LMFDB - Embedded newform 6035.2.a.a.1.10

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			1.10
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)

$f(q)$	$=$	$q-1.14290 q^{2} -1.19489 q^{3} -0.693776 q^{4} +1.00000 q^{5} +1.36564 q^{6} -1.41810 q^{7} +3.07872 q^{8} -1.57223 q^{9} +O(q^{10})$	\(q-1.14290 q^{2} -1.19489 q^{3} -0.693776 q^{4} +1.00000 q^{5} +1.36564 q^{6} -1.41810 q^{7} +3.07872 q^{8} -1.57223 q^{9} -1.14290 q^{10} -1.45595 q^{11} +0.828988 q^{12} -2.13454 q^{13} +1.62075 q^{14} -1.19489 q^{15} -2.13112 q^{16} +1.00000 q^{17} +1.79691 q^{18} -3.86766 q^{19} -0.693776 q^{20} +1.69448 q^{21} +1.66400 q^{22} +0.806721 q^{23} -3.67874 q^{24} +1.00000 q^{25} +2.43956 q^{26} +5.46332 q^{27} +0.983846 q^{28} +0.383262 q^{29} +1.36564 q^{30} +5.73609 q^{31} -3.72178 q^{32} +1.73970 q^{33} -1.14290 q^{34} -1.41810 q^{35} +1.09078 q^{36} +0.651541 q^{37} +4.42035 q^{38} +2.55054 q^{39} +3.07872 q^{40} +11.5480 q^{41} -1.93662 q^{42} -0.386475 q^{43} +1.01010 q^{44} -1.57223 q^{45} -0.922002 q^{46} -5.55119 q^{47} +2.54646 q^{48} -4.98899 q^{49} -1.14290 q^{50} -1.19489 q^{51} +1.48089 q^{52} -8.12698 q^{53} -6.24404 q^{54} -1.45595 q^{55} -4.36594 q^{56} +4.62143 q^{57} -0.438031 q^{58} +4.59181 q^{59} +0.828988 q^{60} +8.05082 q^{61} -6.55578 q^{62} +2.22959 q^{63} +8.51587 q^{64} -2.13454 q^{65} -1.98831 q^{66} +13.5164 q^{67} -0.693776 q^{68} -0.963944 q^{69} +1.62075 q^{70} -1.00000 q^{71} -4.84047 q^{72} +2.57099 q^{73} -0.744647 q^{74} -1.19489 q^{75} +2.68329 q^{76} +2.06468 q^{77} -2.91502 q^{78} -9.66998 q^{79} -2.13112 q^{80} -1.81138 q^{81} -13.1983 q^{82} +2.85555 q^{83} -1.17559 q^{84} +1.00000 q^{85} +0.441703 q^{86} -0.457957 q^{87} -4.48246 q^{88} -6.01322 q^{89} +1.79691 q^{90} +3.02699 q^{91} -0.559684 q^{92} -6.85401 q^{93} +6.34446 q^{94} -3.86766 q^{95} +4.44712 q^{96} -17.0259 q^{97} +5.70192 q^{98} +2.28909 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.14290	−0.808153	−0.404077	−	0.914725i	$-0.632407\pi$
$2$	−1.14290	−0.808153	−0.404077	+	0.914725i	$0.632407\pi$
$3$	−1.19489	−0.689871	−0.344936	−	0.938626i	$-0.612099\pi$
$3$	−1.19489	−0.689871	−0.344936	+	0.938626i	$0.612099\pi$
$4$	−0.693776	−0.346888
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.36564	0.557522
$7$	−1.41810	−0.535992	−0.267996	−	0.963420i	$-0.586361\pi$
$7$	−1.41810	−0.535992	−0.267996	+	0.963420i	$0.586361\pi$
$8$	3.07872	1.08849
$9$	−1.57223	−0.524078
$10$	−1.14290	−0.361417
$11$	−1.45595	−0.438985	−0.219492	−	0.975614i	$-0.570440\pi$
$11$	−1.45595	−0.438985	−0.219492	+	0.975614i	$0.570440\pi$
$12$	0.828988	0.239308
$13$	−2.13454	−0.592014	−0.296007	−	0.955186i	$-0.595655\pi$
$13$	−2.13454	−0.592014	−0.296007	+	0.955186i	$0.595655\pi$
$14$	1.62075	0.433164
$15$	−1.19489	−0.308520
$16$	−2.13112	−0.532780
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.79691	0.423535
$19$	−3.86766	−0.887301	−0.443651	−	0.896200i	$-0.646317\pi$
$19$	−3.86766	−0.887301	−0.443651	+	0.896200i	$0.646317\pi$
$20$	−0.693776	−0.155133
$21$	1.69448	0.369766
$22$	1.66400	0.354767
$23$	0.806721	0.168213	0.0841064	−	0.996457i	$-0.473196\pi$
$23$	0.806721	0.168213	0.0841064	+	0.996457i	$0.473196\pi$
$24$	−3.67874	−0.750919
$25$	1.00000	0.200000
$26$	2.43956	0.478438
$27$	5.46332	1.05142
$28$	0.983846	0.185929
$29$	0.383262	0.0711699	0.0355850	−	0.999367i	$-0.488671\pi$
$29$	0.383262	0.0711699	0.0355850	+	0.999367i	$0.488671\pi$
$30$	1.36564	0.249331
$31$	5.73609	1.03023	0.515116	−	0.857120i	$-0.327749\pi$
$31$	5.73609	1.03023	0.515116	+	0.857120i	$0.327749\pi$
$32$	−3.72178	−0.657924
$33$	1.73970	0.302843
$34$	−1.14290	−0.196006
$35$	−1.41810	−0.239703
$36$	1.09078	0.181796
$37$	0.651541	0.107113	0.0535564	−	0.998565i	$-0.482944\pi$
$37$	0.651541	0.107113	0.0535564	+	0.998565i	$0.482944\pi$
$38$	4.42035	0.717075
$39$	2.55054	0.408413
$40$	3.07872	0.486789
$41$	11.5480	1.80350	0.901750	−	0.432258i	$-0.142283\pi$
$41$	11.5480	1.80350	0.901750	+	0.432258i	$0.142283\pi$
$42$	−1.93662	−0.298827
$43$	−0.386475	−0.0589369	−0.0294685	−	0.999566i	$-0.509381\pi$
$43$	−0.386475	−0.0589369	−0.0294685	+	0.999566i	$0.509381\pi$
$44$	1.01010	0.152279
$45$	−1.57223	−0.234375
$46$	−0.922002	−0.135942
$47$	−5.55119	−0.809724	−0.404862	−	0.914378i	$-0.632680\pi$
$47$	−5.55119	−0.809724	−0.404862	+	0.914378i	$0.632680\pi$
$48$	2.54646	0.367550
$49$	−4.98899	−0.712712
$50$	−1.14290	−0.161631
$51$	−1.19489	−0.167318
$52$	1.48089	0.205363
$53$	−8.12698	−1.11633	−0.558164	−	0.829731i	$-0.688494\pi$
$53$	−8.12698	−1.11633	−0.558164	+	0.829731i	$0.688494\pi$
$54$	−6.24404	−0.849706
$55$	−1.45595	−0.196320
$56$	−4.36594	−0.583423
$57$	4.62143	0.612123
$58$	−0.438031	−0.0575162
$59$	4.59181	0.597803	0.298901	−	0.954284i	$-0.403380\pi$
$59$	4.59181	0.597803	0.298901	+	0.954284i	$0.403380\pi$
$60$	0.828988	0.107022
$61$	8.05082	1.03080	0.515401	−	0.856949i	$-0.327643\pi$
$61$	8.05082	1.03080	0.515401	+	0.856949i	$0.327643\pi$
$62$	−6.55578	−0.832585
$63$	2.22959	0.280902
$64$	8.51587	1.06448
$65$	−2.13454	−0.264757
$66$	−1.98831	−0.244743
$67$	13.5164	1.65129	0.825643	−	0.564193i	$-0.190813\pi$
$67$	13.5164	1.65129	0.825643	+	0.564193i	$0.190813\pi$
$68$	−0.693776	−0.0841327
$69$	−0.963944	−0.116045
$70$	1.62075	0.193717
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	−4.84047	−0.570454
$73$	2.57099	0.300911	0.150456	−	0.988617i	$-0.451926\pi$
$73$	2.57099	0.300911	0.150456	+	0.988617i	$0.451926\pi$
$74$	−0.744647	−0.0865635
$75$	−1.19489	−0.137974
$76$	2.68329	0.307794
$77$	2.06468	0.235292
$78$	−2.91502	−0.330061
