LMFDB - Embedded newform 4034.2.a.b.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$1$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.95232 q^{3} +1.00000 q^{4} -1.60299 q^{5} +1.95232 q^{6} -2.46247 q^{7} -1.00000 q^{8} +0.811553 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.95232 q^{3} +1.00000 q^{4} -1.60299 q^{5} +1.95232 q^{6} -2.46247 q^{7} -1.00000 q^{8} +0.811553 q^{9} +1.60299 q^{10} -1.22325 q^{11} -1.95232 q^{12} -0.0707487 q^{13} +2.46247 q^{14} +3.12954 q^{15} +1.00000 q^{16} -0.614699 q^{17} -0.811553 q^{18} -4.27001 q^{19} -1.60299 q^{20} +4.80752 q^{21} +1.22325 q^{22} +3.57162 q^{23} +1.95232 q^{24} -2.43043 q^{25} +0.0707487 q^{26} +4.27255 q^{27} -2.46247 q^{28} +6.60518 q^{29} -3.12954 q^{30} +6.99329 q^{31} -1.00000 q^{32} +2.38817 q^{33} +0.614699 q^{34} +3.94730 q^{35} +0.811553 q^{36} +3.78421 q^{37} +4.27001 q^{38} +0.138124 q^{39} +1.60299 q^{40} -7.69895 q^{41} -4.80752 q^{42} -2.94677 q^{43} -1.22325 q^{44} -1.30091 q^{45} -3.57162 q^{46} +4.45999 q^{47} -1.95232 q^{48} -0.936264 q^{49} +2.43043 q^{50} +1.20009 q^{51} -0.0707487 q^{52} +5.25896 q^{53} -4.27255 q^{54} +1.96085 q^{55} +2.46247 q^{56} +8.33643 q^{57} -6.60518 q^{58} -1.04102 q^{59} +3.12954 q^{60} +6.55042 q^{61} -6.99329 q^{62} -1.99842 q^{63} +1.00000 q^{64} +0.113409 q^{65} -2.38817 q^{66} +0.787775 q^{67} -0.614699 q^{68} -6.97294 q^{69} -3.94730 q^{70} +0.133893 q^{71} -0.811553 q^{72} +10.6064 q^{73} -3.78421 q^{74} +4.74498 q^{75} -4.27001 q^{76} +3.01220 q^{77} -0.138124 q^{78} +3.58406 q^{79} -1.60299 q^{80} -10.7760 q^{81} +7.69895 q^{82} -9.60951 q^{83} +4.80752 q^{84} +0.985355 q^{85} +2.94677 q^{86} -12.8954 q^{87} +1.22325 q^{88} -6.25366 q^{89} +1.30091 q^{90} +0.174216 q^{91} +3.57162 q^{92} -13.6531 q^{93} -4.45999 q^{94} +6.84477 q^{95} +1.95232 q^{96} +12.6652 q^{97} +0.936264 q^{98} -0.992729 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) $ 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9} - 6 q^{10} - 9 q^{11} - 6 q^{12} - 7 q^{13} + 14 q^{14} - 19 q^{15} + 35 q^{16} + 17 q^{17} - 23 q^{18} - 25 q^{19} + 6 q^{20} - 15 q^{21} + 9 q^{22} - 12 q^{23} + 6 q^{24} + 7 q^{25} + 7 q^{26} - 27 q^{27} - 14 q^{28} - 13 q^{29} + 19 q^{30} - 69 q^{31} - 35 q^{32} + q^{33} - 17 q^{34} - 4 q^{35} + 23 q^{36} - 22 q^{37} + 25 q^{38} - 38 q^{39} - 6 q^{40} + 15 q^{42} - 32 q^{43} - 9 q^{44} + 9 q^{45} + 12 q^{46} - 18 q^{47} - 6 q^{48} - 19 q^{49} - 7 q^{50} - 21 q^{51} - 7 q^{52} + 20 q^{53} + 27 q^{54} - 54 q^{55} + 14 q^{56} + 28 q^{57} + 13 q^{58} - 21 q^{59} - 19 q^{60} - 67 q^{61} + 69 q^{62} - 28 q^{63} + 35 q^{64} + 22 q^{65} - q^{66} - 18 q^{67} + 17 q^{68} - 42 q^{69} + 4 q^{70} - 36 q^{71} - 23 q^{72} - 18 q^{73} + 22 q^{74} - 49 q^{75} - 25 q^{76} + 20 q^{77} + 38 q^{78} - 92 q^{79} + 6 q^{80} - 25 q^{81} + 42 q^{83} - 15 q^{84} - 29 q^{85} + 32 q^{86} - 40 q^{87} + 9 q^{88} - 8 q^{89} - 9 q^{90} - 89 q^{91} - 12 q^{92} - q^{93} + 18 q^{94} - 62 q^{95} + 6 q^{96} - 40 q^{97} + 19 q^{98} - 64 q^{99}+O(q^{100}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9 - 6 * q^10 - 9 * q^11 - 6 * q^12 - 7 * q^13 + 14 * q^14 - 19 * q^15 + 35 * q^16 + 17 * q^17 - 23 * q^18 - 25 * q^19 + 6 * q^20 - 15 * q^21 + 9 * q^22 - 12 * q^23 + 6 * q^24 + 7 * q^25 + 7 * q^26 - 27 * q^27 - 14 * q^28 - 13 * q^29 + 19 * q^30 - 69 * q^31 - 35 * q^32 + q^33 - 17 * q^34 - 4 * q^35 + 23 * q^36 - 22 * q^37 + 25 * q^38 - 38 * q^39 - 6 * q^40 + 15 * q^42 - 32 * q^43 - 9 * q^44 + 9 * q^45 + 12 * q^46 - 18 * q^47 - 6 * q^48 - 19 * q^49 - 7 * q^50 - 21 * q^51 - 7 * q^52 + 20 * q^53 + 27 * q^54 - 54 * q^55 + 14 * q^56 + 28 * q^57 + 13 * q^58 - 21 * q^59 - 19 * q^60 - 67 * q^61 + 69 * q^62 - 28 * q^63 + 35 * q^64 + 22 * q^65 - q^66 - 18 * q^67 + 17 * q^68 - 42 * q^69 + 4 * q^70 - 36 * q^71 - 23 * q^72 - 18 * q^73 + 22 * q^74 - 49 * q^75 - 25 * q^76 + 20 * q^77 + 38 * q^78 - 92 * q^79 + 6 * q^80 - 25 * q^81 + 42 * q^83 - 15 * q^84 - 29 * q^85 + 32 * q^86 - 40 * q^87 + 9 * q^88 - 8 * q^89 - 9 * q^90 - 89 * q^91 - 12 * q^92 - q^93 + 18 * q^94 - 62 * q^95 + 6 * q^96 - 40 * q^97 + 19 * q^98 - 64 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.95232	−1.12717	−0.563586	−	0.826057i	$-0.690579\pi$
$3$	−1.95232	−1.12717	−0.563586	+	0.826057i	$0.690579\pi$
$4$	1.00000	0.500000
$5$	−1.60299	−0.716878	−0.358439	−	0.933553i	$-0.616691\pi$
$5$	−1.60299	−0.716878	−0.358439	+	0.933553i	$0.616691\pi$
$6$	1.95232	0.797031
$7$	−2.46247	−0.930724	−0.465362	−	0.885120i	$-0.654076\pi$
$7$	−2.46247	−0.930724	−0.465362	+	0.885120i	$0.654076\pi$
$8$	−1.00000	−0.353553
$9$	0.811553	0.270518
$10$	1.60299	0.506909
$11$	−1.22325	−0.368822	−0.184411	−	0.982849i	$-0.559038\pi$
$11$	−1.22325	−0.368822	−0.184411	+	0.982849i	$0.559038\pi$
$12$	−1.95232	−0.563586
$13$	−0.0707487	−0.0196222	−0.00981108	−	0.999952i	$-0.503123\pi$
$13$	−0.0707487	−0.0196222	−0.00981108	+	0.999952i	$0.503123\pi$
$14$	2.46247	0.658122
$15$	3.12954	0.808045
$16$	1.00000	0.250000
$17$	−0.614699	−0.149086	−0.0745432	−	0.997218i	$-0.523750\pi$
$17$	−0.614699	−0.149086	−0.0745432	+	0.997218i	$0.523750\pi$
$18$	−0.811553	−0.191285
$19$	−4.27001	−0.979608	−0.489804	−	0.871833i	$-0.662932\pi$
$19$	−4.27001	−0.979608	−0.489804	+	0.871833i	$0.662932\pi$
$20$	−1.60299	−0.358439
$21$	4.80752	1.04909
$22$	1.22325	0.260797
$23$	3.57162	0.744734	0.372367	−	0.928086i	$-0.378546\pi$
$23$	3.57162	0.744734	0.372367	+	0.928086i	$0.378546\pi$
$24$	1.95232	0.398516
$25$	−2.43043	−0.486086
$26$	0.0707487	0.0138750
$27$	4.27255	0.822252
$28$	−2.46247	−0.465362
$29$	6.60518	1.22655	0.613275	−	0.789869i	$-0.289852\pi$
$29$	6.60518	1.22655	0.613275	+	0.789869i	$0.289852\pi$
$30$	−3.12954	−0.571374
$31$	6.99329	1.25603	0.628016	−	0.778200i	$-0.283867\pi$
$31$	6.99329	1.25603	0.628016	+	0.778200i	$0.283867\pi$
$32$	−1.00000	−0.176777
$33$	2.38817	0.415726
$34$	0.614699	0.105420
$35$	3.94730	0.667216
$36$	0.811553	0.135259
$37$	3.78421	0.622120	0.311060	−	0.950390i	$-0.399316\pi$
$37$	3.78421	0.622120	0.311060	+	0.950390i	$0.399316\pi$
$38$	4.27001	0.692687
$39$	0.138124	0.0221176
$40$	1.60299	0.253455
