LMFDB - Embedded newform 6035.2.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6035,2,Mod(1,6035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6035, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6035 = 5 \cdot 17 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6035.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:	$48.1897176198$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.37331 q^{2} +2.40096 q^{3} +3.63259 q^{4} +1.00000 q^{5} -5.69821 q^{6} -2.59145 q^{7} -3.87465 q^{8} +2.76459 q^{9} +O(q^{10})$	\(q-2.37331 q^{2} +2.40096 q^{3} +3.63259 q^{4} +1.00000 q^{5} -5.69821 q^{6} -2.59145 q^{7} -3.87465 q^{8} +2.76459 q^{9} -2.37331 q^{10} +0.912080 q^{11} +8.72170 q^{12} +0.0203183 q^{13} +6.15032 q^{14} +2.40096 q^{15} +1.93055 q^{16} +1.00000 q^{17} -6.56123 q^{18} -1.71796 q^{19} +3.63259 q^{20} -6.22197 q^{21} -2.16465 q^{22} +1.81874 q^{23} -9.30286 q^{24} +1.00000 q^{25} -0.0482216 q^{26} -0.565208 q^{27} -9.41370 q^{28} -3.63731 q^{29} -5.69821 q^{30} +3.56213 q^{31} +3.16751 q^{32} +2.18986 q^{33} -2.37331 q^{34} -2.59145 q^{35} +10.0426 q^{36} -4.84913 q^{37} +4.07725 q^{38} +0.0487833 q^{39} -3.87465 q^{40} -7.46884 q^{41} +14.7666 q^{42} +10.3494 q^{43} +3.31322 q^{44} +2.76459 q^{45} -4.31643 q^{46} -12.8641 q^{47} +4.63517 q^{48} -0.284371 q^{49} -2.37331 q^{50} +2.40096 q^{51} +0.0738081 q^{52} -8.35634 q^{53} +1.34141 q^{54} +0.912080 q^{55} +10.0410 q^{56} -4.12475 q^{57} +8.63246 q^{58} -4.12416 q^{59} +8.72170 q^{60} -4.85394 q^{61} -8.45403 q^{62} -7.16431 q^{63} -11.3786 q^{64} +0.0203183 q^{65} -5.19722 q^{66} -8.85804 q^{67} +3.63259 q^{68} +4.36671 q^{69} +6.15032 q^{70} -1.00000 q^{71} -10.7118 q^{72} +3.13468 q^{73} +11.5085 q^{74} +2.40096 q^{75} -6.24065 q^{76} -2.36361 q^{77} -0.115778 q^{78} -7.65789 q^{79} +1.93055 q^{80} -9.65081 q^{81} +17.7259 q^{82} +12.5752 q^{83} -22.6019 q^{84} +1.00000 q^{85} -24.5624 q^{86} -8.73302 q^{87} -3.53399 q^{88} +1.60745 q^{89} -6.56123 q^{90} -0.0526539 q^{91} +6.60674 q^{92} +8.55252 q^{93} +30.5305 q^{94} -1.71796 q^{95} +7.60504 q^{96} +15.1137 q^{97} +0.674899 q^{98} +2.52153 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9}+O(q^{10}) $ 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9} - 3 q^{10} - 20 q^{11} - 8 q^{12} - 29 q^{13} - 12 q^{14} - 8 q^{15} + q^{16} + 36 q^{17} - 8 q^{18} - 19 q^{19} + 23 q^{20} - 19 q^{21} - 10 q^{22} - 10 q^{23} - 23 q^{24} + 36 q^{25} - 32 q^{26} - 23 q^{27} - 20 q^{28} - 52 q^{29} - 10 q^{30} - 15 q^{31} - 16 q^{32} - 19 q^{33} - 3 q^{34} - 7 q^{35} + 9 q^{36} - 52 q^{37} + 7 q^{38} - 10 q^{39} - 9 q^{40} - 51 q^{41} - 2 q^{42} - 13 q^{43} - 27 q^{44} + 10 q^{45} + 12 q^{46} - 24 q^{47} + 12 q^{48} - 15 q^{49} - 3 q^{50} - 8 q^{51} - 49 q^{52} - 13 q^{53} - 48 q^{54} - 20 q^{55} - 12 q^{56} - 20 q^{57} - 20 q^{58} - 14 q^{59} - 8 q^{60} - 75 q^{61} - 7 q^{62} + 16 q^{63} - 41 q^{64} - 29 q^{65} - q^{66} - 5 q^{67} + 23 q^{68} - 37 q^{69} - 12 q^{70} - 36 q^{71} - 23 q^{72} - 21 q^{73} + q^{74} - 8 q^{75} - 40 q^{76} - 31 q^{77} + 84 q^{78} - 49 q^{79} + q^{80} - 56 q^{81} - 51 q^{82} + 6 q^{83} + 10 q^{84} + 36 q^{85} - 41 q^{86} - 4 q^{87} - 21 q^{88} - 78 q^{89} - 8 q^{90} - 25 q^{91} - 24 q^{92} - 36 q^{93} + 6 q^{94} - 19 q^{95} - 71 q^{96} - 48 q^{97} + 51 q^{98} - 17 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9 - 3 * q^10 - 20 * q^11 - 8 * q^12 - 29 * q^13 - 12 * q^14 - 8 * q^15 + q^16 + 36 * q^17 - 8 * q^18 - 19 * q^19 + 23 * q^20 - 19 * q^21 - 10 * q^22 - 10 * q^23 - 23 * q^24 + 36 * q^25 - 32 * q^26 - 23 * q^27 - 20 * q^28 - 52 * q^29 - 10 * q^30 - 15 * q^31 - 16 * q^32 - 19 * q^33 - 3 * q^34 - 7 * q^35 + 9 * q^36 - 52 * q^37 + 7 * q^38 - 10 * q^39 - 9 * q^40 - 51 * q^41 - 2 * q^42 - 13 * q^43 - 27 * q^44 + 10 * q^45 + 12 * q^46 - 24 * q^47 + 12 * q^48 - 15 * q^49 - 3 * q^50 - 8 * q^51 - 49 * q^52 - 13 * q^53 - 48 * q^54 - 20 * q^55 - 12 * q^56 - 20 * q^57 - 20 * q^58 - 14 * q^59 - 8 * q^60 - 75 * q^61 - 7 * q^62 + 16 * q^63 - 41 * q^64 - 29 * q^65 - q^66 - 5 * q^67 + 23 * q^68 - 37 * q^69 - 12 * q^70 - 36 * q^71 - 23 * q^72 - 21 * q^73 + q^74 - 8 * q^75 - 40 * q^76 - 31 * q^77 + 84 * q^78 - 49 * q^79 + q^80 - 56 * q^81 - 51 * q^82 + 6 * q^83 + 10 * q^84 + 36 * q^85 - 41 * q^86 - 4 * q^87 - 21 * q^88 - 78 * q^89 - 8 * q^90 - 25 * q^91 - 24 * q^92 - 36 * q^93 + 6 * q^94 - 19 * q^95 - 71 * q^96 - 48 * q^97 + 51 * q^98 - 17 * 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 $

$2$	−2.37331	−1.67818	−0.839091	−	0.543991i	$-0.816913\pi$
$2$	−2.37331	−1.67818	−0.839091	+	0.543991i	$0.816913\pi$
$3$	2.40096	1.38619	0.693096	−	0.720845i	$-0.256246\pi$
$3$	2.40096	1.38619	0.693096	+	0.720845i	$0.256246\pi$
$4$	3.63259	1.81630
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−5.69821	−2.32628
$7$	−2.59145	−0.979477	−0.489739	−	0.871869i	$-0.662908\pi$
$7$	−2.59145	−0.979477	−0.489739	+	0.871869i	$0.662908\pi$
$8$	−3.87465	−1.36990
$9$	2.76459	0.921530
$10$	−2.37331	−0.750506
$11$	0.912080	0.275002	0.137501	−	0.990502i	$-0.456093\pi$
$11$	0.912080	0.275002	0.137501	+	0.990502i	$0.456093\pi$
$12$	8.72170	2.51774
$13$	0.0203183	0.00563528	0.00281764	−	0.999996i	$-0.499103\pi$
$13$	0.0203183	0.00563528	0.00281764	+	0.999996i	$0.499103\pi$
$14$	6.15032	1.64374
$15$	2.40096	0.619924
$16$	1.93055	0.482638
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−6.56123	−1.54650
$19$	−1.71796	−0.394127	−0.197063	−	0.980391i	$-0.563141\pi$
$19$	−1.71796	−0.394127	−0.197063	+	0.980391i	$0.563141\pi$
$20$	3.63259	0.812273
$21$	−6.22197	−1.35774
$22$	−2.16465	−0.461504
$23$	1.81874	0.379233	0.189617	−	0.981858i	$-0.439275\pi$
$23$	1.81874	0.379233	0.189617	+	0.981858i	$0.439275\pi$
$24$	−9.30286	−1.89894
$25$	1.00000	0.200000
$26$	−0.0482216	−0.00945703
$27$	−0.565208	−0.108774
$28$	−9.41370	−1.77902
$29$	−3.63731	−0.675432	−0.337716	−	0.941248i	$-0.609654\pi$
$29$	−3.63731	−0.675432	−0.337716	+	0.941248i	$0.609654\pi$
$30$	−5.69821	−1.04035
$31$	3.56213	0.639777	0.319889	−	0.947455i	$-0.396354\pi$
$31$	3.56213	0.639777	0.319889	+	0.947455i	$0.396354\pi$
$32$	3.16751	0.559941
$33$	2.18986	0.381206