$79$	−9.66998	−1.08796	−0.543979	−	0.839099i	$-0.683083\pi$
$79$	−9.66998	−1.08796	−0.543979	+	0.839099i	$0.683083\pi$
$80$	−2.13112	−0.238267
$81$	−1.81138	−0.201265
$82$	−13.1983	−1.45750
$83$	2.85555	0.313437	0.156719	−	0.987643i	$-0.449908\pi$
$83$	2.85555	0.313437	0.156719	+	0.987643i	$0.449908\pi$
$84$	−1.17559	−0.128267
$85$	1.00000	0.108465
$86$	0.441703	0.0476301
$87$	−0.457957	−0.0490981
$88$	−4.48246	−0.477831
$89$	−6.01322	−0.637400	−0.318700	−	0.947856i	$-0.603246\pi$
$89$	−6.01322	−0.637400	−0.318700	+	0.947856i	$0.603246\pi$
$90$	1.79691	0.189411
$91$	3.02699	0.317315
$92$	−0.559684	−0.0583511
$93$	−6.85401	−0.710727
$94$	6.34446	0.654381
$95$	−3.86766	−0.396813
$96$	4.44712	0.453883
$97$	−17.0259	−1.72871	−0.864357	−	0.502879i	$-0.832274\pi$
$97$	−17.0259	−1.72871	−0.864357	+	0.502879i	$0.832274\pi$
$98$	5.70192	0.575981
$99$	2.28909	0.230062
$100$	−0.693776	−0.0693776
$101$	−1.96225	−0.195251	−0.0976254	−	0.995223i	$-0.531125\pi$
$101$	−1.96225	−0.195251	−0.0976254	+	0.995223i	$0.531125\pi$
$102$	1.36564	0.135219
$103$	−0.185934	−0.0183206	−0.00916030	−	0.999958i	$-0.502916\pi$
$103$	−0.185934	−0.0183206	−0.00916030	+	0.999958i	$0.502916\pi$
$104$	−6.57164	−0.644402
$105$	1.69448	0.165364
$106$	9.28834	0.902164
$107$	11.9585	1.15607	0.578034	−	0.816013i	$-0.303820\pi$
$107$	11.9585	1.15607	0.578034	+	0.816013i	$0.303820\pi$
$108$	−3.79033	−0.364724
$109$	15.3208	1.46747	0.733733	−	0.679438i	$-0.237776\pi$
$109$	15.3208	1.46747	0.733733	+	0.679438i	$0.237776\pi$
$110$	1.66400	0.158657
$111$	−0.778521	−0.0738940
$112$	3.02215	0.285566
$113$	−2.10420	−0.197947	−0.0989734	−	0.995090i	$-0.531556\pi$
$113$	−2.10420	−0.197947	−0.0989734	+	0.995090i	$0.531556\pi$
$114$	−5.28184	−0.494690
$115$	0.806721	0.0752271
$116$	−0.265898	−0.0246880
$117$	3.35599	0.310261
$118$	−5.24799	−0.483116
$119$	−1.41810	−0.129997
$120$	−3.67874	−0.335821
$121$	−8.88022	−0.807292
$122$	−9.20130	−0.833046
$123$	−13.7987	−1.24418
$124$	−3.97956	−0.357375
$125$	1.00000	0.0894427
$126$	−2.54820	−0.227011
$127$	−3.68274	−0.326790	−0.163395	−	0.986561i	$-0.552245\pi$
$127$	−3.68274	−0.326790	−0.163395	+	0.986561i	$0.552245\pi$
$128$	−2.28924	−0.202342
$129$	0.461796	0.0406589
$130$	2.43956	0.213964
$131$	−10.6668	−0.931965	−0.465982	−	0.884794i	$-0.654299\pi$
$131$	−10.6668	−0.931965	−0.465982	+	0.884794i	$0.654299\pi$
$132$	−1.20696	−0.105053
$133$	5.48473	0.475586
$134$	−15.4479	−1.33449
$135$	5.46332	0.470208
$136$	3.07872	0.263998
$137$	17.9889	1.53690	0.768448	−	0.639912i	$-0.221029\pi$
$137$	17.9889	1.53690	0.768448	+	0.639912i	$0.221029\pi$
$138$	1.10169	0.0937823
$139$	22.1365	1.87759	0.938796	−	0.344472i	$-0.111942\pi$
$139$	22.1365	1.87759	0.938796	+	0.344472i	$0.111942\pi$
$140$	0.983846	0.0831501
$141$	6.63307	0.558605
$142$	1.14290	0.0959102
$143$	3.10777	0.259885
$144$	3.35062	0.279218
$145$	0.383262	0.0318282
$146$	−2.93838	−0.243182
$147$	5.96130	0.491680
$148$	−0.452024	−0.0371561
$149$	−19.9269	−1.63247	−0.816237	−	0.577717i	$-0.803944\pi$
$149$	−19.9269	−1.63247	−0.816237	+	0.577717i	$0.803944\pi$
$150$	1.36564	0.111504
$151$	−0.510802	−0.0415685	−0.0207842	−	0.999784i	$-0.506616\pi$
$151$	−0.510802	−0.0415685	−0.0207842	+	0.999784i	$0.506616\pi$
$152$	−11.9074	−0.965820
$153$	−1.57223	−0.127108
$154$	−2.35973	−0.190152
$155$	5.73609	0.460734
$156$	−1.76950	−0.141674
$157$	5.93812	0.473913	0.236957	−	0.971520i	$-0.423850\pi$
$157$	5.93812	0.473913	0.236957	+	0.971520i	$0.423850\pi$
$158$	11.0518	0.879237
$159$	9.71087	0.770122
$160$	−3.72178	−0.294233
$161$	−1.14401	−0.0901608
$162$	2.07023	0.162653
$163$	13.2716	1.03951	0.519754	−	0.854316i	$-0.326024\pi$
$163$	13.2716	1.03951	0.519754	+	0.854316i	$0.326024\pi$
$164$	−8.01175	−0.625613
$165$	1.73970	0.135435
$166$	−3.26361	−0.253305
$167$	12.4792	0.965666	0.482833	−	0.875712i	$-0.339608\pi$
$167$	12.4792	0.965666	0.482833	+	0.875712i	$0.339608\pi$
$168$	5.21683	0.402487
$169$	−8.44376	−0.649520
$170$	−1.14290	−0.0876565
$171$	6.08086	0.465015
$172$	0.268128	0.0204445
$173$	−2.56064	−0.194682	−0.0973408	−	0.995251i	$-0.531034\pi$
$173$	−2.56064	−0.194682	−0.0973408	+	0.995251i	$0.531034\pi$
$174$	0.523399	0.0396788
$175$	−1.41810	−0.107198
$176$	3.10280	0.233882
$177$	−5.48672	−0.412407
$178$	6.87252	0.515117
$179$	−0.465192	−0.0347701	−0.0173850	−	0.999849i	$-0.505534\pi$
$179$	−0.465192	−0.0347701	−0.0173850	+	0.999849i	$0.505534\pi$
$180$	1.09078	0.0813018
$181$	−0.872700	−0.0648673	−0.0324336	−	0.999474i	$-0.510326\pi$
$181$	−0.872700	−0.0648673	−0.0324336	+	0.999474i	$0.510326\pi$
$182$	−3.45955	−0.256439
$183$	−9.61987	−0.711121
$184$	2.48367	0.183098
$185$	0.651541	0.0479023
$186$	7.83345	0.574377
$187$	−1.45595	−0.106469
$188$	3.85128	0.280884
$189$	−7.74755	−0.563551
$190$	4.42035	0.320686
$191$	−7.76074	−0.561547	−0.280774	−	0.959774i	$-0.590591\pi$
$191$	−7.76074	−0.561547	−0.280774	+	0.959774i	$0.590591\pi$
$192$	−10.1755	−0.734357
$193$	10.8553	0.781379	0.390690	−	0.920523i	$-0.372237\pi$
$193$	10.8553	0.781379	0.390690	+	0.920523i	$0.372237\pi$
$194$	19.4589	1.39707
$195$	2.55054	0.182648
$196$	3.46124	0.247232
$197$	−5.56876	−0.396758	−0.198379	−	0.980125i	$-0.563568\pi$
$197$	−5.56876	−0.396758	−0.198379	+	0.980125i	$0.563568\pi$
$198$	−2.61620	−0.185925
$199$	15.9135	1.12808	0.564040	−	0.825747i	$-0.309246\pi$
$199$	15.9135	1.12808	0.564040	+	0.825747i	$0.309246\pi$
$200$	3.07872	0.217698
$201$	−16.1506	−1.13917
$202$	2.24265	0.157793
$203$	−0.543504	−0.0381465
$204$	0.828988	0.0580408
$205$	11.5480	0.806550
$206$	0.212504	0.0148059