$41$	−7.69895	−1.20237	−0.601187	−	0.799108i	$-0.705305\pi$
$41$	−7.69895	−1.20237	−0.601187	+	0.799108i	$0.705305\pi$
$42$	−4.80752	−0.741817
$43$	−2.94677	−0.449379	−0.224689	−	0.974430i	$-0.572137\pi$
$43$	−2.94677	−0.449379	−0.224689	+	0.974430i	$0.572137\pi$
$44$	−1.22325	−0.184411
$45$	−1.30091	−0.193928
$46$	−3.57162	−0.526606
$47$	4.45999	0.650556	0.325278	−	0.945618i	$-0.394542\pi$
$47$	4.45999	0.650556	0.325278	+	0.945618i	$0.394542\pi$
$48$	−1.95232	−0.281793
$49$	−0.936264	−0.133752
$50$	2.43043	0.343715
$51$	1.20009	0.168046
$52$	−0.0707487	−0.00981108
$53$	5.25896	0.722374	0.361187	−	0.932493i	$-0.382372\pi$
$53$	5.25896	0.722374	0.361187	+	0.932493i	$0.382372\pi$
$54$	−4.27255	−0.581420
$55$	1.96085	0.264400
$56$	2.46247	0.329061
$57$	8.33643	1.10419
$58$	−6.60518	−0.867303
$59$	−1.04102	−0.135530	−0.0677648	−	0.997701i	$-0.521587\pi$
$59$	−1.04102	−0.135530	−0.0677648	+	0.997701i	$0.521587\pi$
$60$	3.12954	0.404022
$61$	6.55042	0.838696	0.419348	−	0.907826i	$-0.362259\pi$
$61$	6.55042	0.838696	0.419348	+	0.907826i	$0.362259\pi$
$62$	−6.99329	−0.888149
$63$	−1.99842	−0.251778
$64$	1.00000	0.125000
$65$	0.113409	0.0140667
$66$	−2.38817	−0.293963
$67$	0.787775	0.0962420	0.0481210	−	0.998842i	$-0.484677\pi$
$67$	0.787775	0.0962420	0.0481210	+	0.998842i	$0.484677\pi$
$68$	−0.614699	−0.0745432
$69$	−6.97294	−0.839444
$70$	−3.94730	−0.471793
$71$	0.133893	0.0158902	0.00794510	−	0.999968i	$-0.497471\pi$
$71$	0.133893	0.0158902	0.00794510	+	0.999968i	$0.497471\pi$
$72$	−0.811553	−0.0956425
$73$	10.6064	1.24139	0.620693	−	0.784054i	$-0.286852\pi$
$73$	10.6064	1.24139	0.620693	+	0.784054i	$0.286852\pi$
$74$	−3.78421	−0.439905
$75$	4.74498	0.547903
$76$	−4.27001	−0.489804
$77$	3.01220	0.343272
$78$	−0.138124	−0.0156395
$79$	3.58406	0.403239	0.201619	−	0.979464i	$-0.435380\pi$
$79$	3.58406	0.403239	0.201619	+	0.979464i	$0.435380\pi$
$80$	−1.60299	−0.179219
$81$	−10.7760	−1.19734
$82$	7.69895	0.850207
$83$	−9.60951	−1.05478	−0.527390	−	0.849623i	$-0.676829\pi$
$83$	−9.60951	−1.05478	−0.527390	+	0.849623i	$0.676829\pi$
$84$	4.80752	0.524543
$85$	0.985355	0.106877
$86$	2.94677	0.317759
$87$	−12.8954	−1.38253
$88$	1.22325	0.130398
$89$	−6.25366	−0.662887	−0.331444	−	0.943475i	$-0.607536\pi$
$89$	−6.25366	−0.662887	−0.331444	+	0.943475i	$0.607536\pi$
$90$	1.30091	0.137128
$91$	0.174216	0.0182628
$92$	3.57162	0.372367
$93$	−13.6531	−1.41576
$94$	−4.45999	−0.460013
$95$	6.84477	0.702259
$96$	1.95232	0.199258
$97$	12.6652	1.28596	0.642979	−	0.765884i	$-0.277698\pi$
$97$	12.6652	1.28596	0.642979	+	0.765884i	$0.277698\pi$
$98$	0.936264	0.0945770
$99$	−0.992729	−0.0997730
$100$	−2.43043	−0.243043
$101$	−5.70681	−0.567849	−0.283924	−	0.958847i	$-0.591636\pi$
$101$	−5.70681	−0.567849	−0.283924	+	0.958847i	$0.591636\pi$
$102$	−1.20009	−0.118827
$103$	6.46272	0.636791	0.318395	−	0.947958i	$-0.396856\pi$
$103$	6.46272	0.636791	0.318395	+	0.947958i	$0.396856\pi$
$104$	0.0707487	0.00693748
$105$	−7.70639	−0.752067
$106$	−5.25896	−0.510796
$107$	−7.84102	−0.758020	−0.379010	−	0.925393i	$-0.623735\pi$
$107$	−7.84102	−0.758020	−0.379010	+	0.925393i	$0.623735\pi$
$108$	4.27255	0.411126
$109$	12.0178	1.15110	0.575548	−	0.817768i	$-0.304789\pi$
$109$	12.0178	1.15110	0.575548	+	0.817768i	$0.304789\pi$
$110$	−1.96085	−0.186959
$111$	−7.38799	−0.701237
$112$	−2.46247	−0.232681
$113$	13.5531	1.27497	0.637485	−	0.770463i	$-0.279975\pi$
$113$	13.5531	1.27497	0.637485	+	0.770463i	$0.279975\pi$
$114$	−8.33643	−0.780778
$115$	−5.72526	−0.533883
$116$	6.60518	0.613275
$117$	−0.0574163	−0.00530814
$118$	1.04102	0.0958338
$119$	1.51368	0.138758
$120$	−3.12954	−0.285687
$121$	−9.50367	−0.863970
$122$	−6.55042	−0.593047
$123$	15.0308	1.35528
$124$	6.99329	0.628016
$125$	11.9109	1.06534
$126$	1.99842	0.178034
$127$	−16.9649	−1.50539	−0.752695	−	0.658369i	$-0.771246\pi$
$127$	−16.9649	−1.50539	−0.752695	+	0.658369i	$0.771246\pi$
$128$	−1.00000	−0.0883883
$129$	5.75304	0.506527
$130$	−0.113409	−0.00994665
$131$	5.17950	0.452535	0.226268	−	0.974065i	$-0.427348\pi$
$131$	5.17950	0.452535	0.226268	+	0.974065i	$0.427348\pi$
$132$	2.38817	0.207863
$133$	10.5148	0.911745
$134$	−0.787775	−0.0680534
$135$	−6.84884	−0.589454
$136$	0.614699	0.0527100
$137$	11.2522	0.961338	0.480669	−	0.876902i	$-0.340394\pi$
$137$	11.2522	0.961338	0.480669	+	0.876902i	$0.340394\pi$
$138$	6.97294	0.593576
$139$	−5.59529	−0.474586	−0.237293	−	0.971438i	$-0.576260\pi$
$139$	−5.59529	−0.474586	−0.237293	+	0.971438i	$0.576260\pi$
$140$	3.94730	0.333608
$141$	−8.70733	−0.733289
$142$	−0.133893	−0.0112361
$143$	0.0865430	0.00723709
$144$	0.811553	0.0676294
$145$	−10.5880	−0.879287
$146$	−10.6064	−0.877792
$147$	1.82789	0.150762
$148$	3.78421	0.311060
$149$	16.2077	1.32779	0.663895	−	0.747826i	$-0.268902\pi$
$149$	16.2077	1.32779	0.663895	+	0.747826i	$0.268902\pi$
$150$	−4.74498	−0.387426
$151$	−3.84393	−0.312814	−0.156407	−	0.987693i	$-0.549991\pi$
$151$	−3.84393	−0.312814	−0.156407	+	0.987693i	$0.549991\pi$
$152$	4.27001	0.346344
$153$	−0.498861	−0.0403305
$154$	−3.01220	−0.242730
$155$	−11.2102	−0.900422
$156$	0.138124	0.0110588
$157$	−17.8728	−1.42640	−0.713202	−	0.700959i	$-0.752756\pi$
$157$	−17.8728	−1.42640	−0.713202	+	0.700959i	$0.752756\pi$
$158$	−3.58406	−0.285133
$159$	−10.2672	−0.814241
$160$	1.60299	0.126727
$161$	−8.79499	−0.693142
$162$	10.7760	0.846646
$163$	−3.33289	−0.261052	−0.130526	−	0.991445i	$-0.541667\pi$
$163$	−3.33289	−0.261052	−0.130526	+	0.991445i	$0.541667\pi$
$164$	−7.69895	−0.601187
$165$	−3.82820	−0.298025
$166$	9.60951	0.745842
$167$	15.4408	1.19485	0.597423	−	0.801926i	$-0.296191\pi$
$167$	15.4408	1.19485	0.597423	+	0.801926i	$0.296191\pi$
$168$	−4.80752	−0.370908
$169$	−12.9950	−0.999615
$170$	−0.985355	−0.0755733
$171$	−3.46534	−0.265001
$172$	−2.94677	−0.224689
$173$	15.7891	1.20042	0.600211	−	0.799842i	$-0.295083\pi$
$173$	15.7891	1.20042	0.600211	+	0.799842i	$0.295083\pi$
$174$	12.8954	0.977600
$175$	5.98485	0.452412
$176$	−1.22325	−0.0922056
$177$	2.03241	0.152765
$178$	6.25366	0.468732
$179$	−20.8821	−1.56080	−0.780400	−	0.625280i	$-0.784985\pi$
