LMFDB - Embedded newform 4029.2.a.g.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.99316 q^{2} -1.00000 q^{3} +1.97270 q^{4} -1.27823 q^{5} +1.99316 q^{6} +0.558075 q^{7} +0.0544076 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.99316 q^{2} -1.00000 q^{3} +1.97270 q^{4} -1.27823 q^{5} +1.99316 q^{6} +0.558075 q^{7} +0.0544076 q^{8} +1.00000 q^{9} +2.54772 q^{10} +3.37317 q^{11} -1.97270 q^{12} +2.95203 q^{13} -1.11233 q^{14} +1.27823 q^{15} -4.05385 q^{16} -1.00000 q^{17} -1.99316 q^{18} -5.11899 q^{19} -2.52157 q^{20} -0.558075 q^{21} -6.72328 q^{22} +4.39164 q^{23} -0.0544076 q^{24} -3.36612 q^{25} -5.88388 q^{26} -1.00000 q^{27} +1.10092 q^{28} -0.447542 q^{29} -2.54772 q^{30} +10.1334 q^{31} +7.97117 q^{32} -3.37317 q^{33} +1.99316 q^{34} -0.713349 q^{35} +1.97270 q^{36} -9.43079 q^{37} +10.2030 q^{38} -2.95203 q^{39} -0.0695455 q^{40} -8.62551 q^{41} +1.11233 q^{42} -1.04078 q^{43} +6.65426 q^{44} -1.27823 q^{45} -8.75325 q^{46} +0.300155 q^{47} +4.05385 q^{48} -6.68855 q^{49} +6.70924 q^{50} +1.00000 q^{51} +5.82348 q^{52} -10.9672 q^{53} +1.99316 q^{54} -4.31169 q^{55} +0.0303635 q^{56} +5.11899 q^{57} +0.892024 q^{58} +9.17482 q^{59} +2.52157 q^{60} -11.2557 q^{61} -20.1975 q^{62} +0.558075 q^{63} -7.78015 q^{64} -3.77338 q^{65} +6.72328 q^{66} +10.3395 q^{67} -1.97270 q^{68} -4.39164 q^{69} +1.42182 q^{70} +4.59760 q^{71} +0.0544076 q^{72} -1.53582 q^{73} +18.7971 q^{74} +3.36612 q^{75} -10.0982 q^{76} +1.88248 q^{77} +5.88388 q^{78} -1.00000 q^{79} +5.18176 q^{80} +1.00000 q^{81} +17.1921 q^{82} -8.23044 q^{83} -1.10092 q^{84} +1.27823 q^{85} +2.07444 q^{86} +0.447542 q^{87} +0.183526 q^{88} +13.0388 q^{89} +2.54772 q^{90} +1.64745 q^{91} +8.66339 q^{92} -10.1334 q^{93} -0.598259 q^{94} +6.54325 q^{95} -7.97117 q^{96} -4.43052 q^{97} +13.3314 q^{98} +3.37317 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9}+O(q^{10}) $ 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9} - 5 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 7 q^{14} - 5 q^{15} - 22 q^{17} + 2 q^{18} - 36 q^{19} + 4 q^{21} - 9 q^{22} + 21 q^{23} - 6 q^{24} + 9 q^{25} - 16 q^{26} - 22 q^{27} - 17 q^{28} - q^{29} + 5 q^{30} - 12 q^{31} - 11 q^{32} + 2 q^{33} - 2 q^{34} - 14 q^{35} + 16 q^{36} - 6 q^{37} + q^{38} + 11 q^{39} - 24 q^{40} - 17 q^{41} + 7 q^{42} - 36 q^{43} + 16 q^{44} + 5 q^{45} - 23 q^{46} - 17 q^{47} - 6 q^{49} - 33 q^{50} + 22 q^{51} - 57 q^{52} - 2 q^{53} - 2 q^{54} - 24 q^{55} - 64 q^{56} + 36 q^{57} - 7 q^{58} - 59 q^{59} - 30 q^{61} - 4 q^{62} - 4 q^{63} - 22 q^{64} + 36 q^{65} + 9 q^{66} - 16 q^{67} - 16 q^{68} - 21 q^{69} - 39 q^{70} - 11 q^{71} + 6 q^{72} - 19 q^{73} - 28 q^{74} - 9 q^{75} - 