$207$	−1.26835	−0.0881566
$208$	4.54896	0.315413
$209$	5.63110	0.389512
$210$	−1.93662	−0.133640
$211$	1.16945	0.0805085	0.0402543	−	0.999189i	$-0.487183\pi$
$211$	1.16945	0.0805085	0.0402543	+	0.999189i	$0.487183\pi$
$212$	5.63831	0.387241
$213$	1.19489	0.0818727
$214$	−13.6673	−0.934280
$215$	−0.386475	−0.0263574
$216$	16.8201	1.14446
$217$	−8.13436	−0.552196
$218$	−17.5102	−1.18594
$219$	−3.07205	−0.207590
$220$	1.01010	0.0681011
$221$	−2.13454	−0.143584
$222$	0.889773	0.0597177
$223$	20.5967	1.37926	0.689628	−	0.724164i	$-0.257774\pi$
$223$	20.5967	1.37926	0.689628	+	0.724164i	$0.257774\pi$
$224$	5.27786	0.352642
$225$	−1.57223	−0.104816
$226$	2.40490	0.159971
$227$	14.5174	0.963552	0.481776	−	0.876294i	$-0.339992\pi$
$227$	14.5174	0.963552	0.481776	+	0.876294i	$0.339992\pi$
$228$	−3.20624	−0.212338
$229$	−7.93364	−0.524270	−0.262135	−	0.965031i	$-0.584426\pi$
$229$	−7.93364	−0.524270	−0.262135	+	0.965031i	$0.584426\pi$
$230$	−0.922002	−0.0607950
$231$	−2.46707	−0.162321
$232$	1.17996	0.0774679
$233$	−6.31227	−0.413530	−0.206765	−	0.978391i	$-0.566294\pi$
$233$	−6.31227	−0.413530	−0.206765	+	0.978391i	$0.566294\pi$
$234$	−3.83556	−0.250739
$235$	−5.55119	−0.362119
$236$	−3.18569	−0.207371
$237$	11.5546	0.750551
$238$	1.62075	0.105058
$239$	−26.6302	−1.72256	−0.861281	−	0.508130i	$-0.830337\pi$
$239$	−26.6302	−1.72256	−0.861281	+	0.508130i	$0.830337\pi$
$240$	2.54646	0.164373
$241$	−4.16411	−0.268234	−0.134117	−	0.990966i	$-0.542820\pi$
$241$	−4.16411	−0.268234	−0.134117	+	0.990966i	$0.542820\pi$
$242$	10.1492	0.652416
$243$	−14.2256	−0.912570
$244$	−5.58547	−0.357573
$245$	−4.98899	−0.318735
$246$	15.7705	1.00549
$247$	8.25565	0.525294
$248$	17.6598	1.12140
$249$	−3.41207	−0.216231
$250$	−1.14290	−0.0722834
$251$	−4.08972	−0.258141	−0.129070	−	0.991635i	$-0.541199\pi$
$251$	−4.08972	−0.258141	−0.129070	+	0.991635i	$0.541199\pi$
$252$	−1.54683	−0.0974414
$253$	−1.17454	−0.0738429
$254$	4.20901	0.264097
$255$	−1.19489	−0.0748270
$256$	−14.4154	−0.900960
$257$	24.1071	1.50376	0.751881	−	0.659299i	$-0.229147\pi$
$257$	24.1071	1.50376	0.751881	+	0.659299i	$0.229147\pi$
$258$	−0.527788	−0.0328586
$259$	−0.923952	−0.0574116
$260$	1.48089	0.0918409
$261$	−0.602577	−0.0372986
$262$	12.1911	0.753171
$263$	−22.5914	−1.39305	−0.696523	−	0.717534i	$-0.745271\pi$
$263$	−22.5914	−1.39305	−0.696523	+	0.717534i	$0.745271\pi$
$264$	5.35605	0.329642
$265$	−8.12698	−0.499237
$266$	−6.26851	−0.384347
$267$	7.18515	0.439724
$268$	−9.37733	−0.572811
$269$	−22.6102	−1.37857	−0.689283	−	0.724492i	$-0.742074\pi$
$269$	−22.6102	−1.37857	−0.689283	+	0.724492i	$0.742074\pi$
$270$	−6.24404	−0.380000
$271$	−12.0267	−0.730573	−0.365286	−	0.930895i	$-0.619029\pi$
$271$	−12.0267	−0.730573	−0.365286	+	0.930895i	$0.619029\pi$
$272$	−2.13112	−0.129218
$273$	−3.61693	−0.218906
$274$	−20.5595	−1.24205
$275$	−1.45595	−0.0877969
$276$	0.668762	0.0402547
$277$	19.5115	1.17233	0.586167	−	0.810191i	$-0.300636\pi$
$277$	19.5115	1.17233	0.586167	+	0.810191i	$0.300636\pi$
$278$	−25.2998	−1.51738
$279$	−9.01847	−0.539922
$280$	−4.36594	−0.260915
$281$	−18.1137	−1.08057	−0.540286	−	0.841482i	$-0.681684\pi$
$281$	−18.1137	−1.08057	−0.540286	+	0.841482i	$0.681684\pi$
$282$	−7.58094	−0.451439
$283$	−16.7898	−0.998049	−0.499025	−	0.866588i	$-0.666308\pi$
$283$	−16.7898	−0.998049	−0.499025	+	0.866588i	$0.666308\pi$
$284$	0.693776	0.0411681
$285$	4.62143	0.273750
$286$	−3.55188	−0.210027
$287$	−16.3763	−0.966662
$288$	5.85151	0.344803
$289$	1.00000	0.0588235
$290$	−0.438031	−0.0257220
$291$	20.3441	1.19259
$292$	−1.78369	−0.104383
$293$	−19.0336	−1.11195	−0.555977	−	0.831198i	$-0.687656\pi$
$293$	−19.0336	−1.11195	−0.555977	+	0.831198i	$0.687656\pi$
$294$	−6.81318	−0.397353
$295$	4.59181	0.267346
$296$	2.00591	0.116591
$297$	−7.95431	−0.461556
$298$	22.7745	1.31929
$299$	−1.72197	−0.0995843
$300$	0.828988	0.0478616
$301$	0.548062	0.0315897
$302$	0.583796	0.0335937
$303$	2.34467	0.134698
$304$	8.24244	0.472737
$305$	8.05082	0.460989
$306$	1.79691	0.102722
$307$	−26.0214	−1.48512	−0.742559	−	0.669781i	$-0.766388\pi$
$307$	−26.0214	−1.48512	−0.742559	+	0.669781i	$0.766388\pi$
$308$	−1.43243	−0.0816201
$309$	0.222171	0.0126389
$310$	−6.55578	−0.372344
$311$	15.8161	0.896847	0.448423	−	0.893821i	$-0.351986\pi$
$311$	15.8161	0.896847	0.448423	+	0.893821i	$0.351986\pi$
$312$	7.85240	0.444555
$313$	21.8280	1.23379	0.616894	−	0.787046i	$-0.288391\pi$
$313$	21.8280	1.23379	0.616894	+	0.787046i	$0.288391\pi$
$314$	−6.78668	−0.382995
$315$	2.22959	0.125623
$316$	6.70881	0.377400
$317$	−23.4454	−1.31682	−0.658412	−	0.752658i	$-0.728771\pi$
$317$	−23.4454	−1.31682	−0.658412	+	0.752658i	$0.728771\pi$
$318$	−11.0986	−0.622377
$319$	−0.558009	−0.0312425
$320$	8.51587	0.476052
$321$	−14.2891	−0.797538
$322$	1.30749	0.0728637
$323$	−3.86766	−0.215202
$324$	1.25670	0.0698164
$325$	−2.13454	−0.118403
$326$	−15.1681	−0.840082
$327$	−18.3067	−1.01236
$328$	35.5532	1.96310
$329$	7.87215	0.434006
$330$	−1.98831	−0.109453
$331$	2.47128	0.135834	0.0679169	−	0.997691i	$-0.478365\pi$
$331$	2.47128	0.135834	0.0679169	+	0.997691i	$0.478365\pi$
$332$	−1.98111	−0.108728
$333$	−1.02437	−0.0561354
$334$	−14.2624	−0.780406
$335$	13.5164	0.738477
$336$	−3.61114	−0.197004
$337$	−13.9152	−0.758009	−0.379005	−	0.925395i	$-0.623734\pi$
$337$	−13.9152	−0.758009	−0.379005	+	0.925395i	$0.623734\pi$
$338$	9.65038	0.524911
$339$	2.51430	0.136558
$340$	−0.693776	−0.0376253
$341$	−8.35144	−0.452256
$342$	−6.94982	−0.375803
$343$	17.0016	0.918000
$344$	−1.18985	−0.0641524
$345$	−0.963944	−0.0518970
