LMFDB - Embedded newform 4034.2.a.b.1.13

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			1.13
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.35256 q^{3} +1.00000 q^{4} -0.395568 q^{5} +1.35256 q^{6} +1.50560 q^{7} -1.00000 q^{8} -1.17057 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.35256 q^{3} +1.00000 q^{4} -0.395568 q^{5} +1.35256 q^{6} +1.50560 q^{7} -1.00000 q^{8} -1.17057 q^{9} +0.395568 q^{10} +1.06848 q^{11} -1.35256 q^{12} -0.679571 q^{13} -1.50560 q^{14} +0.535031 q^{15} +1.00000 q^{16} -0.116414 q^{17} +1.17057 q^{18} +1.90352 q^{19} -0.395568 q^{20} -2.03642 q^{21} -1.06848 q^{22} -2.44771 q^{23} +1.35256 q^{24} -4.84353 q^{25} +0.679571 q^{26} +5.64096 q^{27} +1.50560 q^{28} +1.89694 q^{29} -0.535031 q^{30} +4.13611 q^{31} -1.00000 q^{32} -1.44518 q^{33} +0.116414 q^{34} -0.595569 q^{35} -1.17057 q^{36} -7.02112 q^{37} -1.90352 q^{38} +0.919163 q^{39} +0.395568 q^{40} +0.146204 q^{41} +2.03642 q^{42} +2.52664 q^{43} +1.06848 q^{44} +0.463041 q^{45} +2.44771 q^{46} +8.25454 q^{47} -1.35256 q^{48} -4.73316 q^{49} +4.84353 q^{50} +0.157457 q^{51} -0.679571 q^{52} -1.27802 q^{53} -5.64096 q^{54} -0.422655 q^{55} -1.50560 q^{56} -2.57463 q^{57} -1.89694 q^{58} -6.85919 q^{59} +0.535031 q^{60} +0.454058 q^{61} -4.13611 q^{62} -1.76242 q^{63} +1.00000 q^{64} +0.268817 q^{65} +1.44518 q^{66} -14.3733 q^{67} -0.116414 q^{68} +3.31068 q^{69} +0.595569 q^{70} +2.75764 q^{71} +1.17057 q^{72} +13.1381 q^{73} +7.02112 q^{74} +6.55117 q^{75} +1.90352 q^{76} +1.60870 q^{77} -0.919163 q^{78} -12.0378 q^{79} -0.395568 q^{80} -4.11804 q^{81} -0.146204 q^{82} +16.0655 q^{83} -2.03642 q^{84} +0.0460497 q^{85} -2.52664 q^{86} -2.56573 q^{87} -1.06848 q^{88} +5.48474 q^{89} -0.463041 q^{90} -1.02317 q^{91} -2.44771 q^{92} -5.59435 q^{93} -8.25454 q^{94} -0.752971 q^{95} +1.35256 q^{96} -4.05519 q^{97} +4.73316 q^{98} -1.25073 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.35256	−0.780903	−0.390451	−	0.920624i	$-0.627681\pi$
$3$	−1.35256	−0.780903	−0.390451	+	0.920624i	$0.627681\pi$
$4$	1.00000	0.500000
$5$	−0.395568	−0.176903	−0.0884517	−	0.996080i	$-0.528192\pi$
$5$	−0.395568	−0.176903	−0.0884517	+	0.996080i	$0.528192\pi$
$6$	1.35256	0.552182
$7$	1.50560	0.569065	0.284532	−	0.958666i	$-0.408162\pi$
$7$	1.50560	0.569065	0.284532	+	0.958666i	$0.408162\pi$
$8$	−1.00000	−0.353553
$9$	−1.17057	−0.390191
$10$	0.395568	0.125090
$11$	1.06848	0.322158	0.161079	−	0.986942i	$-0.448503\pi$
$11$	1.06848	0.322158	0.161079	+	0.986942i	$0.448503\pi$
$12$	−1.35256	−0.390451
$13$	−0.679571	−0.188479	−0.0942396	−	0.995550i	$-0.530042\pi$
$13$	−0.679571	−0.188479	−0.0942396	+	0.995550i	$0.530042\pi$
$14$	−1.50560	−0.402389
$15$	0.535031	0.138144
$16$	1.00000	0.250000
$17$	−0.116414	−0.0282346	−0.0141173	−	0.999900i	$-0.504494\pi$
$17$	−0.116414	−0.0282346	−0.0141173	+	0.999900i	$0.504494\pi$
$18$	1.17057	0.275907
$19$	1.90352	0.436697	0.218348	−	0.975871i	$-0.429933\pi$
$19$	1.90352	0.436697	0.218348	+	0.975871i	$0.429933\pi$
$20$	−0.395568	−0.0884517
$21$	−2.03642	−0.444384
$22$	−1.06848	−0.227800
$23$	−2.44771	−0.510382	−0.255191	−	0.966891i	$-0.582138\pi$
$23$	−2.44771	−0.510382	−0.255191	+	0.966891i	$0.582138\pi$
$24$	1.35256	0.276091
$25$	−4.84353	−0.968705
$26$	0.679571	0.133275
$27$	5.64096	1.08560
$28$	1.50560	0.284532
$29$	1.89694	0.352252	0.176126	−	0.984368i	$-0.443643\pi$
$29$	1.89694	0.352252	0.176126	+	0.984368i	$0.443643\pi$
$30$	−0.535031	−0.0976829
$31$	4.13611	0.742868	0.371434	−	0.928459i	$-0.378866\pi$
$31$	4.13611	0.742868	0.371434	+	0.928459i	$0.378866\pi$
$32$	−1.00000	−0.176777
$33$	−1.44518	−0.251574
$34$	0.116414	0.0199649
$35$	−0.595569	−0.100670
$36$	−1.17057	−0.195095
$37$	−7.02112	−1.15426	−0.577132	−	0.816651i	$-0.695828\pi$
$37$	−7.02112	−1.15426	−0.577132	+	0.816651i	$0.695828\pi$
$38$	−1.90352	−0.308791
$39$	0.919163	0.147184
$40$	0.395568	0.0625448
$41$	0.146204	0.0228332	0.0114166	−	0.999935i	$-0.496366\pi$
$41$	0.146204	0.0228332	0.0114166	+	0.999935i	$0.496366\pi$
$42$	2.03642	0.314227
$43$	2.52664	0.385308	0.192654	−	0.981267i	$-0.438290\pi$
$43$	2.52664	0.385308	0.192654	+	0.981267i	$0.438290\pi$
$44$	1.06848	0.161079
$45$	0.463041	0.0690261
$46$	2.44771	0.360895
$47$	8.25454	1.20405	0.602024	−	0.798478i	$-0.294361\pi$
$47$	8.25454	1.20405	0.602024	+	0.798478i	$0.294361\pi$
$48$	−1.35256	−0.195226
$49$	−4.73316	−0.676165
$50$	4.84353	0.684978
$51$	0.157457	0.0220485
$52$	−0.679571	−0.0942396
$53$	−1.27802	−0.175549	−0.0877746	−	0.996140i	$-0.527976\pi$
$53$	−1.27802	−0.175549	−0.0877746	+	0.996140i	$0.527976\pi$
$54$	−5.64096	−0.767638
$55$	−0.422655	−0.0569908
$56$	−1.50560	−0.201195
$57$	−2.57463	−0.341018
$58$	−1.89694	−0.249080
$59$	−6.85919	−0.892991	−0.446495	−	0.894786i	$-0.647328\pi$
$59$	−6.85919	−0.892991	−0.446495	+	0.894786i	$0.647328\pi$
$60$	0.535031	0.0690722
$61$	0.454058	0.0581362	0.0290681	−	0.999577i	$-0.490746\pi$
$61$	0.454058	0.0581362	0.0290681	+	0.999577i	$0.490746\pi$
$62$	−4.13611	−0.525287
$63$	−1.76242	−0.222044
$64$	1.00000	0.125000
$65$	0.268817	0.0333426
$66$	1.44518	0.177890
$67$	−14.3733	−1.75598	−0.877988	−	0.478683i	$-0.841114\pi$
$67$	−14.3733	−1.75598	−0.877988	+	0.478683i	$0.841114\pi$
$68$	−0.116414	−0.0141173
$69$	3.31068	0.398559
$70$	0.595569	0.0711841
$71$	2.75764	0.327271	0.163636	−	0.986521i	$-0.447678\pi$
$71$	2.75764	0.327271	0.163636	+	0.986521i	$0.447678\pi$
$72$	1.17057	0.137953
$73$	13.1381	1.53770	0.768851	−	0.639427i	$-0.220829\pi$
$73$	13.1381	1.53770	0.768851	+	0.639427i	$0.220829\pi$
$74$	7.02112	0.816188
$75$	6.55117	0.756465
$76$	1.90352	0.218348