77 q^{76} + 2 q^{77} + 16 q^{78} - 22 q^{79} - 2 q^{80} + 22 q^{81} + 33 q^{82} - 23 q^{83} + 17 q^{84} - 5 q^{85} + 6 q^{86} + q^{87} - 23 q^{88} + 12 q^{89} - 5 q^{90} - 24 q^{91} + 66 q^{92} + 12 q^{93} - 61 q^{94} - 11 q^{95} + 11 q^{96} - 9 q^{97} + 17 q^{98} - 2 q^{99}+O(q^{100}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9 - 5 * q^10 - 2 * q^11 - 16 * q^12 - 11 * q^13 - 7 * q^14 - 5 * q^15 - 22 * q^17 + 2 * q^18 - 36 * q^19 + 4 * q^21 - 9 * q^22 + 21 * q^23 - 6 * q^24 + 9 * q^25 - 16 * q^26 - 22 * q^27 - 17 * q^28 - q^29 + 5 * q^30 - 12 * q^31 - 11 * q^32 + 2 * q^33 - 2 * q^34 - 14 * q^35 + 16 * q^36 - 6 * q^37 + q^38 + 11 * q^39 - 24 * q^40 - 17 * q^41 + 7 * q^42 - 36 * q^43 + 16 * q^44 + 5 * q^45 - 23 * q^46 - 17 * q^47 - 6 * q^49 - 33 * q^50 + 22 * q^51 - 57 * q^52 - 2 * q^53 - 2 * q^54 - 24 * q^55 - 64 * q^56 + 36 * q^57 - 7 * q^58 - 59 * q^59 - 30 * q^61 - 4 * q^62 - 4 * q^63 - 22 * q^64 + 36 * q^65 + 9 * q^66 - 16 * q^67 - 16 * q^68 - 21 * q^69 - 39 * q^70 - 11 * q^71 + 6 * q^72 - 19 * q^73 - 28 * q^74 - 9 * q^75 - 77 * q^76 + 2 * q^77 + 16 * q^78 - 22 * q^79 - 2 * q^80 + 22 * q^81 + 33 * q^82 - 23 * q^83 + 17 * q^84 - 5 * q^85 + 6 * q^86 + q^87 - 23 * q^88 + 12 * q^89 - 5 * q^90 - 24 * q^91 + 66 * q^92 + 12 * q^93 - 61 * q^94 - 11 * q^95 + 11 * q^96 - 9 * q^97 + 17 * q^98 - 2 * 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 $

$2$	−1.99316	−1.40938	−0.704690	−	0.709515i	$-0.748914\pi$
$2$	−1.99316	−1.40938	−0.704690	+	0.709515i	$0.748914\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.97270	0.986351
$5$	−1.27823	−0.571642	−0.285821	−	0.958283i	$-0.592266\pi$
$5$	−1.27823	−0.571642	−0.285821	+	0.958283i	$0.592266\pi$
$6$	1.99316	0.813706
$7$	0.558075	0.210932	0.105466	−	0.994423i	$-0.466367\pi$
$7$	0.558075	0.210932	0.105466	+	0.994423i	$0.466367\pi$
$8$	0.0544076	0.0192360
$9$	1.00000	0.333333
$10$	2.54772	0.805661
$11$	3.37317	1.01705	0.508524	−	0.861048i	$-0.330191\pi$
$11$	3.37317	1.01705	0.508524	+	0.861048i	$0.330191\pi$
$12$	−1.97270	−0.569470
$13$	2.95203	0.818746	0.409373	−	0.912367i	$-0.365747\pi$
$13$	2.95203	0.818746	0.409373	+	0.912367i	$0.365747\pi$
$14$	−1.11233	−0.297284
$15$	1.27823	0.330038
$16$	−4.05385	−1.01346
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.99316	−0.469793
$19$	−5.11899	−1.17438	−0.587188	−	0.809451i	$-0.699765\pi$
$19$	−5.11899	−1.17438	−0.587188	+	0.809451i	$0.699765\pi$
$20$	−2.52157	−0.563840
$21$	−0.558075	−0.121782
$22$	−6.72328	−1.43341
$23$	4.39164	0.915719	0.457860	−	0.889024i	$-0.348616\pi$
$23$	4.39164	0.915719	0.457860	+	0.889024i	$0.348616\pi$
$24$	−0.0544076	−0.0111059
$25$	−3.36612	−0.673225
$26$	−5.88388	−1.15392