$346$	2.92656	0.157333
$347$	25.7230	1.38088	0.690441	−	0.723388i	$-0.257416\pi$
$347$	25.7230	1.38088	0.690441	+	0.723388i	$0.257416\pi$
$348$	0.317719	0.0170315
$349$	−23.7269	−1.27007	−0.635035	−	0.772483i	$-0.719014\pi$
$349$	−23.7269	−1.27007	−0.635035	+	0.772483i	$0.719014\pi$
$350$	1.62075	0.0866328
$351$	−11.6617	−0.622454
$352$	5.41872	0.288819
$353$	15.0682	0.802000	0.401000	−	0.916078i	$-0.368663\pi$
$353$	15.0682	0.802000	0.401000	+	0.916078i	$0.368663\pi$
$354$	6.27078	0.333288
$355$	−1.00000	−0.0530745
$356$	4.17183	0.221107
$357$	1.69448	0.0896813
$358$	0.531669	0.0280996
$359$	31.0202	1.63719	0.818593	−	0.574375i	$-0.194755\pi$
$359$	31.0202	1.63719	0.818593	+	0.574375i	$0.194755\pi$
$360$	−4.84047	−0.255115
$361$	−4.04124	−0.212697
$362$	0.997410	0.0524227
$363$	10.6109	0.556928
$364$	−2.10005	−0.110073
$365$	2.57099	0.134572
$366$	10.9946	0.574695
$367$	6.91099	0.360751	0.180375	−	0.983598i	$-0.442269\pi$
$367$	6.91099	0.360751	0.180375	+	0.983598i	$0.442269\pi$
$368$	−1.71922	−0.0896205
$369$	−18.1562	−0.945174
$370$	−0.744647	−0.0387124
$371$	11.5249	0.598343
$372$	4.75515	0.246543
$373$	1.25942	0.0652101	0.0326050	−	0.999468i	$-0.489620\pi$
$373$	1.25942	0.0652101	0.0326050	+	0.999468i	$0.489620\pi$
$374$	1.66400	0.0860436
$375$	−1.19489	−0.0617040
$376$	−17.0906	−0.881378
$377$	−0.818086	−0.0421336
$378$	8.85469	0.455436
$379$	−19.1377	−0.983039	−0.491520	−	0.870867i	$-0.663558\pi$
$379$	−19.1377	−0.983039	−0.491520	+	0.870867i	$0.663558\pi$
$380$	2.68329	0.137650
$381$	4.40048	0.225443
$382$	8.86976	0.453816
$383$	−5.06956	−0.259042	−0.129521	−	0.991577i	$-0.541344\pi$
$383$	−5.06956	−0.259042	−0.129521	+	0.991577i	$0.541344\pi$
$384$	2.73540	0.139590
$385$	2.06468	0.105226
$386$	−12.4065	−0.631474
$387$	0.607629	0.0308875
$388$	11.8121	0.599670
$389$	−27.9511	−1.41718	−0.708589	−	0.705622i	$-0.750668\pi$
$389$	−27.9511	−1.41718	−0.708589	+	0.705622i	$0.750668\pi$
$390$	−2.91502	−0.147608
$391$	0.806721	0.0407976
$392$	−15.3597	−0.775782
$393$	12.7457	0.642936
$394$	6.36454	0.320641
$395$	−9.66998	−0.486550
$396$	−1.58812	−0.0798058
$397$	21.3450	1.07128	0.535638	−	0.844448i	$-0.320071\pi$
$397$	21.3450	1.07128	0.535638	+	0.844448i	$0.320071\pi$
$398$	−18.1876	−0.911662
$399$	−6.55366	−0.328093
$400$	−2.13112	−0.106556
$401$	28.0192	1.39921	0.699607	−	0.714528i	$-0.253359\pi$
$401$	28.0192	1.39921	0.699607	+	0.714528i	$0.253359\pi$
$402$	18.4585	0.920627
$403$	−12.2439	−0.609912
$404$	1.36136	0.0677302
$405$	−1.81138	−0.0900084
$406$	0.621172	0.0308282
$407$	−0.948610	−0.0470208
$408$	−3.67874	−0.182125
$409$	−23.2252	−1.14841	−0.574207	−	0.818710i	$-0.694689\pi$
$409$	−23.2252	−1.14841	−0.574207	+	0.818710i	$0.694689\pi$
$410$	−13.1983	−0.651816
$411$	−21.4948	−1.06026
$412$	0.128996	0.00635520
$413$	−6.51166	−0.320418
$414$	1.44960	0.0712441
$415$	2.85555	0.140173
$416$	7.94427	0.389500
$417$	−26.4507	−1.29530
$418$	−6.43580	−0.314785
$419$	−31.7882	−1.55296	−0.776478	−	0.630144i	$-0.782996\pi$
$419$	−31.7882	−1.55296	−0.776478	+	0.630144i	$0.782996\pi$
$420$	−1.17559	−0.0573629
$421$	5.47968	0.267063	0.133532	−	0.991045i	$-0.457368\pi$
$421$	5.47968	0.267063	0.133532	+	0.991045i	$0.457368\pi$
$422$	−1.33657	−0.0650632
$423$	8.72776	0.424358
$424$	−25.0207	−1.21511
$425$	1.00000	0.0485071
$426$	−1.36564	−0.0661657
$427$	−11.4169	−0.552502
$428$	−8.29649	−0.401026
$429$	−3.71345	−0.179287
$430$	0.441703	0.0213008
$431$	−17.5592	−0.845799	−0.422899	−	0.906177i	$-0.638988\pi$
$431$	−17.5592	−0.845799	−0.422899	+	0.906177i	$0.638988\pi$
$432$	−11.6430	−0.560175
$433$	−16.3837	−0.787353	−0.393676	−	0.919249i	$-0.628797\pi$
$433$	−16.3837	−0.787353	−0.393676	+	0.919249i	$0.628797\pi$
$434$	9.29677	0.446259
$435$	−0.457957	−0.0219573
$436$	−10.6292	−0.509047
$437$	−3.12012	−0.149255
$438$	3.51105	0.167765
$439$	−38.0158	−1.81440	−0.907199	−	0.420702i	$-0.861784\pi$
$439$	−38.0158	−1.81440	−0.907199	+	0.420702i	$0.861784\pi$
$440$	−4.48246	−0.213693
$441$	7.84385	0.373517
$442$	2.43956	0.116038
$443$	−21.2581	−1.01000	−0.505002	−	0.863118i	$-0.668508\pi$
$443$	−21.2581	−1.01000	−0.505002	+	0.863118i	$0.668508\pi$
$444$	0.540120	0.0256330
$445$	−6.01322	−0.285054
$446$	−23.5400	−1.11465
$447$	23.8105	1.12620
$448$	−12.0764	−0.570555
$449$	−28.5350	−1.34665	−0.673324	−	0.739347i	$-0.735134\pi$
$449$	−28.5350	−1.34665	−0.673324	+	0.739347i	$0.735134\pi$
$450$	1.79691	0.0847070
$451$	−16.8133	−0.791709
$452$	1.45985	0.0686654
$453$	0.610353	0.0286769
$454$	−16.5919	−0.778698
$455$	3.02699	0.141907
$456$	14.2281	0.666292
$457$	3.59148	0.168002	0.0840012	−	0.996466i	$-0.473230\pi$
$457$	3.59148	0.168002	0.0840012	+	0.996466i	$0.473230\pi$
$458$	9.06737	0.423690
$459$	5.46332	0.255006
$460$	−0.559684	−0.0260954
$461$	−39.7515	−1.85141	−0.925705	−	0.378246i	$-0.876527\pi$
$461$	−39.7515	−1.85141	−0.925705	+	0.378246i	$0.876527\pi$
$462$	2.81962	0.131181
$463$	−17.1245	−0.795843	−0.397921	−	0.917419i	$-0.630268\pi$
$463$	−17.1245	−0.795843	−0.397921	+	0.917419i	$0.630268\pi$
$464$	−0.816778	−0.0379179
$465$	−6.85401	−0.317847
$466$	7.21430	0.334196
$467$	22.6805	1.04953	0.524764	−	0.851247i	$-0.324153\pi$
$467$	22.6805	1.04953	0.524764	+	0.851247i	$0.324153\pi$
$468$	−2.32831	−0.107626
$469$	−19.1676	−0.885076
$470$	6.34446	0.292648
$471$	−7.09541	−0.326939
$472$	14.1369	0.650704
$473$	0.562688	0.0258724
$474$	−13.2058	−0.606560
$475$	−3.86766	−0.177460
$476$	0.983846	0.0450945
$477$	12.7775	0.585042
$478$	30.4356	1.39209
$479$	−13.5311	−0.618253	−0.309126	−	0.951021i	$-0.600037\pi$
