
$5$	3.58669	1.60402	0.802009	−	0.597312i	$-0.203765\pi$
$5$	3.58669	1.60402	0.802009	+	0.597312i	$0.203765\pi$
$6$	2.44305	0.997371
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−9.21926	−3.25950
$9$	−2.19248	−0.730826
$10$	−9.75100	−3.08354
$11$	−6.15231	−1.85499	−0.927496	−	0.373834i	$-0.878043\pi$
$11$	−6.15231	−1.85499	−0.927496	+	0.373834i	$0.878043\pi$
$12$	−4.84457	−1.39851
$13$	0.437075	0.121223	0.0606114	−	0.998161i	$-0.480695\pi$
$13$	0.437075	0.121223	0.0606114	+	0.998161i	$0.480695\pi$
$14$	−2.71866	−0.726592
$15$	−3.22309	−0.832197
$16$	14.2818	3.57045
$17$	−4.15017	−1.00656	−0.503281	−	0.864123i	$-0.667874\pi$
$17$	−4.15017	−1.00656	−0.503281	+	0.864123i	$0.667874\pi$
$18$	5.96060	1.40493
$19$	−2.98619	−0.685078	−0.342539	−	0.939504i	$-0.611287\pi$
$19$	−2.98619	−0.685078	−0.342539	+	0.939504i	$0.611287\pi$
$20$	19.3362	4.32372
$21$	−0.898623	−0.196096
$22$	16.7260	3.56600
$23$	3.64443	0.759916	0.379958	−	0.925004i	$-0.375939\pi$
$23$	3.64443	0.759916	0.379958	+	0.925004i	$0.375939\pi$
$24$	8.28464	1.69110
$25$	7.86437	1.57287
$26$	−1.18826	−0.233037
$27$	4.66608	0.897987
$28$	5.39111	1.01882
$29$	−7.47833	−1.38869	−0.694345	−	0.719642i	$-0.744306\pi$
$29$	−7.47833	−1.38869	−0.694345	+	0.719642i	$0.744306\pi$
$30$	8.76247	1.59980
$31$	−0.0845463	−0.0151850	−0.00759248	−	0.999971i	$-0.502417\pi$
$31$	−0.0845463	−0.0151850	−0.00759248	+	0.999971i	$0.502417\pi$
$32$	−20.3889	−3.60427
$33$	5.52861	0.962407
$34$	11.2829	1.93500
$35$	3.58669	0.606262
$36$	−11.8199	−1.96998
$37$	4.52200	0.743412	0.371706	−	0.928351i	$-0.378773\pi$
$37$	4.52200	0.743412	0.371706	+	0.928351i	$0.378773\pi$
$38$	8.11843	1.31698
$39$	−0.392766	−0.0628929
$40$	−33.0667	−5.22830
$41$	5.05744	0.789839	0.394920	−	0.918716i	$-0.370772\pi$
$41$	5.05744	0.789839	0.394920	+	0.918716i	$0.370772\pi$
$42$	2.44305	0.376971
$43$	11.2055	1.70882	0.854410	−	0.519600i	$-0.173919\pi$
$43$	11.2055	1.70882	0.854410	+	0.519600i	$0.173919\pi$
$44$	−33.1678	−5.00023
$45$	−7.86374	−1.17226
$46$	−9.90795	−1.46085
$47$	−6.30676	−0.919935	−0.459967	−	0.887936i	$-0.652139\pi$
$47$	−6.30676	−0.919935	−0.459967	+	0.887936i	$0.652139\pi$
$48$	−12.8340	−1.85242
$49$	1.00000	0.142857
$50$	−21.3805	−3.02366
$51$	3.72943	0.522225
$52$	2.35632	0.326763
$53$	−10.0023	−1.37393	−0.686964	−	0.726692i	$-0.741057\pi$
$53$	−10.0023	−1.37393	−0.686964	+	0.726692i	$0.741057\pi$
$54$	−12.6855	−1.72627
$55$	−22.0665	−2.97544
$56$	−9.21926	−1.23198
$57$	2.68346	0.355433
$58$	20.3310	2.66959
$59$	1.07947	0.140536	0.0702678	−	0.997528i	$-0.477615\pi$
$59$	1.07947	0.140536	0.0702678	+	0.997528i	$0.477615\pi$
$60$	−17.3760	−2.24323
$61$	−5.39020	−0.690145	−0.345072	−	0.938576i	$-0.612146\pi$
$61$	−5.39020	−0.690145	−0.345072	+	0.938576i	$0.612146\pi$
$62$	0.229853	0.0291913
$63$	−2.19248	−0.276226
$64$	26.8667	3.35834
$65$	1.56766	0.194444
$66$	−15.0304	−1.85011
$67$	0.429232	0.0524391	0.0262195	−	0.999656i	$-0.491653\pi$
$67$	0.429232	0.0524391	0.0262195	+	0.999656i	$0.491653\pi$
$68$	−22.3740	−2.71324
$69$	−3.27497	−0.394260
$70$	−9.75100	−1.16547
$71$	13.6946	1.62525	0.812627	−	0.582784i	$-0.198037\pi$
$71$	13.6946	1.62525	0.812627	+	0.582784i	$0.198037\pi$
$72$	20.2130	2.38213
$73$	−13.2913	−1.55563	−0.777816	−	0.628492i	$-0.783672\pi$
$73$	−13.2913	−1.55563	−0.777816	+	0.628492i	$0.783672\pi$
$74$	−12.2938	−1.42912
$75$	−7.06710	−0.816039
$76$	−16.0989	−1.84667
$77$	−6.15231	−0.701121
$78$	1.06780	0.120904
$79$	4.10176	0.461484	0.230742	−	0.973015i	$-0.425885\pi$
$79$	4.10176	0.461484	0.230742	+	0.973015i	$0.425885\pi$
$80$	51.2245	5.72707
$81$	2.38438	0.264932
$82$	−13.7494	−1.51837
$83$	−1.17732	−0.129227	−0.0646137	−	0.997910i	$-0.520582\pi$
$83$	−1.17732	−0.129227	−0.0646137	+	0.997910i	$0.520582\pi$
$84$	−4.84457	−0.528586
$85$	−14.8854	−1.61455
$86$	−30.4639	−3.28500
$87$	6.72020	0.720481
$88$	56.7198	6.04635
$89$	−14.0167	−1.48577	−0.742885	−	0.669419i	$-0.766543\pi$
$89$	−14.0167	−1.48577	−0.742885	+	0.669419i	$0.766543\pi$
$90$	21.3788	2.25353
$91$	0.437075	0.0458179
$92$	19.6475	2.04839
$93$	0.0759753	0.00787827
$94$	17.1459	1.76847
$95$	−10.7105	−1.09888
$96$	18.3219	1.86997
$97$	2.83308	0.287655	0.143828	−	0.989603i	$-0.454059\pi$
$97$	2.83308	0.287655	0.143828	+	0.989603i	$0.454059\pi$
$98$	−2.71866	−0.274626
$99$	13.4888	1.35568
$100$	42.3976	4.23976
$101$	10.2894	1.02384	0.511918	−	0.859034i	$-0.328935\pi$
$101$	10.2894	1.02384	0.511918	+	0.859034i	$0.328935\pi$
$102$	−10.1391	−1.00392
$103$	6.29641	0.620404	0.310202	−	0.950671i	$-0.399603\pi$
$103$	6.29641	0.620404	0.310202	+	0.950671i	$0.399603\pi$
$104$	−4.02951	−0.395126
$105$	−3.22309	−0.314541
$106$	27.1930	2.64121
$107$	−13.8880	−1.34261	−0.671303	−	0.741183i	$-0.734265\pi$
$107$	−13.8880	−1.34261	−0.671303	+	0.741183i	$0.734265\pi$
$108$	25.1553	2.42057
$109$	8.66578	0.830031	0.415015	−	0.909814i	$-0.363776\pi$
$109$	8.66578	0.830031	0.415015	+	0.909814i	$0.363776\pi$
$110$	59.9912	5.71993
$111$	−4.06357	−0.385697
$112$	14.2818	1.34950
$113$	12.1592	1.14384	0.571921	−	0.820308i	$-0.306198\pi$
$113$	12.1592	1.14384	0.571921	+	0.820308i	$0.306198\pi$
$114$	−7.29540	−0.683277
$115$	13.0714	1.21892
$116$	−40.3164	−3.74329
$117$	−0.958277	−0.0885928
$118$	−2.93472	−0.270163
$119$	−4.15017	−0.380445
$120$	29.7145	2.71255
$121$	26.8509	2.44099
$122$	14.6541	1.32672
$123$	−4.54473	−0.409784
$124$	−0.455798	−0.0409319
$125$	10.2736	0.918900
$126$	5.96060	0.531012
$127$	−11.9245	−1.05813	−0.529064	−	0.848582i	$-0.677457\pi$