$179$	−20.8821	−1.56080	−0.780400	+	0.625280i	$0.784985\pi$
$180$	−1.30091	−0.0969641
$181$	−2.37926	−0.176849	−0.0884243	−	0.996083i	$-0.528183\pi$
$181$	−2.37926	−0.176849	−0.0884243	+	0.996083i	$0.528183\pi$
$182$	−0.174216	−0.0129138
$183$	−12.7885	−0.945355
$184$	−3.57162	−0.263303
$185$	−6.06604	−0.445984
$186$	13.6531	1.00110
$187$	0.751928	0.0549864
$188$	4.45999	0.325278
$189$	−10.5210	−0.765290
$190$	−6.84477	−0.496572
$191$	−6.90940	−0.499947	−0.249973	−	0.968253i	$-0.580422\pi$
$191$	−6.90940	−0.499947	−0.249973	+	0.968253i	$0.580422\pi$
$192$	−1.95232	−0.140897
$193$	−17.2501	−1.24169	−0.620845	−	0.783934i	$-0.713210\pi$
$193$	−17.2501	−1.24169	−0.620845	+	0.783934i	$0.713210\pi$
$194$	−12.6652	−0.909309
$195$	−0.221411	−0.0158556
$196$	−0.936264	−0.0668760
$197$	6.55335	0.466907	0.233454	−	0.972368i	$-0.424997\pi$
$197$	6.55335	0.466907	0.233454	+	0.972368i	$0.424997\pi$
$198$	0.992729	0.0705501
$199$	−11.1352	−0.789353	−0.394676	−	0.918820i	$-0.629143\pi$
$199$	−11.1352	−0.789353	−0.394676	+	0.918820i	$0.629143\pi$
$200$	2.43043	0.171857
$201$	−1.53799	−0.108481
$202$	5.70681	0.401530
$203$	−16.2650	−1.14158
$204$	1.20009	0.0840230
$205$	12.3413	0.861955
$206$	−6.46272	−0.450279
$207$	2.89856	0.201464
$208$	−0.0707487	−0.00490554
$209$	5.22327	0.361301
$210$	7.70639	0.531792
$211$	0.564385	0.0388539	0.0194269	−	0.999811i	$-0.493816\pi$
$211$	0.564385	0.0388539	0.0194269	+	0.999811i	$0.493816\pi$
$212$	5.25896	0.361187
$213$	−0.261402	−0.0179110
$214$	7.84102	0.536001
$215$	4.72364	0.322150
$216$	−4.27255	−0.290710
$217$	−17.2207	−1.16902
$218$	−12.0178	−0.813948
$219$	−20.7071	−1.39926
$220$	1.96085	0.132200
$221$	0.0434892	0.00292540
$222$	7.38799	0.495849
$223$	−2.82618	−0.189255	−0.0946274	−	0.995513i	$-0.530166\pi$
$223$	−2.82618	−0.189255	−0.0946274	+	0.995513i	$0.530166\pi$
$224$	2.46247	0.164530
$225$	−1.97242	−0.131495
$226$	−13.5531	−0.901540
$227$	−24.6604	−1.63677	−0.818385	−	0.574670i	$-0.805130\pi$
$227$	−24.6604	−1.63677	−0.818385	+	0.574670i	$0.805130\pi$
$228$	8.33643	0.552094
$229$	3.25745	0.215258	0.107629	−	0.994191i	$-0.465674\pi$
$229$	3.25745	0.215258	0.107629	+	0.994191i	$0.465674\pi$
$230$	5.72526	0.377512
$231$	−5.88078	−0.386927
$232$	−6.60518	−0.433651
$233$	18.3415	1.20159	0.600795	−	0.799403i	$-0.294851\pi$
$233$	18.3415	1.20159	0.600795	+	0.799403i	$0.294851\pi$
$234$	0.0574163	0.00375342
$235$	−7.14931	−0.466369
$236$	−1.04102	−0.0677648
$237$	−6.99724	−0.454520
$238$	−1.51368	−0.0981170
$239$	−0.416247	−0.0269248	−0.0134624	−	0.999909i	$-0.504285\pi$
$239$	−0.416247	−0.0269248	−0.0134624	+	0.999909i	$0.504285\pi$
$240$	3.12954	0.202011
$241$	−21.1501	−1.36240	−0.681198	−	0.732100i	$-0.738541\pi$
$241$	−21.1501	−1.36240	−0.681198	+	0.732100i	$0.738541\pi$
$242$	9.50367	0.610919
$243$	8.22064	0.527354
$244$	6.55042	0.419348
$245$	1.50082	0.0958838
$246$	−15.0308	−0.958330
$247$	0.302098	0.0192220
$248$	−6.99329	−0.444074
$249$	18.7608	1.18892
$250$	−11.9109	−0.753311
$251$	14.9152	0.941438	0.470719	−	0.882283i	$-0.343995\pi$
$251$	14.9152	0.941438	0.470719	+	0.882283i	$0.343995\pi$
$252$	−1.99842	−0.125889
$253$	−4.36897	−0.274675
$254$	16.9649	1.06447
$255$	−1.92373	−0.120469
$256$	1.00000	0.0625000
$257$	1.37901	0.0860204	0.0430102	−	0.999075i	$-0.486305\pi$
$257$	1.37901	0.0860204	0.0430102	+	0.999075i	$0.486305\pi$
$258$	−5.75304	−0.358169
$259$	−9.31849	−0.579022
$260$	0.113409	0.00703335
$261$	5.36046	0.331804
$262$	−5.17950	−0.319991
$263$	18.7977	1.15911	0.579556	−	0.814932i	$-0.303226\pi$
$263$	18.7977	1.15911	0.579556	+	0.814932i	$0.303226\pi$
$264$	−2.38817	−0.146981
$265$	−8.43005	−0.517854
$266$	−10.5148	−0.644701
$267$	12.2092	0.747188
$268$	0.787775	0.0481210
$269$	18.5134	1.12878	0.564392	−	0.825507i	$-0.309111\pi$
$269$	18.5134	1.12878	0.564392	+	0.825507i	$0.309111\pi$
$270$	6.84884	0.416807
$271$	−30.6924	−1.86443	−0.932215	−	0.361904i	$-0.882127\pi$
$271$	−30.6924	−1.86443	−0.932215	+	0.361904i	$0.882127\pi$
$272$	−0.614699	−0.0372716
$273$	−0.340126	−0.0205854
$274$	−11.2522	−0.679769
$275$	2.97301	0.179279
$276$	−6.97294	−0.419722
$277$	25.4235	1.52755	0.763775	−	0.645482i	$-0.223344\pi$
$277$	25.4235	1.52755	0.763775	+	0.645482i	$0.223344\pi$
$278$	5.59529	0.335583
$279$	5.67543	0.339779
$280$	−3.94730	−0.235896
$281$	31.3022	1.86734	0.933668	−	0.358141i	$-0.116589\pi$
$281$	31.3022	1.86734	0.933668	+	0.358141i	$0.116589\pi$
$282$	8.70733	0.518514
$283$	−8.54203	−0.507771	−0.253885	−	0.967234i	$-0.581709\pi$
$283$	−8.54203	−0.507771	−0.253885	+	0.967234i	$0.581709\pi$
$284$	0.133893	0.00794510
$285$	−13.3632	−0.791567
$286$	−0.0865430	−0.00511740
$287$	18.9584	1.11908
$288$	−0.811553	−0.0478212
$289$	−16.6221	−0.977773
$290$	10.5880	0.621750
$291$	−24.7266	−1.44950
$292$	10.6064	0.620693
$293$	4.52063	0.264098	0.132049	−	0.991243i	$-0.457844\pi$
$293$	4.52063	0.264098	0.132049	+	0.991243i	$0.457844\pi$
$294$	−1.82789	−0.106605
$295$	1.66874	0.0971581
$296$	−3.78421	−0.219953
$297$	−5.22637	−0.303265
$298$	−16.2077	−0.938889
$299$	−0.252687	−0.0146133
$300$	4.74498	0.273952
$301$	7.25633	0.418248
$302$	3.84393	0.221193
$303$	11.1415	0.640063
$304$	−4.27001	−0.244902
$305$	−10.5002	−0.601242
$306$	0.498861	0.0285180
$307$	8.09519	0.462017	0.231008	−	0.972952i	$-0.425797\pi$
$307$	8.09519	0.462017	0.231008	+	0.972952i	$0.425797\pi$
$308$	3.01220	0.171636
$309$	−12.6173	−0.717773
$310$	11.2102	0.636694
$311$	−19.0488	−1.08016	−0.540079	−	0.841614i	$-0.681606\pi$
$311$	−19.0488	−1.08016	−0.540079	+	0.841614i	$0.681606\pi$
$312$	−0.138124	−0.00781974
$313$	−32.0293	−1.81040	−0.905201	−	0.424983i	$-0.860280\pi$
$313$	−32.0293	−1.81040	−0.905201	+	0.424983i	$0.860280\pi$
$314$	17.8728	1.00862
$315$	3.20345	0.180494
$316$	3.58406	0.201619
$317$	−9.34848	−0.525063	−0.262532	−	0.964923i	$-0.584557\pi$
$317$	−9.34848	−0.525063	−0.262532	+	0.964923i	$0.584557\pi$
$318$	10.2672	0.575755
$319$	−8.07975	−0.452379
$320$	−1.60299	−0.0896097
$321$	15.3082	0.854419
$322$	8.79499	0.490126
$323$	2.62477	0.146046
$324$	−10.7760	−0.598669
$325$	0.171950	0.00953806
$326$	3.33289	0.184592
$327$	−23.4626	−1.29748