$479$	−13.5311	−0.618253	−0.309126	+	0.951021i	$0.600037\pi$
$480$	4.44712	0.202983
$481$	−1.39074	−0.0634122
$482$	4.75917	0.216774
$483$	1.36697	0.0621993
$484$	6.16088	0.280040
$485$	−17.0259	−0.773104
$486$	16.2584	0.737497
$487$	−37.9229	−1.71845	−0.859224	−	0.511599i	$-0.829053\pi$
$487$	−37.9229	−1.71845	−0.859224	+	0.511599i	$0.829053\pi$
$488$	24.7862	1.12202
$489$	−15.8581	−0.717127
$490$	5.70192	0.257587
$491$	24.8748	1.12258	0.561291	−	0.827618i	$-0.310305\pi$
$491$	24.8748	1.12258	0.561291	+	0.827618i	$0.310305\pi$
$492$	9.57318	0.431592
$493$	0.383262	0.0172612
$494$	−9.43540	−0.424518
$495$	2.28909	0.102887
$496$	−12.2243	−0.548887
$497$	1.41810	0.0636106
$498$	3.89966	0.174748
$499$	−3.98025	−0.178180	−0.0890902	−	0.996024i	$-0.528396\pi$
$499$	−3.98025	−0.178180	−0.0890902	+	0.996024i	$0.528396\pi$
$500$	−0.693776	−0.0310266
$501$	−14.9112	−0.666185
$502$	4.67415	0.208617
$503$	−5.55722	−0.247784	−0.123892	−	0.992296i	$-0.539538\pi$
$503$	−5.55722	−0.247784	−0.123892	+	0.992296i	$0.539538\pi$
$504$	6.86427	0.305759
$505$	−1.96225	−0.0873188
$506$	1.34239	0.0596764
$507$	10.0894	0.448085
$508$	2.55500	0.113360
$509$	−0.573086	−0.0254016	−0.0127008	−	0.999919i	$-0.504043\pi$
$509$	−0.573086	−0.0254016	−0.0127008	+	0.999919i	$0.504043\pi$
$510$	1.36564	0.0604717
$511$	−3.64592	−0.161286
$512$	21.0538	0.930456
$513$	−21.1303	−0.932924
$514$	−27.5521	−1.21527
$515$	−0.185934	−0.00819322
$516$	−0.320383	−0.0141041
$517$	8.08224	0.355456
$518$	1.05599	0.0463974
$519$	3.05969	0.134305
$520$	−6.57164	−0.288186
$521$	22.8333	1.00035	0.500174	−	0.865925i	$-0.333270\pi$
$521$	22.8333	1.00035	0.500174	+	0.865925i	$0.333270\pi$
$522$	0.688686	0.0301430
$523$	1.71586	0.0750292	0.0375146	−	0.999296i	$-0.488056\pi$
$523$	1.71586	0.0750292	0.0375146	+	0.999296i	$0.488056\pi$
$524$	7.40039	0.323288
$525$	1.69448	0.0739531
$526$	25.8198	1.12579
$527$	5.73609	0.249868
$528$	−3.70751	−0.161349
$529$	−22.3492	−0.971704
$530$	9.28834	0.403460
$531$	−7.21940	−0.313295
$532$	−3.80518	−0.164975
$533$	−24.6497	−1.06770
$534$	−8.21192	−0.355365
$535$	11.9585	0.517009
$536$	41.6131	1.79741
$537$	0.555854	0.0239869
$538$	25.8412	1.11409
$539$	7.26370	0.312870
$540$	−3.79033	−0.163110
$541$	−38.9339	−1.67390	−0.836950	−	0.547280i	$-0.815663\pi$
$541$	−38.9339	−1.67390	−0.836950	+	0.547280i	$0.815663\pi$
$542$	13.7454	0.590415
$543$	1.04278	0.0447501
$544$	−3.72178	−0.159570
$545$	15.3208	0.656271
$546$	4.13379	0.176910
$547$	−31.8226	−1.36064	−0.680318	−	0.732917i	$-0.738159\pi$
$547$	−31.8226	−1.36064	−0.680318	+	0.732917i	$0.738159\pi$
$548$	−12.4803	−0.533131
$549$	−12.6578	−0.540221
$550$	1.66400	0.0709534
$551$	−1.48232	−0.0631492
$552$	−2.96771	−0.126314
$553$	13.7130	0.583137
$554$	−22.2997	−0.947425
$555$	−0.778521	−0.0330464
$556$	−15.3578	−0.651315
$557$	−22.4641	−0.951834	−0.475917	−	0.879490i	$-0.657884\pi$
$557$	−22.4641	−0.951834	−0.475917	+	0.879490i	$0.657884\pi$
$558$	10.3072	0.436339
$559$	0.824946	0.0348915
$560$	3.02215	0.127709
$561$	1.73970	0.0734502
$562$	20.7021	0.873267
$563$	19.2941	0.813150	0.406575	−	0.913617i	$-0.366723\pi$
$563$	19.2941	0.813150	0.406575	+	0.913617i	$0.366723\pi$
$564$	−4.60187	−0.193774
$565$	−2.10420	−0.0885245
$566$	19.1891	0.806577
$567$	2.56873	0.107876
$568$	−3.07872	−0.129180
$569$	2.56632	0.107586	0.0537929	−	0.998552i	$-0.482869\pi$
$569$	2.56632	0.107586	0.0537929	+	0.998552i	$0.482869\pi$
$570$	−5.28184	−0.221232
$571$	22.2379	0.930626	0.465313	−	0.885146i	$-0.345942\pi$
$571$	22.2379	0.930626	0.465313	+	0.885146i	$0.345942\pi$
$572$	−2.15610	−0.0901510
$573$	9.27324	0.387395
$574$	18.7165	0.781211
$575$	0.806721	0.0336426
$576$	−13.3889	−0.557872
$577$	−39.1758	−1.63091	−0.815454	−	0.578822i	$-0.803513\pi$
$577$	−39.1758	−1.63091	−0.815454	+	0.578822i	$0.803513\pi$
$578$	−1.14290	−0.0475384
$579$	−12.9709	−0.539051
$580$	−0.265898	−0.0110408
$581$	−4.04946	−0.168000
$582$	−23.2513	−0.963796
$583$	11.8325	0.490050
$584$	7.91535	0.327540
$585$	3.35599	0.138753
$586$	21.7535	0.898629
$587$	−13.9595	−0.576172	−0.288086	−	0.957605i	$-0.593019\pi$
$587$	−13.9595	−0.576172	−0.288086	+	0.957605i	$0.593019\pi$
$588$	−4.13581	−0.170558
$589$	−22.1852	−0.914126
$590$	−5.24799	−0.216056
$591$	6.65407	0.273712
$592$	−1.38851	−0.0570676
$593$	16.7158	0.686437	0.343219	−	0.939256i	$-0.388483\pi$
$593$	16.7158	0.686437	0.343219	+	0.939256i	$0.388483\pi$
$594$	9.09100	0.373008
$595$	−1.41810	−0.0581365
$596$	13.8248	0.566286
$597$	−19.0150	−0.778230
$598$	1.96805	0.0804794
$599$	40.4066	1.65097	0.825484	−	0.564425i	$-0.190902\pi$
$599$	40.4066	1.65097	0.825484	+	0.564425i	$0.190902\pi$
$600$	−3.67874	−0.150184
$601$	3.83840	0.156571	0.0782857	−	0.996931i	$-0.475055\pi$
$601$	3.83840	0.156571	0.0782857	+	0.996931i	$0.475055\pi$
$602$	−0.626380	−0.0255294
$603$	−21.2509	−0.865402
$604$	0.354382	0.0144196
$605$	−8.88022	−0.361032
$606$	−2.67973	−0.108857
$607$	−6.50603	−0.264072	−0.132036	−	0.991245i	$-0.542151\pi$
$607$	−6.50603	−0.264072	−0.132036	+	0.991245i	$0.542151\pi$
$608$	14.3946	0.583777
$609$	0.649429	0.0263162
$610$	−9.20130	−0.372550
$611$	11.8492	0.479368
$612$	1.09078	0.0440921
$613$	41.9514	1.69440	0.847200	−	0.531273i	$-0.178286\pi$
$613$	41.9514	1.69440	0.847200	+	0.531273i	$0.178286\pi$
$614$	29.7398	1.20020
$615$	−13.7987	−0.556416
$616$	6.35658	0.256114
$617$	−19.3643	−0.779578	−0.389789	−	0.920904i	$-0.627452\pi$
$617$	−19.3643	−0.779578	−0.389789	+	0.920904i	$0.627452\pi$
$618$	−0.253919	−0.0102141
$619$	−39.5273	−1.58874	−0.794369	−	0.607436i	$-0.792198\pi$