$34$	−2.37331	−0.407019
$35$	−2.59145	−0.438036
$36$	10.0426	1.67377
$37$	−4.84913	−0.797192	−0.398596	−	0.917127i	$-0.630502\pi$
$37$	−4.84913	−0.797192	−0.398596	+	0.917127i	$0.630502\pi$
$38$	4.07725	0.661417
$39$	0.0487833	0.00781158
$40$	−3.87465	−0.612636
$41$	−7.46884	−1.16644	−0.583218	−	0.812315i	$-0.698207\pi$
$41$	−7.46884	−1.16644	−0.583218	+	0.812315i	$0.698207\pi$
$42$	14.7666	2.27854
$43$	10.3494	1.57827	0.789136	−	0.614218i	$-0.210529\pi$
$43$	10.3494	1.57827	0.789136	+	0.614218i	$0.210529\pi$
$44$	3.31322	0.499486
$45$	2.76459	0.412121
$46$	−4.31643	−0.636423
$47$	−12.8641	−1.87643	−0.938213	−	0.346058i	$-0.887520\pi$
$47$	−12.8641	−1.87643	−0.938213	+	0.346058i	$0.887520\pi$
$48$	4.63517	0.669029
$49$	−0.284371	−0.0406244
$50$	−2.37331	−0.335637
$51$	2.40096	0.336201
$52$	0.0738081	0.0102353
$53$	−8.35634	−1.14783	−0.573916	−	0.818914i	$-0.694576\pi$
$53$	−8.35634	−1.14783	−0.573916	+	0.818914i	$0.694576\pi$
$54$	1.34141	0.182543
$55$	0.912080	0.122985
$56$	10.0410	1.34178
$57$	−4.12475	−0.546336
$58$	8.63246	1.13350
$59$	−4.12416	−0.536919	−0.268460	−	0.963291i	$-0.586515\pi$
$59$	−4.12416	−0.536919	−0.268460	+	0.963291i	$0.586515\pi$
$60$	8.72170	1.12597
$61$	−4.85394	−0.621484	−0.310742	−	0.950494i	$-0.600577\pi$
$61$	−4.85394	−0.621484	−0.310742	+	0.950494i	$0.600577\pi$
$62$	−8.45403	−1.07366
$63$	−7.16431	−0.902618
$64$	−11.3786	−1.42232
$65$	0.0203183	0.00252017
$66$	−5.19722	−0.639734
$67$	−8.85804	−1.08218	−0.541091	−	0.840964i	$-0.681988\pi$
$67$	−8.85804	−1.08218	−0.541091	+	0.840964i	$0.681988\pi$
$68$	3.63259	0.440517
$69$	4.36671	0.525690
$70$	6.15032	0.735104
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	−10.7118	−1.26240
$73$	3.13468	0.366886	0.183443	−	0.983030i	$-0.441276\pi$
$73$	3.13468	0.366886	0.183443	+	0.983030i	$0.441276\pi$
$74$	11.5085	1.33783
$75$	2.40096	0.277239
$76$	−6.24065	−0.715852
$77$	−2.36361	−0.269359
$78$	−0.115778	−0.0131093
$79$	−7.65789	−0.861579	−0.430790	−	0.902452i	$-0.641765\pi$
$79$	−7.65789	−0.861579	−0.430790	+	0.902452i	$0.641765\pi$
$80$	1.93055	0.215842
$81$	−9.65081	−1.07231
$82$	17.7259	1.95749
$83$	12.5752	1.38030	0.690152	−	0.723664i	$-0.257544\pi$
$83$	12.5752	1.38030	0.690152	+	0.723664i	$0.257544\pi$
$84$	−22.6019	−2.46607
$85$	1.00000	0.108465
$86$	−24.5624	−2.64863
$87$	−8.73302	−0.936278
$88$	−3.53399	−0.376725
$89$	1.60745	0.170389	0.0851947	−	0.996364i	$-0.472849\pi$
$89$	1.60745	0.170389	0.0851947	+	0.996364i	$0.472849\pi$
$90$	−6.56123	−0.691614
$91$	−0.0526539	−0.00551963
$92$	6.60674	0.688800
$93$	8.55252	0.886855
$94$	30.5305	3.14899
$95$	−1.71796	−0.176259
$96$	7.60504	0.776186
$97$	15.1137	1.53457	0.767283	−	0.641309i	$-0.221608\pi$
$97$	15.1137	1.53457	0.767283	+	0.641309i	$0.221608\pi$
$98$	0.674899	0.0681751
$99$	2.52153	0.253423
$100$	3.63259	0.363259
$101$	−1.35661	−0.134988	−0.0674938	−	0.997720i	$-0.521500\pi$
$101$	−1.35661	−0.134988	−0.0674938	+	0.997720i	$0.521500\pi$
$102$	−5.69821	−0.564207
$103$	−4.67905	−0.461040	−0.230520	−	0.973068i	$-0.574043\pi$
$103$	−4.67905	−0.461040	−0.230520	+	0.973068i	$0.574043\pi$
$104$	−0.0787262	−0.00771974
$105$	−6.22197	−0.607202
$106$	19.8322	1.92627
$107$	18.3694	1.77584	0.887918	−	0.460001i	$-0.152151\pi$
$107$	18.3694	1.77584	0.887918	+	0.460001i	$0.152151\pi$
$108$	−2.05317	−0.197567
$109$	12.1620	1.16491	0.582456	−	0.812862i	$-0.302092\pi$
$109$	12.1620	1.16491	0.582456	+	0.812862i	$0.302092\pi$
$110$	−2.16465	−0.206391
$111$	−11.6425	−1.10506
$112$	−5.00293	−0.472733
$113$	−15.3623	−1.44517	−0.722583	−	0.691284i	$-0.757045\pi$
$113$	−15.3623	−1.44517	−0.722583	+	0.691284i	$0.757045\pi$
$114$	9.78930	0.916852
$115$	1.81874	0.169598
$116$	−13.2129	−1.22678
$117$	0.0561717	0.00519308
$118$	9.78790	0.901049
$119$	−2.59145	−0.237558
$120$	−9.30286	−0.849231
$121$	−10.1681	−0.924374
$122$	11.5199	1.04296
$123$	−17.9324	−1.61691
$124$	12.9398	1.16203
$125$	1.00000	0.0894427
$126$	17.0031	1.51476
$127$	−10.5612	−0.937158	−0.468579	−	0.883421i	$-0.655234\pi$
$127$	−10.5612	−0.937158	−0.468579	+	0.883421i	$0.655234\pi$
$128$	20.6698	1.82697
$129$	24.8485	2.18779
$130$	−0.0482216	−0.00422931
$131$	−10.4468	−0.912742	−0.456371	−	0.889790i	$-0.650851\pi$
$131$	−10.4468	−0.912742	−0.456371	+	0.889790i	$0.650851\pi$
$132$	7.95489	0.692384
$133$	4.45201	0.386038
$134$	21.0229	1.81610
$135$	−0.565208	−0.0486454
$136$	−3.87465	−0.332248
$137$	18.2099	1.55578	0.777890	−	0.628400i	$-0.216290\pi$
$137$	18.2099	1.55578	0.777890	+	0.628400i	$0.216290\pi$
$138$	−10.3636	−0.882205
$139$	12.1818	1.03324	0.516621	−	0.856214i	$-0.327189\pi$
$139$	12.1818	1.03324	0.516621	+	0.856214i	$0.327189\pi$
$140$	−9.41370	−0.795603
$141$	−30.8862	−2.60109
$142$	2.37331	0.199164
$143$	0.0185319	0.00154972
$144$	5.33718	0.444765
$145$	−3.63731	−0.302062
$146$	−7.43955	−0.615702
$147$	−0.682761	−0.0563132
$148$	−17.6149	−1.44794
$149$	12.6475	1.03613	0.518063	−	0.855342i	$-0.326653\pi$
$149$	12.6475	1.03613	0.518063	+	0.855342i	$0.326653\pi$
$150$	−5.69821	−0.465257
$151$	−12.4058	−1.00957	−0.504786	−	0.863244i	$-0.668429\pi$
$151$	−12.4058	−1.00957	−0.504786	+	0.863244i	$0.668429\pi$
$152$	6.65649	0.539913
$153$	2.76459	0.223504
$154$	5.60958	0.452033
$155$	3.56213	0.286117
$156$	0.177210	0.0141882
$157$	−18.5732	−1.48231	−0.741153	−	0.671336i	$-0.765721\pi$
$157$	−18.5732	−1.48231	−0.741153	+	0.671336i	$0.765721\pi$
$158$	18.1745	1.44589
$159$	−20.0632	−1.59112
$160$	3.16751	0.250413
$161$	−4.71318	−0.371450
$162$	22.9044	1.79954
$163$	−0.726868	−0.0569327	−0.0284663	−	0.999595i	$-0.509062\pi$
$163$	−0.726868	−0.0569327	−0.0284663	+	0.999595i	$0.509062\pi$
$164$	−27.1313	−2.11860
$165$	2.18986	0.170481
$166$	−29.8448	−2.31640
$167$	−24.9942	−1.93411	−0.967053	−	0.254575i	$-0.918064\pi$
$167$	−24.9942	−1.93411	−0.967053	+	0.254575i	$0.918064\pi$
$168$	24.1079	1.85997
$169$	−12.9996	−0.999968
$170$	−2.37331	−0.182024
$171$	−4.74946	−0.363200
$172$	37.5953	2.86661
$173$	19.3651	1.47230	0.736150	−	0.676818i	$-0.236642\pi$
$173$	19.3651	1.47230	0.736150	+	0.676818i	$0.236642\pi$
$174$	20.7262	1.57125
$175$	−2.59145	−0.195895
$176$	1.76082	0.132727