$127$	−11.9245	−1.05813	−0.529064	+	0.848582i	$0.677457\pi$
$128$	−32.2637	−2.85174
$129$	−10.0695	−0.886570
$130$	−4.26192	−0.373795
$131$	10.5085	0.918135	0.459068	−	0.888401i	$-0.348184\pi$
$131$	10.5085	0.918135	0.459068	+	0.888401i	$0.348184\pi$
$132$	29.8053	2.59422
$133$	−2.98619	−0.258935
$134$	−1.16694	−0.100808
$135$	16.7358	1.44039
$136$	38.2615	3.28089
$137$	4.88617	0.417454	0.208727	−	0.977974i	$-0.433068\pi$
$137$	4.88617	0.417454	0.208727	+	0.977974i	$0.433068\pi$
$138$	8.90352	0.757918
$139$	−16.0765	−1.36359	−0.681795	−	0.731543i	$-0.738801\pi$
$139$	−16.0765	−1.36359	−0.681795	+	0.731543i	$0.738801\pi$
$140$	19.3362	1.63421
$141$	5.66740	0.477281
$142$	−37.2310	−3.12436
$143$	−2.68902	−0.224867
$144$	−31.3125	−2.60938
$145$	−26.8225	−2.22748
$146$	36.1346	2.99052
$147$	−0.898623	−0.0741172
$148$	24.3786	2.00391
$149$	16.2761	1.33339	0.666694	−	0.745332i	$-0.267709\pi$
$149$	16.2761	1.33339	0.666694	+	0.745332i	$0.267709\pi$
$150$	19.2130	1.56874
$151$	−12.4912	−1.01652	−0.508259	−	0.861204i	$-0.669711\pi$
$151$	−12.4912	−1.01652	−0.508259	+	0.861204i	$0.669711\pi$
$152$	27.5304	2.23301
$153$	9.09914	0.735622
$154$	16.7260	1.34782
$155$	−0.303242	−0.0243570
$156$	−2.11744	−0.169531
$157$	19.2088	1.53303	0.766516	−	0.642225i	$-0.221989\pi$
$157$	19.2088	1.53303	0.766516	+	0.642225i	$0.221989\pi$
$158$	−11.1513	−0.887148
$159$	8.98834	0.712822
$160$	−73.1286	−5.78132
$161$	3.64443	0.287221
$162$	−6.48233	−0.509300
$163$	−4.70230	−0.368313	−0.184156	−	0.982897i	$-0.558955\pi$
$163$	−4.70230	−0.368313	−0.184156	+	0.982897i	$0.558955\pi$
$164$	27.2652	2.12905
$165$	19.8294	1.54372
$166$	3.20073	0.248424
$167$	16.3733	1.26701	0.633503	−	0.773740i	$-0.281616\pi$
$167$	16.3733	1.26701	0.633503	+	0.773740i	$0.281616\pi$
$168$	8.28464	0.639174
$169$	−12.8090	−0.985305
$170$	40.4682	3.10377
$171$	6.54715	0.500673
$172$	60.4099	4.60621
$173$	−0.149213	−0.0113444	−0.00567222	−	0.999984i	$-0.501806\pi$
$173$	−0.149213	−0.0113444	−0.00567222	+	0.999984i	$0.501806\pi$
$174$	−18.2699	−1.38504
$175$	7.86437	0.594490
$176$	−87.8662	−6.62316
$177$	−0.970041	−0.0729127
$178$	38.1067	2.85622
$179$	−8.21822	−0.614258	−0.307129	−	0.951668i	$-0.599368\pi$
$179$	−8.21822	−0.614258	−0.307129	+	0.951668i	$0.599368\pi$
$180$	−42.3943	−3.15988
$181$	21.2890	1.58240	0.791198	−	0.611561i	$-0.209458\pi$
$181$	21.2890	1.58240	0.791198	+	0.611561i	$0.209458\pi$
$182$	−1.18826	−0.0880796
$183$	4.84376	0.358061
$184$	−33.5989	−2.47695
$185$	16.2190	1.19245
$186$	−0.206551	−0.0151450
$187$	25.5331	1.86717
$188$	−34.0004	−2.47973
$189$	4.66608	0.339407
$190$	29.1183	2.11246
$191$	19.2441	1.39245	0.696226	−	0.717823i	$-0.254861\pi$
$191$	19.2441	1.39245	0.696226	+	0.717823i	$0.254861\pi$
$192$	−24.1430	−1.74237
$193$	1.70644	0.122832	0.0614160	−	0.998112i	$-0.480438\pi$
$193$	1.70644	0.122832	0.0614160	+	0.998112i	$0.480438\pi$
$194$	−7.70217	−0.552984
$195$	−1.40873	−0.100881
$196$	5.39111	0.385079
$197$	−11.3972	−0.812016	−0.406008	−	0.913869i	$-0.633080\pi$
$197$	−11.3972	−0.812016	−0.406008	+	0.913869i	$0.633080\pi$
$198$	−36.6714	−2.60613
$199$	18.3993	1.30429	0.652144	−	0.758095i	$-0.273870\pi$
$199$	18.3993	1.30429	0.652144	+	0.758095i	$0.273870\pi$
$200$	−72.5037	−5.12678
$201$	−0.385718	−0.0272064
$202$	−27.9734	−1.96820
$203$	−7.47833	−0.524876
$204$	20.1058	1.40769
$205$	18.1395	1.26692
$206$	−17.1178	−1.19265
$207$	−7.99032	−0.555366
$208$	6.24223	0.432821
$209$	18.3720	1.27081
$210$	8.76247	0.604668
$211$	5.86906	0.404043	0.202021	−	0.979381i	$-0.435249\pi$
$211$	5.86906	0.404043	0.202021	+	0.979381i	$0.435249\pi$
$212$	−53.9237	−3.70350
$213$	−12.3063	−0.843214
$214$	37.7568	2.58100
$215$	40.1906	2.74098
$216$	−43.0178	−2.92699
$217$	−0.0845463	−0.00573938
$218$	−23.5593	−1.59564
$219$	11.9439	0.807093
$220$	−118.963	−8.02046
$221$	−1.81393	−0.122018
$222$	11.0475	0.741457
$223$	−0.238872	−0.0159960	−0.00799802	−	0.999968i	$-0.502546\pi$
$223$	−0.238872	−0.0159960	−0.00799802	+	0.999968i	$0.502546\pi$
$224$	−20.3889	−1.36229
$225$	−17.2424	−1.14950
$226$	−33.0568	−2.19890
$227$	−23.3285	−1.54837	−0.774183	−	0.632962i	$-0.781839\pi$
$227$	−23.3285	−1.54837	−0.774183	+	0.632962i	$0.781839\pi$
$228$	14.4668	0.958087
$229$	−22.6685	−1.49798	−0.748989	−	0.662582i	$-0.769461\pi$
$229$	−22.6685	−1.49798	−0.748989	+	0.662582i	$0.769461\pi$
$230$	−35.5368	−2.34323
$231$	5.52861	0.363756
$232$	68.9446	4.52644
$233$	−11.7360	−0.768849	−0.384424	−	0.923156i	$-0.625600\pi$
$233$	−11.7360	−0.768849	−0.384424	+	0.923156i	$0.625600\pi$
$234$	2.60523	0.170309
$235$	−22.6204	−1.47559
$236$	5.81956	0.378821
$237$	−3.68593	−0.239427
$238$	11.2829	0.731361
$239$	25.4338	1.64518	0.822588	−	0.568638i	$-0.192530\pi$
$239$	25.4338	1.64518	0.822588	+	0.568638i	$0.192530\pi$
$240$	−46.0315	−2.97132
$241$	−4.81627	−0.310244	−0.155122	−	0.987895i	$-0.549577\pi$
$241$	−4.81627	−0.310244	−0.155122	+	0.987895i	$0.549577\pi$
$242$	−72.9985	−4.69252
$243$	−16.1409	−1.03544
$244$	−29.0592	−1.86032
$245$	3.58669	0.229145
$246$	12.3556	0.787762
$247$	−1.30519	−0.0830472
$248$	0.779455	0.0494954
$249$	1.05796	0.0670458
$250$	−27.9305	−1.76648
$251$	18.2117	1.14951	0.574757	−	0.818324i	$-0.305097\pi$
$251$	18.2117	1.14951	0.574757	+	0.818324i	$0.305097\pi$
$252$	−11.8199	−0.744582
$253$	−22.4217	−1.40964
$254$	32.4186	2.03412
$255$	13.3763	0.837659
$256$	33.9806	2.12379
$257$	−1.85367	−0.115629	−0.0578144	−	0.998327i	$-0.518413\pi$
$257$	−1.85367	−0.115629	−0.0578144	+	0.998327i	$0.518413\pi$