$619$	−39.5273	−1.58874	−0.794369	+	0.607436i	$0.792198\pi$
$620$	−3.97956	−0.159823
$621$	4.40738	0.176862
$622$	−18.0762	−0.724790
$623$	8.52736	0.341642
$624$	−5.43551	−0.217595
$625$	1.00000	0.0400000
$626$	−24.9472	−0.997091
$627$	−6.72856	−0.268713
$628$	−4.11973	−0.164395
$629$	0.651541	0.0259787
$630$	−2.54820	−0.101523
$631$	−17.4445	−0.694454	−0.347227	−	0.937781i	$-0.612877\pi$
$631$	−17.4445	−0.694454	−0.347227	+	0.937781i	$0.612877\pi$
$632$	−29.7712	−1.18423
$633$	−1.39737	−0.0555405
$634$	26.7957	1.06420
$635$	−3.68274	−0.146145
$636$	−6.73717	−0.267146
$637$	10.6492	0.421936
$638$	0.637749	0.0252487
$639$	1.57223	0.0621966
$640$	−2.28924	−0.0904902
$641$	36.7309	1.45078	0.725391	−	0.688337i	$-0.241659\pi$
$641$	36.7309	1.45078	0.725391	+	0.688337i	$0.241659\pi$
$642$	16.3310	0.644533
$643$	−2.39378	−0.0944013	−0.0472006	−	0.998885i	$-0.515030\pi$
$643$	−2.39378	−0.0944013	−0.0472006	+	0.998885i	$0.515030\pi$
$644$	0.793688	0.0312757
$645$	0.461796	0.0181832
$646$	4.42035	0.173916
$647$	13.6283	0.535783	0.267892	−	0.963449i	$-0.413673\pi$
$647$	13.6283	0.535783	0.267892	+	0.963449i	$0.413673\pi$
$648$	−5.57675	−0.219075
$649$	−6.68544	−0.262426
$650$	2.43956	0.0956876
$651$	9.71968	0.380944
$652$	−9.20749	−0.360593
$653$	−37.9809	−1.48631	−0.743154	−	0.669121i	$-0.766671\pi$
$653$	−37.9809	−1.48631	−0.743154	+	0.669121i	$0.766671\pi$
$654$	20.9228	0.818144
$655$	−10.6668	−0.416787
$656$	−24.6103	−0.960870
$657$	−4.04219	−0.157701
$658$	−8.99709	−0.350743
$659$	−19.7228	−0.768292	−0.384146	−	0.923272i	$-0.625504\pi$
$659$	−19.7228	−0.768292	−0.384146	+	0.923272i	$0.625504\pi$
$660$	−1.20696	−0.0469810
$661$	−41.3583	−1.60865	−0.804326	−	0.594189i	$-0.797473\pi$
$661$	−41.3583	−1.60865	−0.804326	+	0.594189i	$0.797473\pi$
$662$	−2.82443	−0.109775
$663$	2.55054	0.0990548
$664$	8.79144	0.341174
$665$	5.48473	0.212689
$666$	1.17076	0.0453660
$667$	0.309185	0.0119717
$668$	−8.65775	−0.334978
$669$	−24.6108	−0.951508
$670$	−15.4479	−0.596803
$671$	−11.7216	−0.452506
$672$	−6.30648	−0.243278
$673$	−19.7251	−0.760345	−0.380173	−	0.924916i	$-0.624135\pi$
$673$	−19.7251	−0.760345	−0.380173	+	0.924916i	$0.624135\pi$
$674$	15.9037	0.612588
$675$	5.46332	0.210283
$676$	5.85808	0.225311
$677$	−0.737462	−0.0283430	−0.0141715	−	0.999900i	$-0.504511\pi$
$677$	−0.737462	−0.0283430	−0.0141715	+	0.999900i	$0.504511\pi$
$678$	−2.87359	−0.110360
$679$	24.1444	0.926577
$680$	3.07872	0.118064
$681$	−17.3467	−0.664727
$682$	9.54488	0.365492
$683$	−1.76767	−0.0676381	−0.0338190	−	0.999428i	$-0.510767\pi$
$683$	−1.76767	−0.0676381	−0.0338190	+	0.999428i	$0.510767\pi$
$684$	−4.21875	−0.161308
$685$	17.9889	0.687321
$686$	−19.4312	−0.741885
$687$	9.47984	0.361678
$688$	0.823626	0.0314005
$689$	17.3473	0.660881
$690$	1.10169	0.0419407
$691$	40.5244	1.54162	0.770811	−	0.637064i	$-0.219851\pi$
$691$	40.5244	1.54162	0.770811	+	0.637064i	$0.219851\pi$
$692$	1.77651	0.0675328
$693$	−3.24616	−0.123311
$694$	−29.3988	−1.11596
$695$	22.1365	0.839685
$696$	−1.40992	−0.0534429
$697$	11.5480	0.437413
$698$	27.1175	1.02641
$699$	7.54248	0.285283
$700$	0.983846	0.0371859
$701$	10.6822	0.403460	0.201730	−	0.979441i	$-0.435344\pi$
$701$	10.6822	0.403460	0.201730	+	0.979441i	$0.435344\pi$
$702$	13.3281	0.503038
$703$	−2.51994	−0.0950412
$704$	−12.3987	−0.467292
$705$	6.63307	0.249816
$706$	−17.2215	−0.648139
$707$	2.78267	0.104653
$708$	3.80656	0.143059
$709$	−30.5452	−1.14715	−0.573574	−	0.819154i	$-0.694444\pi$
$709$	−30.5452	−1.14715	−0.573574	+	0.819154i	$0.694444\pi$
$710$	1.14290	0.0428923
$711$	15.2035	0.570175
$712$	−18.5130	−0.693805
$713$	4.62742	0.173298
$714$	−1.93662	−0.0724763
$715$	3.10777	0.116224
$716$	0.322739	0.0120613
$717$	31.8202	1.18835
$718$	−35.4531	−1.32310
$719$	6.30240	0.235040	0.117520	−	0.993071i	$-0.462506\pi$
$719$	6.30240	0.235040	0.117520	+	0.993071i	$0.462506\pi$
$720$	3.35062	0.124870
$721$	0.263673	0.00981970
$722$	4.61874	0.171892
$723$	4.97566	0.185047
$724$	0.605458	0.0225017
$725$	0.383262	0.0142340
$726$	−12.1272	−0.450083
$727$	8.07300	0.299411	0.149705	−	0.988731i	$-0.452167\pi$
$727$	8.07300	0.299411	0.149705	+	0.988731i	$0.452167\pi$
$728$	9.31926	0.345395
$729$	22.4322	0.830821
$730$	−2.93838	−0.108755
$731$	−0.386475	−0.0142943
$732$	6.67404	0.246679
$733$	49.2546	1.81926	0.909631	−	0.415417i	$-0.136364\pi$
$733$	49.2546	1.81926	0.909631	+	0.415417i	$0.136364\pi$
$734$	−7.89858	−0.291542
$735$	5.96130	0.219886
$736$	−3.00244	−0.110671
$737$	−19.6791	−0.724889
$738$	20.7508	0.763846
$739$	−18.2217	−0.670295	−0.335147	−	0.942166i	$-0.608786\pi$
$739$	−18.2217	−0.670295	−0.335147	+	0.942166i	$0.608786\pi$
$740$	−0.452024	−0.0166167
$741$	−9.86461	−0.362386
$742$	−13.1718	−0.483553
$743$	−27.1141	−0.994718	−0.497359	−	0.867545i	$-0.665697\pi$
$743$	−27.1141	−0.994718	−0.497359	+	0.867545i	$0.665697\pi$
$744$	−21.1016	−0.773621
$745$	−19.9269	−0.730065
$746$	−1.43939	−0.0526998
$747$	−4.48959	−0.164265
$748$	1.01010	0.0369330
$749$	−16.9583	−0.619643
$750$	1.36564	0.0498663
$751$	−28.3154	−1.03324	−0.516622	−	0.856214i	$-0.672811\pi$
$751$	−28.3154	−1.03324	−0.516622	+	0.856214i	$0.672811\pi$
$752$	11.8303	0.431405
$753$	4.88677	0.178084
$754$	0.934992	0.0340504
$755$	−0.510802	−0.0185900
$756$	5.37507	0.195489
$757$	−1.77818	−0.0646289	−0.0323145	−	0.999478i	$-0.510288\pi$
$757$	−1.77818	−0.0646289	−0.0323145	+	0.999478i	$0.510288\pi$
$758$	21.8725	0.794446
$759$	1.40345	0.0509421
$760$	−11.9074	−0.431928
$761$	−32.0382	−1.16138	−0.580692	−	0.814123i	$-0.697218\pi$