$27$	−1.00000	−0.192450
$28$	1.10092	0.208053
$29$	−0.447542	−0.0831064	−0.0415532	−	0.999136i	$-0.513231\pi$
$29$	−0.447542	−0.0831064	−0.0415532	+	0.999136i	$0.513231\pi$
$30$	−2.54772	−0.465149
$31$	10.1334	1.82001	0.910003	−	0.414601i	$-0.136079\pi$
$31$	10.1334	1.82001	0.910003	+	0.414601i	$0.136079\pi$
$32$	7.97117	1.40912
$33$	−3.37317	−0.587193
$34$	1.99316	0.341825
$35$	−0.713349	−0.120578
$36$	1.97270	0.328784
$37$	−9.43079	−1.55041	−0.775206	−	0.631708i	$-0.782354\pi$
$37$	−9.43079	−1.55041	−0.775206	+	0.631708i	$0.782354\pi$
$38$	10.2030	1.65514
$39$	−2.95203	−0.472703
$40$	−0.0695455	−0.0109961
$41$	−8.62551	−1.34708	−0.673539	−	0.739152i	$-0.735227\pi$
$41$	−8.62551	−1.34708	−0.673539	+	0.739152i	$0.735227\pi$
$42$	1.11233	0.171637
$43$	−1.04078	−0.158717	−0.0793586	−	0.996846i	$-0.525287\pi$
$43$	−1.04078	−0.158717	−0.0793586	+	0.996846i	$0.525287\pi$
$44$	6.65426	1.00317
$45$	−1.27823	−0.190547
$46$	−8.75325	−1.29060
$47$	0.300155	0.0437822	0.0218911	−	0.999760i	$-0.493031\pi$
$47$	0.300155	0.0437822	0.0218911	+	0.999760i	$0.493031\pi$
$48$	4.05385	0.585123
$49$	−6.68855	−0.955508
$50$	6.70924	0.948830
$51$	1.00000	0.140028
$52$	5.82348	0.807572
$53$	−10.9672	−1.50645	−0.753227	−	0.657760i	$-0.771504\pi$
$53$	−10.9672	−1.50645	−0.753227	+	0.657760i	$0.771504\pi$
$54$	1.99316	0.271235
$55$	−4.31169	−0.581388
$56$	0.0303635	0.00405749
$57$	5.11899	0.678026
$58$	0.892024	0.117128
$59$	9.17482	1.19446	0.597230	−	0.802070i	$-0.296268\pi$
$59$	9.17482	1.19446	0.597230	+	0.802070i	$0.296268\pi$
$60$	2.52157	0.325533
$61$	−11.2557	−1.44114	−0.720570	−	0.693383i	$-0.756120\pi$
$61$	−11.2557	−1.44114	−0.720570	+	0.693383i	$0.756120\pi$
$62$	−20.1975	−2.56508
$63$	0.558075	0.0703108
$64$	−7.78015	−0.972519
$65$	−3.77338	−0.468030
$66$	6.72328	0.827578
$67$	10.3395	1.26317	0.631587	−	0.775305i	$-0.282404\pi$
$67$	10.3395	1.26317	0.631587	+	0.775305i	$0.282404\pi$
$68$	−1.97270	−0.239225
$69$	−4.39164	−0.528691
$70$	1.42182	0.169940
$71$	4.59760	0.545635	0.272817	−	0.962066i	$-0.412045\pi$
$71$	4.59760	0.545635	0.272817	+	0.962066i	$0.412045\pi$
$72$	0.0544076	0.00641199
$73$	−1.53582	−0.179754	−0.0898770	−	0.995953i	$-0.528647\pi$
$73$	−1.53582	−0.179754	−0.0898770	+	0.995953i	$0.528647\pi$
$74$	18.7971	2.18512
$75$	3.36612	0.388687
$76$	−10.0982	−1.15835
$77$	1.88248	0.214528
$78$	5.88388	0.666219
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	5.18176	0.579338
$81$	1.00000	0.111111
$82$	17.1921	1.89854
$83$	−8.23044	−0.903409	−0.451704	−	0.892168i	$-0.649184\pi$
$83$	−8.23044	−0.903409	−0.451704	+	0.892168i	$0.649184\pi$
$84$	−1.10092	−0.120120
$85$	1.27823	0.138644
$86$	2.07444	0.223693
$87$	0.447542	0.0479815