$328$	7.69895	0.425103
$329$	−10.9826	−0.605489
$330$	3.82820	0.210735
$331$	−9.35946	−0.514442	−0.257221	−	0.966353i	$-0.582807\pi$
$331$	−9.35946	−0.514442	−0.257221	+	0.966353i	$0.582807\pi$
$332$	−9.60951	−0.527390
$333$	3.07109	0.168295
$334$	−15.4408	−0.844884
$335$	−1.26279	−0.0689938
$336$	4.80752	0.262272
$337$	−9.01843	−0.491265	−0.245633	−	0.969363i	$-0.578996\pi$
$337$	−9.01843	−0.491265	−0.245633	+	0.969363i	$0.578996\pi$
$338$	12.9950	0.706835
$339$	−26.4600	−1.43711
$340$	0.985355	0.0534384
$341$	−8.55451	−0.463253
$342$	3.46534	0.187384
$343$	19.5428	1.05521
$344$	2.94677	0.158879
$345$	11.1775	0.601779
$346$	−15.7891	−0.848827
$347$	−7.84730	−0.421265	−0.210633	−	0.977565i	$-0.567552\pi$
$347$	−7.84730	−0.421265	−0.210633	+	0.977565i	$0.567552\pi$
$348$	−12.8954	−0.691267
$349$	−15.2849	−0.818182	−0.409091	−	0.912494i	$-0.634154\pi$
$349$	−15.2849	−0.818182	−0.409091	+	0.912494i	$0.634154\pi$
$350$	−5.98485	−0.319904
$351$	−0.302277	−0.0161344
$352$	1.22325	0.0651992
$353$	−5.35814	−0.285185	−0.142593	−	0.989781i	$-0.545544\pi$
$353$	−5.35814	−0.285185	−0.142593	+	0.989781i	$0.545544\pi$
$354$	−2.03241	−0.108021
$355$	−0.214629	−0.0113913
$356$	−6.25366	−0.331444
$357$	−2.95518	−0.156405
$358$	20.8821	1.10365
$359$	−6.78175	−0.357927	−0.178964	−	0.983856i	$-0.557274\pi$
$359$	−6.78175	−0.357927	−0.178964	+	0.983856i	$0.557274\pi$
$360$	1.30091	0.0685640
$361$	−0.767000	−0.0403684
$362$	2.37926	0.125051
$363$	18.5542	0.973843
$364$	0.174216	0.00913141
$365$	−17.0019	−0.889921
$366$	12.7885	0.668467
$367$	−17.7023	−0.924051	−0.462026	−	0.886867i	$-0.652877\pi$
$367$	−17.7023	−0.924051	−0.462026	+	0.886867i	$0.652877\pi$
$368$	3.57162	0.186184
$369$	−6.24811	−0.325264
$370$	6.06604	0.315358
$371$	−12.9500	−0.672331
$372$	−13.6531	−0.707882
$373$	26.4213	1.36804	0.684022	−	0.729461i	$-0.260229\pi$
$373$	26.4213	1.36804	0.684022	+	0.729461i	$0.260229\pi$
$374$	−0.751928	−0.0388812
$375$	−23.2539	−1.20082
$376$	−4.45999	−0.230006
$377$	−0.467308	−0.0240676
$378$	10.5210	0.541142
$379$	−16.1931	−0.831786	−0.415893	−	0.909414i	$-0.636531\pi$
$379$	−16.1931	−0.831786	−0.415893	+	0.909414i	$0.636531\pi$
$380$	6.84477	0.351130
$381$	33.1209	1.69683
$382$	6.90940	0.353516
$383$	−23.0182	−1.17617	−0.588087	−	0.808797i	$-0.700119\pi$
$383$	−23.0182	−1.17617	−0.588087	+	0.808797i	$0.700119\pi$
$384$	1.95232	0.0996289
$385$	−4.82852	−0.246084
$386$	17.2501	0.878007
$387$	−2.39146	−0.121565
$388$	12.6652	0.642979
$389$	−22.3500	−1.13319	−0.566595	−	0.823996i	$-0.691740\pi$
$389$	−22.3500	−1.13319	−0.566595	+	0.823996i	$0.691740\pi$
$390$	0.221411	0.0112116
$391$	−2.19547	−0.111030
$392$	0.936264	0.0472885
$393$	−10.1120	−0.510085
$394$	−6.55335	−0.330153
$395$	−5.74521	−0.289073
$396$	−0.992729	−0.0498865
$397$	−8.41709	−0.422442	−0.211221	−	0.977438i	$-0.567744\pi$
$397$	−8.41709	−0.422442	−0.211221	+	0.977438i	$0.567744\pi$
$398$	11.1352	0.558157
$399$	−20.5282	−1.02769
$400$	−2.43043	−0.121522
$401$	−13.8499	−0.691632	−0.345816	−	0.938302i	$-0.612398\pi$
$401$	−13.8499	−0.691632	−0.345816	+	0.938302i	$0.612398\pi$
$402$	1.53799	0.0767079
$403$	−0.494766	−0.0246461
$404$	−5.70681	−0.283924
$405$	17.2739	0.858345
$406$	16.2650	0.807220
$407$	−4.62902	−0.229452
$408$	−1.20009	−0.0594133
$409$	−2.09556	−0.103619	−0.0518094	−	0.998657i	$-0.516499\pi$
$409$	−2.09556	−0.103619	−0.0518094	+	0.998657i	$0.516499\pi$
$410$	−12.3413	−0.609494
$411$	−21.9678	−1.08359
$412$	6.46272	0.318395
$413$	2.56348	0.126141
$414$	−2.89856	−0.142456
$415$	15.4039	0.756149
$416$	0.0707487	0.00346874
$417$	10.9238	0.534940
$418$	−5.22327	−0.255479
$419$	−36.7103	−1.79342	−0.896708	−	0.442623i	$-0.854048\pi$
$419$	−36.7103	−1.79342	−0.896708	+	0.442623i	$0.854048\pi$
$420$	−7.70639	−0.376034
$421$	−6.99348	−0.340841	−0.170421	−	0.985371i	$-0.554513\pi$
$421$	−6.99348	−0.340841	−0.170421	+	0.985371i	$0.554513\pi$
$422$	−0.564385	−0.0274738
$423$	3.61952	0.175987
$424$	−5.25896	−0.255398
$425$	1.49398	0.0724689
$426$	0.261402	0.0126650
$427$	−16.1302	−0.780595
$428$	−7.84102	−0.379010
$429$	−0.168960	−0.00815745
$430$	−4.72364	−0.227794
$431$	10.7142	0.516086	0.258043	−	0.966133i	$-0.416922\pi$
$431$	10.7142	0.516086	0.258043	+	0.966133i	$0.416922\pi$
$432$	4.27255	0.205563
$433$	−21.4336	−1.03003	−0.515017	−	0.857180i	$-0.672215\pi$
$433$	−21.4336	−1.03003	−0.515017	+	0.857180i	$0.672215\pi$
$434$	17.2207	0.826622
$435$	20.6712	0.991108
$436$	12.0178	0.575548
$437$	−15.2509	−0.729547
$438$	20.7071	0.989423
$439$	−10.9962	−0.524822	−0.262411	−	0.964956i	$-0.584518\pi$
$439$	−10.9962	−0.524822	−0.262411	+	0.964956i	$0.584518\pi$
$440$	−1.96085	−0.0934797
$441$	−0.759828	−0.0361823
$442$	−0.0434892	−0.00206857
$443$	17.6451	0.838343	0.419171	−	0.907907i	$-0.362321\pi$
$443$	17.6451	0.838343	0.419171	+	0.907907i	$0.362321\pi$
$444$	−7.38799	−0.350618
$445$	10.0245	0.475209
$446$	2.82618	0.133823
$447$	−31.6427	−1.49665
$448$	−2.46247	−0.116341
$449$	21.7676	1.02728	0.513638	−	0.858007i	$-0.328298\pi$
$449$	21.7676	1.02728	0.513638	+	0.858007i	$0.328298\pi$
$450$	1.97242	0.0929810
$451$	9.41770	0.443462
$452$	13.5531	0.637485
$453$	7.50458	0.352596
$454$	24.6604	1.15737
$455$	−0.279266	−0.0130922
$456$	−8.33643	−0.390389
$457$	−39.0215	−1.82535	−0.912673	−	0.408690i	$-0.865986\pi$
$457$	−39.0215	−1.82535	−0.912673	+	0.408690i	$0.865986\pi$
$458$	−3.25745	−0.152211
$459$	−2.62633	−0.122587
$460$	−5.72526	−0.266942
$461$	15.1542	0.705800	0.352900	−	0.935661i	$-0.385196\pi$
$461$	15.1542	0.705800	0.352900	+	0.935661i	$0.385196\pi$
$462$	5.88078	0.273598
$463$	15.3111	0.711566	0.355783	−	0.934569i	$-0.384214\pi$
$463$	15.3111	0.711566	0.355783	+	0.934569i	$0.384214\pi$
$464$	6.60518	0.306638
$465$	21.8858	1.01493
$466$	−18.3415	−0.849652
$467$	−29.0304	−1.34337	−0.671684	−	0.740838i	$-0.734429\pi$
$467$	−29.0304	−1.34337	−0.671684	+	0.740838i	$0.734429\pi$
$468$	−0.0574163	−0.00265407
$469$	−1.93987	−0.0895748
$470$	7.14931	0.329773
$471$	34.8934	1.60780
$472$	1.04102	0.0479169
$473$	3.60463	0.165741
$474$	6.99724	0.321394
$475$	10.3780	0.476174
$476$	1.51368	0.0693792