$77$	1.60870	0.183329
$78$	−0.919163	−0.104075
$79$	−12.0378	−1.35436	−0.677178	−	0.735819i	$-0.736797\pi$
$79$	−12.0378	−1.35436	−0.677178	+	0.735819i	$0.736797\pi$
$80$	−0.395568	−0.0442259
$81$	−4.11804	−0.457560
$82$	−0.146204	−0.0161455
$83$	16.0655	1.76342	0.881711	−	0.471790i	$-0.156392\pi$
$83$	16.0655	1.76342	0.881711	+	0.471790i	$0.156392\pi$
$84$	−2.03642	−0.222192
$85$	0.0460497	0.00499479
$86$	−2.52664	−0.272454
$87$	−2.56573	−0.275075
$88$	−1.06848	−0.113900
$89$	5.48474	0.581381	0.290691	−	0.956817i	$-0.406115\pi$
$89$	5.48474	0.581381	0.290691	+	0.956817i	$0.406115\pi$
$90$	−0.463041	−0.0488088
$91$	−1.02317	−0.107257
$92$	−2.44771	−0.255191
$93$	−5.59435	−0.580107
$94$	−8.25454	−0.851390
$95$	−0.752971	−0.0772532
$96$	1.35256	0.138045
$97$	−4.05519	−0.411743	−0.205871	−	0.978579i	$-0.566003\pi$
$97$	−4.05519	−0.411743	−0.205871	+	0.978579i	$0.566003\pi$
$98$	4.73316	0.478121
$99$	−1.25073	−0.125703
$100$	−4.84353	−0.484353
$101$	−10.4663	−1.04144	−0.520720	−	0.853727i	$-0.674337\pi$
$101$	−10.4663	−1.04144	−0.520720	+	0.853727i	$0.674337\pi$
$102$	−0.157457	−0.0155906
$103$	−1.03084	−0.101571	−0.0507857	−	0.998710i	$-0.516173\pi$
$103$	−1.03084	−0.101571	−0.0507857	+	0.998710i	$0.516173\pi$
$104$	0.679571	0.0666375
$105$	0.805545	0.0786131
$106$	1.27802	0.124132
$107$	7.10794	0.687150	0.343575	−	0.939125i	$-0.388362\pi$
$107$	7.10794	0.687150	0.343575	+	0.939125i	$0.388362\pi$
$108$	5.64096	0.542802
$109$	−12.3658	−1.18443	−0.592215	−	0.805780i	$-0.701747\pi$
$109$	−12.3658	−1.18443	−0.592215	+	0.805780i	$0.701747\pi$
$110$	0.422655	0.0402986
$111$	9.49650	0.901368
$112$	1.50560	0.142266
$113$	15.8673	1.49267	0.746333	−	0.665573i	$-0.231813\pi$
$113$	15.8673	1.49267	0.746333	+	0.665573i	$0.231813\pi$
$114$	2.57463	0.241136
$115$	0.968235	0.0902884
$116$	1.89694	0.176126
$117$	0.795488	0.0735429
$118$	6.85919	0.631440
$119$	−0.175273	−0.0160673
$120$	−0.535031	−0.0488414
$121$	−9.85836	−0.896214
$122$	−0.454058	−0.0411085
$123$	−0.197750	−0.0178305
$124$	4.13611	0.371434
$125$	3.89379	0.348271
$126$	1.76242	0.157009
$127$	4.44200	0.394164	0.197082	−	0.980387i	$-0.436854\pi$
$127$	4.44200	0.394164	0.197082	+	0.980387i	$0.436854\pi$
$128$	−1.00000	−0.0883883
$129$	−3.41743	−0.300888
$130$	−0.268817	−0.0235768
$131$	−3.44238	−0.300762	−0.150381	−	0.988628i	$-0.548050\pi$
$131$	−3.44238	−0.300762	−0.150381	+	0.988628i	$0.548050\pi$
$132$	−1.44518	−0.125787
$133$	2.86594	0.248509
$134$	14.3733	1.24166
$135$	−2.23139	−0.192047
$136$	0.116414	0.00998243
$137$	−14.7080	−1.25659	−0.628293	−	0.777977i	$-0.716246\pi$
$137$	−14.7080	−1.25659	−0.628293	+	0.777977i	$0.716246\pi$
$138$	−3.31068	−0.281824
$139$	11.3215	0.960277	0.480138	−	0.877193i	$-0.340586\pi$
$139$	11.3215	0.960277	0.480138	+	0.877193i	$0.340586\pi$
$140$	−0.595569	−0.0503348
$141$	−11.1648	−0.940244
$142$	−2.75764	−0.231416
$143$	−0.726106	−0.0607200
$144$	−1.17057	−0.0975477
$145$	−0.750368	−0.0623146
$146$	−13.1381	−1.08732
$147$	6.40190	0.528019
$148$	−7.02112	−0.577132
$149$	8.56801	0.701919	0.350959	−	0.936391i	$-0.385855\pi$
$149$	8.56801	0.701919	0.350959	+	0.936391i	$0.385855\pi$
$150$	−6.55117	−0.534901
$151$	−4.54726	−0.370051	−0.185026	−	0.982734i	$-0.559237\pi$
$151$	−4.54726	−0.370051	−0.185026	+	0.982734i	$0.559237\pi$
$152$	−1.90352	−0.154396
$153$	0.136271	0.0110169
$154$	−1.60870	−0.129633
$155$	−1.63611	−0.131416
$156$	0.919163	0.0735920
$157$	7.44260	0.593984	0.296992	−	0.954880i	$-0.404017\pi$
$157$	7.44260	0.593984	0.296992	+	0.954880i	$0.404017\pi$
$158$	12.0378	0.957674
$159$	1.72860	0.137087
$160$	0.395568	0.0312724
$161$	−3.68527	−0.290440
$162$	4.11804	0.323544
$163$	−7.20905	−0.564656	−0.282328	−	0.959318i	$-0.591107\pi$
$163$	−7.20905	−0.564656	−0.282328	+	0.959318i	$0.591107\pi$
$164$	0.146204	0.0114166
$165$	0.571668	0.0445043
$166$	−16.0655	−1.24693
$167$	−19.5626	−1.51380	−0.756900	−	0.653531i	$-0.773287\pi$
$167$	−19.5626	−1.51380	−0.756900	+	0.653531i	$0.773287\pi$
$168$	2.03642	0.157114
$169$	−12.5382	−0.964476
$170$	−0.0460497	−0.00353185
$171$	−2.22820	−0.170395
$172$	2.52664	0.192654
$173$	−6.76217	−0.514118	−0.257059	−	0.966396i	$-0.582754\pi$
$173$	−6.76217	−0.514118	−0.257059	+	0.966396i	$0.582754\pi$
$174$	2.56573	0.194507
$175$	−7.29243	−0.551256
$176$	1.06848	0.0805394
$177$	9.27749	0.697339
$178$	−5.48474	−0.411099
$179$	7.71632	0.576745	0.288373	−	0.957518i	$-0.406886\pi$
$179$	7.71632	0.576745	0.288373	+	0.957518i	$0.406886\pi$
$180$	0.463041	0.0345131
$181$	2.39062	0.177693	0.0888467	−	0.996045i	$-0.471682\pi$
$181$	2.39062	0.177693	0.0888467	+	0.996045i	$0.471682\pi$
$182$	1.02317	0.0758420
$183$	−0.614142	−0.0453987
$184$	2.44771	0.180447
$185$	2.77733	0.204193
$186$	5.59435	0.410198
$187$	−0.124386	−0.00909598
$188$	8.25454	0.602024
$189$	8.49305	0.617779
$190$	0.752971	0.0546262
$191$	−9.88079	−0.714949	−0.357474	−	0.933923i	$-0.616362\pi$
$191$	−9.88079	−0.714949	−0.357474	+	0.933923i	$0.616362\pi$
$192$	−1.35256	−0.0976128
$193$	−5.26642	−0.379085	−0.189542	−	0.981873i	$-0.560700\pi$
$193$	−5.26642	−0.379085	−0.189542	+	0.981873i	$0.560700\pi$
$194$	4.05519	0.291146
$195$	−0.363592	−0.0260374
$196$	−4.73316	−0.338083
$197$	15.2491	1.08645	0.543225	−	0.839587i	$-0.317203\pi$
$197$	15.2491	1.08645	0.543225	+	0.839587i	$0.317203\pi$
$198$	1.25073	0.0888855
$199$	6.97944	0.494760	0.247380	−	0.968919i	$-0.420430\pi$
$199$	6.97944	0.494760	0.247380	+	0.968919i	$0.420430\pi$
$200$	4.84353	0.342489
$201$	19.4408	1.37125
$202$	10.4663	0.736410
$203$	2.85603	0.200454
$204$	0.157457	0.0110242
$205$	−0.0578337	−0.00403928