$177$	−9.90192	−0.744274
$178$	−3.81498	−0.285945
$179$	1.36200	0.101801	0.0509004	−	0.998704i	$-0.483791\pi$
$179$	1.36200	0.101801	0.0509004	+	0.998704i	$0.483791\pi$
$180$	10.0426	0.748534
$181$	13.2571	0.985396	0.492698	−	0.870200i	$-0.336011\pi$
$181$	13.2571	0.985396	0.492698	+	0.870200i	$0.336011\pi$
$182$	0.124964	0.00926294
$183$	−11.6541	−0.861496
$184$	−7.04698	−0.519510
$185$	−4.84913	−0.356515
$186$	−20.2978	−1.48830
$187$	0.912080	0.0666979
$188$	−46.7302	−3.40815
$189$	1.46471	0.106542
$190$	4.07725	0.295795
$191$	−22.5578	−1.63222	−0.816112	−	0.577894i	$-0.803875\pi$
$191$	−22.5578	−1.63222	−0.816112	+	0.577894i	$0.803875\pi$
$192$	−27.3194	−1.97161
$193$	−16.0068	−1.15220	−0.576099	−	0.817380i	$-0.695426\pi$
$193$	−16.0068	−1.15220	−0.576099	+	0.817380i	$0.695426\pi$
$194$	−35.8695	−2.57528
$195$	0.0487833	0.00349345
$196$	−1.03300	−0.0737859
$197$	17.3496	1.23611	0.618054	−	0.786136i	$-0.287921\pi$
$197$	17.3496	1.23611	0.618054	+	0.786136i	$0.287921\pi$
$198$	−5.98436	−0.425290
$199$	−27.0498	−1.91751	−0.958754	−	0.284238i	$-0.908259\pi$
$199$	−27.0498	−1.91751	−0.958754	+	0.284238i	$0.908259\pi$
$200$	−3.87465	−0.273979
$201$	−21.2678	−1.50011
$202$	3.21965	0.226534
$203$	9.42592	0.661570
$204$	8.72170	0.610641
$205$	−7.46884	−0.521646
$206$	11.1048	0.773710
$207$	5.02807	0.349475
$208$	0.0392255	0.00271980
$209$	−1.56692	−0.108386
$210$	14.7666	1.01900
$211$	−11.6667	−0.803168	−0.401584	−	0.915822i	$-0.631540\pi$
$211$	−11.6667	−0.803168	−0.401584	+	0.915822i	$0.631540\pi$
$212$	−30.3552	−2.08480
$213$	−2.40096	−0.164511
$214$	−43.5962	−2.98018
$215$	10.3494	0.705825
$216$	2.18998	0.149010
$217$	−9.23109	−0.626647
$218$	−28.8643	−1.95493
$219$	7.52622	0.508575
$220$	3.31322	0.223377
$221$	0.0203183	0.00136676
$222$	27.6313	1.85449
$223$	14.4394	0.966936	0.483468	−	0.875362i	$-0.339377\pi$
$223$	14.4394	0.966936	0.483468	+	0.875362i	$0.339377\pi$
$224$	−8.20844	−0.548450
$225$	2.76459	0.184306
$226$	36.4595	2.42525
$227$	16.2703	1.07990	0.539948	−	0.841698i	$-0.318444\pi$
$227$	16.2703	1.07990	0.539948	+	0.841698i	$0.318444\pi$
$228$	−14.9835	−0.992308
$229$	6.46703	0.427353	0.213677	−	0.976904i	$-0.431456\pi$
$229$	6.46703	0.427353	0.213677	+	0.976904i	$0.431456\pi$
$230$	−4.31643	−0.284617
$231$	−5.67493	−0.373383
$232$	14.0933	0.925271
$233$	−13.4033	−0.878076	−0.439038	−	0.898468i	$-0.644681\pi$
$233$	−13.4033	−0.878076	−0.439038	+	0.898468i	$0.644681\pi$
$234$	−0.133313	−0.00871493
$235$	−12.8641	−0.839163
$236$	−14.9814	−0.975205
$237$	−18.3862	−1.19432
$238$	6.15032	0.398666
$239$	−0.926394	−0.0599234	−0.0299617	−	0.999551i	$-0.509539\pi$
$239$	−0.926394	−0.0599234	−0.0299617	+	0.999551i	$0.509539\pi$
$240$	4.63517	0.299199
$241$	1.97714	0.127359	0.0636795	−	0.997970i	$-0.479716\pi$
$241$	1.97714	0.127359	0.0636795	+	0.997970i	$0.479716\pi$
$242$	24.1321	1.55127
$243$	−21.4755	−1.37766
$244$	−17.6324	−1.12880
$245$	−0.284371	−0.0181678
$246$	42.5590	2.71346
$247$	−0.0349060	−0.00222102
$248$	−13.8020	−0.876428
$249$	30.1924	1.91337
$250$	−2.37331	−0.150101
$251$	−2.17266	−0.137137	−0.0685685	−	0.997646i	$-0.521843\pi$
$251$	−2.17266	−0.137137	−0.0685685	+	0.997646i	$0.521843\pi$
$252$	−26.0250	−1.63942
$253$	1.65884	0.104290
$254$	25.0651	1.57272
$255$	2.40096	0.150354
$256$	−26.2988	−1.64367
$257$	−1.64986	−0.102916	−0.0514578	−	0.998675i	$-0.516387\pi$
$257$	−1.64986	−0.102916	−0.0514578	+	0.998675i	$0.516387\pi$
$258$	−58.9732	−3.67151
$259$	12.5663	0.780831
$260$	0.0738081	0.00457738
$261$	−10.0557	−0.622431
$262$	24.7935	1.53175
$263$	−22.7717	−1.40416	−0.702082	−	0.712096i	$-0.747746\pi$
$263$	−22.7717	−1.40416	−0.702082	+	0.712096i	$0.747746\pi$
$264$	−8.48495	−0.522213
$265$	−8.35634	−0.513326
$266$	−10.5660	−0.647843
$267$	3.85942	0.236193
$268$	−32.1777	−1.96556
$269$	−11.0528	−0.673898	−0.336949	−	0.941523i	$-0.609395\pi$
$269$	−11.0528	−0.673898	−0.336949	+	0.941523i	$0.609395\pi$
$270$	1.34141	0.0816358
$271$	7.18262	0.436313	0.218157	−	0.975914i	$-0.429996\pi$
$271$	7.18262	0.436313	0.218157	+	0.975914i	$0.429996\pi$
$272$	1.93055	0.117057
$273$	−0.126420	−0.00765127
$274$	−43.2178	−2.61088
$275$	0.912080	0.0550005
$276$	15.8625	0.954810
$277$	−28.1042	−1.68862	−0.844308	−	0.535858i	$-0.819988\pi$
$277$	−28.1042	−1.68862	−0.844308	+	0.535858i	$0.819988\pi$
$278$	−28.9111	−1.73397
$279$	9.84783	0.589574
$280$	10.0410	0.600063
$281$	−24.2941	−1.44927	−0.724633	−	0.689135i	$-0.757991\pi$
$281$	−24.2941	−1.44927	−0.724633	+	0.689135i	$0.757991\pi$
$282$	73.3025	4.36510
$283$	4.82597	0.286874	0.143437	−	0.989659i	$-0.454185\pi$
$283$	4.82597	0.286874	0.143437	+	0.989659i	$0.454185\pi$
$284$	−3.63259	−0.215555
$285$	−4.12475	−0.244329
$286$	−0.0439819	−0.00260071
$287$	19.3552	1.14250
$288$	8.75686	0.516003
$289$	1.00000	0.0588235
$290$	8.63246	0.506916
$291$	36.2874	2.12720
$292$	11.3870	0.666374
$293$	30.0855	1.75761	0.878806	−	0.477178i	$-0.158340\pi$
$293$	30.0855	1.75761	0.878806	+	0.477178i	$0.158340\pi$
$294$	1.62040	0.0945038
$295$	−4.12416	−0.240118
$296$	18.7887	1.09207
$297$	−0.515515	−0.0299132
$298$	−30.0165	−1.73881
$299$	0.0369537	0.00213709
$300$	8.72170	0.503548
$301$	−26.8200	−1.54588
$302$	29.4429	1.69425
$303$	−3.25716	−0.187119
$304$	−3.31661	−0.190221
$305$	−4.85394	−0.277936
$306$	−6.56123	−0.375080
$307$	−18.6715	−1.06564	−0.532821	−	0.846228i	$-0.678868\pi$
$307$	−18.6715	−1.06564	−0.532821	+	0.846228i	$0.678868\pi$
$308$	−8.58604	−0.489235
$309$	−11.2342	−0.639091
$310$	−8.45403	−0.480157
$311$	−8.11584	−0.460207	−0.230104	−	0.973166i	$-0.573906\pi$
$311$	−8.11584	−0.460207	−0.230104	+	0.973166i	$0.573906\pi$
$312$	−0.189018	−0.0107010
$313$	21.2813	1.20289	0.601446	−	0.798913i	$-0.294591\pi$
$313$	21.2813	1.20289	0.601446	+	0.798913i	$0.294591\pi$
$314$	44.0800	2.48758
$315$	−7.16431	−0.403663
$316$	−27.8180	−1.56488
$317$	6.28005	0.352723	0.176361	−	0.984325i	$-0.443567\pi$
$317$	6.28005	0.352723	0.176361	+	0.984325i	$0.443567\pi$
$318$	47.6162	2.67018
$319$	−3.31752	−0.185745
$320$	−11.3786	−0.636081
$321$	44.1041	2.46165
$322$	11.1858	0.623362
$323$	−1.71796	−0.0955898
$324$	−35.0575	−1.94764