$477$	4.26793	0.195415
$478$	0.416247	0.0190387
$479$	−4.56957	−0.208789	−0.104395	−	0.994536i	$-0.533290\pi$
$479$	−4.56957	−0.208789	−0.104395	+	0.994536i	$0.533290\pi$
$480$	−3.12954	−0.142843
$481$	−0.267728	−0.0122073
$482$	21.1501	0.963359
$483$	17.1706	0.781291
$484$	−9.50367	−0.431985
$485$	−20.3022	−0.921875
$486$	−8.22064	−0.372896
$487$	39.7226	1.80000	0.900000	−	0.435889i	$-0.143566\pi$
$487$	39.7226	1.80000	0.900000	+	0.435889i	$0.143566\pi$
$488$	−6.55042	−0.296524
$489$	6.50687	0.294251
$490$	−1.50082	−0.0678001
$491$	26.0299	1.17472	0.587358	−	0.809328i	$-0.300168\pi$
$491$	26.0299	1.17472	0.587358	+	0.809328i	$0.300168\pi$
$492$	15.0308	0.677641
$493$	−4.06020	−0.182862
$494$	−0.302098	−0.0135920
$495$	1.59133	0.0715250
$496$	6.99329	0.314008
$497$	−0.329707	−0.0147894
$498$	−18.7608	−0.840693
$499$	−27.2533	−1.22003	−0.610013	−	0.792391i	$-0.708836\pi$
$499$	−27.2533	−1.22003	−0.610013	+	0.792391i	$0.708836\pi$
$500$	11.9109	0.532671
$501$	−30.1454	−1.34680
$502$	−14.9152	−0.665697
$503$	−11.9999	−0.535049	−0.267525	−	0.963551i	$-0.586206\pi$
$503$	−11.9999	−0.535049	−0.267525	+	0.963551i	$0.586206\pi$
$504$	1.99842	0.0890168
$505$	9.14794	0.407078
$506$	4.36897	0.194224
$507$	25.3704	1.12674
$508$	−16.9649	−0.752695
$509$	32.5306	1.44189	0.720946	−	0.692991i	$-0.243707\pi$
$509$	32.5306	1.44189	0.720946	+	0.692991i	$0.243707\pi$
$510$	1.92373	0.0851841
$511$	−26.1179	−1.15539
$512$	−1.00000	−0.0441942
$513$	−18.2438	−0.805485
$514$	−1.37901	−0.0608256
$515$	−10.3597	−0.456501
$516$	5.75304	0.253264
$517$	−5.45566	−0.239940
$518$	9.31849	0.409431
$519$	−30.8254	−1.35308
$520$	−0.113409	−0.00497333
$521$	−14.1617	−0.620435	−0.310217	−	0.950666i	$-0.600402\pi$
$521$	−14.1617	−0.620435	−0.310217	+	0.950666i	$0.600402\pi$
$522$	−5.36046	−0.234621
$523$	14.8194	0.648006	0.324003	−	0.946056i	$-0.394971\pi$
$523$	14.8194	0.648006	0.324003	+	0.946056i	$0.394971\pi$
$524$	5.17950	0.226268
$525$	−11.6843	−0.509947
$526$	−18.7977	−0.819617
$527$	−4.29877	−0.187257
$528$	2.38817	0.103932
$529$	−10.2435	−0.445371
$530$	8.43005	0.366178
$531$	−0.844845	−0.0366631
$532$	10.5148	0.455872
$533$	0.544691	0.0235932
$534$	−12.2092	−0.528342
$535$	12.5691	0.543408
$536$	−0.787775	−0.0340267
$537$	40.7685	1.75929
$538$	−18.5134	−0.798170
$539$	1.14528	0.0493307
$540$	−6.84884	−0.294727
$541$	−37.5096	−1.61266	−0.806332	−	0.591463i	$-0.798551\pi$
$541$	−37.5096	−1.61266	−0.806332	+	0.591463i	$0.798551\pi$
$542$	30.6924	1.31835
$543$	4.64507	0.199339
$544$	0.614699	0.0263550
$545$	−19.2644	−0.825195
$546$	0.340126	0.0145560
$547$	15.0828	0.644892	0.322446	−	0.946588i	$-0.395495\pi$
$547$	15.0828	0.644892	0.322446	+	0.946588i	$0.395495\pi$
$548$	11.2522	0.480669
$549$	5.31602	0.226882
$550$	−2.97301	−0.126770
$551$	−28.2042	−1.20154
$552$	6.97294	0.296788
$553$	−8.82563	−0.375304
$554$	−25.4235	−1.08014
$555$	11.8429	0.502701
$556$	−5.59529	−0.237293
$557$	−0.372288	−0.0157743	−0.00788717	−	0.999969i	$-0.502511\pi$
$557$	−0.372288	−0.0157743	−0.00788717	+	0.999969i	$0.502511\pi$
$558$	−5.67543	−0.240260
$559$	0.208480	0.00881778
$560$	3.94730	0.166804
$561$	−1.46800	−0.0619791
$562$	−31.3022	−1.32041
$563$	−19.7409	−0.831981	−0.415990	−	0.909369i	$-0.636565\pi$
$563$	−19.7409	−0.831981	−0.415990	+	0.909369i	$0.636565\pi$
$564$	−8.70733	−0.366645
$565$	−21.7255	−0.913997
$566$	8.54203	0.359048
$567$	26.5356	1.11439
$568$	−0.133893	−0.00561803
$569$	33.6636	1.41125	0.705625	−	0.708586i	$-0.250666\pi$
$569$	33.6636	1.41125	0.705625	+	0.708586i	$0.250666\pi$
$570$	13.3632	0.559722
$571$	−29.2250	−1.22303	−0.611514	−	0.791234i	$-0.709439\pi$
$571$	−29.2250	−1.22303	−0.611514	+	0.791234i	$0.709439\pi$
$572$	0.0865430	0.00361854
$573$	13.4894	0.563526
$574$	−18.9584	−0.791308
$575$	−8.68058	−0.362005
$576$	0.811553	0.0338147
$577$	18.3233	0.762808	0.381404	−	0.924408i	$-0.375441\pi$
$577$	18.3233	0.762808	0.381404	+	0.924408i	$0.375441\pi$
$578$	16.6221	0.691390
$579$	33.6777	1.39960
$580$	−10.5880	−0.439644
$581$	23.6631	0.981710
$582$	24.7266	1.02495
$583$	−6.43300	−0.266428
$584$	−10.6064	−0.438896
$585$	0.0920377	0.00380529
$586$	−4.52063	−0.186745
$587$	31.1849	1.28714	0.643569	−	0.765388i	$-0.277453\pi$
$587$	31.1849	1.28714	0.643569	+	0.765388i	$0.277453\pi$
$588$	1.82789	0.0753808
$589$	−29.8614	−1.23042
$590$	−1.66874	−0.0687011
$591$	−12.7942	−0.526285
$592$	3.78421	0.155530
$593$	−26.3115	−1.08048	−0.540241	−	0.841510i	$-0.681667\pi$
$593$	−26.3115	−1.08048	−0.540241	+	0.841510i	$0.681667\pi$
$594$	5.22637	0.214441
$595$	−2.42640	−0.0994728
$596$	16.2077	0.663895
$597$	21.7395	0.889737
$598$	0.252687	0.0103332
$599$	8.96600	0.366341	0.183170	−	0.983081i	$-0.441364\pi$
$599$	8.96600	0.366341	0.183170	+	0.983081i	$0.441364\pi$
$600$	−4.74498	−0.193713
$601$	26.1380	1.06619	0.533096	−	0.846055i	$-0.321029\pi$
$601$	26.1380	1.06619	0.533096	+	0.846055i	$0.321029\pi$
$602$	−7.25633	−0.295746
$603$	0.639321	0.0260352
$604$	−3.84393	−0.156407
$605$	15.2343	0.619361
$606$	−11.1415	−0.452593
$607$	29.7126	1.20600	0.602998	−	0.797743i	$-0.293973\pi$
$607$	29.7126	1.20600	0.602998	+	0.797743i	$0.293973\pi$
$608$	4.27001	0.173172
$609$	31.7545	1.28676
$610$	10.5002	0.425142
$611$	−0.315538	−0.0127653
$612$	−0.498861	−0.0201653
$613$	−8.02069	−0.323953	−0.161976	−	0.986795i	$-0.551787\pi$
$613$	−8.02069	−0.323953	−0.161976	+	0.986795i	$0.551787\pi$
$614$	−8.09519	−0.326695
$615$	−24.0942	−0.971572
$616$	−3.01220	−0.121365
$617$	10.4272	0.419785	0.209892	−	0.977725i	$-0.432689\pi$
$617$	10.4272	0.419785	0.209892	+	0.977725i	$0.432689\pi$
$618$	12.6173	0.507542
$619$	−16.1761	−0.650173	−0.325087	−	0.945684i	$-0.605393\pi$
$619$	−16.1761	−0.650173	−0.325087	+	0.945684i	$0.605393\pi$
$620$	−11.2102	−0.450211
$621$	15.2599	0.612359
$622$	19.0488	0.763787
$623$	15.3994	0.616965
$624$	0.138124	0.00552939
$625$	−6.94084	−0.277634
$626$	32.0293	1.28015
$627$	−10.1975	−0.407249
$628$	−17.8728	−0.713202
$629$	−2.32615	−0.0927497
$630$	−3.20345	−0.127628
$631$	−3.29879	−0.131323	−0.0656614	−	0.997842i	$-0.520916\pi$
$631$	−3.29879	−0.131323	−0.0656614	+	0.997842i	$0.520916\pi$