$206$	1.03084	0.0718218
$207$	2.86522	0.199146
$208$	−0.679571	−0.0471198
$209$	2.03386	0.140685
$210$	−0.805545	−0.0555879
$211$	−25.6146	−1.76338	−0.881691	−	0.471828i	$-0.843594\pi$
$211$	−25.6146	−1.76338	−0.881691	+	0.471828i	$0.843594\pi$
$212$	−1.27802	−0.0877746
$213$	−3.72988	−0.255567
$214$	−7.10794	−0.485889
$215$	−0.999457	−0.0681624
$216$	−5.64096	−0.383819
$217$	6.22734	0.422740
$218$	12.3658	0.837519
$219$	−17.7702	−1.20080
$220$	−0.422655	−0.0284954
$221$	0.0791117	0.00532163
$222$	−9.49650	−0.637364
$223$	−4.86757	−0.325957	−0.162978	−	0.986630i	$-0.552110\pi$
$223$	−4.86757	−0.325957	−0.162978	+	0.986630i	$0.552110\pi$
$224$	−1.50560	−0.100597
$225$	5.66970	0.377980
$226$	−15.8673	−1.05547
$227$	−2.73845	−0.181757	−0.0908785	−	0.995862i	$-0.528968\pi$
$227$	−2.73845	−0.181757	−0.0908785	+	0.995862i	$0.528968\pi$
$228$	−2.57463	−0.170509
$229$	25.6694	1.69628	0.848141	−	0.529770i	$-0.177722\pi$
$229$	25.6694	1.69628	0.848141	+	0.529770i	$0.177722\pi$
$230$	−0.968235	−0.0638435
$231$	−2.17587	−0.143162
$232$	−1.89694	−0.124540
$233$	−5.38061	−0.352495	−0.176248	−	0.984346i	$-0.556396\pi$
$233$	−5.38061	−0.352495	−0.176248	+	0.984346i	$0.556396\pi$
$234$	−0.795488	−0.0520027
$235$	−3.26523	−0.213000
$236$	−6.85919	−0.446495
$237$	16.2819	1.05762
$238$	0.175273	0.0113613
$239$	−17.5326	−1.13409	−0.567045	−	0.823686i	$-0.691914\pi$
$239$	−17.5326	−1.13409	−0.567045	+	0.823686i	$0.691914\pi$
$240$	0.535031	0.0345361
$241$	4.85052	0.312450	0.156225	−	0.987722i	$-0.450068\pi$
$241$	4.85052	0.312450	0.156225	+	0.987722i	$0.450068\pi$
$242$	9.85836	0.633719
$243$	−11.3530	−0.728294
$244$	0.454058	0.0290681
$245$	1.87229	0.119616
$246$	0.197750	0.0126081
$247$	−1.29358	−0.0823082
$248$	−4.13611	−0.262643
$249$	−21.7297	−1.37706
$250$	−3.89379	−0.246265
$251$	−13.0716	−0.825073	−0.412537	−	0.910941i	$-0.635357\pi$
$251$	−13.0716	−0.825073	−0.412537	+	0.910941i	$0.635357\pi$
$252$	−1.76242	−0.111022
$253$	−2.61532	−0.164424
$254$	−4.44200	−0.278716
$255$	−0.0622852	−0.00390045
$256$	1.00000	0.0625000
$257$	−20.1296	−1.25565	−0.627825	−	0.778355i	$-0.716055\pi$
$257$	−20.1296	−1.25565	−0.627825	+	0.778355i	$0.716055\pi$
$258$	3.41743	0.212760
$259$	−10.5710	−0.656851
$260$	0.268817	0.0166713
$261$	−2.22050	−0.137446
$262$	3.44238	0.212671
$263$	10.7114	0.660494	0.330247	−	0.943894i	$-0.392868\pi$
$263$	10.7114	0.660494	0.330247	+	0.943894i	$0.392868\pi$
$264$	1.44518	0.0889448
$265$	0.505543	0.0310553
$266$	−2.86594	−0.175722
$267$	−7.41846	−0.454002
$268$	−14.3733	−0.877988
$269$	8.69319	0.530033	0.265017	−	0.964244i	$-0.414623\pi$
$269$	8.69319	0.530033	0.265017	+	0.964244i	$0.414623\pi$
$270$	2.23139	0.135798
$271$	−21.3229	−1.29527	−0.647636	−	0.761950i	$-0.724242\pi$
$271$	−21.3229	−1.29527	−0.647636	+	0.761950i	$0.724242\pi$
$272$	−0.116414	−0.00705864
$273$	1.38390	0.0837572
$274$	14.7080	0.888541
$275$	−5.17519	−0.312076
$276$	3.31068	0.199279
$277$	−19.1917	−1.15311	−0.576557	−	0.817057i	$-0.695604\pi$
$277$	−19.1917	−1.15311	−0.576557	+	0.817057i	$0.695604\pi$
$278$	−11.3215	−0.679018
$279$	−4.84162	−0.289860
$280$	0.595569	0.0355920
$281$	−17.4771	−1.04260	−0.521299	−	0.853374i	$-0.674552\pi$
$281$	−17.4771	−1.04260	−0.521299	+	0.853374i	$0.674552\pi$
$282$	11.1648	0.664853
$283$	−21.9318	−1.30371	−0.651855	−	0.758344i	$-0.726009\pi$
$283$	−21.9318	−1.30371	−0.651855	+	0.758344i	$0.726009\pi$
$284$	2.75764	0.163636
$285$	1.01844	0.0603272
$286$	0.726106	0.0429355
$287$	0.220125	0.0129936
$288$	1.17057	0.0689767
$289$	−16.9864	−0.999203
$290$	0.750368	0.0440631
$291$	5.48491	0.321531
$292$	13.1381	0.768851
$293$	−16.1080	−0.941042	−0.470521	−	0.882389i	$-0.655934\pi$
$293$	−16.1080	−0.941042	−0.470521	+	0.882389i	$0.655934\pi$
$294$	−6.40190	−0.373366
$295$	2.71328	0.157973
$296$	7.02112	0.408094
$297$	6.02724	0.349736
$298$	−8.56801	−0.496332
$299$	1.66339	0.0961964
$300$	6.55117	0.378232
$301$	3.80411	0.219265
$302$	4.54726	0.261666
$303$	14.1564	0.813264
$304$	1.90352	0.109174
$305$	−0.179611	−0.0102845
$306$	−0.136271	−0.00779010
$307$	−20.6517	−1.17866	−0.589328	−	0.807894i	$-0.700607\pi$
$307$	−20.6517	−1.17866	−0.589328	+	0.807894i	$0.700607\pi$
$308$	1.60870	0.0916643
$309$	1.39427	0.0793174
$310$	1.63611	0.0929251
$311$	−0.371278	−0.0210532	−0.0105266	−	0.999945i	$-0.503351\pi$
$311$	−0.371278	−0.0210532	−0.0105266	+	0.999945i	$0.503351\pi$
$312$	−0.919163	−0.0520374
$313$	30.6791	1.73408	0.867042	−	0.498235i	$-0.166018\pi$
$313$	30.6791	1.73408	0.867042	+	0.498235i	$0.166018\pi$
$314$	−7.44260	−0.420010
$315$	0.697157	0.0392803
$316$	−12.0378	−0.677178
$317$	22.9920	1.29136	0.645678	−	0.763609i	$-0.276575\pi$
$317$	22.9920	1.29136	0.645678	+	0.763609i	$0.276575\pi$
$318$	−1.72860	−0.0969350
$319$	2.02683	0.113481
$320$	−0.395568	−0.0221129
$321$	−9.61394	−0.536598
$322$	3.68527	0.205372
$323$	−0.221596	−0.0123299
$324$	−4.11804	−0.228780
$325$	3.29152	0.182581
$326$	7.20905	0.399272
$327$	16.7256	0.924925
$328$	−0.146204	−0.00807277
$329$	12.4281	0.685181
$330$	−0.571668	−0.0314693
$331$	−10.3236	−0.567436	−0.283718	−	0.958908i	$-0.591568\pi$
$331$	−10.3236	−0.567436	−0.283718	+	0.958908i	$0.591568\pi$
$332$	16.0655	0.881711
$333$	8.21873	0.450383
$334$	19.5626	1.07042
$335$	5.68561	0.310638
$336$	−2.03642	−0.111096
$337$	12.9181	0.703693	0.351847	−	0.936058i	$-0.385554\pi$
$337$	12.9181	0.703693	0.351847	+	0.936058i	$0.385554\pi$
$338$	12.5382	0.681987
$339$	−21.4615	−1.16563
$340$	0.0460497	0.00249740
$341$	4.41934	0.239321
$342$	2.22820	0.120487
$343$	−17.6655	−0.953846
$344$	−2.52664	−0.136227
$345$	−1.30960	−0.0705064