$258$	27.3755	1.70433
$259$	4.52200	0.280983
$260$	8.45139	0.524133
$261$	16.3961	1.01489
$262$	−28.5691	−1.76501
$263$	−15.3998	−0.949591	−0.474795	−	0.880096i	$-0.657478\pi$
$263$	−15.3998	−0.949591	−0.474795	+	0.880096i	$0.657478\pi$
$264$	−50.9697	−3.13697
$265$	−35.8753	−2.20381
$266$	8.11843	0.497773
$267$	12.5958	0.770848
$268$	2.31404	0.141352
$269$	−18.4640	−1.12577	−0.562884	−	0.826536i	$-0.690308\pi$
$269$	−18.4640	−1.12577	−0.562884	+	0.826536i	$0.690308\pi$
$270$	−45.4989	−2.76898
$271$	1.99413	0.121135	0.0605673	−	0.998164i	$-0.480709\pi$
$271$	1.99413	0.121135	0.0605673	+	0.998164i	$0.480709\pi$
$272$	−59.2719	−3.59389
$273$	−0.392766	−0.0237713
$274$	−13.2838	−0.802506
$275$	−48.3840	−2.91767
$276$	−17.6557	−1.06275
$277$	27.2755	1.63882	0.819412	−	0.573205i	$-0.194300\pi$
$277$	27.2755	1.63882	0.819412	+	0.573205i	$0.194300\pi$
$278$	43.7065	2.62134
$279$	0.185366	0.0110976
$280$	−33.0667	−1.97611
$281$	21.7734	1.29889	0.649447	−	0.760407i	$-0.275000\pi$
$281$	21.7734	1.29889	0.649447	+	0.760407i	$0.275000\pi$
$282$	−15.4077	−0.917516
$283$	15.5606	0.924983	0.462491	−	0.886624i	$-0.346956\pi$
$283$	15.5606	0.924983	0.462491	+	0.886624i	$0.346956\pi$
$284$	73.8292	4.38096
$285$	9.62474	0.570120
$286$	7.31054	0.432281
$287$	5.05744	0.298531
$288$	44.7021	2.63410
$289$	0.223872	0.0131689
$290$	72.9211	4.28208
$291$	−2.54587	−0.149241
$292$	−71.6549	−4.19329
$293$	−20.3666	−1.18983	−0.594916	−	0.803788i	$-0.702815\pi$
$293$	−20.3666	−1.18983	−0.594916	+	0.803788i	$0.702815\pi$
$294$	2.44305	0.142482
$295$	3.87174	0.225422
$296$	−41.6895	−2.42315
$297$	−28.7072	−1.66576
$298$	−44.2491	−2.56328
$299$	1.59289	0.0921192
$300$	−38.0995	−2.19968
$301$	11.2055	0.645873
$302$	33.9593	1.95414
$303$	−9.24632	−0.531187
$304$	−42.6482	−2.44604
$305$	−19.3330	−1.10700
$306$	−24.7375	−1.41415
$307$	22.5602	1.28758	0.643788	−	0.765204i	$-0.277362\pi$
$307$	22.5602	1.28758	0.643788	+	0.765204i	$0.277362\pi$
$308$	−33.1678	−1.88991
$309$	−5.65810	−0.321878
$310$	0.824411	0.0468234
$311$	11.9761	0.679104	0.339552	−	0.940587i	$-0.389724\pi$
$311$	11.9761	0.679104	0.339552	+	0.940587i	$0.389724\pi$
$312$	3.62101	0.204999
$313$	24.1029	1.36237	0.681187	−	0.732109i	$-0.261464\pi$
$313$	24.1029	1.36237	0.681187	+	0.732109i	$0.261464\pi$
$314$	−52.2223	−2.94707
$315$	−7.86374	−0.443072
$316$	22.1130	1.24395
$317$	6.87592	0.386190	0.193095	−	0.981180i	$-0.438147\pi$
$317$	6.87592	0.386190	0.193095	+	0.981180i	$0.438147\pi$
$318$	−24.4362	−1.37032
$319$	46.0090	2.57601
$320$	96.3627	5.38684
$321$	12.4801	0.696572
$322$	−9.90795	−0.552149
$323$	12.3932	0.689575
$324$	12.8545	0.714137
$325$	3.43732	0.190668
$326$	12.7840	0.708038
$327$	−7.78727	−0.430637
$328$	−46.6258	−2.57448
$329$	−6.30676	−0.347703
$330$	−53.9094	−2.96762
$331$	30.1696	1.65827	0.829136	−	0.559047i	$-0.188833\pi$
$331$	30.1696	1.65827	0.829136	+	0.559047i	$0.188833\pi$
$332$	−6.34704	−0.348339
$333$	−9.91437	−0.543304
$334$	−44.5135	−2.43567
$335$	1.53952	0.0841132
$336$	−12.8340	−0.700150
$337$	−31.4116	−1.71110	−0.855549	−	0.517721i	$-0.826780\pi$
$337$	−31.4116	−1.71110	−0.855549	+	0.517721i	$0.826780\pi$
$338$	34.8232	1.89413
$339$	−10.9266	−0.593449
$340$	−80.2486	−4.35209
$341$	0.520155	0.0281680
$342$	−17.7995	−0.962485
$343$	1.00000	0.0539949
$344$	−103.306	−5.56990
$345$	−11.7463	−0.632400
$346$	0.405659	0.0218084
$347$	−0.429830	−0.0230745	−0.0115372	−	0.999933i	$-0.503673\pi$
$347$	−0.429830	−0.0230745	−0.0115372	+	0.999933i	$0.503673\pi$
$348$	36.2293	1.94209
$349$	23.7478	1.27119	0.635595	−	0.772023i	$-0.280755\pi$
$349$	23.7478	1.27119	0.635595	+	0.772023i	$0.280755\pi$
$350$	−21.3805	−1.14284
$351$	2.03943	0.108857
$352$	125.439	6.68590
$353$	−1.83516	−0.0976759	−0.0488379	−	0.998807i	$-0.515552\pi$
$353$	−1.83516	−0.0976759	−0.0488379	+	0.998807i	$0.515552\pi$
$354$	2.63721	0.140166
$355$	49.1184	2.60694
$356$	−75.5657	−4.00497
$357$	3.72943	0.197383
$358$	22.3425	1.18084
$359$	16.7364	0.883311	0.441656	−	0.897185i	$-0.354391\pi$
$359$	16.7364	0.883311	0.441656	+	0.897185i	$0.354391\pi$
$360$	72.4979	3.82097
$361$	−10.0827	−0.530667
$362$	−57.8774	−3.04197
$363$	−24.1289	−1.26644
$364$	2.35632	0.123505
$365$	−47.6719	−2.49526
$366$	−13.1685	−0.688330
$367$	31.3254	1.63517	0.817586	−	0.575807i	$-0.195312\pi$
$367$	31.3254	1.63517	0.817586	+	0.575807i	$0.195312\pi$
$368$	52.0490	2.71324
$369$	−11.0883	−0.577235
$370$	−44.0940	−2.29234
$371$	−10.0023	−0.519296
$372$	0.409591	0.0212363
$373$	−5.13661	−0.265964	−0.132982	−	0.991118i	$-0.542455\pi$
$373$	−5.13661	−0.265964	−0.132982	+	0.991118i	$0.542455\pi$
$374$	−69.4158	−3.58941
$375$	−9.23211	−0.476744
$376$	58.1436	2.99853
$377$	−3.26859	−0.168341
$378$	−12.6855	−0.652471
$379$	−2.11173	−0.108472	−0.0542361	−	0.998528i	$-0.517272\pi$
$379$	−2.11173	−0.108472	−0.0542361	+	0.998528i	$0.517272\pi$
$380$	−57.7417	−2.96208
$381$	10.7156	0.548978
$382$	−52.3180	−2.67682
$383$	19.5018	0.996494	0.498247	−	0.867035i	$-0.333977\pi$
$383$	19.5018	0.996494	0.498247	+	0.867035i	$0.333977\pi$
$384$	28.9929	1.47954
$385$	−22.0665	−1.12461
$386$	−4.63922	−0.236130
$387$	−24.5678	−1.24885
$388$	15.2734	0.775390
$389$	−13.7410	−0.696695	−0.348348	−	0.937365i	$-0.613257\pi$
$389$	−13.7410	−0.696695	−0.348348	+	0.937365i	$0.613257\pi$
$390$	3.82986	0.193932
$391$	−15.1250	−0.764903
$392$	−9.21926	−0.465643
$393$	−9.44321	−0.476347
$394$	30.9851	1.56101
$395$	14.7118	0.740229
$396$	72.7195	3.65429