$632$	−3.58406	−0.142566
$633$	−1.10186	−0.0437950
$634$	9.34848	0.371276
$635$	27.1945	1.07918
$636$	−10.2672	−0.407120
$637$	0.0662395	0.00262450
$638$	8.07975	0.319880
$639$	0.108661	0.00429858
$640$	1.60299	0.0633636
$641$	−24.3065	−0.960047	−0.480024	−	0.877256i	$-0.659372\pi$
$641$	−24.3065	−0.960047	−0.480024	+	0.877256i	$0.659372\pi$
$642$	−15.3082	−0.604166
$643$	16.5468	0.652543	0.326272	−	0.945276i	$-0.394208\pi$
$643$	16.5468	0.652543	0.326272	+	0.945276i	$0.394208\pi$
$644$	−8.79499	−0.346571
$645$	−9.22206	−0.363118
$646$	−2.62477	−0.103270
$647$	−29.9888	−1.17898	−0.589491	−	0.807775i	$-0.700672\pi$
$647$	−29.9888	−1.17898	−0.589491	+	0.807775i	$0.700672\pi$
$648$	10.7760	0.423323
$649$	1.27342	0.0499863
$650$	−0.171950	−0.00674443
$651$	33.6204	1.31769
$652$	−3.33289	−0.130526
$653$	−10.2287	−0.400280	−0.200140	−	0.979767i	$-0.564140\pi$
$653$	−10.2287	−0.400280	−0.200140	+	0.979767i	$0.564140\pi$
$654$	23.4626	0.917460
$655$	−8.30268	−0.324412
$656$	−7.69895	−0.300594
$657$	8.60766	0.335817
$658$	10.9826	0.428145
$659$	21.9892	0.856577	0.428288	−	0.903642i	$-0.359117\pi$
$659$	21.9892	0.856577	0.428288	+	0.903642i	$0.359117\pi$
$660$	−3.82820	−0.149012
$661$	46.2286	1.79808	0.899042	−	0.437863i	$-0.144264\pi$
$661$	46.2286	1.79808	0.899042	+	0.437863i	$0.144264\pi$
$662$	9.35946	0.363766
$663$	−0.0849048	−0.00329743
$664$	9.60951	0.372921
$665$	−16.8550	−0.653610
$666$	−3.07109	−0.119002
$667$	23.5912	0.913454
$668$	15.4408	0.597423
$669$	5.51760	0.213323
$670$	1.26279	0.0487860
$671$	−8.01277	−0.309330
$672$	−4.80752	−0.185454
$673$	47.0650	1.81422	0.907112	−	0.420890i	$-0.138282\pi$
$673$	47.0650	1.81422	0.907112	+	0.420890i	$0.138282\pi$
$674$	9.01843	0.347377
$675$	−10.3841	−0.399686
$676$	−12.9950	−0.499807
$677$	27.4409	1.05464	0.527319	−	0.849667i	$-0.323197\pi$
$677$	27.4409	1.05464	0.527319	+	0.849667i	$0.323197\pi$
$678$	26.4600	1.01619
$679$	−31.1877	−1.19687
$680$	−0.985355	−0.0377866
$681$	48.1450	1.84492
$682$	8.55451	0.327569
$683$	37.6264	1.43974	0.719868	−	0.694111i	$-0.244202\pi$
$683$	37.6264	1.43974	0.719868	+	0.694111i	$0.244202\pi$
$684$	−3.46534	−0.132501
$685$	−18.0371	−0.689162
$686$	−19.5428	−0.746147
$687$	−6.35958	−0.242633
$688$	−2.94677	−0.112345
$689$	−0.372065	−0.0141745
$690$	−11.1775	−0.425522
$691$	7.06457	0.268749	0.134374	−	0.990931i	$-0.457098\pi$
$691$	7.06457	0.268749	0.134374	+	0.990931i	$0.457098\pi$
$692$	15.7891	0.600211
$693$	2.44456	0.0928611
$694$	7.84730	0.297879
$695$	8.96917	0.340220
$696$	12.8954	0.488800
$697$	4.73254	0.179258
$698$	15.2849	0.578542
$699$	−35.8084	−1.35440
$700$	5.98485	0.226206
$701$	19.3985	0.732670	0.366335	−	0.930483i	$-0.380612\pi$
$701$	19.3985	0.732670	0.366335	+	0.930483i	$0.380612\pi$
$702$	0.302277	0.0114087
$703$	−16.1586	−0.609434
$704$	−1.22325	−0.0461028
$705$	13.9577	0.525679
$706$	5.35814	0.201656
$707$	14.0528	0.528510
$708$	2.03241	0.0763826
$709$	25.2890	0.949750	0.474875	−	0.880053i	$-0.342493\pi$
$709$	25.2890	0.949750	0.474875	+	0.880053i	$0.342493\pi$
$710$	0.214629	0.00805488
$711$	2.90866	0.109083
$712$	6.25366	0.234366
$713$	24.9774	0.935410
$714$	2.95518	0.110595
$715$	−0.138727	−0.00518811
$716$	−20.8821	−0.780400
$717$	0.812648	0.0303489
$718$	6.78175	0.253093
$719$	−39.4671	−1.47187	−0.735937	−	0.677050i	$-0.763258\pi$
$719$	−39.4671	−1.47187	−0.735937	+	0.677050i	$0.763258\pi$
$720$	−1.30091	−0.0484820
$721$	−15.9142	−0.592677
$722$	0.767000	0.0285448
$723$	41.2917	1.53565
$724$	−2.37926	−0.0884243
$725$	−16.0534	−0.596210
$726$	−18.5542	−0.688611
$727$	−18.2438	−0.676625	−0.338313	−	0.941034i	$-0.609856\pi$
$727$	−18.2438	−0.676625	−0.338313	+	0.941034i	$0.609856\pi$
$728$	−0.174216	−0.00645688
$729$	16.2788	0.602919
$730$	17.0019	0.629269
$731$	1.81138	0.0669962
$732$	−12.7885	−0.472677
$733$	22.6126	0.835217	0.417609	−	0.908627i	$-0.362868\pi$
$733$	22.6126	0.835217	0.417609	+	0.908627i	$0.362868\pi$
$734$	17.7023	0.653403
$735$	−2.93008	−0.108078
$736$	−3.57162	−0.131652
$737$	−0.963642	−0.0354962
$738$	6.24811	0.229996
$739$	−0.275537	−0.0101358	−0.00506790	−	0.999987i	$-0.501613\pi$
$739$	−0.275537	−0.0101358	−0.00506790	+	0.999987i	$0.501613\pi$
$740$	−6.06604	−0.222992
$741$	−0.589792	−0.0216665
$742$	12.9500	0.475410
$743$	24.5549	0.900830	0.450415	−	0.892819i	$-0.351276\pi$
$743$	24.5549	0.900830	0.450415	+	0.892819i	$0.351276\pi$
$744$	13.6531	0.500548
$745$	−25.9808	−0.951863
$746$	−26.4213	−0.967353
$747$	−7.79863	−0.285337
$748$	0.751928	0.0274932
$749$	19.3082	0.705508
$750$	23.2539	0.849111
$751$	−9.77934	−0.356853	−0.178427	−	0.983953i	$-0.557101\pi$
$751$	−9.77934	−0.356853	−0.178427	+	0.983953i	$0.557101\pi$
$752$	4.45999	0.162639
$753$	−29.1192	−1.06116
$754$	0.467308	0.0170183
$755$	6.16177	0.224250
$756$	−10.5210	−0.382645
$757$	−27.1059	−0.985181	−0.492591	−	0.870261i	$-0.663950\pi$
$757$	−27.1059	−0.985181	−0.492591	+	0.870261i	$0.663950\pi$
$758$	16.1931	0.588162
$759$	8.52962	0.309606
$760$	−6.84477	−0.248286
$761$	−46.3297	−1.67945	−0.839725	−	0.543012i	$-0.817284\pi$
$761$	−46.3297	−1.67945	−0.839725	+	0.543012i	$0.817284\pi$
$762$	−33.1209	−1.19984
$763$	−29.5934	−1.07135
$764$	−6.90940	−0.249973
$765$	0.799668	0.0289121
$766$	23.0182	0.831681
$767$	0.0736510	0.00265938
$768$	−1.95232	−0.0704483
$769$	4.84136	0.174584	0.0872920	−	0.996183i	$-0.472179\pi$
$769$	4.84136	0.174584	0.0872920	+	0.996183i	$0.472179\pi$
$770$	4.82852	0.174008
$771$	−2.69227	−0.0969599
$772$	−17.2501	−0.620845
$773$	12.6018	0.453256	0.226628	−	0.973981i	$-0.427230\pi$
$773$	12.6018	0.453256	0.226628	+	0.973981i	$0.427230\pi$
$774$	2.39146	0.0859594
$775$	−16.9967	−0.610540
$776$	−12.6652	−0.454655
$777$	18.1927	0.652658
$778$	22.3500	0.801287
$779$	32.8746	1.17786
$780$	−0.221411	−0.00792779
$781$	−0.163784	−0.00586066
$782$	2.19547	0.0785099
$783$	28.2209	1.00853
$784$	−0.936264	−0.0334380
$785$	28.6498	1.02256
$786$	10.1120	0.360685
$787$	−42.7137	−1.52258	−0.761289	−	0.648413i	$-0.775433\pi$
$787$	−42.7137	−1.52258	−0.761289	+	0.648413i	$0.775433\pi$
$788$	6.55335	0.233454
$789$	−36.6990	−1.30652