$346$	6.76217	0.363537
$347$	−18.1403	−0.973820	−0.486910	−	0.873452i	$-0.661876\pi$
$347$	−18.1403	−0.973820	−0.486910	+	0.873452i	$0.661876\pi$
$348$	−2.56573	−0.137537
$349$	−29.6318	−1.58616	−0.793078	−	0.609121i	$-0.791523\pi$
$349$	−29.6318	−1.58616	−0.793078	+	0.609121i	$0.791523\pi$
$350$	7.29243	0.389797
$351$	−3.83344	−0.204614
$352$	−1.06848	−0.0569500
$353$	−30.3110	−1.61329	−0.806645	−	0.591036i	$-0.798719\pi$
$353$	−30.3110	−1.61329	−0.806645	+	0.591036i	$0.798719\pi$
$354$	−9.27749	−0.493093
$355$	−1.09083	−0.0578954
$356$	5.48474	0.290691
$357$	0.237068	0.0125470
$358$	−7.71632	−0.407820
$359$	0.971662	0.0512823	0.0256412	−	0.999671i	$-0.491837\pi$
$359$	0.971662	0.0512823	0.0256412	+	0.999671i	$0.491837\pi$
$360$	−0.463041	−0.0244044
$361$	−15.3766	−0.809296
$362$	−2.39062	−0.125648
$363$	13.3341	0.699856
$364$	−1.02317	−0.0536284
$365$	−5.19703	−0.272025
$366$	0.614142	0.0321017
$367$	−12.2843	−0.641235	−0.320618	−	0.947209i	$-0.603890\pi$
$367$	−12.2843	−0.641235	−0.320618	+	0.947209i	$0.603890\pi$
$368$	−2.44771	−0.127595
$369$	−0.171142	−0.00890932
$370$	−2.77733	−0.144387
$371$	−1.92419	−0.0998988
$372$	−5.59435	−0.290054
$373$	−27.0718	−1.40173	−0.700864	−	0.713295i	$-0.747202\pi$
$373$	−27.0718	−1.40173	−0.700864	+	0.713295i	$0.747202\pi$
$374$	0.124386	0.00643183
$375$	−5.26659	−0.271966
$376$	−8.25454	−0.425695
$377$	−1.28910	−0.0663922
$378$	−8.49305	−0.436836
$379$	4.49022	0.230647	0.115324	−	0.993328i	$-0.463210\pi$
$379$	4.49022	0.230647	0.115324	+	0.993328i	$0.463210\pi$
$380$	−0.752971	−0.0386266
$381$	−6.00809	−0.307804
$382$	9.88079	0.505545
$383$	21.3209	1.08945	0.544725	−	0.838615i	$-0.316634\pi$
$383$	21.3209	1.08945	0.544725	+	0.838615i	$0.316634\pi$
$384$	1.35256	0.0690227
$385$	−0.636351	−0.0324315
$386$	5.26642	0.268054
$387$	−2.95761	−0.150344
$388$	−4.05519	−0.205871
$389$	−12.2961	−0.623436	−0.311718	−	0.950175i	$-0.600904\pi$
$389$	−12.2961	−0.623436	−0.311718	+	0.950175i	$0.600904\pi$
$390$	0.363592	0.0184112
$391$	0.284947	0.0144104
$392$	4.73316	0.239061
$393$	4.65604	0.234866
$394$	−15.2491	−0.768237
$395$	4.76176	0.239590
$396$	−1.25073	−0.0628515
$397$	−20.7364	−1.04073	−0.520366	−	0.853943i	$-0.674204\pi$
$397$	−20.7364	−1.04073	−0.520366	+	0.853943i	$0.674204\pi$
$398$	−6.97944	−0.349848
$399$	−3.87637	−0.194061
$400$	−4.84353	−0.242176
$401$	−6.83314	−0.341231	−0.170615	−	0.985338i	$-0.554576\pi$
$401$	−6.83314	−0.341231	−0.170615	+	0.985338i	$0.554576\pi$
$402$	−19.4408	−0.969617
$403$	−2.81078	−0.140015
$404$	−10.4663	−0.520720
$405$	1.62897	0.0809440
$406$	−2.85603	−0.141743
$407$	−7.50190	−0.371855
$408$	−0.157457	−0.00779530
$409$	−7.93478	−0.392350	−0.196175	−	0.980569i	$-0.562852\pi$
$409$	−7.93478	−0.392350	−0.196175	+	0.980569i	$0.562852\pi$
$410$	0.0578337	0.00285620
$411$	19.8935	0.981272
$412$	−1.03084	−0.0507857
$413$	−10.3272	−0.508169
$414$	−2.86522	−0.140818
$415$	−6.35502	−0.311956
$416$	0.679571	0.0333187
$417$	−15.3130	−0.749883
$418$	−2.03386	−0.0994795
$419$	7.86943	0.384447	0.192223	−	0.981351i	$-0.438430\pi$
$419$	7.86943	0.384447	0.192223	+	0.981351i	$0.438430\pi$
$420$	0.805545	0.0393066
$421$	−13.5945	−0.662557	−0.331279	−	0.943533i	$-0.607480\pi$
$421$	−13.5945	−0.662557	−0.331279	+	0.943533i	$0.607480\pi$
$422$	25.6146	1.24690
$423$	−9.66253	−0.469808
$424$	1.27802	0.0620660
$425$	0.563855	0.0273510
$426$	3.72988	0.180713
$427$	0.683631	0.0330832
$428$	7.10794	0.343575
$429$	0.982104	0.0474164
$430$	0.999457	0.0481981
$431$	−24.4001	−1.17531	−0.587657	−	0.809110i	$-0.699949\pi$
$431$	−24.4001	−1.17531	−0.587657	+	0.809110i	$0.699949\pi$
$432$	5.64096	0.271401
$433$	−10.6097	−0.509867	−0.254934	−	0.966959i	$-0.582054\pi$
$433$	−10.6097	−0.509867	−0.254934	+	0.966959i	$0.582054\pi$
$434$	−6.22734	−0.298922
$435$	1.01492	0.0486617
$436$	−12.3658	−0.592215
$437$	−4.65925	−0.222882
$438$	17.7702	0.849091
$439$	−14.1920	−0.677349	−0.338675	−	0.940904i	$-0.609979\pi$
$439$	−14.1920	−0.677349	−0.338675	+	0.940904i	$0.609979\pi$
$440$	0.422655	0.0201493
$441$	5.54051	0.263834
$442$	−0.0791117	−0.00376296
$443$	21.1493	1.00483	0.502417	−	0.864625i	$-0.332444\pi$
$443$	21.1493	1.00483	0.502417	+	0.864625i	$0.332444\pi$
$444$	9.49650	0.450684
$445$	−2.16959	−0.102848
$446$	4.86757	0.230486
$447$	−11.5888	−0.548130
$448$	1.50560	0.0711331
$449$	41.3879	1.95322	0.976609	−	0.215025i	$-0.0689834\pi$
$449$	41.3879	1.95322	0.976609	+	0.215025i	$0.0689834\pi$
$450$	−5.66970	−0.267272
$451$	0.156216	0.00735590
$452$	15.8673	0.746333
$453$	6.15046	0.288974
$454$	2.73845	0.128522
$455$	0.404732	0.0189741
$456$	2.57463	0.120568
$457$	23.4724	1.09799	0.548997	−	0.835824i	$-0.315010\pi$
$457$	23.4724	1.09799	0.548997	+	0.835824i	$0.315010\pi$
$458$	−25.6694	−1.19945
$459$	−0.656688	−0.0306516
$460$	0.968235	0.0451442
$461$	−29.0799	−1.35438	−0.677192	−	0.735806i	$-0.736804\pi$
$461$	−29.0799	−1.35438	−0.677192	+	0.735806i	$0.736804\pi$
$462$	2.17587	0.101231
$463$	−7.15965	−0.332737	−0.166369	−	0.986064i	$-0.553204\pi$
$463$	−7.15965	−0.332737	−0.166369	+	0.986064i	$0.553204\pi$
$464$	1.89694	0.0880630
$465$	2.21295	0.102623
$466$	5.38061	0.249252
$467$	−41.8797	−1.93796	−0.968981	−	0.247136i	$-0.920511\pi$
$467$	−41.8797	−1.93796	−0.968981	+	0.247136i	$0.920511\pi$
$468$	0.795488	0.0367714
$469$	−21.6405	−0.999263
$470$	3.26523	0.150614
$471$	−10.0666	−0.463844
$472$	6.85919	0.315720
$473$	2.69965	0.124130
$474$	−16.2819	−0.747851
$475$	−9.21973	−0.423030
$476$	−0.175273	−0.00803365
$477$	1.49601	0.0684977
$478$	17.5326	0.801923
$479$	−0.693668	−0.0316945	−0.0158473	−	0.999874i	$-0.505045\pi$