$761$	−32.0382	−1.16138	−0.580692	+	0.814123i	$0.697218\pi$
$762$	−5.02931	−0.182193
$763$	−21.7265	−0.786550
$764$	5.38422	0.194794
$765$	−1.57223	−0.0568442
$766$	5.79400	0.209346
$767$	−9.80139	−0.353908
$768$	17.2248	0.621547
$769$	36.1557	1.30381	0.651904	−	0.758301i	$-0.273970\pi$
$769$	36.1557	1.30381	0.651904	+	0.758301i	$0.273970\pi$
$770$	−2.35973	−0.0850387
$771$	−28.8054	−1.03740
$772$	−7.53113	−0.271051
$773$	15.8537	0.570219	0.285109	−	0.958495i	$-0.407970\pi$
$773$	15.8537	0.570219	0.285109	+	0.958495i	$0.407970\pi$
$774$	−0.694461	−0.0249619
$775$	5.73609	0.206046
$776$	−52.4179	−1.88169
$777$	1.10402	0.0396066
$778$	31.9454	1.14530
$779$	−44.6638	−1.60025
$780$	−1.76950	−0.0633584
$781$	1.45595	0.0520979
$782$	−0.922002	−0.0329707
$783$	2.09388	0.0748293
$784$	10.6321	0.379719
$785$	5.93812	0.211941
$786$	−14.5671	−0.519591
$787$	−5.71704	−0.203790	−0.101895	−	0.994795i	$-0.532491\pi$
$787$	−5.71704	−0.203790	−0.101895	+	0.994795i	$0.532491\pi$
$788$	3.86347	0.137631
$789$	26.9943	0.961023
$790$	11.0518	0.393207
$791$	2.98398	0.106098
$792$	7.04746	0.250421
$793$	−17.1848	−0.610249
$794$	−24.3953	−0.865755
$795$	9.71087	0.344409
$796$	−11.0404	−0.391318
$797$	−46.1077	−1.63322	−0.816609	−	0.577192i	$-0.804149\pi$
$797$	−46.1077	−1.63322	−0.816609	+	0.577192i	$0.804149\pi$
$798$	7.49019	0.265150
$799$	−5.55119	−0.196387
$800$	−3.72178	−0.131585
$801$	9.45419	0.334047
$802$	−32.0232	−1.13078
$803$	−3.74322	−0.132095
$804$	11.2049	0.395166
$805$	−1.14401	−0.0403211
$806$	13.9936	0.492902
$807$	27.0167	0.951033
$808$	−6.04121	−0.212529
$809$	−22.7058	−0.798293	−0.399147	−	0.916887i	$-0.630694\pi$
$809$	−22.7058	−0.798293	−0.399147	+	0.916887i	$0.630694\pi$
$810$	2.07023	0.0727406
$811$	47.5135	1.66842	0.834212	−	0.551444i	$-0.185923\pi$
$811$	47.5135	1.66842	0.834212	+	0.551444i	$0.185923\pi$
$812$	0.377070	0.0132326
$813$	14.3707	0.504001
$814$	1.08417	0.0380001
$815$	13.2716	0.464882
$816$	2.54646	0.0891439
$817$	1.49475	0.0522948
$818$	26.5441	0.928094
$819$	−4.75913	−0.166298
$820$	−8.01175	−0.279783
$821$	19.3864	0.676589	0.338295	−	0.941040i	$-0.390150\pi$
$821$	19.3864	0.676589	0.338295	+	0.941040i	$0.390150\pi$
$822$	24.5664	0.856853
$823$	39.7973	1.38725	0.693624	−	0.720337i	$-0.256013\pi$
$823$	39.7973	1.38725	0.693624	+	0.720337i	$0.256013\pi$
$824$	−0.572438	−0.0199418
$825$	1.73970	0.0605686
$826$	7.44218	0.258947
$827$	−17.1569	−0.596603	−0.298301	−	0.954472i	$-0.596420\pi$
$827$	−17.1569	−0.596603	−0.298301	+	0.954472i	$0.596420\pi$
$828$	0.879953	0.0305805
$829$	33.7508	1.17222	0.586108	−	0.810233i	$-0.300660\pi$
$829$	33.7508	1.17222	0.586108	+	0.810233i	$0.300660\pi$
$830$	−3.26361	−0.113282
$831$	−23.3142	−0.808759
$832$	−18.1774	−0.630189
$833$	−4.98899	−0.172858
$834$	30.2306	1.04680
$835$	12.4792	0.431859
$836$	−3.90673	−0.135117
$837$	31.3381	1.08320
$838$	36.3308	1.25503
$839$	40.8261	1.40947	0.704737	−	0.709469i	$-0.251065\pi$
$839$	40.8261	1.40947	0.704737	+	0.709469i	$0.251065\pi$
$840$	5.21683	0.179998
$841$	−28.8531	−0.994935
$842$	−6.26273	−0.215828
$843$	21.6439	0.745455
$844$	−0.811339	−0.0279275
$845$	−8.44376	−0.290474
$846$	−9.97497	−0.342946
$847$	12.5931	0.432702
$848$	17.3196	0.594757
$849$	20.0620	0.688525
$850$	−1.14290	−0.0392012
$851$	0.525612	0.0180177
$852$	−0.828988	−0.0284007
$853$	−52.5717	−1.80002	−0.900011	−	0.435868i	$-0.856442\pi$
$853$	−52.5717	−1.80002	−0.900011	+	0.435868i	$0.856442\pi$
$854$	13.0484	0.446506
$855$	6.08086	0.207961
$856$	36.8167	1.25837
$857$	33.3137	1.13797	0.568986	−	0.822347i	$-0.307336\pi$
$857$	33.3137	1.13797	0.568986	+	0.822347i	$0.307336\pi$
$858$	4.24411	0.144892
$859$	43.0968	1.47044	0.735222	−	0.677826i	$-0.237078\pi$
$859$	43.0968	1.47044	0.735222	+	0.677826i	$0.237078\pi$
$860$	0.268128	0.00914307
$861$	19.5679	0.666872
$862$	20.0685	0.683535
$863$	11.8269	0.402592	0.201296	−	0.979530i	$-0.435485\pi$
$863$	11.8269	0.402592	0.201296	+	0.979530i	$0.435485\pi$
$864$	−20.3333	−0.691753
$865$	−2.56064	−0.0870643
$866$	18.7250	0.636302
$867$	−1.19489	−0.0405807
$868$	5.64343	0.191550
$869$	14.0790	0.477597
$870$	0.523399	0.0177449
$871$	−28.8511	−0.977584
$872$	47.1685	1.59733
$873$	26.7686	0.905980
$874$	3.56599	0.120621
$875$	−1.41810	−0.0479406
$876$	2.13132	0.0720105
$877$	−6.30613	−0.212943	−0.106471	−	0.994316i	$-0.533955\pi$
$877$	−6.30613	−0.212943	−0.106471	+	0.994316i	$0.533955\pi$
$878$	43.4484	1.46631
$879$	22.7431	0.767105
$880$	3.10280	0.104595
$881$	39.6553	1.33602	0.668011	−	0.744152i	$-0.267146\pi$
$881$	39.6553	1.33602	0.668011	+	0.744152i	$0.267146\pi$
$882$	−8.96475	−0.301859
$883$	−51.1866	−1.72257	−0.861283	−	0.508126i	$-0.830339\pi$
$883$	−51.1866	−1.72257	−0.861283	+	0.508126i	$0.830339\pi$
$884$	1.48089	0.0498077
$885$	−5.48672	−0.184434
$886$	24.2959	0.816238
$887$	−35.4430	−1.19006	−0.595030	−	0.803703i	$-0.702860\pi$
$887$	−35.4430	−1.19006	−0.595030	+	0.803703i	$0.702860\pi$
$888$	−2.39685	−0.0804330
$889$	5.22250	0.175157
$890$	6.87252	0.230367
$891$	2.63728	0.0883522
$892$	−14.2895	−0.478447
$893$	21.4701	0.718469
$894$	−27.2130	−0.910140
$895$	−0.465192	−0.0155497
$896$	3.24638	0.108454
$897$	2.05757	0.0687004
$898$	32.6126	1.08830
$899$	2.19842	0.0733215
$900$	1.09078	0.0363593
$901$	−8.12698	−0.270749
$902$	19.2160	0.639822
$903$	−0.654874	−0.0217929
$904$	−6.47826	−0.215464
$905$	−0.872700	−0.0290095
$906$	−0.697573	−0.0231753
$907$	−4.89099	−0.162403	−0.0812014	−	0.996698i	$-0.525876\pi$
$907$	−4.89099	−0.162403	−0.0812014	+	0.996698i	$0.525876\pi$
$908$	−10.0718	−0.334245