$790$	5.74521	0.204405
$791$	−33.3741	−1.18665
$792$	0.992729	0.0352751
$793$	−0.463434	−0.0164570
$794$	8.41709	0.298711
$795$	16.4582	0.583711
$796$	−11.1352	−0.394676
$797$	12.1565	0.430604	0.215302	−	0.976547i	$-0.430926\pi$
$797$	12.1565	0.430604	0.215302	+	0.976547i	$0.430926\pi$
$798$	20.5282	0.726689
$799$	−2.74155	−0.0969891
$800$	2.43043	0.0859287
$801$	−5.07518	−0.179323
$802$	13.8499	0.489058
$803$	−12.9742	−0.457850
$804$	−1.53799	−0.0542407
$805$	14.0983	0.496898
$806$	0.494766	0.0174274
$807$	−36.1441	−1.27233
$808$	5.70681	0.200765
$809$	34.5659	1.21527	0.607636	−	0.794216i	$-0.292118\pi$
$809$	34.5659	1.21527	0.607636	+	0.794216i	$0.292118\pi$
$810$	−17.2739	−0.606941
$811$	33.4899	1.17599	0.587994	−	0.808865i	$-0.299918\pi$
$811$	33.4899	1.17599	0.587994	+	0.808865i	$0.299918\pi$
$812$	−16.2650	−0.570790
$813$	59.9214	2.10154
$814$	4.62902	0.162247
$815$	5.34258	0.187142
$816$	1.20009	0.0420115
$817$	12.5828	0.440215
$818$	2.09556	0.0732696
$819$	0.141386	0.00494042
$820$	12.3413	0.430978
$821$	16.5968	0.579231	0.289615	−	0.957143i	$-0.406473\pi$
$821$	16.5968	0.579231	0.289615	+	0.957143i	$0.406473\pi$
$822$	21.9678	0.766216
$823$	−4.91009	−0.171155	−0.0855774	−	0.996332i	$-0.527273\pi$
$823$	−4.91009	−0.171155	−0.0855774	+	0.996332i	$0.527273\pi$
$824$	−6.46272	−0.225140
$825$	−5.80427	−0.202079
$826$	−2.56348	−0.0891949
$827$	23.5704	0.819623	0.409812	−	0.912170i	$-0.365594\pi$
$827$	23.5704	0.819623	0.409812	+	0.912170i	$0.365594\pi$
$828$	2.89856	0.100732
$829$	−24.0509	−0.835323	−0.417662	−	0.908603i	$-0.637150\pi$
$829$	−24.0509	−0.835323	−0.417662	+	0.908603i	$0.637150\pi$
$830$	−15.4039	−0.534678
$831$	−49.6348	−1.72181
$832$	−0.0707487	−0.00245277
$833$	0.575521	0.0199406
$834$	−10.9238	−0.378260
$835$	−24.7514	−0.856559
$836$	5.22327	0.180651
$837$	29.8792	1.03278
$838$	36.7103	1.26814
$839$	−12.6046	−0.435159	−0.217580	−	0.976043i	$-0.569816\pi$
$839$	−12.6046	−0.435159	−0.217580	+	0.976043i	$0.569816\pi$
$840$	7.70639	0.265896
$841$	14.6284	0.504427
$842$	6.99348	0.241011
$843$	−61.1120	−2.10481
$844$	0.564385	0.0194269
$845$	20.8308	0.716602
$846$	−3.61952	−0.124442
$847$	23.4025	0.804118
$848$	5.25896	0.180594
$849$	16.6768	0.572345
$850$	−1.49398	−0.0512432
$851$	13.5158	0.463314
$852$	−0.261402	−0.00895550
$853$	42.0838	1.44092	0.720461	−	0.693495i	$-0.243930\pi$
$853$	42.0838	1.44092	0.720461	+	0.693495i	$0.243930\pi$
$854$	16.1302	0.551964
$855$	5.55490	0.189974
$856$	7.84102	0.268001
$857$	−31.1898	−1.06542	−0.532711	−	0.846297i	$-0.678827\pi$
$857$	−31.1898	−1.06542	−0.532711	+	0.846297i	$0.678827\pi$
$858$	0.168960	0.00576819
$859$	7.85153	0.267891	0.133945	−	0.990989i	$-0.457235\pi$
$859$	7.85153	0.267891	0.133945	+	0.990989i	$0.457235\pi$
$860$	4.72364	0.161075
$861$	−37.0129	−1.26140
$862$	−10.7142	−0.364928
$863$	−23.4259	−0.797426	−0.398713	−	0.917076i	$-0.630543\pi$
$863$	−23.4259	−0.797426	−0.398713	+	0.917076i	$0.630543\pi$
$864$	−4.27255	−0.145355
$865$	−25.3097	−0.860556
$866$	21.4336	0.728345
$867$	32.4517	1.10212
$868$	−17.2207	−0.584510
$869$	−4.38419	−0.148723
$870$	−20.6712	−0.700819
$871$	−0.0557341	−0.00188848
$872$	−12.0178	−0.406974
$873$	10.2785	0.347874
$874$	15.2509	0.515868
$875$	−29.3301	−0.991540
$876$	−20.7071	−0.699628
$877$	43.6347	1.47344	0.736719	−	0.676199i	$-0.236374\pi$
$877$	43.6347	1.47344	0.736719	+	0.676199i	$0.236374\pi$
$878$	10.9962	0.371105
$879$	−8.82571	−0.297684
$880$	1.96085	0.0661001
$881$	−28.4467	−0.958395	−0.479197	−	0.877707i	$-0.659072\pi$
$881$	−28.4467	−0.958395	−0.479197	+	0.877707i	$0.659072\pi$
$882$	0.759828	0.0255847
$883$	−41.3342	−1.39101	−0.695503	−	0.718523i	$-0.744818\pi$
$883$	−41.3342	−1.39101	−0.695503	+	0.718523i	$0.744818\pi$
$884$	0.0434892	0.00146270
$885$	−3.25792	−0.109514
$886$	−17.6451	−0.592798
$887$	−18.9353	−0.635784	−0.317892	−	0.948127i	$-0.602975\pi$
$887$	−18.9353	−0.635784	−0.317892	+	0.948127i	$0.602975\pi$
$888$	7.38799	0.247925
$889$	41.7754	1.40110
$890$	−10.0245	−0.336023
$891$	13.1817	0.441605
$892$	−2.82618	−0.0946274
$893$	−19.0442	−0.637290
$894$	31.6427	1.05829
$895$	33.4737	1.11890
$896$	2.46247	0.0822652
$897$	0.493327	0.0164717
$898$	−21.7676	−0.726394
$899$	46.1919	1.54059
$900$	−1.97242	−0.0657475
$901$	−3.23268	−0.107696
$902$	−9.41770	−0.313575
$903$	−14.1667	−0.471437
$904$	−13.5531	−0.450770
$905$	3.81392	0.126779
$906$	−7.50458	−0.249323
$907$	9.62768	0.319682	0.159841	−	0.987143i	$-0.448902\pi$
$907$	9.62768	0.319682	0.159841	+	0.987143i	$0.448902\pi$
$908$	−24.6604	−0.818385
$909$	−4.63138	−0.153613
$910$	0.279266	0.00925759
$911$	44.6679	1.47991	0.739956	−	0.672655i	$-0.234846\pi$
$911$	44.6679	1.47991	0.739956	+	0.672655i	$0.234846\pi$
$912$	8.33643	0.276047
$913$	11.7548	0.389026
$914$	39.0215	1.29071
$915$	20.4998	0.677704
$916$	3.25745	0.107629
$917$	−12.7543	−0.421186
$918$	2.62633	0.0866818
$919$	−4.47815	−0.147721	−0.0738603	−	0.997269i	$-0.523532\pi$
$919$	−4.47815	−0.147721	−0.0738603	+	0.997269i	$0.523532\pi$
$920$	5.72526	0.188756
$921$	−15.8044	−0.520773
$922$	−15.1542	−0.499076
$923$	−0.00947277	−0.000311800 0
$924$	−5.88078	−0.193463
$925$	−9.19726	−0.302404
$926$	−15.3111	−0.503153
$927$	5.24484	0.172263
$928$	−6.60518	−0.216826
$929$	45.0422	1.47779	0.738894	−	0.673822i	$-0.235349\pi$
$929$	45.0422	1.47779	0.738894	+	0.673822i	$0.235349\pi$
$930$	−21.8858	−0.717664
$931$	3.99786	0.131025
$932$	18.3415	0.600795
$933$	37.1894	1.21753
$934$	29.0304	0.949905
$935$	−1.20533	−0.0394185
$936$	0.0574163	0.00187671
$937$	−34.1445	−1.11545	−0.557725	−	0.830026i	$-0.688326\pi$
$937$	−34.1445	−1.11545	−0.557725	+	0.830026i	$0.688326\pi$
$938$	1.93987	0.0633389
$939$	62.5314	2.04064
$940$	−7.14931	−0.233185
$941$	−11.9814	−0.390582	−0.195291	−	0.980745i	$-0.562565\pi$
$941$	−11.9814	−0.390582	−0.195291	+	0.980745i	$0.562565\pi$
$942$	−34.8934	−1.13689
$943$	−27.4977	−0.895449
$944$	−1.04102	−0.0338824
$945$	16.8650	0.548620
$946$	−3.60463	−0.117196
$947$	15.4470	0.501961	0.250980	−	0.967992i	$-0.419247\pi$
$947$	15.4470	0.501961	0.250980	+	0.967992i	$0.419247\pi$
$948$	−6.99724	−0.227260