$88$	0.183526	0.0195639
$89$	13.0388	1.38211	0.691055	−	0.722802i	$-0.257146\pi$
$89$	13.0388	1.38211	0.691055	+	0.722802i	$0.257146\pi$
$90$	2.54772	0.268554
$91$	1.64745	0.172700
$92$	8.66339	0.903221
$93$	−10.1334	−1.05078
$94$	−0.598259	−0.0617057
$95$	6.54325	0.671323
$96$	−7.97117	−0.813554
$97$	−4.43052	−0.449851	−0.224926	−	0.974376i	$-0.572214\pi$
$97$	−4.43052	−0.449851	−0.224926	+	0.974376i	$0.572214\pi$
$98$	13.3314	1.34667
$99$	3.37317	0.339016
$100$	−6.64036	−0.664036
$101$	19.8635	1.97649	0.988244	−	0.152886i	$-0.0488566\pi$
$101$	19.8635	1.97649	0.988244	+	0.152886i	$0.0488566\pi$
$102$	−1.99316	−0.197353
$103$	−6.43144	−0.633709	−0.316854	−	0.948474i	$-0.602627\pi$
$103$	−6.43144	−0.633709	−0.316854	+	0.948474i	$0.602627\pi$
$104$	0.160613	0.0157494
$105$	0.713349	0.0696157
$106$	21.8593	2.12317
$107$	8.82922	0.853553	0.426777	−	0.904357i	$-0.359649\pi$
$107$	8.82922	0.853553	0.426777	+	0.904357i	$0.359649\pi$
$108$	−1.97270	−0.189823
$109$	−16.0253	−1.53494	−0.767470	−	0.641084i	$-0.778485\pi$
$109$	−16.0253	−1.53494	−0.767470	+	0.641084i	$0.778485\pi$
$110$	8.59390	0.819396
$111$	9.43079	0.895131
$112$	−2.26235	−0.213772
$113$	10.3479	0.973453	0.486726	−	0.873554i	$-0.338191\pi$
$113$	10.3479	0.973453	0.486726	+	0.873554i	$0.338191\pi$
$114$	−10.2030	−0.955597
$115$	−5.61353	−0.523464
$116$	−0.882867	−0.0819721
$117$	2.95203	0.272915
$118$	−18.2869	−1.68345
$119$	−0.558075	−0.0511586
$120$	0.0695455	0.00634860
$121$	0.378257	0.0343870
$122$	22.4344	2.03111
$123$	8.62551	0.777736
$124$	19.9901	1.79517
$125$	10.6938	0.956486
$126$	−1.11233	−0.0990946
$127$	−1.90483	−0.169027	−0.0845133	−	0.996422i	$-0.526934\pi$
$127$	−1.90483	−0.169027	−0.0845133	+	0.996422i	$0.526934\pi$
$128$	−0.435220	−0.0384684
$129$	1.04078	0.0916355
$130$	7.52096	0.659632
$131$	4.06698	0.355334	0.177667	−	0.984091i	$-0.443145\pi$
$131$	4.06698	0.355334	0.177667	+	0.984091i	$0.443145\pi$
$132$	−6.65426	−0.579179
$133$	−2.85678	−0.247714
$134$	−20.6084	−1.78029
$135$	1.27823	0.110013
$136$	−0.0544076	−0.00466541
$137$	4.60220	0.393192	0.196596	−	0.980485i	$-0.437011\pi$
$137$	4.60220	0.393192	0.196596	+	0.980485i	$0.437011\pi$
$138$	8.75325	0.745126
$139$	−7.84280	−0.665218	−0.332609	−	0.943065i	$-0.607929\pi$
$139$	−7.84280	−0.665218	−0.332609	+	0.943065i	$0.607929\pi$
$140$	−1.40722	−0.118932
$141$	−0.300155	−0.0252776
$142$	−9.16377	−0.769007
$143$	9.95770	0.832704
$144$	−4.05385	−0.337821
$145$	0.572062	0.0475072
$146$	3.06114	0.253342
$147$	6.68855	0.551663
$148$	−18.6041	−1.52925
$149$	−18.8556	−1.54471	−0.772355	−	0.635192i	$-0.780921\pi$
$149$	−18.8556	−1.54471	−0.772355	+	0.635192i	$0.780921\pi$
$150$	−6.70924	−0.547807