$397$	30.6331	1.53743	0.768715	−	0.639592i	$-0.220897\pi$
$397$	30.6331	1.53743	0.768715	+	0.639592i	$0.220897\pi$
$398$	−50.0213	−2.50734
$399$	2.68346	0.134341
$400$	112.317	5.61587
$401$	9.37442	0.468136	0.234068	−	0.972220i	$-0.424796\pi$
$401$	9.37442	0.468136	0.234068	+	0.972220i	$0.424796\pi$
$402$	1.04864	0.0523012
$403$	−0.0369531	−0.00184077
$404$	55.4714	2.75981
$405$	8.55205	0.424955
$406$	20.3310	1.00901
$407$	−27.8207	−1.37902
$408$	−34.3826	−1.70219
$409$	16.3209	0.807014	0.403507	−	0.914977i	$-0.367791\pi$
$409$	16.3209	0.807014	0.403507	+	0.914977i	$0.367791\pi$
$410$	−49.3151	−2.43550
$411$	−4.39083	−0.216584
$412$	33.9446	1.67233
$413$	1.07947	0.0531175
$414$	21.7230	1.06763
$415$	−4.22268	−0.207283
$416$	−8.91146	−0.436920
$417$	14.4467	0.707459
$418$	−49.9471	−2.44299
$419$	17.9286	0.875867	0.437934	−	0.899007i	$-0.355711\pi$
$419$	17.9286	0.875867	0.437934	+	0.899007i	$0.355711\pi$
$420$	−17.3760	−0.847862
$421$	−9.07939	−0.442502	−0.221251	−	0.975217i	$-0.571014\pi$
$421$	−9.07939	−0.442502	−0.221251	+	0.975217i	$0.571014\pi$
$422$	−15.9560	−0.776725
$423$	13.8274	0.672312
$424$	92.2142	4.47832
$425$	−32.6384	−1.58320
$426$	33.4567	1.62098
$427$	−5.39020	−0.260850
$428$	−74.8719	−3.61907
$429$	2.41642	0.116666
$430$	−109.265	−5.26921
$431$	26.7123	1.28669	0.643344	−	0.765577i	$-0.277547\pi$
$431$	26.7123	1.28669	0.643344	+	0.765577i	$0.277547\pi$
$432$	66.6401	3.20622
$433$	−25.7496	−1.23745	−0.618723	−	0.785609i	$-0.712350\pi$
$433$	−25.7496	−1.23745	−0.618723	+	0.785609i	$0.712350\pi$
$434$	0.229853	0.0110333
$435$	24.1033	1.15566
$436$	46.7181	2.23739
$437$	−10.8829	−0.520602
$438$	−32.4714	−1.55154
$439$	18.0350	0.860763	0.430381	−	0.902647i	$-0.358379\pi$
$439$	18.0350	0.860763	0.430381	+	0.902647i	$0.358379\pi$
$440$	203.436	9.69845
$441$	−2.19248	−0.104404
$442$	4.93147	0.234566
$443$	33.9536	1.61318	0.806592	−	0.591109i	$-0.201310\pi$
$443$	33.9536	1.61318	0.806592	+	0.591109i	$0.201310\pi$
$444$	−21.9071	−1.03967
$445$	−50.2737	−2.38320
$446$	0.649411	0.0307505
$447$	−14.6261	−0.691789
$448$	26.8667	1.26933
$449$	35.9164	1.69500	0.847500	−	0.530795i	$-0.178107\pi$
$449$	35.9164	1.69500	0.847500	+	0.530795i	$0.178107\pi$
$450$	46.8763	2.20977
$451$	−31.1149	−1.46514
$452$	65.5516	3.08329
$453$	11.2249	0.527390
$454$	63.4222	2.97655
$455$	1.56766	0.0734928
$456$	−24.7395	−1.15853
$457$	15.7647	0.737441	0.368721	−	0.929540i	$-0.379796\pi$
$457$	15.7647	0.737441	0.368721	+	0.929540i	$0.379796\pi$
$458$	61.6280	2.87969
$459$	−19.3650	−0.903881
$460$	70.4695	3.28566
$461$	−1.11400	−0.0518843	−0.0259421	−	0.999663i	$-0.508259\pi$
$461$	−1.11400	−0.0518843	−0.0259421	+	0.999663i	$0.508259\pi$
$462$	−15.0304	−0.699278
$463$	−9.68434	−0.450069	−0.225035	−	0.974351i	$-0.572250\pi$
$463$	−9.68434	−0.450069	−0.225035	+	0.974351i	$0.572250\pi$
$464$	−106.804	−4.95825
$465$	0.272500	0.0126369
$466$	31.9061	1.47802
$467$	−16.2219	−0.750659	−0.375329	−	0.926891i	$-0.622470\pi$
$467$	−16.2219	−0.750659	−0.375329	+	0.926891i	$0.622470\pi$
$468$	−5.16617	−0.238807
$469$	0.429232	0.0198201
$470$	61.4971	2.83665
$471$	−17.2615	−0.795368
$472$	−9.95196	−0.458076
$473$	−68.9396	−3.16985
$474$	10.0208	0.460271
$475$	−23.4845	−1.07754
$476$	−22.3740	−1.02551
$477$	21.9299	1.00410
$478$	−69.1458	−3.16266
$479$	24.4008	1.11490	0.557450	−	0.830211i	$-0.311780\pi$
$479$	24.4008	1.11490	0.557450	+	0.830211i	$0.311780\pi$
$480$	65.7150	2.99947
$481$	1.97645	0.0901185
$482$	13.0938	0.596407
$483$	−3.27497	−0.149016
$484$	144.756	6.57983
$485$	10.1614	0.461404
$486$	43.8816	1.99051
$487$	−16.0977	−0.729454	−0.364727	−	0.931114i	$-0.618838\pi$
$487$	−16.0977	−0.729454	−0.364727	+	0.931114i	$0.618838\pi$
$488$	49.6937	2.24953
$489$	4.22560	0.191088
$490$	−9.75100	−0.440505
$491$	1.04602	0.0472063	0.0236031	−	0.999721i	$-0.492486\pi$
$491$	1.04602	0.0472063	0.0236031	+	0.999721i	$0.492486\pi$
$492$	−24.5011	−1.10460
$493$	31.0363	1.39780
$494$	3.54836	0.159648
$495$	48.3802	2.17453
$496$	−1.20747	−0.0542172
$497$	13.6946	0.614288
$498$	−2.87625	−0.128888
$499$	18.8517	0.843919	0.421959	−	0.906615i	$-0.361342\pi$
$499$	18.8517	0.843919	0.421959	+	0.906615i	$0.361342\pi$
$500$	55.3861	2.47694
$501$	−14.7135	−0.657349
$502$	−49.5114	−2.20980
$503$	−9.67865	−0.431550	−0.215775	−	0.976443i	$-0.569228\pi$
$503$	−9.67865	−0.431550	−0.215775	+	0.976443i	$0.569228\pi$
$504$	20.2130	0.900359
$505$	36.9050	1.64225
$506$	60.9568	2.70986
$507$	11.5104	0.511196
$508$	−64.2862	−2.85224
$509$	14.5048	0.642913	0.321457	−	0.946924i	$-0.395828\pi$
$509$	14.5048	0.642913	0.321457	+	0.946924i	$0.395828\pi$
$510$	−36.3657	−1.61030
$511$	−13.2913	−0.587974
$512$	−27.8543	−1.23100
$513$	−13.9338	−0.615192
$514$	5.03950	0.222283
$515$	22.5833	0.995139
$516$	−54.2858	−2.38980
$517$	38.8011	1.70647
$518$	−12.2938	−0.540157
$519$	0.134086	0.00588573
$520$	−14.4526	−0.633789
$521$	−18.4533	−0.808453	−0.404226	−	0.914659i	$-0.632459\pi$
$521$	−18.4533	−0.808453	−0.404226	+	0.914659i	$0.632459\pi$
$522$	−44.5753	−1.95101
$523$	27.7331	1.21268	0.606342	−	0.795204i	$-0.292636\pi$
$523$	27.7331	1.21268	0.606342	+	0.795204i	$0.292636\pi$
$524$	56.6526	2.47488
$525$	−7.06710	−0.308434
$526$	41.8667	1.82548
$527$	0.350881	0.0152846
$528$	78.9585	3.43623
$529$	−9.71815	−0.422528
$530$	97.5328	4.23656
$531$	−2.36672	−0.102707
$532$	−16.0989	−0.697974
$533$	2.21048	0.0957466
$534$	−34.2436	−1.48186
$535$	−49.8121	−2.15357
$536$	−3.95720	−0.170925
$537$	7.38508	0.318690
$538$	50.1972	2.16416