$949$	−0.750389	−0.0243587
$950$	−10.3780	−0.336706
$951$	18.2512	0.591837
$952$	−1.51368	−0.0490585
$953$	16.6843	0.540458	0.270229	−	0.962796i	$-0.412901\pi$
$953$	16.6843	0.540458	0.270229	+	0.962796i	$0.412901\pi$
$954$	−4.26793	−0.138179
$955$	11.0757	0.358401
$956$	−0.416247	−0.0134624
$957$	15.7743	0.509910
$958$	4.56957	0.147636
$959$	−27.7081	−0.894741
$960$	3.12954	0.101006
$961$	17.9061	0.577617
$962$	0.267728	0.00863190
$963$	−6.36341	−0.205058
$964$	−21.1501	−0.681198
$965$	27.6517	0.890140
$966$	−17.1706	−0.552456
$967$	33.8297	1.08789	0.543945	−	0.839121i	$-0.316930\pi$
$967$	33.8297	1.08789	0.543945	+	0.839121i	$0.316930\pi$
$968$	9.50367	0.305460
$969$	−5.12439	−0.164619
$970$	20.3022	0.651864
$971$	34.0555	1.09289	0.546446	−	0.837494i	$-0.315980\pi$
$971$	34.0555	1.09289	0.546446	+	0.837494i	$0.315980\pi$
$972$	8.22064	0.263677
$973$	13.7782	0.441709
$974$	−39.7226	−1.27279
$975$	−0.335701	−0.0107510
$976$	6.55042	0.209674
$977$	−33.6393	−1.07622	−0.538109	−	0.842875i	$-0.680861\pi$
$977$	−33.6393	−1.07622	−0.538109	+	0.842875i	$0.680861\pi$
$978$	−6.50687	−0.208067
$979$	7.64976	0.244487
$980$	1.50082	0.0479419
$981$	9.75309	0.311392
$982$	−26.0299	−0.830649
$983$	42.7925	1.36487	0.682434	−	0.730947i	$-0.260922\pi$
$983$	42.7925	1.36487	0.682434	+	0.730947i	$0.260922\pi$
$984$	−15.0308	−0.479165
$985$	−10.5049	−0.334715
$986$	4.06020	0.129303
$987$	21.4415	0.682490
$988$	0.302098	0.00961101
$989$	−10.5247	−0.334668
$990$	−1.59133	−0.0505758
$991$	−31.1166	−0.988452	−0.494226	−	0.869333i	$-0.664549\pi$
$991$	−31.1166	−0.988452	−0.494226	+	0.869333i	$0.664549\pi$
$992$	−6.99329	−0.222037
$993$	18.2727	0.579865
$994$	0.329707	0.0104577
$995$	17.8496	0.565869
$996$	18.7608	0.594460
$997$	41.7900	1.32350	0.661752	−	0.749723i	$-0.269813\pi$
$997$	41.7900	1.32350	0.661752	+	0.749723i	$0.269813\pi$
$998$	27.2533	0.862689
$999$	16.1682	0.511540

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.b.1.9	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.b.1.9	✓	35	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.95232 q^{3} +1.00000 q^{4} -1.60299 q^{5} +1.95232 q^{6} -2.46247 q^{7} -1.00000 q^{8} +0.811553 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.95232 q^{3} +1.00000 q^{4} -1.60299 q^{5} +1.95232 q^{6} -2.46247 q^{7} -1.00000 q^{8} +0.811553 q^{9} +1.60299 q^{10} -1.22325 q^{11} -1.95232 q^{12} -0.0707487 q^{13} +2.46247 q^{14} +3.12954 q^{15} +1.00000 q^{16} -0.614699 q^{17} -0.811553 q^{18} -4.27001 q^{19} -1.60299 q^{20} +4.80752 q^{21} +1.22325 q^{22} +3.57162 q^{23} +1.95232 q^{24} -2.43043 q^{25} +0.0707487 q^{26} +4.27255 q^{27} -2.46247 q^{28} +6.60518 q^{29} -3.12954 q^{30} +6.99329 q^{31} -1.00000 q^{32} +2.38817 q^{33} +0.614699 q^{34} +3.94730 q^{35} +0.811553 q^{36} +3.78421 q^{37} +4.27001 q^{38} +0.138124 q^{39} +1.60299 q^{40} -7.69895 q^{41} -4.80752 q^{42} -2.94677 q^{43} -1.22325 q^{44} -1.30091 q^{45} -3.57162 q^{46} +4.45999 q^{47} -1.95232 q^{48} -0.936264 q^{49} +2.43043 q^{50} +1.20009 q^{51} -0.0707487 q^{52} +5.25896 q^{53} -4.27255 q^{54} +1.96085 q^{55} +2.46247 q^{56} +8.33643 q^{57} -6.60518 q^{58} -1.04102 q^{59} +3.12954 q^{60} +6.55042 q^{61} -6.99329 q^{62} -1.99842 q^{63} +1.00000 q^{64} +0.113409 q^{65} -2.38817 q^{66} +0.787775 q^{67} -0.614699 q^{68} -6.97294 q^{69} -3.94730 q^{70} +0.133893 q^{71} -0.811553 q^{72} +10.6064 q^{73} -3.78421 q^{74} +4.74498 q^{75} -4.27001 q^{76} +3.01220 q^{77} -0.138124 q^{78} +3.58406 q^{79} -1.60299 q^{80} -10.7760 q^{81} +7.69895 q^{82} -9.60951 q^{83} +4.80752 q^{84} +0.985355 q^{85} +2.94677 q^{86} -12.8954 q^{87} +1.22325 q^{88} -6.25366 q^{89} +1.30091 q^{90} +0.174216 q^{91} +3.57162 q^{92} -13.6531 q^{93} -4.45999 q^{94} +6.84477 q^{95} +1.95232 q^{96} +12.6652 q^{97} +0.936264 q^{98} -0.992729 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9} - 6 q^{10} - 9 q^{11} - 6 q^{12} - 7 q^{13} + 14 q^{14} - 19 q^{15} + 35 q^{16} + 17 q^{17} - 23 q^{18} - 25 q^{19} + 6 q^{20} - 15 q^{21} + 9 q^{22} - 12 q^{23} + 6 q^{24} + 7 q^{25} + 7 q^{26} - 27 q^{27} - 14 q^{28} - 13 q^{29} + 19 q^{30} - 69 q^{31} - 35 q^{32} + q^{33} - 17 q^{34} - 4 q^{35} + 23 q^{36} - 22 q^{37} + 25 q^{38} - 38 q^{39} - 6 q^{40} + 15 q^{42} - 32 q^{43} - 9 q^{44} + 9 q^{45} + 12 q^{46} - 18 q^{47} - 6 q^{48} - 19 q^{49} - 7 q^{50} - 21 q^{51} - 7 q^{52} + 20 q^{53} + 27 q^{54} - 54 q^{55} + 14 q^{56} + 28 q^{57} + 13 q^{58} - 21 q^{59} - 19 q^{60} - 67 q^{61} + 69 q^{62} - 28 q^{63} + 35 q^{64} + 22 q^{65} - q^{66} - 18 q^{67} + 17 q^{68} - 42 q^{69} + 4 q^{70} - 36 q^{71} - 23 q^{72} - 18 q^{73} + 22 q^{74} - 49 q^{75} - 25 q^{76} + 20 q^{77} + 38 q^{78} - 92 q^{79} + 6 q^{80} - 25 q^{81} + 42 q^{83} - 15 q^{84} - 29 q^{85} + 32 q^{86} - 40 q^{87} + 9 q^{88} - 8 q^{89} - 9 q^{90} - 89 q^{91} - 12 q^{92} - q^{93} + 18 q^{94} - 62 q^{95} + 6 q^{96} - 40 q^{97} + 19 q^{98} - 64 q^{99}+O(q^{100}) \) 35 * q - 35 * q^2 - 6 * q^3 + 35 * q^4 + 6 * q^5 + 6 * q^6 - 14 * q^7 - 35 * q^8 + 23 * q^9 - 6 * q^10 - 9 * q^11 - 6 * q^12 - 7 * q^13 + 14 * q^14 - 19 * q^15 + 35 * q^16 + 17 * q^17 - 23 * q^18 - 25 * q^19 + 6 * q^20 - 15 * q^21 + 9 * q^22 - 12 * q^23 + 6 * q^24 + 7 * q^25 + 7 * q^26 - 27 * q^27 - 14 * q^28 - 13 * q^29 + 19 * q^30 - 69 * q^31 - 35 * q^32 + q^33 - 17 * q^34 - 4 * q^35 + 23 * q^36 - 22 * q^37 + 25 * q^38 - 38 * q^39 - 6 * q^40 + 15 * q^42 - 32 * q^43 - 9 * q^44 + 9 * q^45 + 12 * q^46 - 18 * q^47 - 6 * q^48 - 19 * q^49 - 7 * q^50 - 21 * q^51 - 7 * q^52 + 20 * q^53 + 27 * q^54 - 54 * q^55 + 14 * q^56 + 28 * q^57 + 13 * q^58 - 21 * q^59 - 19 * q^60 - 67 * q^61 + 69 * q^62 - 28 * q^63 + 35 * q^64 + 22 * q^65 - q^66 - 18 * q^67 + 17 * q^68 - 42 * q^69 + 4 * q^70 - 36 * q^71 - 23 * q^72 - 18 * q^73 + 22 * q^74 - 49 * q^75 - 25 * q^76 + 20 * q^77 + 38 * q^78 - 92 * q^79 + 6 * q^80 - 25 * q^81 + 42 * q^83 - 15 * q^84 - 29 * q^85 + 32 * q^86 - 40 * q^87 + 9 * q^88 - 8 * q^89 - 9 * q^90 - 89 * q^91 - 12 * q^92 - q^93 + 18 * q^94 - 62 * q^95 + 6 * q^96 - 40 * q^97 + 19 * q^98 - 64 * q^99

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