$479$	−0.693668	−0.0316945	−0.0158473	+	0.999874i	$0.505045\pi$
$480$	−0.535031	−0.0244207
$481$	4.77135	0.217555
$482$	−4.85052	−0.220935
$483$	4.98457	0.226806
$484$	−9.85836	−0.448107
$485$	1.60411	0.0728387
$486$	11.3530	0.514982
$487$	−35.0836	−1.58979	−0.794895	−	0.606748i	$-0.792474\pi$
$487$	−35.0836	−1.58979	−0.794895	+	0.606748i	$0.792474\pi$
$488$	−0.454058	−0.0205542
$489$	9.75069	0.440942
$490$	−1.87229	−0.0845813
$491$	−13.8160	−0.623505	−0.311753	−	0.950163i	$-0.600916\pi$
$491$	−13.8160	−0.623505	−0.311753	+	0.950163i	$0.600916\pi$
$492$	−0.197750	−0.00891527
$493$	−0.220830	−0.00994569
$494$	1.29358	0.0582007
$495$	0.494749	0.0222373
$496$	4.13611	0.185717
$497$	4.15191	0.186238
$498$	21.7297	0.973729
$499$	20.6857	0.926021	0.463011	−	0.886353i	$-0.346769\pi$
$499$	20.6857	0.926021	0.463011	+	0.886353i	$0.346769\pi$
$500$	3.89379	0.174135
$501$	26.4597	1.18213
$502$	13.0716	0.583415
$503$	33.2970	1.48464	0.742321	−	0.670044i	$-0.233725\pi$
$503$	33.2970	1.48464	0.742321	+	0.670044i	$0.233725\pi$
$504$	1.76242	0.0785043
$505$	4.14016	0.184234
$506$	2.61532	0.116265
$507$	16.9587	0.753162
$508$	4.44200	0.197082
$509$	20.8749	0.925265	0.462633	−	0.886550i	$-0.346905\pi$
$509$	20.8749	0.925265	0.462633	+	0.886550i	$0.346905\pi$
$510$	0.0622852	0.00275803
$511$	19.7808	0.875052
$512$	−1.00000	−0.0441942
$513$	10.7377	0.474080
$514$	20.1296	0.887879
$515$	0.407766	0.0179683
$516$	−3.41743	−0.150444
$517$	8.81978	0.387893
$518$	10.5710	0.464464
$519$	9.14627	0.401477
$520$	−0.268817	−0.0117884
$521$	−12.1112	−0.530602	−0.265301	−	0.964166i	$-0.585471\pi$
$521$	−12.1112	−0.530602	−0.265301	+	0.964166i	$0.585471\pi$
$522$	2.22050	0.0971887
$523$	27.8176	1.21638	0.608190	−	0.793792i	$-0.291896\pi$
$523$	27.8176	1.21638	0.608190	+	0.793792i	$0.291896\pi$
$524$	−3.44238	−0.150381
$525$	9.86347	0.430477
$526$	−10.7114	−0.467040
$527$	−0.481502	−0.0209745
$528$	−1.44518	−0.0628935
$529$	−17.0087	−0.739510
$530$	−0.505543	−0.0219594
$531$	8.02918	0.348437
$532$	2.86594	0.124254
$533$	−0.0993561	−0.00430359
$534$	7.41846	0.321028
$535$	−2.81167	−0.121559
$536$	14.3733	0.620831
$537$	−10.4368	−0.450382
$538$	−8.69319	−0.374790
$539$	−5.05727	−0.217832
$540$	−2.23139	−0.0960236
$541$	17.7585	0.763497	0.381749	−	0.924266i	$-0.375322\pi$
$541$	17.7585	0.763497	0.381749	+	0.924266i	$0.375322\pi$
$542$	21.3229	0.915895
$543$	−3.23346	−0.138761
$544$	0.116414	0.00499121
$545$	4.89153	0.209530
$546$	−1.38390	−0.0592253
$547$	−35.7144	−1.52704	−0.763519	−	0.645785i	$-0.776530\pi$
$547$	−35.7144	−1.52704	−0.763519	+	0.645785i	$0.776530\pi$
$548$	−14.7080	−0.628293
$549$	−0.531508	−0.0226842
$550$	5.17519	0.220671
$551$	3.61085	0.153827
$552$	−3.31068	−0.140912
$553$	−18.1241	−0.770716
$554$	19.1917	0.815375
$555$	−3.75652	−0.159455
$556$	11.3215	0.480138
$557$	−24.7855	−1.05020	−0.525098	−	0.851042i	$-0.675971\pi$
$557$	−24.7855	−1.05020	−0.525098	+	0.851042i	$0.675971\pi$
$558$	4.84162	0.204962
$559$	−1.71703	−0.0726226
$560$	−0.595569	−0.0251674
$561$	0.168240	0.00710308
$562$	17.4771	0.737228
$563$	1.08361	0.0456686	0.0228343	−	0.999739i	$-0.492731\pi$
$563$	1.08361	0.0456686	0.0228343	+	0.999739i	$0.492731\pi$
$564$	−11.1648	−0.470122
$565$	−6.27658	−0.264058
$566$	21.9318	0.921862
$567$	−6.20014	−0.260381
$568$	−2.75764	−0.115708
$569$	33.9472	1.42314	0.711571	−	0.702615i	$-0.247984\pi$
$569$	33.9472	1.42314	0.711571	+	0.702615i	$0.247984\pi$
$570$	−1.01844	−0.0426578
$571$	13.4685	0.563640	0.281820	−	0.959467i	$-0.409062\pi$
$571$	13.4685	0.563640	0.281820	+	0.959467i	$0.409062\pi$
$572$	−0.726106	−0.0303600
$573$	13.3644	0.558305
$574$	−0.220125	−0.00918785
$575$	11.8555	0.494410
$576$	−1.17057	−0.0487739
$577$	35.5943	1.48181	0.740904	−	0.671611i	$-0.234397\pi$
$577$	35.5943	1.48181	0.740904	+	0.671611i	$0.234397\pi$
$578$	16.9864	0.706543
$579$	7.12316	0.296028
$580$	−0.750368	−0.0311573
$581$	24.1883	1.00350
$582$	−5.48491	−0.227357
$583$	−1.36553	−0.0565545
$584$	−13.1381	−0.543660
$585$	−0.314670	−0.0130100
$586$	16.1080	0.665417
$587$	−12.5135	−0.516488	−0.258244	−	0.966080i	$-0.583144\pi$
$587$	−12.5135	−0.516488	−0.258244	+	0.966080i	$0.583144\pi$
$588$	6.40190	0.264010
$589$	7.87316	0.324408
$590$	−2.71328	−0.111704
$591$	−20.6253	−0.848412
$592$	−7.02112	−0.288566
$593$	−32.1534	−1.32038	−0.660191	−	0.751098i	$-0.729525\pi$
$593$	−32.1534	−1.32038	−0.660191	+	0.751098i	$0.729525\pi$
$594$	−6.02724	−0.247300
$595$	0.0693326	0.00284236
$596$	8.56801	0.350959
$597$	−9.44014	−0.386359
$598$	−1.66339	−0.0680211
$599$	−45.4319	−1.85630	−0.928148	−	0.372211i	$-0.878600\pi$
$599$	−45.4319	−1.85630	−0.928148	+	0.372211i	$0.878600\pi$
$600$	−6.55117	−0.267451
$601$	0.100841	0.00411338	0.00205669	−	0.999998i	$-0.499345\pi$
$601$	0.100841	0.00411338	0.00205669	+	0.999998i	$0.499345\pi$
$602$	−3.80411	−0.155044
$603$	16.8250	0.685166
$604$	−4.54726	−0.185026
$605$	3.89965	0.158543
$606$	−14.1564	−0.575064
$607$	29.1196	1.18193	0.590964	−	0.806698i	$-0.298747\pi$
$607$	29.1196	1.18193	0.590964	+	0.806698i	$0.298747\pi$
$608$	−1.90352	−0.0771978
$609$	−3.86297	−0.156535
$610$	0.179611	0.00727223
$611$	−5.60955	−0.226938
$612$	0.136271	0.00550844
$613$	21.6353	0.873842	0.436921	−	0.899500i	$-0.356069\pi$
$613$	21.6353	0.873842	0.436921	+	0.899500i	$0.356069\pi$
$614$	20.6517	0.833435
$615$	0.0782237	0.00315428
$616$	−1.60870	−0.0648164
$617$	−11.3169	−0.455603	−0.227801	−	0.973708i	$-0.573154\pi$
$617$	−11.3169	−0.455603	−0.227801	+	0.973708i	$0.573154\pi$
$618$	−1.39427	−0.0560859
$619$	19.2536	0.773866	0.386933	−	0.922108i	$-0.373534\pi$