$325$	0.0203183	0.00112706
$326$	1.72508	0.0955434
$327$	29.2005	1.61479
$328$	28.9391	1.59790
$329$	33.3368	1.83792
$330$	−5.19722	−0.286098
$331$	−24.8544	−1.36612	−0.683061	−	0.730362i	$-0.739351\pi$
$331$	−24.8544	−1.36612	−0.683061	+	0.730362i	$0.739351\pi$
$332$	45.6805	2.50704
$333$	−13.4059	−0.734636
$334$	59.3189	3.24578
$335$	−8.85804	−0.483966
$336$	−12.0118	−0.655299
$337$	0.792548	0.0431728	0.0215864	−	0.999767i	$-0.493128\pi$
$337$	0.792548	0.0431728	0.0215864	+	0.999767i	$0.493128\pi$
$338$	30.8520	1.67813
$339$	−36.8843	−2.00328
$340$	3.63259	0.197005
$341$	3.24895	0.175940
$342$	11.2719	0.609516
$343$	18.8771	1.01927
$344$	−40.1004	−2.16207
$345$	4.36671	0.235096
$346$	−45.9593	−2.47079
$347$	30.0530	1.61333	0.806666	−	0.591008i	$-0.201270\pi$
$347$	30.0530	1.61333	0.806666	+	0.591008i	$0.201270\pi$
$348$	−31.7235	−1.70056
$349$	27.6810	1.48173	0.740866	−	0.671653i	$-0.234415\pi$
$349$	27.6810	1.48173	0.740866	+	0.671653i	$0.234415\pi$
$350$	6.15032	0.328748
$351$	−0.0114841	−0.000612974 0
$352$	2.88902	0.153985
$353$	−3.94428	−0.209933	−0.104967	−	0.994476i	$-0.533474\pi$
$353$	−3.94428	−0.209933	−0.104967	+	0.994476i	$0.533474\pi$
$354$	23.5003	1.24903
$355$	−1.00000	−0.0530745
$356$	5.83921	0.309478
$357$	−6.22197	−0.329301
$358$	−3.23245	−0.170840
$359$	7.14325	0.377007	0.188503	−	0.982073i	$-0.439636\pi$
$359$	7.14325	0.377007	0.188503	+	0.982073i	$0.439636\pi$
$360$	−10.7118	−0.564562
$361$	−16.0486	−0.844664
$362$	−31.4633	−1.65367
$363$	−24.4132	−1.28136
$364$	−0.191270	−0.0100253
$365$	3.13468	0.164076
$366$	27.6588	1.44575
$367$	−13.1754	−0.687748	−0.343874	−	0.939016i	$-0.611739\pi$
$367$	−13.1754	−0.687748	−0.343874	+	0.939016i	$0.611739\pi$
$368$	3.51117	0.183032
$369$	−20.6483	−1.07491
$370$	11.5085	0.598297
$371$	21.6551	1.12428
$372$	31.0678	1.61079
$373$	−21.5240	−1.11447	−0.557235	−	0.830355i	$-0.688138\pi$
$373$	−21.5240	−1.11447	−0.557235	+	0.830355i	$0.688138\pi$
$374$	−2.16465	−0.111931
$375$	2.40096	0.123985
$376$	49.8440	2.57051
$377$	−0.0739039	−0.00380624
$378$	−3.47621	−0.178797
$379$	−27.0927	−1.39166	−0.695829	−	0.718207i	$-0.744963\pi$
$379$	−27.0927	−1.39166	−0.695829	+	0.718207i	$0.744963\pi$
$380$	−6.24065	−0.320139
$381$	−25.3571	−1.29908
$382$	53.5366	2.73917
$383$	36.8608	1.88350	0.941749	−	0.336317i	$-0.109181\pi$
$383$	36.8608	1.88350	0.941749	+	0.336317i	$0.109181\pi$
$384$	49.6274	2.53254
$385$	−2.36361	−0.120461
$386$	37.9892	1.93360
$387$	28.6119	1.45443
$388$	54.9020	2.78723
$389$	−16.8046	−0.852026	−0.426013	−	0.904717i	$-0.640082\pi$
$389$	−16.8046	−0.852026	−0.426013	+	0.904717i	$0.640082\pi$
$390$	−0.115778	−0.00586264
$391$	1.81874	0.0919776
$392$	1.10184	0.0556511
$393$	−25.0823	−1.26524
$394$	−41.1760	−2.07442
$395$	−7.65789	−0.385310
$396$	9.15969	0.460291
$397$	−22.2138	−1.11488	−0.557439	−	0.830218i	$-0.688216\pi$
$397$	−22.2138	−1.11488	−0.557439	+	0.830218i	$0.688216\pi$
$398$	64.1975	3.21793
$399$	10.6891	0.535124
$400$	1.93055	0.0965275
$401$	15.0743	0.752773	0.376386	−	0.926463i	$-0.377167\pi$
$401$	15.0743	0.752773	0.376386	+	0.926463i	$0.377167\pi$
$402$	50.4750	2.51746
$403$	0.0723764	0.00360532
$404$	−4.92801	−0.245178
$405$	−9.65081	−0.479553
$406$	−22.3706	−1.11024
$407$	−4.42279	−0.219230
$408$	−9.30286	−0.460560
$409$	−5.19102	−0.256680	−0.128340	−	0.991730i	$-0.540965\pi$
$409$	−5.19102	−0.256680	−0.128340	+	0.991730i	$0.540965\pi$
$410$	17.7259	0.875418
$411$	43.7213	2.15661
$412$	−16.9971	−0.837386
$413$	10.6876	0.525900
$414$	−11.9332	−0.586483
$415$	12.5752	0.617291
$416$	0.0643583	0.00315542
$417$	29.2479	1.43227
$418$	3.71878	0.181891
$419$	25.4563	1.24362	0.621810	−	0.783168i	$-0.286398\pi$
$419$	25.4563	1.24362	0.621810	+	0.783168i	$0.286398\pi$
$420$	−22.6019	−1.10286
$421$	−29.4834	−1.43693	−0.718465	−	0.695563i	$-0.755155\pi$
$421$	−29.4834	−1.43693	−0.718465	+	0.695563i	$0.755155\pi$
$422$	27.6886	1.34786
$423$	−35.5640	−1.72918
$424$	32.3779	1.57241
$425$	1.00000	0.0485071
$426$	5.69821	0.276079
$427$	12.5788	0.608729
$428$	66.7285	3.22545
$429$	0.0444943	0.00214820
$430$	−24.5624	−1.18450
$431$	27.9236	1.34503	0.672517	−	0.740082i	$-0.265213\pi$
$431$	27.9236	1.34503	0.672517	+	0.740082i	$0.265213\pi$
$432$	−1.09116	−0.0524986
$433$	−15.6172	−0.750514	−0.375257	−	0.926921i	$-0.622446\pi$
$433$	−15.6172	−0.750514	−0.375257	+	0.926921i	$0.622446\pi$
$434$	21.9082	1.05163
$435$	−8.73302	−0.418716
$436$	44.1797	2.11583
$437$	−3.12452	−0.149466
$438$	−17.8620	−0.853481
$439$	−0.909778	−0.0434213	−0.0217107	−	0.999764i	$-0.506911\pi$
$439$	−0.909778	−0.0434213	−0.0217107	+	0.999764i	$0.506911\pi$
$440$	−3.53399	−0.168476
$441$	−0.786168	−0.0374366
$442$	−0.0482216	−0.00229367
$443$	−2.18805	−0.103957	−0.0519787	−	0.998648i	$-0.516553\pi$
$443$	−2.18805	−0.103957	−0.0519787	+	0.998648i	$0.516553\pi$
$444$	−42.2926	−2.00712
$445$	1.60745	0.0762005
$446$	−34.2692	−1.62270
$447$	30.3662	1.43627
$448$	29.4870	1.39313
$449$	−11.0504	−0.521503	−0.260751	−	0.965406i	$-0.583970\pi$
$449$	−11.0504	−0.521503	−0.260751	+	0.965406i	$0.583970\pi$
$450$	−6.56123	−0.309299
$451$	−6.81218	−0.320773
$452$	−55.8051	−2.62485
$453$	−29.7859	−1.39946
$454$	−38.6144	−1.81226
$455$	−0.0526539	−0.00246845
$456$	15.9819	0.748423
$457$	13.9561	0.652840	0.326420	−	0.945225i	$-0.394158\pi$
$457$	13.9561	0.652840	0.326420	+	0.945225i	$0.394158\pi$
$458$	−15.3483	−0.717177
$459$	−0.565208	−0.0263817
$460$	6.60674	0.308041
$461$	25.2659	1.17675	0.588374	−	0.808589i	$-0.299768\pi$
$461$	25.2659	1.17675	0.588374	+	0.808589i	$0.299768\pi$
$462$	13.4684	0.626605
$463$	−29.5848	−1.37492	−0.687462	−	0.726221i	$-0.741275\pi$
$463$	−29.5848	−1.37492	−0.687462	+	0.726221i	$0.741275\pi$
$464$	−7.02201	−0.325989
$465$	8.55252	0.396613
$466$	31.8101	1.47357
$467$	3.44712	0.159514	0.0797569	−	0.996814i	$-0.474586\pi$
$467$	3.44712	0.159514	0.0797569	+	0.996814i	$0.474586\pi$
$468$	0.204049	0.00943217
$469$	22.9552	1.05997
$470$	30.5305	1.40827
$471$	−44.5935	−2.05476
$472$	15.9797	0.735524
$473$	9.43950	0.434029
$474$	43.6362	2.00428
$475$	−1.71796	−0.0788254
$476$	−9.41370	−0.431476
$477$	−23.1019	−1.05776