$151$	−9.32924	−0.759203	−0.379602	−	0.925150i	$-0.623939\pi$
$151$	−9.32924	−0.759203	−0.379602	+	0.925150i	$0.623939\pi$
$152$	−0.278512	−0.0225903
$153$	−1.00000	−0.0808452
$154$	−3.75209	−0.302352
$155$	−12.9528	−1.04039
$156$	−5.82348	−0.466252
$157$	24.9351	1.99003	0.995017	−	0.0997055i	$-0.0317901\pi$
$157$	24.9351	1.99003	0.995017	+	0.0997055i	$0.0317901\pi$
$158$	1.99316	0.158568
$159$	10.9672	0.869752
$160$	−10.1890	−0.805511
$161$	2.45086	0.193155
$162$	−1.99316	−0.156598
$163$	−8.86915	−0.694685	−0.347343	−	0.937738i	$-0.612916\pi$
$163$	−8.86915	−0.694685	−0.347343	+	0.937738i	$0.612916\pi$
$164$	−17.0156	−1.32869
$165$	4.31169	0.335664
$166$	16.4046	1.27325
$167$	−14.8847	−1.15181	−0.575907	−	0.817515i	$-0.695351\pi$
$167$	−14.8847	−1.15181	−0.575907	+	0.817515i	$0.695351\pi$
$168$	−0.0303635	−0.00234259
$169$	−4.28551	−0.329655
$170$	−2.54772	−0.195402
$171$	−5.11899	−0.391459
$172$	−2.05315	−0.156551
$173$	3.09388	0.235223	0.117612	−	0.993060i	$-0.462476\pi$
$173$	3.09388	0.235223	0.117612	+	0.993060i	$0.462476\pi$
$174$	−0.892024	−0.0676242
$175$	−1.87855	−0.142005
$176$	−13.6743	−1.03074
$177$	−9.17482	−0.689622
$178$	−25.9885	−1.94792
$179$	−18.2877	−1.36689	−0.683443	−	0.730004i	$-0.739518\pi$
$179$	−18.2877	−1.36689	−0.683443	+	0.730004i	$0.739518\pi$
$180$	−2.52157	−0.187947
$181$	−0.765844	−0.0569247	−0.0284624	−	0.999595i	$-0.509061\pi$
$181$	−0.765844	−0.0569247	−0.0284624	+	0.999595i	$0.509061\pi$
$182$	−3.28365	−0.243400
$183$	11.2557	0.832042
$184$	0.238938	0.0176148
$185$	12.0547	0.886282
$186$	20.1975	1.48095
$187$	−3.37317	−0.246670
$188$	0.592117	0.0431846
$189$	−0.558075	−0.0405940
$190$	−13.0418	−0.946149
$191$	24.1682	1.74875	0.874374	−	0.485253i	$-0.161273\pi$
$191$	24.1682	1.74875	0.874374	+	0.485253i	$0.161273\pi$
$192$	7.78015	0.561484
$193$	18.8668	1.35806	0.679032	−	0.734109i	$-0.262400\pi$
$193$	18.8668	1.35806	0.679032	+	0.734109i	$0.262400\pi$
$194$	8.83075	0.634011
$195$	3.77338	0.270217
$196$	−13.1945	−0.942466
$197$	−14.5162	−1.03423	−0.517117	−	0.855915i	$-0.672995\pi$
$197$	−14.5162	−1.03423	−0.517117	+	0.855915i	$0.672995\pi$
$198$	−6.72328	−0.477802
$199$	2.47928	0.175751	0.0878757	−	0.996131i	$-0.471992\pi$
$199$	2.47928	0.175751	0.0878757	+	0.996131i	$0.471992\pi$
$200$	−0.183143	−0.0129501
$201$	−10.3395	−0.729294
$202$	−39.5911	−2.78562
$203$	−0.249762	−0.0175298
$204$	1.97270	0.138117
$205$	11.0254	0.770047
$206$	12.8189	0.893137
$207$	4.39164	0.305240
$208$	−11.9671	−0.829768
$209$	−17.2672	−1.19440
$210$	−1.42182	−0.0981150
$211$	−8.31689	−0.572559	−0.286279	−	0.958146i	$-0.592419\pi$
$211$	−8.31689	−0.572559	−0.286279	+	0.958146i	$0.592419\pi$
$212$	−21.6349	−1.48589