$619$	19.2536	0.773866	0.386933	+	0.922108i	$0.373534\pi$
$620$	−1.63611	−0.0657079
$621$	−13.8074	−0.554073
$622$	0.371278	0.0148869
$623$	8.25784	0.330843
$624$	0.919163	0.0367960
$625$	22.6774	0.907095
$626$	−30.6791	−1.22618
$627$	−2.75093	−0.109861
$628$	7.44260	0.296992
$629$	0.817357	0.0325902
$630$	−0.697157	−0.0277754
$631$	−19.0977	−0.760266	−0.380133	−	0.924932i	$-0.624122\pi$
$631$	−19.0977	−0.760266	−0.380133	+	0.924932i	$0.624122\pi$
$632$	12.0378	0.478837
$633$	34.6454	1.37703
$634$	−22.9920	−0.913127
$635$	−1.75711	−0.0697290
$636$	1.72860	0.0685434
$637$	3.21652	0.127443
$638$	−2.02683	−0.0802430
$639$	−3.22801	−0.127698
$640$	0.395568	0.0156362
$641$	11.3721	0.449171	0.224585	−	0.974454i	$-0.427897\pi$
$641$	11.3721	0.449171	0.224585	+	0.974454i	$0.427897\pi$
$642$	9.61394	0.379432
$643$	0.490036	0.0193251	0.00966257	−	0.999953i	$-0.496924\pi$
$643$	0.490036	0.0193251	0.00966257	+	0.999953i	$0.496924\pi$
$644$	−3.68527	−0.145220
$645$	1.35183	0.0532282
$646$	0.221596	0.00871858
$647$	29.0759	1.14309	0.571547	−	0.820570i	$-0.306344\pi$
$647$	29.0759	1.14309	0.571547	+	0.820570i	$0.306344\pi$
$648$	4.11804	0.161772
$649$	−7.32889	−0.287684
$650$	−3.29152	−0.129104
$651$	−8.42288	−0.330119
$652$	−7.20905	−0.282328
$653$	34.2051	1.33855	0.669275	−	0.743015i	$-0.266605\pi$
$653$	34.2051	1.33855	0.669275	+	0.743015i	$0.266605\pi$
$654$	−16.7256	−0.654021
$655$	1.36170	0.0532059
$656$	0.146204	0.00570831
$657$	−15.3791	−0.599998
$658$	−12.4281	−0.484496
$659$	26.1806	1.01985	0.509926	−	0.860218i	$-0.329673\pi$
$659$	26.1806	1.01985	0.509926	+	0.860218i	$0.329673\pi$
$660$	0.571668	0.0222521
$661$	−34.5137	−1.34243	−0.671214	−	0.741263i	$-0.734227\pi$
$661$	−34.5137	−1.34243	−0.671214	+	0.741263i	$0.734227\pi$
$662$	10.3236	0.401238
$663$	−0.107004	−0.00415567
$664$	−16.0655	−0.623464
$665$	−1.13368	−0.0439620
$666$	−8.21873	−0.318469
$667$	−4.64314	−0.179783
$668$	−19.5626	−0.756900
$669$	6.58370	0.254540
$670$	−5.68561	−0.219654
$671$	0.485150	0.0187290
$672$	2.03642	0.0785568
$673$	−6.86992	−0.264816	−0.132408	−	0.991195i	$-0.542271\pi$
$673$	−6.86992	−0.264816	−0.132408	+	0.991195i	$0.542271\pi$
$674$	−12.9181	−0.497586
$675$	−27.3222	−1.05163
$676$	−12.5382	−0.482238
$677$	7.10369	0.273017	0.136508	−	0.990639i	$-0.456412\pi$
$677$	7.10369	0.273017	0.136508	+	0.990639i	$0.456412\pi$
$678$	21.4615	0.824223
$679$	−6.10552	−0.234308
$680$	−0.0460497	−0.00176593
$681$	3.70392	0.141935
$682$	−4.41934	−0.169225
$683$	16.0769	0.615165	0.307582	−	0.951521i	$-0.400480\pi$
$683$	16.0769	0.615165	0.307582	+	0.951521i	$0.400480\pi$
$684$	−2.22820	−0.0851975
$685$	5.81800	0.222294
$686$	17.6655	0.674471
$687$	−34.7195	−1.32463
$688$	2.52664	0.0963271
$689$	0.868504	0.0330874
$690$	1.30960	0.0498556
$691$	−28.9672	−1.10197	−0.550983	−	0.834517i	$-0.685747\pi$
$691$	−28.9672	−1.10197	−0.550983	+	0.834517i	$0.685747\pi$
$692$	−6.76217	−0.257059
$693$	−1.88310	−0.0715331
$694$	18.1403	0.688595
$695$	−4.47842	−0.169876
$696$	2.56573	0.0972536
$697$	−0.0170202	−0.000644686 0
$698$	29.6318	1.12158
$699$	7.27761	0.275264
$700$	−7.29243	−0.275628
$701$	46.1539	1.74321	0.871604	−	0.490210i	$-0.163080\pi$
$701$	46.1539	1.74321	0.871604	+	0.490210i	$0.163080\pi$
$702$	3.83344	0.144684
$703$	−13.3648	−0.504063
$704$	1.06848	0.0402697
$705$	4.41643	0.166332
$706$	30.3110	1.14077
$707$	−15.7582	−0.592647
$708$	9.27749	0.348670
$709$	12.3876	0.465228	0.232614	−	0.972569i	$-0.425272\pi$
$709$	12.3876	0.465228	0.232614	+	0.972569i	$0.425272\pi$
$710$	1.09083	0.0409382
$711$	14.0911	0.528457
$712$	−5.48474	−0.205549
$713$	−10.1240	−0.379146
$714$	−0.237068	−0.00887206
$715$	0.287224	0.0107416
$716$	7.71632	0.288373
$717$	23.7140	0.885615
$718$	−0.971662	−0.0362621
$719$	−50.5336	−1.88459	−0.942294	−	0.334788i	$-0.891335\pi$
$719$	−50.5336	−1.88459	−0.942294	+	0.334788i	$0.891335\pi$
$720$	0.463041	0.0172565
$721$	−1.55203	−0.0578007
$722$	15.3766	0.572259
$723$	−6.56064	−0.243993
$724$	2.39062	0.0888467
$725$	−9.18786	−0.341228
$726$	−13.3341	−0.494873
$727$	−35.3451	−1.31088	−0.655438	−	0.755249i	$-0.727516\pi$
$727$	−35.3451	−1.31088	−0.655438	+	0.755249i	$0.727516\pi$
$728$	1.02317	0.0379210
$729$	27.7097	1.02629
$730$	5.19703	0.192351
$731$	−0.294136	−0.0108790
$732$	−0.614142	−0.0226993
$733$	29.1633	1.07717	0.538585	−	0.842571i	$-0.318959\pi$
$733$	29.1633	1.07717	0.538585	+	0.842571i	$0.318959\pi$
$734$	12.2843	0.453422
$735$	−2.53239	−0.0934085
$736$	2.44771	0.0902236
$737$	−15.3575	−0.565701
$738$	0.171142	0.00629984
$739$	1.19446	0.0439389	0.0219694	−	0.999759i	$-0.493006\pi$
$739$	1.19446	0.0439389	0.0219694	+	0.999759i	$0.493006\pi$
$740$	2.77733	0.102097
$741$	1.74964	0.0642747
$742$	1.92419	0.0706391
$743$	4.60586	0.168973	0.0844863	−	0.996425i	$-0.473075\pi$
$743$	4.60586	0.168973	0.0844863	+	0.996425i	$0.473075\pi$
$744$	5.59435	0.205099
$745$	−3.38923	−0.124172
$746$	27.0718	0.991171
$747$	−18.8059	−0.688071
$748$	−0.124386	−0.00454799
$749$	10.7017	0.391033
$750$	5.26659	0.192309
$751$	−9.51571	−0.347233	−0.173617	−	0.984813i	$-0.555545\pi$
$751$	−9.51571	−0.347233	−0.173617	+	0.984813i	$0.555545\pi$
$752$	8.25454	0.301012
$753$	17.6802	0.644302
$754$	1.28910	0.0469464
$755$	1.79875	0.0654633
$756$	8.49305	0.308889
$757$	53.5531	1.94642	0.973210	−	0.229917i	$-0.0738456\pi$
$757$	53.5531	1.94642	0.973210	+	0.229917i	$0.0738456\pi$
$758$	−4.49022	−0.163092
$759$	3.53738	0.128399
$760$	0.752971	0.0273131
$761$	−2.31444	−0.0838984	−0.0419492	−	0.999120i	$-0.513357\pi$
$761$	−2.31444	−0.0838984	−0.0419492	+	0.999120i	$0.513357\pi$