$478$	2.19862	0.100562
$479$	−42.0553	−1.92156	−0.960778	−	0.277318i	$-0.910554\pi$
$479$	−42.0553	−1.92156	−0.960778	+	0.277318i	$0.910554\pi$
$480$	7.60504	0.347121
$481$	−0.0985259	−0.00449240
$482$	−4.69237	−0.213732
$483$	−11.3161	−0.514902
$484$	−36.9366	−1.67894
$485$	15.1137	0.686279
$486$	50.9681	2.31196
$487$	18.6454	0.844902	0.422451	−	0.906386i	$-0.361170\pi$
$487$	18.6454	0.844902	0.422451	+	0.906386i	$0.361170\pi$
$488$	18.8073	0.851368
$489$	−1.74518	−0.0789196
$490$	0.674899	0.0304888
$491$	10.0312	0.452702	0.226351	−	0.974046i	$-0.427320\pi$
$491$	10.0312	0.452702	0.226351	+	0.974046i	$0.427320\pi$
$492$	−65.1410	−2.93678
$493$	−3.63731	−0.163816
$494$	0.0828427	0.00372727
$495$	2.52153	0.113334
$496$	6.87687	0.308781
$497$	2.59145	0.116243
$498$	−71.6559	−3.21098
$499$	−13.5082	−0.604711	−0.302356	−	0.953195i	$-0.597773\pi$
$499$	−13.5082	−0.604711	−0.302356	+	0.953195i	$0.597773\pi$
$500$	3.63259	0.162455
$501$	−60.0099	−2.68104
$502$	5.15639	0.230141
$503$	−32.1625	−1.43406	−0.717028	−	0.697044i	$-0.754498\pi$
$503$	−32.1625	−1.43406	−0.717028	+	0.697044i	$0.754498\pi$
$504$	27.7592	1.23649
$505$	−1.35661	−0.0603683
$506$	−3.93693	−0.175018
$507$	−31.2114	−1.38615
$508$	−38.3647	−1.70216
$509$	41.9611	1.85989	0.929946	−	0.367696i	$-0.119853\pi$
$509$	41.9611	1.85989	0.929946	+	0.367696i	$0.119853\pi$
$510$	−5.69821	−0.252321
$511$	−8.12337	−0.359357
$512$	21.0754	0.931412
$513$	0.971005	0.0428709
$514$	3.91563	0.172711
$515$	−4.67905	−0.206184
$516$	90.2645	3.97368
$517$	−11.7331	−0.516022
$518$	−29.8237	−1.31038
$519$	46.4947	2.04089
$520$	−0.0787262	−0.00345237
$521$	18.0801	0.792105	0.396052	−	0.918228i	$-0.370380\pi$
$521$	18.0801	0.792105	0.396052	+	0.918228i	$0.370380\pi$
$522$	23.8652	1.04455
$523$	−9.28440	−0.405978	−0.202989	−	0.979181i	$-0.565066\pi$
$523$	−9.28440	−0.405978	−0.202989	+	0.979181i	$0.565066\pi$
$524$	−37.9490	−1.65781
$525$	−6.22197	−0.271549
$526$	54.0443	2.35644
$527$	3.56213	0.155169
$528$	4.22764	0.183985
$529$	−19.6922	−0.856182
$530$	19.8322	0.861455
$531$	−11.4016	−0.494787
$532$	16.1724	0.701160
$533$	−0.151754	−0.00657320
$534$	−9.15959	−0.396374
$535$	18.3694	0.794178
$536$	34.3218	1.48248
$537$	3.27010	0.141115
$538$	26.2316	1.13092
$539$	−0.259369	−0.0111718
$540$	−2.05317	−0.0883544
$541$	0.107472	0.00462057	0.00231029	−	0.999997i	$-0.499265\pi$
$541$	0.107472	0.00462057	0.00231029	+	0.999997i	$0.499265\pi$
$542$	−17.0466	−0.732213
$543$	31.8298	1.36595
$544$	3.16751	0.135806
$545$	12.1620	0.520964
$546$	0.300033	0.0128402
$547$	10.8157	0.462447	0.231224	−	0.972901i	$-0.425727\pi$
$547$	10.8157	0.462447	0.231224	+	0.972901i	$0.425727\pi$
$548$	66.1493	2.82576
$549$	−13.4192	−0.572716
$550$	−2.16465	−0.0923009
$551$	6.24875	0.266206
$552$	−16.9195	−0.720141
$553$	19.8451	0.843897
$554$	66.6999	2.83381
$555$	−11.6425	−0.494198
$556$	44.2514	1.87668
$557$	−0.517959	−0.0219466	−0.0109733	−	0.999940i	$-0.503493\pi$
$557$	−0.517959	−0.0219466	−0.0109733	+	0.999940i	$0.503493\pi$
$558$	−23.3719	−0.989413
$559$	0.210283	0.00889400
$560$	−5.00293	−0.211412
$561$	2.18986	0.0924561
$562$	57.6575	2.43213
$563$	12.9902	0.547471	0.273735	−	0.961805i	$-0.411741\pi$
$563$	12.9902	0.547471	0.273735	+	0.961805i	$0.411741\pi$
$564$	−112.197	−4.72435
$565$	−15.3623	−0.646298
$566$	−11.4535	−0.481427
$567$	25.0096	1.05031
$568$	3.87465	0.162577
$569$	21.7177	0.910454	0.455227	−	0.890376i	$-0.349558\pi$
$569$	21.7177	0.910454	0.455227	+	0.890376i	$0.349558\pi$
$570$	9.78930	0.410028
$571$	28.2885	1.18383	0.591917	−	0.805999i	$-0.298371\pi$
$571$	28.2885	1.18383	0.591917	+	0.805999i	$0.298371\pi$
$572$	0.0673189	0.00281474
$573$	−54.1602	−2.26258
$574$	−45.9357	−1.91732
$575$	1.81874	0.0758467
$576$	−31.4571	−1.31071
$577$	46.2725	1.92635	0.963175	−	0.268875i	$-0.0866517\pi$
$577$	46.2725	1.92635	0.963175	+	0.268875i	$0.0866517\pi$
$578$	−2.37331	−0.0987166
$579$	−38.4317	−1.59717
$580$	−13.2129	−0.548635
$581$	−32.5880	−1.35198
$582$	−86.1211	−3.56984
$583$	−7.62165	−0.315657
$584$	−12.1458	−0.502596
$585$	0.0561717	0.00232242
$586$	−71.4021	−2.94960
$587$	−11.6086	−0.479138	−0.239569	−	0.970879i	$-0.577006\pi$
$587$	−11.6086	−0.479138	−0.239569	+	0.970879i	$0.577006\pi$
$588$	−2.48019	−0.102282
$589$	−6.11959	−0.252153
$590$	9.78790	0.402961
$591$	41.6556	1.71348
$592$	−9.36149	−0.384755
$593$	−35.0442	−1.43909	−0.719547	−	0.694444i	$-0.755650\pi$
$593$	−35.0442	−1.43909	−0.719547	+	0.694444i	$0.755650\pi$
$594$	1.22348	0.0501998
$595$	−2.59145	−0.106239
$596$	45.9434	1.88191
$597$	−64.9453	−2.65803
$598$	−0.0877024	−0.00358642
$599$	−24.2254	−0.989824	−0.494912	−	0.868943i	$-0.664800\pi$
$599$	−24.2254	−0.989824	−0.494912	+	0.868943i	$0.664800\pi$
$600$	−9.30286	−0.379788
$601$	−36.4608	−1.48727	−0.743634	−	0.668587i	$-0.766899\pi$
$601$	−36.4608	−1.48727	−0.743634	+	0.668587i	$0.766899\pi$
$602$	63.6522	2.59427
$603$	−24.4888	−0.997263
$604$	−45.0654	−1.83368
$605$	−10.1681	−0.413392
$606$	7.73024	0.314019
$607$	20.4279	0.829145	0.414572	−	0.910016i	$-0.363931\pi$
$607$	20.4279	0.829145	0.414572	+	0.910016i	$0.363931\pi$
$608$	−5.44165	−0.220688
$609$	22.6312	0.917063
$610$	11.5199	0.466427
$611$	−0.261377	−0.0105742
$612$	10.0426	0.405949
$613$	−11.7878	−0.476106	−0.238053	−	0.971252i	$-0.576509\pi$
$613$	−11.7878	−0.476106	−0.238053	+	0.971252i	$0.576509\pi$
$614$	44.3133	1.78834
$615$	−17.9324	−0.723103
$616$	9.15817	0.368993
$617$	−23.3808	−0.941277	−0.470638	−	0.882326i	$-0.655976\pi$
$617$	−23.3808	−0.941277	−0.470638	+	0.882326i	$0.655976\pi$
$618$	26.6622	1.07251
$619$	−20.4660	−0.822596	−0.411298	−	0.911501i	$-0.634925\pi$
$619$	−20.4660	−0.822596	−0.411298	+	0.911501i	$0.634925\pi$
$620$	12.9398	0.519674
$621$	−1.02797	−0.0412509
$622$	19.2614	0.772311
$623$	−4.16563	−0.166893
$624$	0.0941787	0.00377016
$625$	1.00000	0.0400000
$626$	−50.5072	−2.01867
$627$	−3.76210	−0.150244
$628$	−67.4691	−2.69231
$629$	−4.84913	−0.193347
$630$	17.0031	0.677420
$631$	20.6536	0.822206	0.411103	−	0.911589i	$-0.365144\pi$
$631$	20.6536	0.822206	0.411103	+	0.911589i	$0.365144\pi$
$632$	29.6716	1.18027
$633$	−28.0112	−1.11335