$539$	−6.15231	−0.264999
$540$	90.2244	3.88264
$541$	−22.1720	−0.953249	−0.476625	−	0.879107i	$-0.658140\pi$
$541$	−22.1720	−0.953249	−0.476625	+	0.879107i	$0.658140\pi$
$542$	−5.42135	−0.232867
$543$	−19.1307	−0.820979
$544$	84.6171	3.62793
$545$	31.0815	1.33138
$546$	1.06780	0.0456975
$547$	45.5619	1.94809	0.974043	−	0.226364i	$-0.0726838\pi$
$547$	45.5619	1.94809	0.974043	+	0.226364i	$0.0726838\pi$
$548$	26.3419	1.12527
$549$	11.8179	0.504375
$550$	131.540	5.60887
$551$	22.3317	0.951362
$552$	30.1928	1.28509
$553$	4.10176	0.174425
$554$	−74.1527	−3.15045
$555$	−14.5748	−0.618665
$556$	−86.6701	−3.67563
$557$	−20.2511	−0.858066	−0.429033	−	0.903289i	$-0.641146\pi$
$557$	−20.2511	−0.858066	−0.429033	+	0.903289i	$0.641146\pi$
$558$	−0.503947	−0.0213338
$559$	4.89764	0.207148
$560$	51.2245	2.16463
$561$	−22.9446	−0.968723
$562$	−59.1945	−2.49697
$563$	−3.17345	−0.133745	−0.0668724	−	0.997762i	$-0.521302\pi$
$563$	−3.17345	−0.133745	−0.0668724	+	0.997762i	$0.521302\pi$
$564$	30.5535	1.28654
$565$	43.6114	1.83474
$566$	−42.3040	−1.77817
$567$	2.38438	0.100135
$568$	−126.254	−5.29752
$569$	−13.8716	−0.581529	−0.290764	−	0.956795i	$-0.593910\pi$
$569$	−13.8716	−0.581529	−0.290764	+	0.956795i	$0.593910\pi$
$570$	−26.1664	−1.09599
$571$	−24.4837	−1.02461	−0.512305	−	0.858803i	$-0.671208\pi$
$571$	−24.4837	−1.02461	−0.512305	+	0.858803i	$0.671208\pi$
$572$	−14.4968	−0.606142
$573$	−17.2932	−0.722432
$574$	−13.7494	−0.573891
$575$	28.6611	1.19525
$576$	−58.9046	−2.45436
$577$	−43.9290	−1.82879	−0.914393	−	0.404827i	$-0.867332\pi$
$577$	−43.9290	−1.82879	−0.914393	+	0.404827i	$0.867332\pi$
$578$	−0.608630	−0.0253157
$579$	−1.53344	−0.0637277
$580$	−144.603	−6.00430
$581$	−1.17732	−0.0488434
$582$	6.92135	0.286899
$583$	61.5375	2.54862
$584$	122.536	5.07058
$585$	−3.43705	−0.142104
$586$	55.3699	2.28731
$587$	−15.8458	−0.654027	−0.327014	−	0.945020i	$-0.606042\pi$
$587$	−15.8458	−0.654027	−0.327014	+	0.945020i	$0.606042\pi$
$588$	−4.84457	−0.199787
$589$	0.252471	0.0104029
$590$	−10.5260	−0.433347
$591$	10.2418	0.421290
$592$	64.5823	2.65432
$593$	26.0204	1.06853	0.534264	−	0.845317i	$-0.320589\pi$
$593$	26.0204	1.06853	0.534264	+	0.845317i	$0.320589\pi$
$594$	78.0450	3.20223
$595$	−14.8854	−0.610241
$596$	87.7460	3.59422
$597$	−16.5340	−0.676691
$598$	−4.33052	−0.177088
$599$	16.7520	0.684466	0.342233	−	0.939615i	$-0.388817\pi$
$599$	16.7520	0.684466	0.342233	+	0.939615i	$0.388817\pi$
$600$	65.1535	2.65988
$601$	−36.0258	−1.46952	−0.734762	−	0.678325i	$-0.762706\pi$
$601$	−36.0258	−1.46952	−0.734762	+	0.678325i	$0.762706\pi$
$602$	−30.4639	−1.24162
$603$	−0.941082	−0.0383238
$604$	−67.3413	−2.74008
$605$	96.3061	3.91540
$606$	25.1376	1.02114
$607$	30.4832	1.23728	0.618638	−	0.785676i	$-0.287685\pi$
$607$	30.4832	1.23728	0.618638	+	0.785676i	$0.287685\pi$
$608$	60.8849	2.46921
$609$	6.72020	0.272316
$610$	52.5598	2.12809
$611$	−2.75653	−0.111517
$612$	49.0544	1.98291
$613$	−16.4618	−0.664886	−0.332443	−	0.943123i	$-0.607873\pi$
$613$	−16.4618	−0.664886	−0.332443	+	0.943123i	$0.607873\pi$
$614$	−61.3334	−2.47521
$615$	−16.3006	−0.657302
$616$	56.7198	2.28530
$617$	−41.2887	−1.66222	−0.831110	−	0.556107i	$-0.812294\pi$
$617$	−41.2887	−1.66222	−0.831110	+	0.556107i	$0.812294\pi$
$618$	15.3824	0.618773
$619$	−21.8387	−0.877772	−0.438886	−	0.898543i	$-0.644627\pi$
$619$	−21.8387	−0.877772	−0.438886	+	0.898543i	$0.644627\pi$
$620$	−1.63481	−0.0656555
$621$	17.0052	0.682395
$622$	−32.5590	−1.30550
$623$	−14.0167	−0.561568
$624$	−5.60941	−0.224556
$625$	−2.47354	−0.0989416
$626$	−65.5274	−2.61900
$627$	−16.5095	−0.659324
$628$	103.557	4.13237
$629$	−18.7670	−0.748291
$630$	21.3788	0.851753
$631$	−8.38874	−0.333951	−0.166975	−	0.985961i	$-0.553400\pi$
$631$	−8.38874	−0.333951	−0.166975	+	0.985961i	$0.553400\pi$
$632$	−37.8152	−1.50421
$633$	−5.27407	−0.209626
$634$	−18.6933	−0.742405
$635$	−42.7695	−1.69725
$636$	48.4571	1.92145
$637$	0.437075	0.0173176
$638$	−125.083	−4.95207
$639$	−30.0252	−1.18778
$640$	−115.720	−4.57424
$641$	32.6795	1.29076	0.645382	−	0.763860i	$-0.276698\pi$
$641$	32.6795	1.29076	0.645382	+	0.763860i	$0.276698\pi$
$642$	−33.9291	−1.33908
$643$	14.7099	0.580100	0.290050	−	0.957012i	$-0.406328\pi$
$643$	14.7099	0.580100	0.290050	+	0.957012i	$0.406328\pi$
$644$	19.6475	0.774220
$645$	−36.1162	−1.42207
$646$	−33.6928	−1.32563
$647$	8.99013	0.353438	0.176719	−	0.984261i	$-0.443452\pi$
$647$	8.99013	0.353438	0.176719	+	0.984261i	$0.443452\pi$
$648$	−21.9823	−0.863545
$649$	−6.64126	−0.260692
$650$	−9.34490	−0.366537
$651$	0.0759753	0.00297771
$652$	−25.3506	−0.992807
$653$	14.7857	0.578610	0.289305	−	0.957237i	$-0.406576\pi$
$653$	14.7857	0.578610	0.289305	+	0.957237i	$0.406576\pi$
$654$	21.1709	0.827849
$655$	37.6909	1.47271
$656$	72.2294	2.82008
$657$	29.1409	1.13690
$658$	17.1459	0.668417
$659$	20.1464	0.784794	0.392397	−	0.919796i	$-0.371646\pi$
$659$	20.1464	0.784794	0.392397	+	0.919796i	$0.371646\pi$
$660$	106.903	4.16118
$661$	7.15641	0.278352	0.139176	−	0.990268i	$-0.455555\pi$
$661$	7.15641	0.278352	0.139176	+	0.990268i	$0.455555\pi$
$662$	−82.0209	−3.18783
$663$	1.63004	0.0633056
$664$	10.8540	0.421217
$665$	−10.7105	−0.415337
$666$	26.9538	1.04444
$667$	−27.2542	−1.05529
$668$	88.2704	3.41528
$669$	0.214656	0.00829907
$670$	−4.18544	−0.161698
$671$	33.1622	1.28021
$672$	18.3219	0.706782
$673$	5.64587	0.217632	0.108816	−	0.994062i	$-0.465294\pi$
$673$	5.64587	0.217632	0.108816	+	0.994062i	$0.465294\pi$
$674$	85.3974	3.28939