$762$	6.00809	0.217650
$763$	−18.6180	−0.674018
$764$	−9.88079	−0.357474
$765$	−0.0539045	−0.00194892
$766$	−21.3209	−0.770357
$767$	4.66131	0.168310
$768$	−1.35256	−0.0488064
$769$	29.0362	1.04707	0.523536	−	0.852004i	$-0.324613\pi$
$769$	29.0362	1.04707	0.523536	+	0.852004i	$0.324613\pi$
$770$	0.636351	0.0229325
$771$	27.2266	0.980541
$772$	−5.26642	−0.189542
$773$	21.4610	0.771897	0.385949	−	0.922520i	$-0.373874\pi$
$773$	21.4610	0.771897	0.385949	+	0.922520i	$0.373874\pi$
$774$	2.95761	0.106309
$775$	−20.0334	−0.719620
$776$	4.05519	0.145573
$777$	14.2980	0.512937
$778$	12.2961	0.440836
$779$	0.278302	0.00997120
$780$	−0.363592	−0.0130187
$781$	2.94647	0.105433
$782$	−0.284947	−0.0101897
$783$	10.7005	0.382406
$784$	−4.73316	−0.169041
$785$	−2.94405	−0.105078
$786$	−4.65604	−0.166075
$787$	−14.7287	−0.525022	−0.262511	−	0.964929i	$-0.584551\pi$
$787$	−14.7287	−0.525022	−0.262511	+	0.964929i	$0.584551\pi$
$788$	15.2491	0.543225
$789$	−14.4879	−0.515782
$790$	−4.76176	−0.169416
$791$	23.8898	0.849424
$792$	1.25073	0.0444427
$793$	−0.308565	−0.0109575
$794$	20.7364	0.735908
$795$	−0.683779	−0.0242511
$796$	6.97944	0.247380
$797$	−19.4454	−0.688790	−0.344395	−	0.938825i	$-0.611916\pi$
$797$	−19.4454	−0.688790	−0.344395	+	0.938825i	$0.611916\pi$
$798$	3.87637	0.137222
$799$	−0.960944	−0.0339958
$800$	4.84353	0.171244
$801$	−6.42029	−0.226850
$802$	6.83314	0.241287
$803$	14.0378	0.495383
$804$	19.4408	0.685623
$805$	1.45778	0.0513799
$806$	2.81078	0.0990056
$807$	−11.7581	−0.413904
$808$	10.4663	0.368205
$809$	1.76408	0.0620219	0.0310109	−	0.999519i	$-0.490127\pi$
$809$	1.76408	0.0620219	0.0310109	+	0.999519i	$0.490127\pi$
$810$	−1.62897	−0.0572360
$811$	−56.1616	−1.97210	−0.986050	−	0.166449i	$-0.946770\pi$
$811$	−56.1616	−1.97210	−0.986050	+	0.166449i	$0.946770\pi$
$812$	2.85603	0.100227
$813$	28.8405	1.01148
$814$	7.50190	0.262941
$815$	2.85167	0.0998897
$816$	0.157457	0.00551211
$817$	4.80949	0.168263
$818$	7.93478	0.277433
$819$	1.19769	0.0418506
$820$	−0.0578337	−0.00201964
$821$	−34.1250	−1.19097	−0.595485	−	0.803367i	$-0.703040\pi$
$821$	−34.1250	−1.19097	−0.595485	+	0.803367i	$0.703040\pi$
$822$	−19.8935	−0.693864
$823$	−34.4517	−1.20091	−0.600455	−	0.799658i	$-0.705014\pi$
$823$	−34.4517	−1.20091	−0.600455	+	0.799658i	$0.705014\pi$
$824$	1.03084	0.0359109
$825$	6.99978	0.243701
$826$	10.3272	0.359330
$827$	39.0942	1.35944	0.679719	−	0.733472i	$-0.262102\pi$
$827$	39.0942	1.35944	0.679719	+	0.733472i	$0.262102\pi$
$828$	2.86522	0.0995732
$829$	22.4732	0.780527	0.390264	−	0.920703i	$-0.372384\pi$
$829$	22.4732	0.780527	0.390264	+	0.920703i	$0.372384\pi$
$830$	6.35502	0.220586
$831$	25.9579	0.900470
$832$	−0.679571	−0.0235599
$833$	0.551006	0.0190912
$834$	15.3130	0.530247
$835$	7.73834	0.267796
$836$	2.03386	0.0703426
$837$	23.3317	0.806460
$838$	−7.86943	−0.271845
$839$	25.2778	0.872687	0.436344	−	0.899780i	$-0.356273\pi$
$839$	25.2778	0.872687	0.436344	+	0.899780i	$0.356273\pi$
$840$	−0.805545	−0.0277939
$841$	−25.4016	−0.875918
$842$	13.5945	0.468499
$843$	23.6389	0.814167
$844$	−25.6146	−0.881691
$845$	4.95971	0.170619
$846$	9.66253	0.332205
$847$	−14.8428	−0.510004
$848$	−1.27802	−0.0438873
$849$	29.6641	1.01807
$850$	−0.563855	−0.0193401
$851$	17.1856	0.589116
$852$	−3.72988	−0.127783
$853$	−37.5715	−1.28642	−0.643211	−	0.765689i	$-0.722398\pi$
$853$	−37.5715	−1.28642	−0.643211	+	0.765689i	$0.722398\pi$
$854$	−0.683631	−0.0233934
$855$	0.881407	0.0301435
$856$	−7.10794	−0.242944
$857$	6.14373	0.209866	0.104933	−	0.994479i	$-0.466537\pi$
$857$	6.14373	0.209866	0.104933	+	0.994479i	$0.466537\pi$
$858$	−0.982104	−0.0335285
$859$	36.7675	1.25449	0.627245	−	0.778822i	$-0.284182\pi$
$859$	36.7675	1.25449	0.627245	+	0.778822i	$0.284182\pi$
$860$	−0.999457	−0.0340812
$861$	−0.297733	−0.0101467
$862$	24.4001	0.831072
$863$	31.9230	1.08667	0.543336	−	0.839515i	$-0.317161\pi$
$863$	31.9230	1.08667	0.543336	+	0.839515i	$0.317161\pi$
$864$	−5.64096	−0.191909
$865$	2.67490	0.0909494
$866$	10.6097	0.360531
$867$	22.9752	0.780280
$868$	6.22734	0.211370
$869$	−12.8621	−0.436316
$870$	−1.01492	−0.0344090
$871$	9.76767	0.330965
$872$	12.3658	0.418760
$873$	4.74690	0.160658
$874$	4.65925	0.157601
$875$	5.86250	0.198189
$876$	−17.7702	−0.600398
$877$	5.22580	0.176463	0.0882314	−	0.996100i	$-0.471879\pi$
$877$	5.22580	0.176463	0.0882314	+	0.996100i	$0.471879\pi$
$878$	14.1920	0.478958
$879$	21.7872	0.734862
$880$	−0.422655	−0.0142477
$881$	4.10257	0.138219	0.0691095	−	0.997609i	$-0.477984\pi$
$881$	4.10257	0.138219	0.0691095	+	0.997609i	$0.477984\pi$
$882$	−5.54051	−0.186559
$883$	38.7112	1.30274	0.651368	−	0.758762i	$-0.274195\pi$
$883$	38.7112	1.30274	0.651368	+	0.758762i	$0.274195\pi$
$884$	0.0791117	0.00266081
$885$	−3.66988	−0.123362
$886$	−21.1493	−0.710525
$887$	15.7015	0.527206	0.263603	−	0.964631i	$-0.415089\pi$
$887$	15.7015	0.527206	0.263603	+	0.964631i	$0.415089\pi$
$888$	−9.49650	−0.318682
$889$	6.68789	0.224305
$890$	2.16959	0.0727248
$891$	−4.40003	−0.147407
$892$	−4.86757	−0.162978
$893$	15.7126	0.525804
$894$	11.5888	0.387587
$895$	−3.05233	−0.102028
$896$	−1.50560	−0.0502987
$897$	−2.24984	−0.0751200
$898$	−41.3879	−1.38113
$899$	7.84594	0.261677
$900$	5.66970	0.188990
$901$	0.148779	0.00495656
$902$	−0.156216	−0.00520141
$903$	−5.14530	−0.171225
$904$	−15.8673	−0.527737
$905$	−0.945653	−0.0314346
$906$	−6.15046	−0.204335
$907$	31.3791	1.04192	0.520962	−	0.853580i	$-0.325573\pi$
$907$	31.3791	1.04192	0.520962	+	0.853580i	$0.325573\pi$
$908$	−2.73845	−0.0908785
$909$	12.2516	0.406361
$910$	−0.404732	−0.0134167