$634$	−14.9045	−0.591933
$635$	−10.5612	−0.419110
$636$	−72.8815	−2.88994
$637$	−0.00577792	−0.000228930 0
$638$	7.87349	0.311715
$639$	−2.76459	−0.109366
$640$	20.6698	0.817047
$641$	−27.9597	−1.10434	−0.552170	−	0.833731i	$-0.686200\pi$
$641$	−27.9597	−1.10434	−0.552170	+	0.833731i	$0.686200\pi$
$642$	−104.673	−4.13110
$643$	29.6348	1.16868	0.584342	−	0.811508i	$-0.301353\pi$
$643$	29.6348	1.16868	0.584342	+	0.811508i	$0.301353\pi$
$644$	−17.1211	−0.674664
$645$	24.8485	0.978409
$646$	4.07725	0.160417
$647$	−30.5566	−1.20130	−0.600652	−	0.799510i	$-0.705092\pi$
$647$	−30.5566	−1.20130	−0.600652	+	0.799510i	$0.705092\pi$
$648$	37.3935	1.46896
$649$	−3.76156	−0.147654
$650$	−0.0482216	−0.00189141
$651$	−22.1634	−0.868654
$652$	−2.64041	−0.103407
$653$	31.6460	1.23841	0.619203	−	0.785231i	$-0.287456\pi$
$653$	31.6460	1.23841	0.619203	+	0.785231i	$0.287456\pi$
$654$	−69.3018	−2.70992
$655$	−10.4468	−0.408191
$656$	−14.4190	−0.562966
$657$	8.66609	0.338097
$658$	−79.1185	−3.08436
$659$	8.32873	0.324441	0.162221	−	0.986755i	$-0.448134\pi$
$659$	8.32873	0.324441	0.162221	+	0.986755i	$0.448134\pi$
$660$	7.95489	0.309644
$661$	−12.6803	−0.493207	−0.246604	−	0.969116i	$-0.579315\pi$
$661$	−12.6803	−0.493207	−0.246604	+	0.969116i	$0.579315\pi$
$662$	58.9871	2.29260
$663$	0.0487833	0.00189459
$664$	−48.7244	−1.89087
$665$	4.45201	0.172642
$666$	31.8162	1.23285
$667$	−6.61532	−0.256146
$668$	−90.7936	−3.51291
$669$	34.6685	1.34036
$670$	21.0229	0.812184
$671$	−4.42718	−0.170910
$672$	−19.7081	−0.760257
$673$	−17.2742	−0.665870	−0.332935	−	0.942950i	$-0.608039\pi$
$673$	−17.2742	−0.665870	−0.332935	+	0.942950i	$0.608039\pi$
$674$	−1.88096	−0.0724519
$675$	−0.565208	−0.0217549
$676$	−47.2222	−1.81624
$677$	46.5241	1.78807	0.894033	−	0.448001i	$-0.147864\pi$
$677$	46.5241	1.78807	0.894033	+	0.448001i	$0.147864\pi$
$678$	87.5378	3.36187
$679$	−39.1665	−1.50307
$680$	−3.87465	−0.148586
$681$	39.0642	1.49695
$682$	−7.71075	−0.295260
$683$	6.24006	0.238769	0.119385	−	0.992848i	$-0.461908\pi$
$683$	6.24006	0.238769	0.119385	+	0.992848i	$0.461908\pi$
$684$	−17.2528	−0.659679
$685$	18.2099	0.695766
$686$	−44.8012	−1.71052
$687$	15.5271	0.592394
$688$	19.9801	0.761734
$689$	−0.169787	−0.00646835
$690$	−10.3636	−0.394534
$691$	−7.15386	−0.272146	−0.136073	−	0.990699i	$-0.543448\pi$
$691$	−7.15386	−0.272146	−0.136073	+	0.990699i	$0.543448\pi$
$692$	70.3455	2.67414
$693$	−6.53442	−0.248222
$694$	−71.3251	−2.70746
$695$	12.1818	0.462080
$696$	33.8374	1.28260
$697$	−7.46884	−0.282903
$698$	−65.6956	−2.48662
$699$	−32.1806	−1.21718
$700$	−9.41370	−0.355804
$701$	3.05752	0.115481	0.0577404	−	0.998332i	$-0.481610\pi$
$701$	3.05752	0.115481	0.0577404	+	0.998332i	$0.481610\pi$
$702$	0.0272552	0.00102868
$703$	8.33061	0.314195
$704$	−10.3782	−0.391142
$705$	−30.8862	−1.16324
$706$	9.36100	0.352306
$707$	3.51559	0.132217
$708$	−35.9697	−1.35182
$709$	−7.92567	−0.297655	−0.148827	−	0.988863i	$-0.547550\pi$
$709$	−7.92567	−0.297655	−0.148827	+	0.988863i	$0.547550\pi$
$710$	2.37331	0.0890687
$711$	−21.1709	−0.793971
$712$	−6.22831	−0.233416
$713$	6.47858	0.242625
$714$	14.7666	0.552628
$715$	0.0185319	0.000693054 0
$716$	4.94760	0.184900
$717$	−2.22423	−0.0830654
$718$	−16.9531	−0.632686
$719$	45.6777	1.70349	0.851745	−	0.523956i	$-0.175544\pi$
$719$	45.6777	1.70349	0.851745	+	0.523956i	$0.175544\pi$
$720$	5.33718	0.198905
$721$	12.1255	0.451579
$722$	38.0883	1.41750
$723$	4.74703	0.176544
$724$	48.1578	1.78977
$725$	−3.63731	−0.135086
$726$	57.9400	2.15036
$727$	−46.2064	−1.71370	−0.856851	−	0.515565i	$-0.827582\pi$
$727$	−46.2064	−1.71370	−0.856851	+	0.515565i	$0.827582\pi$
$728$	0.204015	0.00756131
$729$	−22.6094	−0.837386
$730$	−7.43955	−0.275350
$731$	10.3494	0.382787
$732$	−42.3346	−1.56473
$733$	−19.0776	−0.704648	−0.352324	−	0.935878i	$-0.614608\pi$
$733$	−19.0776	−0.704648	−0.352324	+	0.935878i	$0.614608\pi$
$734$	31.2692	1.15417
$735$	−0.682761	−0.0251840
$736$	5.76087	0.212348
$737$	−8.07924	−0.297603
$738$	49.0048	1.80389
$739$	4.32475	0.159089	0.0795443	−	0.996831i	$-0.474653\pi$
$739$	4.32475	0.159089	0.0795443	+	0.996831i	$0.474653\pi$
$740$	−17.6149	−0.647537
$741$	−0.0838078	−0.00307876
$742$	−51.3942	−1.88674
$743$	−14.7981	−0.542889	−0.271444	−	0.962454i	$-0.587501\pi$
$743$	−14.7981	−0.542889	−0.271444	+	0.962454i	$0.587501\pi$
$744$	−33.1380	−1.21490
$745$	12.6475	0.463370
$746$	51.0831	1.87028
$747$	34.7652	1.27199
$748$	3.31322	0.121143
$749$	−47.6034	−1.73939
$750$	−5.69821	−0.208069
$751$	18.9794	0.692569	0.346285	−	0.938129i	$-0.387443\pi$
$751$	18.9794	0.692569	0.346285	+	0.938129i	$0.387443\pi$
$752$	−24.8349	−0.905634
$753$	−5.21646	−0.190098
$754$	0.175397	0.00638757
$755$	−12.4058	−0.451495
$756$	5.32070	0.193512
$757$	−0.918722	−0.0333915	−0.0166958	−	0.999861i	$-0.505315\pi$
$757$	−0.918722	−0.0333915	−0.0166958	+	0.999861i	$0.505315\pi$
$758$	64.2993	2.33546
$759$	3.98279	0.144566
$760$	6.65649	0.241456
$761$	18.8713	0.684085	0.342043	−	0.939684i	$-0.388881\pi$
$761$	18.8713	0.684085	0.342043	+	0.939684i	$0.388881\pi$
$762$	60.1802	2.18010
$763$	−31.5173	−1.14100
$764$	−81.9433	−2.96460
$765$	2.76459	0.0999540
$766$	−87.4820	−3.16085
$767$	−0.0837958	−0.00302569
$768$	−63.1422	−2.27845
$769$	−44.3626	−1.59975	−0.799877	−	0.600163i	$-0.795102\pi$
$769$	−44.3626	−1.59975	−0.799877	+	0.600163i	$0.795102\pi$
$770$	5.60958	0.202155
$771$	−3.96124	−0.142661
$772$	−58.1463	−2.09273
$773$	−15.7914	−0.567978	−0.283989	−	0.958828i	$-0.591658\pi$
$773$	−15.7914	−0.567978	−0.283989	+	0.958828i	$0.591658\pi$
$774$	−67.9049	−2.44079
$775$	3.56213	0.127955
$776$	−58.5604	−2.10219
$777$	30.1711	1.08238
$778$	39.8825	1.42986
$779$	12.8312	0.459724
$780$	0.177210	0.00634513
$781$	−0.912080	−0.0326368
$782$	−4.31643	−0.154355
$783$	2.05584	0.0734696
$784$	−0.548992	−0.0196069
$785$	−18.5732	−0.662908
$786$	59.5281	2.12330
$787$	−23.8809	−0.851263	−0.425632	−	0.904897i	$-0.639948\pi$
$787$	−23.8809	−0.851263	−0.425632	+	0.904897i	$0.639948\pi$
$788$	63.0241	2.24514
$789$	−54.6739	−1.94644
$790$	18.1745	0.646621
$791$	39.8107	1.41551
$792$	−9.77003	−0.347163