$675$	36.6958	1.41242
$676$	−69.0545	−2.65594
$677$	−35.2244	−1.35378	−0.676892	−	0.736083i	$-0.736673\pi$
$677$	−35.2244	−1.35378	−0.676892	+	0.736083i	$0.736673\pi$
$678$	29.7056	1.14084
$679$	2.83308	0.108724
$680$	137.232	5.26261
$681$	20.9635	0.803323
$682$	−1.41412	−0.0541496
$683$	−14.2553	−0.545463	−0.272732	−	0.962090i	$-0.587927\pi$
$683$	−14.2553	−0.545463	−0.272732	+	0.962090i	$0.587927\pi$
$684$	35.2964	1.34959
$685$	17.5252	0.669604
$686$	−2.71866	−0.103799
$687$	20.3705	0.777182
$688$	160.035	6.10126
$689$	−4.37178	−0.166551
$690$	31.9342	1.21571
$691$	2.85379	0.108563	0.0542817	−	0.998526i	$-0.482713\pi$
$691$	2.85379	0.108563	0.0542817	+	0.998526i	$0.482713\pi$
$692$	−0.804422	−0.0305795
$693$	13.4888	0.512397
$694$	1.16856	0.0443580
$695$	−57.6615	−2.18722
$696$	−61.9552	−2.34841
$697$	−20.9892	−0.795023
$698$	−64.5621	−2.44371
$699$	10.5462	0.398894
$700$	42.3976	1.60248
$701$	−4.62937	−0.174849	−0.0874245	−	0.996171i	$-0.527864\pi$
$701$	−4.62937	−0.174849	−0.0874245	+	0.996171i	$0.527864\pi$
$702$	−5.54451	−0.209264
$703$	−13.5035	−0.509295
$704$	−165.292	−6.22969
$705$	20.3272	0.765567
$706$	4.98918	0.187770
$707$	10.2894	0.386974
$708$	−5.22959	−0.196540
$709$	−12.1823	−0.457515	−0.228758	−	0.973483i	$-0.573466\pi$
$709$	−12.1823	−0.457515	−0.228758	+	0.973483i	$0.573466\pi$
$710$	−133.536	−5.01153
$711$	−8.99301	−0.337264
$712$	129.224	4.84287
$713$	−0.308123	−0.0115393
$714$	−10.1391	−0.379445
$715$	−9.64470	−0.360691
$716$	−44.3053	−1.65577
$717$	−22.8554	−0.853550
$718$	−45.5004	−1.69806
$719$	−17.4261	−0.649882	−0.324941	−	0.945734i	$-0.605344\pi$
$719$	−17.4261	−0.649882	−0.324941	+	0.945734i	$0.605344\pi$
$720$	−112.308	−4.18549
$721$	6.29641	0.234491
$722$	27.4114	1.02015
$723$	4.32802	0.160961
$724$	114.771	4.26543
$725$	−58.8123	−2.18423
$726$	65.5982	2.43458
$727$	−0.430594	−0.0159698	−0.00798492	−	0.999968i	$-0.502542\pi$
$727$	−0.430594	−0.0159698	−0.00798492	+	0.999968i	$0.502542\pi$
$728$	−4.02951	−0.149344
$729$	7.35143	0.272275
$730$	129.604	4.79685
$731$	−46.5046	−1.72003
$732$	26.1132	0.965173
$733$	−15.5938	−0.575969	−0.287984	−	0.957635i	$-0.592985\pi$
$733$	−15.5938	−0.575969	−0.287984	+	0.957635i	$0.592985\pi$
$734$	−85.1630	−3.14342
$735$	−3.22309	−0.118885
$736$	−74.3057	−2.73894
$737$	−2.64077	−0.0972740
$738$	30.1453	1.10967
$739$	−22.4872	−0.827206	−0.413603	−	0.910457i	$-0.635730\pi$
$739$	−22.4872	−0.827206	−0.413603	+	0.910457i	$0.635730\pi$
$740$	87.4384	3.21430
$741$	1.17287	0.0430866
$742$	27.1930	0.998285
$743$	−31.3730	−1.15096	−0.575481	−	0.817815i	$-0.695185\pi$
$743$	−31.3730	−1.15096	−0.575481	+	0.817815i	$0.695185\pi$
$744$	−0.700436	−0.0256792
$745$	58.3773	2.13878
$746$	13.9647	0.511284
$747$	2.58124	0.0944427
$748$	137.652	5.03304
$749$	−13.8880	−0.507458
$750$	25.0990	0.916484
$751$	47.3544	1.72799	0.863993	−	0.503505i	$-0.167956\pi$
$751$	47.3544	1.72799	0.863993	+	0.503505i	$0.167956\pi$
$752$	−90.0719	−3.28458
$753$	−16.3655	−0.596391
$754$	8.88618	0.323616
$755$	−44.8020	−1.63051
$756$	25.1553	0.914890
$757$	32.1157	1.16726	0.583632	−	0.812018i	$-0.301631\pi$
$757$	32.1157	1.16726	0.583632	+	0.812018i	$0.301631\pi$
$758$	5.74107	0.208525
$759$	20.1486	0.731348
$760$	98.7433	3.58179
$761$	41.6987	1.51158	0.755788	−	0.654816i	$-0.227254\pi$
$761$	41.6987	1.51158	0.755788	+	0.654816i	$0.227254\pi$
$762$	−29.1321	−1.05535
$763$	8.66578	0.313722
$764$	103.747	3.75343
$765$	32.6358	1.17995
$766$	−53.0186	−1.91564
$767$	0.471812	0.0170361
$768$	−30.5358	−1.10186
$769$	32.8642	1.18511	0.592556	−	0.805529i	$-0.298119\pi$
$769$	32.8642	1.18511	0.592556	+	0.805529i	$0.298119\pi$
$770$	59.9912	2.16193
$771$	1.66575	0.0599906
$772$	9.19958	0.331100
$773$	−22.3320	−0.803227	−0.401613	−	0.915809i	$-0.631550\pi$
$773$	−22.3320	−0.803227	−0.401613	+	0.915809i	$0.631550\pi$
$774$	66.7913	2.40077
$775$	−0.664904	−0.0238840
$776$	−26.1189	−0.937613
$777$	−4.06357	−0.145780
$778$	37.3570	1.33931
$779$	−15.1025	−0.541102
$780$	−7.59462	−0.271931
$781$	−84.2536	−3.01483
$782$	41.1196	1.47044
$783$	−34.8945	−1.24703
$784$	14.2818	0.510065
$785$	68.8962	2.45901
$786$	25.6729	0.915721
$787$	−21.2017	−0.755758	−0.377879	−	0.925855i	$-0.623346\pi$
$787$	−21.2017	−0.755758	−0.377879	+	0.925855i	$0.623346\pi$
$788$	−61.4435	−2.18883
$789$	13.8386	0.492667
$790$	−39.9962	−1.42300
$791$	12.1592	0.432332
$792$	−124.357	−4.41882
$793$	−2.35592	−0.0836613
$794$	−83.2809	−2.95553
$795$	32.2384	1.14338
$796$	99.1923	3.51578
$797$	35.2053	1.24704	0.623518	−	0.781809i	$-0.285703\pi$
$797$	35.2053	1.24704	0.623518	+	0.781809i	$0.285703\pi$
$798$	−7.29540	−0.258255
$799$	26.1741	0.925972
$800$	−160.345	−5.66907
$801$	30.7313	1.08584
$802$	−25.4859	−0.899937
$803$	81.7724	2.88568
$804$	−2.07945	−0.0733364
$805$	13.0714	0.460708
$806$	0.100463	0.00353865
$807$	16.5921	0.584071
$808$	−94.8609	−3.33720
$809$	6.41510	0.225543	0.112771	−	0.993621i	$-0.464027\pi$
$809$	6.41510	0.225543	0.112771	+	0.993621i	$0.464027\pi$
$810$	−23.2501	−0.816926
$811$	12.0851	0.424366	0.212183	−	0.977230i	$-0.431943\pi$
$811$	12.0851	0.424366	0.212183	+	0.977230i	$0.431943\pi$
$812$	−40.3164	−1.41483
$813$	−1.79197	−0.0628471
$814$	75.6351	2.65101
$815$	−16.8657	−0.590780
$816$	53.2631	1.86458
$817$	−33.4617	−1.17068
$818$	−44.3708	−1.55139
$819$	−0.958277	−0.0334849
$820$	97.7918	3.41504
$821$	−7.47828	−0.260994	−0.130497	−	0.991449i	$-0.541657\pi$
$821$	−7.47828	−0.260994	−0.130497	+	0.991449i	$0.541657\pi$
$822$	11.9372	0.416356