$911$	−25.7575	−0.853384	−0.426692	−	0.904397i	$-0.640321\pi$
$911$	−25.7575	−0.853384	−0.426692	+	0.904397i	$0.640321\pi$
$912$	−2.57463	−0.0852544
$913$	17.1656	0.568100
$914$	−23.4724	−0.776399
$915$	0.242935	0.00803119
$916$	25.6694	0.848141
$917$	−5.18286	−0.171153
$918$	0.656688	0.0216739
$919$	−8.38694	−0.276660	−0.138330	−	0.990386i	$-0.544173\pi$
$919$	−8.38694	−0.276660	−0.138330	+	0.990386i	$0.544173\pi$
$920$	−0.968235	−0.0319218
$921$	27.9328	0.920416
$922$	29.0799	0.957695
$923$	−1.87401	−0.0616838
$924$	−2.17587	−0.0715809
$925$	34.0070	1.11814
$926$	7.15965	0.235281
$927$	1.20667	0.0396322
$928$	−1.89694	−0.0622700
$929$	−59.7705	−1.96100	−0.980502	−	0.196507i	$-0.937040\pi$
$929$	−59.7705	−1.96100	−0.980502	+	0.196507i	$0.937040\pi$
$930$	−2.21295	−0.0725654
$931$	−9.00964	−0.295279
$932$	−5.38061	−0.176248
$933$	0.502177	0.0164405
$934$	41.8797	1.37035
$935$	0.0492030	0.00160911
$936$	−0.795488	−0.0260013
$937$	42.1175	1.37592	0.687959	−	0.725750i	$-0.258507\pi$
$937$	42.1175	1.37592	0.687959	+	0.725750i	$0.258507\pi$
$938$	21.6405	0.706586
$939$	−41.4954	−1.35415
$940$	−3.26523	−0.106500
$941$	−7.01159	−0.228571	−0.114286	−	0.993448i	$-0.536458\pi$
$941$	−7.01159	−0.228571	−0.114286	+	0.993448i	$0.536458\pi$
$942$	10.0666	0.327987
$943$	−0.357864	−0.0116537
$944$	−6.85919	−0.223248
$945$	−3.35958	−0.109287
$946$	−2.69965	−0.0877732
$947$	3.86051	0.125450	0.0627248	−	0.998031i	$-0.480021\pi$
$947$	3.86051	0.125450	0.0627248	+	0.998031i	$0.480021\pi$
$948$	16.2819	0.528810
$949$	−8.92830	−0.289825
$950$	9.21973	0.299128
$951$	−31.0981	−1.00842
$952$	0.175273	0.00568065
$953$	45.8306	1.48460	0.742300	−	0.670068i	$-0.233735\pi$
$953$	45.8306	1.48460	0.742300	+	0.670068i	$0.233735\pi$
$954$	−1.49601	−0.0484352
$955$	3.90853	0.126477
$956$	−17.5326	−0.567045
$957$	−2.74142	−0.0886174
$958$	0.693668	0.0224114
$959$	−22.1444	−0.715079
$960$	0.535031	0.0172681
$961$	−13.8926	−0.448148
$962$	−4.77135	−0.153834
$963$	−8.32036	−0.268120
$964$	4.85052	0.156225
$965$	2.08323	0.0670615
$966$	−4.98457	−0.160376
$967$	−19.0114	−0.611364	−0.305682	−	0.952134i	$-0.598884\pi$
$967$	−19.0114	−0.611364	−0.305682	+	0.952134i	$0.598884\pi$
$968$	9.85836	0.316860
$969$	0.299723	0.00962848
$970$	−1.60411	−0.0515048
$971$	−6.75621	−0.216817	−0.108409	−	0.994106i	$-0.534575\pi$
$971$	−6.75621	−0.216817	−0.108409	+	0.994106i	$0.534575\pi$
$972$	−11.3530	−0.364147
$973$	17.0457	0.546460
$974$	35.0836	1.12415
$975$	−4.45199	−0.142578
$976$	0.454058	0.0145340
$977$	2.26162	0.0723556	0.0361778	−	0.999345i	$-0.488482\pi$
$977$	2.26162	0.0723556	0.0361778	+	0.999345i	$0.488482\pi$
$978$	−9.75069	−0.311793
$979$	5.86031	0.187296
$980$	1.87229	0.0598080
$981$	14.4751	0.462154
$982$	13.8160	0.440885
$983$	49.6088	1.58227	0.791137	−	0.611638i	$-0.209489\pi$
$983$	49.6088	1.58227	0.791137	+	0.611638i	$0.209489\pi$
$984$	0.197750	0.00630405
$985$	−6.03204	−0.192197
$986$	0.220830	0.00703266
$987$	−16.8097	−0.535060
$988$	−1.29358	−0.0411541
$989$	−6.18446	−0.196654
$990$	−0.494749	−0.0157241
$991$	13.0455	0.414405	0.207203	−	0.978298i	$-0.433564\pi$
$991$	13.0455	0.414405	0.207203	+	0.978298i	$0.433564\pi$
$992$	−4.13611	−0.131322
$993$	13.9633	0.443112
$994$	−4.15191	−0.131690
$995$	−2.76085	−0.0875247
$996$	−21.7297	−0.688531
$997$	37.8423	1.19848	0.599239	−	0.800570i	$-0.295470\pi$
$997$	37.8423	1.19848	0.599239	+	0.800570i	$0.295470\pi$
$998$	−20.6857	−0.654796
$999$	−39.6059	−1.25307

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.b.1.13	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.b.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.35256 q^{3} +1.00000 q^{4} -0.395568 q^{5} +1.35256 q^{6} +1.50560 q^{7} -1.00000 q^{8} -1.17057 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.35256 q^{3} +1.00000 q^{4} -0.395568 q^{5} +1.35256 q^{6} +1.50560 q^{7} -1.00000 q^{8} -1.17057 q^{9} +0.395568 q^{10} +1.06848 q^{11} -1.35256 q^{12} -0.679571 q^{13} -1.50560 q^{14} +0.535031 q^{15} +1.00000 q^{16} -0.116414 q^{17} +1.17057 q^{18} +1.90352 q^{19} -0.395568 q^{20} -2.03642 q^{21} -1.06848 q^{22} -2.44771 q^{23} +1.35256 q^{24} -4.84353 q^{25} +0.679571 q^{26} +5.64096 q^{27} +1.50560 q^{28} +1.89694 q^{29} -0.535031 q^{30} +4.13611 q^{31} -1.00000 q^{32} -1.44518 q^{33} +0.116414 q^{34} -0.595569 q^{35} -1.17057 q^{36} -7.02112 q^{37} -1.90352 q^{38} +0.919163 q^{39} +0.395568 q^{40} +0.146204 q^{41} +2.03642 q^{42} +2.52664 q^{43} +1.06848 q^{44} +0.463041 q^{45} +2.44771 q^{46} +8.25454 q^{47} -1.35256 q^{48} -4.73316 q^{49} +4.84353 q^{50} +0.157457 q^{51} -0.679571 q^{52} -1.27802 q^{53} -5.64096 q^{54} -0.422655 q^{55} -1.50560 q^{56} -2.57463 q^{57} -1.89694 q^{58} -6.85919 q^{59} +0.535031 q^{60} +0.454058 q^{61} -4.13611 q^{62} -1.76242 q^{63} +1.00000 q^{64} +0.268817 q^{65} +1.44518 q^{66} -14.3733 q^{67} -0.116414 q^{68} +3.31068 q^{69} +0.595569 q^{70} +2.75764 q^{71} +1.17057 q^{72} +13.1381 q^{73} +7.02112 q^{74} +6.55117 q^{75} +1.90352 q^{76} +1.60870 q^{77} -0.919163 q^{78} -12.0378 q^{79} -0.395568 q^{80} -4.11804 q^{81} -0.146204 q^{82} +16.0655 q^{83} -2.03642 q^{84} +0.0460497 q^{85} -2.52664 q^{86} -2.56573 q^{87} -1.06848 q^{88} +5.48474 q^{89} -0.463041 q^{90} -1.02317 q^{91} -2.44771 q^{92} -5.59435 q^{93} -8.25454 q^{94} -0.752971 q^{95} +1.35256 q^{96} -4.05519 q^{97} +4.73316 q^{98} -1.25073 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 35 q^{2} - 6 q^{3} + 35 q^{4} + 6 q^{5} + 6 q^{6} - 14 q^{7} - 35 q^{8} + 23 q^{9}+O(q^{10}) \) 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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