$793$	−0.0986238	−0.00350223
$794$	52.7202	1.87097
$795$	−20.0632	−0.711569
$796$	−98.2608	−3.48276
$797$	26.6700	0.944700	0.472350	−	0.881411i	$-0.343406\pi$
$797$	26.6700	0.944700	0.472350	+	0.881411i	$0.343406\pi$
$798$	−25.3685	−0.898035
$799$	−12.8641	−0.455100
$800$	3.16751	0.111988
$801$	4.44394	0.157019
$802$	−35.7759	−1.26329
$803$	2.85907	0.100895
$804$	−77.2571	−2.72465
$805$	−4.71318	−0.166118
$806$	−0.171771	−0.00605039
$807$	−26.5372	−0.934153
$808$	5.25638	0.184919
$809$	−20.3285	−0.714713	−0.357356	−	0.933968i	$-0.616322\pi$
$809$	−20.3285	−0.714713	−0.357356	+	0.933968i	$0.616322\pi$
$810$	22.9044	0.804777
$811$	−10.7577	−0.377755	−0.188878	−	0.982001i	$-0.560485\pi$
$811$	−10.7577	−0.377755	−0.188878	+	0.982001i	$0.560485\pi$
$812$	34.2405	1.20161
$813$	17.2452	0.604814
$814$	10.4966	0.367907
$815$	−0.726868	−0.0254611
$816$	4.63517	0.162263
$817$	−17.7799	−0.622040
$818$	12.3199	0.430755
$819$	−0.145566	−0.00508650
$820$	−27.1313	−0.947465
$821$	−51.7175	−1.80495	−0.902476	−	0.430740i	$-0.858253\pi$
$821$	−51.7175	−1.80495	−0.902476	+	0.430740i	$0.858253\pi$
$822$	−103.764	−3.61919
$823$	40.0860	1.39731	0.698656	−	0.715458i	$-0.253782\pi$
$823$	40.0860	1.39731	0.698656	+	0.715458i	$0.253782\pi$
$824$	18.1297	0.631577
$825$	2.18986	0.0762413
$826$	−25.3649	−0.882557
$827$	15.0956	0.524927	0.262463	−	0.964942i	$-0.415465\pi$
$827$	15.0956	0.524927	0.262463	+	0.964942i	$0.415465\pi$
$828$	18.2649	0.634750
$829$	−48.0423	−1.66858	−0.834288	−	0.551328i	$-0.814121\pi$
$829$	−48.0423	−1.66858	−0.834288	+	0.551328i	$0.814121\pi$
$830$	−29.8448	−1.03593
$831$	−67.4769	−2.34075
$832$	−0.231193	−0.00801518
$833$	−0.284371	−0.00985286
$834$	−69.4142	−2.40362
$835$	−24.9942	−0.864959
$836$	−5.69197	−0.196861
$837$	−2.01334	−0.0695914
$838$	−60.4156	−2.08702
$839$	−13.7624	−0.475130	−0.237565	−	0.971372i	$-0.576349\pi$
$839$	−13.7624	−0.475130	−0.237565	+	0.971372i	$0.576349\pi$
$840$	24.1079	0.831803
$841$	−15.7700	−0.543792
$842$	69.9731	2.41143
$843$	−58.3291	−2.00896
$844$	−42.3803	−1.45879
$845$	−12.9996	−0.447199
$846$	84.4045	2.90188
$847$	26.3502	0.905403
$848$	−16.1323	−0.553987
$849$	11.5869	0.397663
$850$	−2.37331	−0.0814038
$851$	−8.81930	−0.302322
$852$	−8.72170	−0.298800
$853$	−32.2099	−1.10285	−0.551424	−	0.834225i	$-0.685915\pi$
$853$	−32.2099	−1.10285	−0.551424	+	0.834225i	$0.685915\pi$
$854$	−29.8533	−1.02156
$855$	−4.74946	−0.162428
$856$	−71.1750	−2.43271
$857$	−51.3129	−1.75281	−0.876407	−	0.481571i	$-0.840066\pi$
$857$	−51.3129	−1.75281	−0.876407	+	0.481571i	$0.840066\pi$
$858$	−0.105599	−0.00360508
$859$	4.93312	0.168316	0.0841579	−	0.996452i	$-0.473180\pi$
$859$	4.93312	0.168316	0.0841579	+	0.996452i	$0.473180\pi$
$860$	37.5953	1.28199
$861$	46.4709	1.58372
$862$	−66.2714	−2.25721
$863$	16.8598	0.573914	0.286957	−	0.957943i	$-0.407356\pi$
$863$	16.8598	0.573914	0.286957	+	0.957943i	$0.407356\pi$
$864$	−1.79030	−0.0609072
$865$	19.3651	0.658433
$866$	37.0644	1.25950
$867$	2.40096	0.0815407
$868$	−33.5328	−1.13818
$869$	−6.98460	−0.236936
$870$	20.7262	0.702683
$871$	−0.179980	−0.00609839
$872$	−47.1236	−1.59581
$873$	41.7832	1.41415
$874$	7.41545	0.250831
$875$	−2.59145	−0.0876071
$876$	27.3397	0.923723
$877$	35.4076	1.19563	0.597815	−	0.801634i	$-0.296036\pi$
$877$	35.4076	1.19563	0.597815	+	0.801634i	$0.296036\pi$
$878$	2.15918	0.0728689
$879$	72.2339	2.43639
$880$	1.76082	0.0593571
$881$	5.87506	0.197936	0.0989679	−	0.995091i	$-0.468446\pi$
$881$	5.87506	0.197936	0.0989679	+	0.995091i	$0.468446\pi$
$882$	1.86582	0.0628254
$883$	39.6021	1.33272	0.666358	−	0.745632i	$-0.267852\pi$
$883$	39.6021	1.33272	0.666358	+	0.745632i	$0.267852\pi$
$884$	0.0738081	0.00248243
$885$	−9.90192	−0.332849
$886$	5.19292	0.174459
$887$	55.1172	1.85065	0.925327	−	0.379169i	$-0.123790\pi$
$887$	55.1172	1.85065	0.925327	+	0.379169i	$0.123790\pi$
$888$	45.1108	1.51382
$889$	27.3690	0.917925
$890$	−3.81498	−0.127878
$891$	−8.80231	−0.294889
$892$	52.4526	1.75624
$893$	22.1001	0.739550
$894$	−72.0683	−2.41033
$895$	1.36200	0.0455267
$896$	−53.5649	−1.78948
$897$	0.0887241	0.00296241
$898$	26.2261	0.875177
$899$	−12.9566	−0.432126
$900$	10.0426	0.334754
$901$	−8.35634	−0.278390
$902$	16.1674	0.538316
$903$	−64.3937	−2.14289
$904$	59.5236	1.97973
$905$	13.2571	0.440682
$906$	70.6911	2.34855
$907$	50.3308	1.67121	0.835604	−	0.549333i	$-0.185118\pi$
$907$	50.3308	1.67121	0.835604	+	0.549333i	$0.185118\pi$
$908$	59.1033	1.96141
$909$	−3.75047	−0.124395
$910$	0.124964	0.00414251
$911$	−39.3200	−1.30273	−0.651364	−	0.758765i	$-0.725803\pi$
$911$	−39.3200	−1.30273	−0.651364	+	0.758765i	$0.725803\pi$
$912$	−7.96303	−0.263682
$913$	11.4696	0.379587
$914$	−33.1222	−1.09558
$915$	−11.6541	−0.385273
$916$	23.4921	0.776200
$917$	27.0724	0.894010
$918$	1.34141	0.0442732
$919$	34.7300	1.14564	0.572818	−	0.819682i	$-0.305850\pi$
$919$	34.7300	1.14564	0.572818	+	0.819682i	$0.305850\pi$
$920$	−7.04698	−0.232332
$921$	−44.8296	−1.47718
$922$	−59.9637	−1.97480
$923$	−0.0203183	−0.000668784 0
$924$	−20.6147	−0.678174
$925$	−4.84913	−0.159438
$926$	70.2139	2.30737
$927$	−12.9357	−0.424863
$928$	−11.5212	−0.378202
$929$	2.54007	0.0833372	0.0416686	−	0.999131i	$-0.486733\pi$
$929$	2.54007	0.0833372	0.0416686	+	0.999131i	$0.486733\pi$
$930$	−20.2978	−0.665590
$931$	0.488537	0.0160112
$932$	−48.6886	−1.59485
$933$	−19.4858	−0.637936
$934$	−8.18109	−0.267693
$935$	0.912080	0.0298282
$936$	−0.217646	−0.00711397
$937$	−30.1935	−0.986378	−0.493189	−	0.869922i	$-0.664169\pi$
$937$	−30.1935	−0.986378	−0.493189	+	0.869922i	$0.664169\pi$
$938$	−54.4797	−1.77883
$939$	51.0955	1.66744
$940$	−46.7302	−1.52417
$941$	−39.8411	−1.29878	−0.649392	−	0.760454i	$-0.724976\pi$
$941$	−39.8411	−1.29878	−0.649392	+	0.760454i	$0.724976\pi$
$942$	105.834	3.44827
$943$	−13.5839	−0.442352
$944$	−7.96189	−0.259138
$945$	1.46471	0.0476470
$946$	−22.4028	−0.728379
$947$	−41.2564	−1.34065	−0.670327	−	0.742066i	$-0.733846\pi$
$947$	−41.2564	−1.34065	−0.670327	+	0.742066i	$0.733846\pi$
$948$	−66.7898	−2.16923
$949$	0.0636912	0.00206751
$950$	4.07725	0.132283
$951$	15.0781	0.488942
$952$	10.0410	0.325430