$823$	46.6206	1.62509	0.812547	−	0.582896i	$-0.198080\pi$
$823$	46.6206	1.62509	0.812547	+	0.582896i	$0.198080\pi$
$824$	−58.0482	−2.02221
$825$	43.4790	1.51375
$826$	−2.93472	−0.102112
$827$	−19.7120	−0.685454	−0.342727	−	0.939435i	$-0.611351\pi$
$827$	−19.7120	−0.685454	−0.342727	+	0.939435i	$0.611351\pi$
$828$	−43.0767	−1.49702
$829$	10.1066	0.351017	0.175508	−	0.984478i	$-0.443843\pi$
$829$	10.1066	0.351017	0.175508	+	0.984478i	$0.443843\pi$
$830$	11.4800	0.398477
$831$	−24.5104	−0.850255
$832$	11.7428	0.407108
$833$	−4.15017	−0.143795
$834$	−39.2757	−1.36001
$835$	58.7261	2.03230
$836$	99.0452	3.42555
$837$	−0.394500	−0.0136359
$838$	−48.7416	−1.68375
$839$	7.33493	0.253230	0.126615	−	0.991952i	$-0.459589\pi$
$839$	7.33493	0.253230	0.126615	+	0.991952i	$0.459589\pi$
$840$	29.7145	1.02525
$841$	26.9254	0.928460
$842$	24.6838	0.850659
$843$	−19.5661	−0.673892
$844$	31.6407	1.08912
$845$	−45.9418	−1.58045
$846$	−37.5920	−1.29244
$847$	26.8509	0.922609
$848$	−142.852	−4.90554
$849$	−13.9831	−0.479900
$850$	88.7328	3.04351
$851$	16.4801	0.564930
$852$	−66.3446	−2.27293
$853$	−27.7324	−0.949539	−0.474770	−	0.880110i	$-0.657469\pi$
$853$	−27.7324	−0.949539	−0.474770	+	0.880110i	$0.657469\pi$
$854$	14.6541	0.501454
$855$	23.4826	0.803088
$856$	128.037	4.37623
$857$	−49.5757	−1.69347	−0.846737	−	0.532012i	$-0.821436\pi$
$857$	−49.5757	−1.69347	−0.846737	+	0.532012i	$0.821436\pi$
$858$	−6.56942	−0.224276
$859$	5.67823	0.193739	0.0968694	−	0.995297i	$-0.469117\pi$
$859$	5.67823	0.193739	0.0968694	+	0.995297i	$0.469117\pi$
$860$	216.672	7.38845
$861$	−4.54473	−0.154884
$862$	−72.6217	−2.47351
$863$	−1.00000	−0.0340404
$863$	−1.00000	−0.0340404
$864$	−95.1360	−3.23659
$865$	−0.535181	−0.0181967
$866$	70.0044	2.37885
$867$	−0.201176	−0.00683230
$868$	−0.455798	−0.0154708
$869$	−25.2353	−0.856049
$870$	−65.5286	−2.22163
$871$	0.187607	0.00635681
$872$	−79.8921	−2.70549
$873$	−6.21146	−0.210226
$874$	29.5870	1.00080
$875$	10.2736	0.347312
$876$	64.3908	2.17556
$877$	−47.0585	−1.58905	−0.794527	−	0.607229i	$-0.792281\pi$
$877$	−47.0585	−1.58905	−0.794527	+	0.607229i	$0.792281\pi$
$878$	−49.0310	−1.65472
$879$	18.3019	0.617308
$880$	−315.149	−10.6237
$881$	39.7337	1.33866	0.669331	−	0.742964i	$-0.266581\pi$
$881$	39.7337	1.33866	0.669331	+	0.742964i	$0.266581\pi$
$882$	5.96060	0.200704
$883$	−2.08887	−0.0702961	−0.0351481	−	0.999382i	$-0.511190\pi$
$883$	−2.08887	−0.0702961	−0.0351481	+	0.999382i	$0.511190\pi$
$884$	−9.77911	−0.328907
$885$	−3.47924	−0.116953
$886$	−92.3082	−3.10116
$887$	−25.1053	−0.842955	−0.421477	−	0.906839i	$-0.638488\pi$
$887$	−25.1053	−0.842955	−0.421477	+	0.906839i	$0.638488\pi$
$888$	37.4631	1.25718
$889$	−11.9245	−0.399934
$890$	136.677	4.58142
$891$	−14.6695	−0.491446
$892$	−1.28778	−0.0431182
$893$	18.8332	0.630228
$894$	39.7632	1.32988
$895$	−29.4762	−0.985282
$896$	−32.2637	−1.07786
$897$	−1.43141	−0.0477933
$898$	−97.6445	−3.25844
$899$	0.632265	0.0210872
$900$	−92.9559	−3.09853
$901$	41.5114	1.38294
$902$	84.5909	2.81657
$903$	−10.0695	−0.335092
$904$	−112.099	−3.72836
$905$	76.3569	2.53819
$906$	−30.5166	−1.01385
$907$	3.58011	0.118876	0.0594378	−	0.998232i	$-0.481069\pi$
$907$	3.58011	0.118876	0.0594378	+	0.998232i	$0.481069\pi$
$908$	−125.766	−4.17370
$909$	−22.5593	−0.748246
$910$	−4.26192	−0.141281
$911$	−36.1281	−1.19698	−0.598489	−	0.801131i	$-0.704232\pi$
$911$	−36.1281	−1.19698	−0.598489	+	0.801131i	$0.704232\pi$
$912$	38.3246	1.26906
$913$	7.24322	0.239716
$914$	−42.8588	−1.41764
$915$	17.3731	0.574336
$916$	−122.208	−4.03788
$917$	10.5085	0.347022
$918$	52.6468	1.73760
$919$	33.8793	1.11757	0.558787	−	0.829311i	$-0.311267\pi$
$919$	33.8793	1.11757	0.558787	+	0.829311i	$0.311267\pi$
$920$	−120.509	−3.97307
$921$	−20.2731	−0.668021
$922$	3.02859	0.0997414
$923$	5.98558	0.197018
$924$	29.8053	0.980523
$925$	35.5627	1.16929
$926$	26.3284	0.865205
$927$	−13.8047	−0.453407
$928$	152.474	5.00522
$929$	35.1702	1.15390	0.576949	−	0.816780i	$-0.304243\pi$
$929$	35.1702	1.15390	0.576949	+	0.816780i	$0.304243\pi$
$930$	−0.740835	−0.0242929
$931$	−2.98619	−0.0978684
$932$	−63.2699	−2.07247
$933$	−10.7620	−0.352333
$934$	44.1017	1.44305
$935$	91.5794	2.99497
$936$	8.83461	0.288768
$937$	7.59282	0.248047	0.124023	−	0.992279i	$-0.460420\pi$
$937$	7.59282	0.248047	0.124023	+	0.992279i	$0.460420\pi$
$938$	−1.16694	−0.0381018
$939$	−21.6594	−0.706827
$940$	−121.949	−3.97754
$941$	−38.4311	−1.25282	−0.626408	−	0.779495i	$-0.715476\pi$
$941$	−38.4311	−1.25282	−0.626408	+	0.779495i	$0.715476\pi$
$942$	46.9281	1.52900
$943$	18.4315	0.600211
$944$	15.4169	0.501776
$945$	16.7358	0.544415
$946$	187.423	6.09366
$947$	−23.8402	−0.774703	−0.387351	−	0.921932i	$-0.626610\pi$
$947$	−23.8402	−0.774703	−0.387351	+	0.921932i	$0.626610\pi$
$948$	−19.8713	−0.645389
$949$	−5.80931	−0.188578
$950$	63.8463	2.07145
$951$	−6.17886	−0.200363
$952$	38.2615	1.24006
$953$	−19.7189	−0.638758	−0.319379	−	0.947627i	$-0.603474\pi$
$953$	−19.7189	−0.638758	−0.319379	+	0.947627i	$0.603474\pi$
$954$	−59.6199	−1.93027
$955$	69.0225	2.23352
$956$	137.116	4.43466
$957$	−41.3447	−1.33649
$958$	−66.3373	−2.14326
$959$	4.88617	0.157783
$960$	−86.5937	−2.79480
$961$	−30.9929	−0.999769
$962$	−5.37330	−0.173242
$963$	30.4492	0.981211
$964$	−25.9650	−0.836278
$965$	6.12047	0.197025
$966$	8.90352	0.286466
$967$	35.2356	1.13310	0.566550	−	0.824027i	$-0.308278\pi$
$967$	35.2356	1.13310	0.566550	+	0.824027i	$0.308278\pi$
$968$	−247.546	−7.95642
$969$	−11.1368	−0.357765