$909$	3.08511	0.102327
$910$	−3.45955	−0.114683
$911$	−17.0473	−0.564803	−0.282402	−	0.959296i	$-0.591131\pi$
$911$	−17.0473	−0.564803	−0.282402	+	0.959296i	$0.591131\pi$
$912$	−9.84883	−0.326127
$913$	−4.15753	−0.137594
$914$	−4.10471	−0.135772
$915$	−9.61987	−0.318023
$916$	5.50417	0.181863
$917$	15.1266	0.499526
$918$	−6.24404	−0.206084
$919$	28.7615	0.948756	0.474378	−	0.880321i	$-0.342673\pi$
$919$	28.7615	0.948756	0.474378	+	0.880321i	$0.342673\pi$
$920$	2.48367	0.0818841
$921$	31.0927	1.02454
$922$	45.4320	1.49622
$923$	2.13454	0.0702591
$924$	1.71160	0.0563074
$925$	0.651541	0.0214225
$926$	19.5716	0.643163
$927$	0.292331	0.00960142
$928$	−1.42642	−0.0468244
$929$	8.77796	0.287996	0.143998	−	0.989578i	$-0.454004\pi$
$929$	8.77796	0.287996	0.143998	+	0.989578i	$0.454004\pi$
$930$	7.83345	0.256869
$931$	19.2957	0.632390
$932$	4.37930	0.143449
$933$	−18.8985	−0.618709
$934$	−25.9216	−0.848180
$935$	−1.45595	−0.0476146
$936$	10.3322	0.337717
$937$	−49.3272	−1.61145	−0.805725	−	0.592290i	$-0.798224\pi$
$937$	−49.3272	−1.61145	−0.805725	+	0.592290i	$0.798224\pi$
$938$	21.9066	0.715277
$939$	−26.0820	−0.851155
$940$	3.85128	0.125615
$941$	24.5561	0.800504	0.400252	−	0.916405i	$-0.368923\pi$
$941$	24.5561	0.800504	0.400252	+	0.916405i	$0.368923\pi$
$942$	8.10936	0.264217
$943$	9.31604	0.303372
$944$	−9.78571	−0.318498
$945$	−7.74755	−0.252028
$946$	−0.643097	−0.0209089
$947$	35.7481	1.16166	0.580829	−	0.814025i	$-0.302728\pi$
$947$	35.7481	1.16166	0.580829	+	0.814025i	$0.302728\pi$
$948$	−8.01630	−0.260357
$949$	−5.48786	−0.178144
$950$	4.42035	0.143415
$951$	28.0147	0.908439
$952$	−4.36594	−0.141501
$953$	−19.9222	−0.645343	−0.322671	−	0.946511i	$-0.604581\pi$
$953$	−19.9222	−0.645343	−0.322671	+	0.946511i	$0.604581\pi$
$954$	−14.6034	−0.472804
$955$	−7.76074	−0.251132
$956$	18.4754	0.597536
$957$	0.666761	0.0215533
$958$	15.4647	0.499643
$959$	−25.5101	−0.823764
$960$	−10.1755	−0.328414
$961$	1.90271	0.0613778
$962$	1.58948	0.0512468
$963$	−18.8015	−0.605869
$964$	2.88896	0.0930471
$965$	10.8553	0.349443
$966$	−1.56231	−0.0502666
$967$	−7.03659	−0.226282	−0.113141	−	0.993579i	$-0.536091\pi$
$967$	−7.03659	−0.226282	−0.113141	+	0.993579i	$0.536091\pi$
$968$	−27.3397	−0.878732
$969$	4.62143	0.148462
$970$	19.4589	0.624787
$971$	−32.2341	−1.03444	−0.517220	−	0.855852i	$-0.673033\pi$
$971$	−32.2341	−1.03444	−0.517220	+	0.855852i	$0.673033\pi$
$972$	9.86936	0.316560
$973$	−31.3918	−1.00638
$974$	43.3421	1.38877
$975$	2.55054	0.0816827
$976$	−17.1573	−0.549191
$977$	33.4530	1.07026	0.535129	−	0.844770i	$-0.320263\pi$
$977$	33.4530	1.07026	0.535129	+	0.844770i	$0.320263\pi$
$978$	18.1242	0.579548
$979$	8.75494	0.279809
$980$	3.46124	0.110565
$981$	−24.0879	−0.769066
$982$	−28.4294	−0.907219
$983$	20.0803	0.640461	0.320231	−	0.947340i	$-0.396240\pi$
$983$	20.0803	0.640461	0.320231	+	0.947340i	$0.396240\pi$
$984$	−42.4822	−1.35428
$985$	−5.56876	−0.177435
$986$	−0.438031	−0.0139497
$987$	−9.40637	−0.299408
$988$	−5.72758	−0.182218
$989$	−0.311778	−0.00991395
$990$	−2.61620	−0.0831484
$991$	−24.1280	−0.766453	−0.383226	−	0.923654i	$-0.625187\pi$
$991$	−24.1280	−0.766453	−0.383226	+	0.923654i	$0.625187\pi$
$992$	−21.3485	−0.677814
$993$	−2.95291	−0.0937078
$994$	−1.62075	−0.0514071
$995$	15.9135	0.504493
$996$	2.36721	0.0750081
$997$	−0.939731	−0.0297616	−0.0148808	−	0.999889i	$-0.504737\pi$
$997$	−0.939731	−0.0297616	−0.0148808	+	0.999889i	$0.504737\pi$
$998$	4.54903	0.143997
$999$	3.55958	0.112620

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.a.1.10	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.a.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-1.14290 q^{2} -1.19489 q^{3} -0.693776 q^{4} +1.00000 q^{5} +1.36564 q^{6} -1.41810 q^{7} +3.07872 q^{8} -1.57223 q^{9} +O(q^{10})\)	\(q-1.14290 q^{2} -1.19489 q^{3} -0.693776 q^{4} +1.00000 q^{5} +1.36564 q^{6} -1.41810 q^{7} +3.07872 q^{8} -1.57223 q^{9} -1.14290 q^{10} -1.45595 q^{11} +0.828988 q^{12} -2.13454 q^{13} +1.62075 q^{14} -1.19489 q^{15} -2.13112 q^{16} +1.00000 q^{17} +1.79691 q^{18} -3.86766 q^{19} -0.693776 q^{20} +1.69448 q^{21} +1.66400 q^{22} +0.806721 q^{23} -3.67874 q^{24} +1.00000 q^{25} +2.43956 q^{26} +5.46332 q^{27} +0.983846 q^{28} +0.383262 q^{29} +1.36564 q^{30} +5.73609 q^{31} -3.72178 q^{32} +1.73970 q^{33} -1.14290 q^{34} -1.41810 q^{35} +1.09078 q^{36} +0.651541 q^{37} +4.42035 q^{38} +2.55054 q^{39} +3.07872 q^{40} +11.5480 q^{41} -1.93662 q^{42} -0.386475 q^{43} +1.01010 q^{44} -1.57223 q^{45} -0.922002 q^{46} -5.55119 q^{47} +2.54646 q^{48} -4.98899 q^{49} -1.14290 q^{50} -1.19489 q^{51} +1.48089 q^{52} -8.12698 q^{53} -6.24404 q^{54} -1.45595 q^{55} -4.36594 q^{56} +4.62143 q^{57} -0.438031 q^{58} +4.59181 q^{59} +0.828988 q^{60} +8.05082 q^{61} -6.55578 q^{62} +2.22959 q^{63} +8.51587 q^{64} -2.13454 q^{65} -1.98831 q^{66} +13.5164 q^{67} -0.693776 q^{68} -0.963944 q^{69} +1.62075 q^{70} -1.00000 q^{71} -4.84047 q^{72} +2.57099 q^{73} -0.744647 q^{74} -1.19489 q^{75} +2.68329 q^{76} +2.06468 q^{77} -2.91502 q^{78} -9.66998 q^{79} -2.13112 q^{80} -1.81138 q^{81} -13.1983 q^{82} +2.85555 q^{83} -1.17559 q^{84} +1.00000 q^{85} +0.441703 q^{86} -0.457957 q^{87} -4.48246 q^{88} -6.01322 q^{89} +1.79691 q^{90} +3.02699 q^{91} -0.559684 q^{92} -6.85401 q^{93} +6.34446 q^{94} -3.86766 q^{95} +4.44712 q^{96} -17.0259 q^{97} +5.70192 q^{98} +2.28909 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9}+O(q^{10}) \) 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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