$953$	−27.9244	−0.904560	−0.452280	−	0.891876i	$-0.649389\pi$
$953$	−27.9244	−0.904560	−0.452280	+	0.891876i	$0.649389\pi$
$954$	54.8279	1.77512
$955$	−22.5578	−0.729953
$956$	−3.36521	−0.108839
$957$	−7.96521	−0.257479
$958$	99.8102	3.22472
$959$	−47.1902	−1.52385
$960$	−27.3194	−0.881731
$961$	−18.3112	−0.590685
$962$	0.233832	0.00753906
$963$	50.7838	1.63649
$964$	7.18216	0.231322
$965$	−16.0068	−0.515278
$966$	26.8567	0.864099
$967$	30.1985	0.971120	0.485560	−	0.874203i	$-0.338616\pi$
$967$	30.1985	0.971120	0.485560	+	0.874203i	$0.338616\pi$
$968$	39.3979	1.26630
$969$	−4.12475	−0.132506
$970$	−35.8695	−1.15170
$971$	38.0077	1.21973	0.609863	−	0.792507i	$-0.291224\pi$
$971$	38.0077	1.21973	0.609863	+	0.792507i	$0.291224\pi$
$972$	−78.0120	−2.50223
$973$	−31.5684	−1.01204
$974$	−44.2512	−1.41790
$975$	0.0487833	0.00156232
$976$	−9.37078	−0.299951
$977$	15.4423	0.494042	0.247021	−	0.969010i	$-0.420548\pi$
$977$	15.4423	0.494042	0.247021	+	0.969010i	$0.420548\pi$
$978$	4.14184	0.132442
$979$	1.46612	0.0468575
$980$	−1.03300	−0.0329981
$981$	33.6230	1.07350
$982$	−23.8071	−0.759716
$983$	54.3259	1.73273	0.866363	−	0.499414i	$-0.166451\pi$
$983$	54.3259	1.73273	0.866363	+	0.499414i	$0.166451\pi$
$984$	69.4816	2.21499
$985$	17.3496	0.552804
$986$	8.63246	0.274914
$987$	80.0402	2.54771
$988$	−0.126799	−0.00403402
$989$	18.8229	0.598533
$990$	−5.98436	−0.190196
$991$	−4.17404	−0.132593	−0.0662963	−	0.997800i	$-0.521118\pi$
$991$	−4.17404	−0.132593	−0.0662963	+	0.997800i	$0.521118\pi$
$992$	11.2831	0.358238
$993$	−59.6743	−1.89371
$994$	−6.15032	−0.195076
$995$	−27.0498	−0.857535
$996$	109.677	3.47524
$997$	−24.9767	−0.791021	−0.395510	−	0.918462i	$-0.629432\pi$
$997$	−24.9767	−0.791021	−0.395510	+	0.918462i	$0.629432\pi$
$998$	32.0592	1.01482
$999$	2.74077	0.0867140

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.a.1.3	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.a.1.3	✓	36	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:	\( N \)	\(=\)	\( 6035 = 5 \cdot 17 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.37331 q^{2} +2.40096 q^{3} +3.63259 q^{4} +1.00000 q^{5} -5.69821 q^{6} -2.59145 q^{7} -3.87465 q^{8} +2.76459 q^{9} +O(q^{10})\)	\(q-2.37331 q^{2} +2.40096 q^{3} +3.63259 q^{4} +1.00000 q^{5} -5.69821 q^{6} -2.59145 q^{7} -3.87465 q^{8} +2.76459 q^{9} -2.37331 q^{10} +0.912080 q^{11} +8.72170 q^{12} +0.0203183 q^{13} +6.15032 q^{14} +2.40096 q^{15} +1.93055 q^{16} +1.00000 q^{17} -6.56123 q^{18} -1.71796 q^{19} +3.63259 q^{20} -6.22197 q^{21} -2.16465 q^{22} +1.81874 q^{23} -9.30286 q^{24} +1.00000 q^{25} -0.0482216 q^{26} -0.565208 q^{27} -9.41370 q^{28} -3.63731 q^{29} -5.69821 q^{30} +3.56213 q^{31} +3.16751 q^{32} +2.18986 q^{33} -2.37331 q^{34} -2.59145 q^{35} +10.0426 q^{36} -4.84913 q^{37} +4.07725 q^{38} +0.0487833 q^{39} -3.87465 q^{40} -7.46884 q^{41} +14.7666 q^{42} +10.3494 q^{43} +3.31322 q^{44} +2.76459 q^{45} -4.31643 q^{46} -12.8641 q^{47} +4.63517 q^{48} -0.284371 q^{49} -2.37331 q^{50} +2.40096 q^{51} +0.0738081 q^{52} -8.35634 q^{53} +1.34141 q^{54} +0.912080 q^{55} +10.0410 q^{56} -4.12475 q^{57} +8.63246 q^{58} -4.12416 q^{59} +8.72170 q^{60} -4.85394 q^{61} -8.45403 q^{62} -7.16431 q^{63} -11.3786 q^{64} +0.0203183 q^{65} -5.19722 q^{66} -8.85804 q^{67} +3.63259 q^{68} +4.36671 q^{69} +6.15032 q^{70} -1.00000 q^{71} -10.7118 q^{72} +3.13468 q^{73} +11.5085 q^{74} +2.40096 q^{75} -6.24065 q^{76} -2.36361 q^{77} -0.115778 q^{78} -7.65789 q^{79} +1.93055 q^{80} -9.65081 q^{81} +17.7259 q^{82} +12.5752 q^{83} -22.6019 q^{84} +1.00000 q^{85} -24.5624 q^{86} -8.73302 q^{87} -3.53399 q^{88} +1.60745 q^{89} -6.56123 q^{90} -0.0526539 q^{91} +6.60674 q^{92} +8.55252 q^{93} +30.5305 q^{94} -1.71796 q^{95} +7.60504 q^{96} +15.1137 q^{97} +0.674899 q^{98} +2.52153 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9}+O(q^{10}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9} - 3 q^{10} - 20 q^{11} - 8 q^{12} - 29 q^{13} - 12 q^{14} - 8 q^{15} + q^{16} + 36 q^{17} - 8 q^{18} - 19 q^{19} + 23 q^{20} - 19 q^{21} - 10 q^{22} - 10 q^{23} - 23 q^{24} + 36 q^{25} - 32 q^{26} - 23 q^{27} - 20 q^{28} - 52 q^{29} - 10 q^{30} - 15 q^{31} - 16 q^{32} - 19 q^{33} - 3 q^{34} - 7 q^{35} + 9 q^{36} - 52 q^{37} + 7 q^{38} - 10 q^{39} - 9 q^{40} - 51 q^{41} - 2 q^{42} - 13 q^{43} - 27 q^{44} + 10 q^{45} + 12 q^{46} - 24 q^{47} + 12 q^{48} - 15 q^{49} - 3 q^{50} - 8 q^{51} - 49 q^{52} - 13 q^{53} - 48 q^{54} - 20 q^{55} - 12 q^{56} - 20 q^{57} - 20 q^{58} - 14 q^{59} - 8 q^{60} - 75 q^{61} - 7 q^{62} + 16 q^{63} - 41 q^{64} - 29 q^{65} - q^{66} - 5 q^{67} + 23 q^{68} - 37 q^{69} - 12 q^{70} - 36 q^{71} - 23 q^{72} - 21 q^{73} + q^{74} - 8 q^{75} - 40 q^{76} - 31 q^{77} + 84 q^{78} - 49 q^{79} + q^{80} - 56 q^{81} - 51 q^{82} + 6 q^{83} + 10 q^{84} + 36 q^{85} - 41 q^{86} - 4 q^{87} - 21 q^{88} - 78 q^{89} - 8 q^{90} - 25 q^{91} - 24 q^{92} - 36 q^{93} + 6 q^{94} - 19 q^{95} - 71 q^{96} - 48 q^{97} + 51 q^{98} - 17 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9 - 3 * q^10 - 20 * q^11 - 8 * q^12 - 29 * q^13 - 12 * q^14 - 8 * q^15 + q^16 + 36 * q^17 - 8 * q^18 - 19 * q^19 + 23 * q^20 - 19 * q^21 - 10 * q^22 - 10 * q^23 - 23 * q^24 + 36 * q^25 - 32 * q^26 - 23 * q^27 - 20 * q^28 - 52 * q^29 - 10 * q^30 - 15 * q^31 - 16 * q^32 - 19 * q^33 - 3 * q^34 - 7 * q^35 + 9 * q^36 - 52 * q^37 + 7 * q^38 - 10 * q^39 - 9 * q^40 - 51 * q^41 - 2 * q^42 - 13 * q^43 - 27 * q^44 + 10 * q^45 + 12 * q^46 - 24 * q^47 + 12 * q^48 - 15 * q^49 - 3 * q^50 - 8 * q^51 - 49 * q^52 - 13 * q^53 - 48 * q^54 - 20 * q^55 - 12 * q^56 - 20 * q^57 - 20 * q^58 - 14 * q^59 - 8 * q^60 - 75 * q^61 - 7 * q^62 + 16 * q^63 - 41 * q^64 - 29 * q^65 - q^66 - 5 * q^67 + 23 * q^68 - 37 * q^69 - 12 * q^70 - 36 * q^71 - 23 * q^72 - 21 * q^73 + q^74 - 8 * q^75 - 40 * q^76 - 31 * q^77 + 84 * q^78 - 49 * q^79 + q^80 - 56 * q^81 - 51 * q^82 + 6 * q^83 + 10 * q^84 + 36 * q^85 - 41 * q^86 - 4 * q^87 - 21 * q^88 - 78 * q^89 - 8 * q^90 - 25 * q^91 - 24 * q^92 - 36 * q^93 + 6 * q^94 - 19 * q^95 - 71 * q^96 - 48 * q^97 + 51 * q^98 - 17 * q^99

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