$970$	−27.6253	−0.886996
$971$	2.30692	0.0740326	0.0370163	−	0.999315i	$-0.488215\pi$
$971$	2.30692	0.0740326	0.0370163	+	0.999315i	$0.488215\pi$
$972$	−87.0173	−2.79108
$973$	−16.0765	−0.515389
$974$	43.7640	1.40229
$975$	−3.08886	−0.0989226
$976$	−76.9819	−2.46413
$977$	29.8815	0.955995	0.477997	−	0.878361i	$-0.341363\pi$
$977$	29.8815	0.955995	0.477997	+	0.878361i	$0.341363\pi$
$978$	−11.4880	−0.367344
$979$	86.2353	2.75609
$980$	19.3362	0.617674
$981$	−18.9995	−0.606608
$982$	−2.84377	−0.0907485
$983$	−49.1865	−1.56881	−0.784403	−	0.620252i	$-0.787030\pi$
$983$	−49.1865	−1.56881	−0.784403	+	0.620252i	$0.787030\pi$
$984$	41.8990	1.33569
$985$	−40.8782	−1.30249
$986$	−84.3771	−2.68711
$987$	5.66740	0.180395
$988$	−7.03641	−0.223858
$989$	40.8376	1.29856
$990$	−131.529	−4.18027
$991$	−27.9441	−0.887675	−0.443837	−	0.896107i	$-0.646383\pi$
$991$	−27.9441	−0.887675	−0.443837	+	0.896107i	$0.646383\pi$
$992$	1.72380	0.0547308
$993$	−27.1111	−0.860345
$994$	−37.2310	−1.18090
$995$	65.9925	2.09210
$996$	5.70360	0.180725
$997$	58.9359	1.86652	0.933259	−	0.359205i	$-0.116952\pi$
$997$	58.9359	1.86652	0.933259	+	0.359205i	$0.116952\pi$
$998$	−51.2514	−1.62233
$999$	21.1000	0.667574

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.f.1.5	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.f.1.5	✓	132	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.71866 q^{2} -0.898623 q^{3} +5.39111 q^{4} +3.58669 q^{5} +2.44305 q^{6} +1.00000 q^{7} -9.21926 q^{8} -2.19248 q^{9} +O(q^{10})\)	\(q-2.71866 q^{2} -0.898623 q^{3} +5.39111 q^{4} +3.58669 q^{5} +2.44305 q^{6} +1.00000 q^{7} -9.21926 q^{8} -2.19248 q^{9} -9.75100 q^{10} -6.15231 q^{11} -4.84457 q^{12} +0.437075 q^{13} -2.71866 q^{14} -3.22309 q^{15} +14.2818 q^{16} -4.15017 q^{17} +5.96060 q^{18} -2.98619 q^{19} +19.3362 q^{20} -0.898623 q^{21} +16.7260 q^{22} +3.64443 q^{23} +8.28464 q^{24} +7.86437 q^{25} -1.18826 q^{26} +4.66608 q^{27} +5.39111 q^{28} -7.47833 q^{29} +8.76247 q^{30} -0.0845463 q^{31} -20.3889 q^{32} +5.52861 q^{33} +11.2829 q^{34} +3.58669 q^{35} -11.8199 q^{36} +4.52200 q^{37} +8.11843 q^{38} -0.392766 q^{39} -33.0667 q^{40} +5.05744 q^{41} +2.44305 q^{42} +11.2055 q^{43} -33.1678 q^{44} -7.86374 q^{45} -9.90795 q^{46} -6.30676 q^{47} -12.8340 q^{48} +1.00000 q^{49} -21.3805 q^{50} +3.72943 q^{51} +2.35632 q^{52} -10.0023 q^{53} -12.6855 q^{54} -22.0665 q^{55} -9.21926 q^{56} +2.68346 q^{57} +20.3310 q^{58} +1.07947 q^{59} -17.3760 q^{60} -5.39020 q^{61} +0.229853 q^{62} -2.19248 q^{63} +26.8667 q^{64} +1.56766 q^{65} -15.0304 q^{66} +0.429232 q^{67} -22.3740 q^{68} -3.27497 q^{69} -9.75100 q^{70} +13.6946 q^{71} +20.2130 q^{72} -13.2913 q^{73} -12.2938 q^{74} -7.06710 q^{75} -16.0989 q^{76} -6.15231 q^{77} +1.06780 q^{78} +4.10176 q^{79} +51.2245 q^{80} +2.38438 q^{81} -13.7494 q^{82} -1.17732 q^{83} -4.84457 q^{84} -14.8854 q^{85} -30.4639 q^{86} +6.72020 q^{87} +56.7198 q^{88} -14.0167 q^{89} +21.3788 q^{90} +0.437075 q^{91} +19.6475 q^{92} +0.0759753 q^{93} +17.1459 q^{94} -10.7105 q^{95} +18.3219 q^{96} +2.83308 q^{97} -2.71866 q^{98} +13.4888 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9}+O(q^{10}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9} + 22 q^{10} + 32 q^{11} + 30 q^{12} + 16 q^{13} + 8 q^{14} + 59 q^{15} + 254 q^{16} + 11 q^{17} + 33 q^{18} + 40 q^{19} + 4 q^{20} + 10 q^{21} + 66 q^{22} + 62 q^{23} + 36 q^{24} + 235 q^{25} + 25 q^{26} + 37 q^{27} + 174 q^{28} + 28 q^{29} + 45 q^{30} + 121 q^{31} + 53 q^{32} - 13 q^{33} + 44 q^{34} + 11 q^{35} + 274 q^{36} + 61 q^{37} - 28 q^{38} + 114 q^{39} + 32 q^{40} - q^{41} + 16 q^{42} + 105 q^{43} + 54 q^{44} + 29 q^{45} + 104 q^{46} + 33 q^{47} + 16 q^{48} + 132 q^{49} - 14 q^{50} + 53 q^{51} - 11 q^{52} + 48 q^{53} + 11 q^{54} + 118 q^{55} + 30 q^{56} + 93 q^{57} + 87 q^{58} + 12 q^{59} + 41 q^{60} + 54 q^{61} - 28 q^{62} + 178 q^{63} + 376 q^{64} + 22 q^{65} + 6 q^{66} + 123 q^{67} - 47 q^{68} + 58 q^{69} + 22 q^{70} + 108 q^{71} + 97 q^{72} + q^{73} - 10 q^{74} + 23 q^{75} + 71 q^{76} + 32 q^{77} + 5 q^{78} + 204 q^{79} - 10 q^{80} + 296 q^{81} + 80 q^{82} - 10 q^{83} + 30 q^{84} + 94 q^{85} + 48 q^{86} + 4 q^{87} + 155 q^{88} + q^{89} - 66 q^{90} + 16 q^{91} + 49 q^{92} + 90 q^{93} + 79 q^{94} + 100 q^{95} + q^{96} + 18 q^{97} + 8 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9 + 22 * q^10 + 32 * q^11 + 30 * q^12 + 16 * q^13 + 8 * q^14 + 59 * q^15 + 254 * q^16 + 11 * q^17 + 33 * q^18 + 40 * q^19 + 4 * q^20 + 10 * q^21 + 66 * q^22 + 62 * q^23 + 36 * q^24 + 235 * q^25 + 25 * q^26 + 37 * q^27 + 174 * q^28 + 28 * q^29 + 45 * q^30 + 121 * q^31 + 53 * q^32 - 13 * q^33 + 44 * q^34 + 11 * q^35 + 274 * q^36 + 61 * q^37 - 28 * q^38 + 114 * q^39 + 32 * q^40 - q^41 + 16 * q^42 + 105 * q^43 + 54 * q^44 + 29 * q^45 + 104 * q^46 + 33 * q^47 + 16 * q^48 + 132 * q^49 - 14 * q^50 + 53 * q^51 - 11 * q^52 + 48 * q^53 + 11 * q^54 + 118 * q^55 + 30 * q^56 + 93 * q^57 + 87 * q^58 + 12 * q^59 + 41 * q^60 + 54 * q^61 - 28 * q^62 + 178 * q^63 + 376 * q^64 + 22 * q^65 + 6 * q^66 + 123 * q^67 - 47 * q^68 + 58 * q^69 + 22 * q^70 + 108 * q^71 + 97 * q^72 + q^73 - 10 * q^74 + 23 * q^75 + 71 * q^76 + 32 * q^77 + 5 * q^78 + 204 * q^79 - 10 * q^80 + 296 * q^81 + 80 * q^82 - 10 * q^83 + 30 * q^84 + 94 * q^85 + 48 * q^86 + 4 * q^87 + 155 * q^88 + q^89 - 66 * q^90 + 16 * q^91 + 49 * q^92 + 90 * q^93 + 79 * q^94 + 100 * q^95 + q^96 + 18 * q^97 + 8 * q^98 + 96 * q^99

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