$213$	−4.59760	−0.315022
$214$	−17.5981	−1.20298
$215$	1.33036	0.0907295
$216$	−0.0544076	−0.00370197
$217$	5.65518	0.383898
$218$	31.9410	2.16331
$219$	1.53582	0.103781
$220$	−8.50568	−0.573453
$221$	−2.95203	−0.198575
$222$	−18.7971	−1.26158
$223$	19.8244	1.32754	0.663770	−	0.747937i	$-0.268956\pi$
$223$	19.8244	1.32754	0.663770	+	0.747937i	$0.268956\pi$
$224$	4.44851	0.297228
$225$	−3.36612	−0.224408
$226$	−20.6252	−1.37196
$227$	−13.2085	−0.876678	−0.438339	−	0.898810i	$-0.644433\pi$
$227$	−13.2085	−0.876678	−0.438339	+	0.898810i	$0.644433\pi$
$228$	10.0982	0.668772
$229$	−16.0345	−1.05959	−0.529795	−	0.848126i	$-0.677731\pi$
$229$	−16.0345	−1.05959	−0.529795	+	0.848126i	$0.677731\pi$
$230$	11.1887	0.737760
$231$	−1.88248	−0.123858
$232$	−0.0243497	−0.00159863
$233$	13.2575	0.868529	0.434265	−	0.900785i	$-0.357008\pi$
$233$	13.2575	0.868529	0.434265	+	0.900785i	$0.357008\pi$
$234$	−5.88388	−0.384641
$235$	−0.383668	−0.0250277
$236$	18.0992	1.17816
$237$	1.00000	0.0649570
$238$	1.11233	0.0721019
$239$	−18.6218	−1.20454	−0.602272	−	0.798291i	$-0.705738\pi$
$239$	−18.6218	−1.20454	−0.602272	+	0.798291i	$0.705738\pi$
$240$	−5.18176	−0.334481
$241$	−1.22869	−0.0791469	−0.0395735	−	0.999217i	$-0.512600\pi$
$241$	−1.22869	−0.0791469	−0.0395735	+	0.999217i	$0.512600\pi$
$242$	−0.753929	−0.0484644
$243$	−1.00000	−0.0641500
$244$	−22.2041	−1.42147
$245$	8.54952	0.546209
$246$	−17.1921	−1.09613
$247$	−15.1114	−0.961516
$248$	0.551332	0.0350096
$249$	8.23044	0.521583
$250$	−21.3146	−1.34805
$251$	9.62142	0.607299	0.303649	−	0.952784i	$-0.401795\pi$
$251$	9.62142	0.607299	0.303649	+	0.952784i	$0.401795\pi$
$252$	1.10092	0.0693512
$253$	14.8137	0.931331
$254$	3.79664	0.238223
$255$	−1.27823	−0.0800460
$256$	16.4278	1.02674
$257$	−4.60183	−0.287054	−0.143527	−	0.989646i	$-0.545844\pi$
$257$	−4.60183	−0.287054	−0.143527	+	0.989646i	$0.545844\pi$
$258$	−2.07444	−0.129149
$259$	−5.26308	−0.327032
$260$	−7.44376	−0.461642
$261$	−0.447542	−0.0277021
$262$	−8.10617	−0.500801
$263$	−6.78162	−0.418172	−0.209086	−	0.977897i	$-0.567049\pi$
$263$	−6.78162	−0.418172	−0.209086	+	0.977897i	$0.567049\pi$
$264$	−0.183526	−0.0112952
$265$	14.0186	0.861154
$266$	5.69402	0.349123
$267$	−13.0388	−0.797961
$268$	20.3968	1.24593
$269$	0.498794	0.0304120	0.0152060	−	0.999884i	$-0.495160\pi$
$269$	0.498794	0.0304120	0.0152060	+	0.999884i	$0.495160\pi$
$270$	−2.54772	−0.155050
$271$	−5.24460	−0.318587	−0.159293	−	0.987231i	$-0.550922\pi$
$271$	−5.24460	−0.318587	−0.159293	+	0.987231i	$0.550922\pi$
$272$	4.05385	0.245801
$273$	−1.64745	−0.0997085
$274$	−9.17294	−0.554157
$275$	−11.3545	−0.684702
$276$	−8.66339	−0.521475
$277$	21.1976	1.27364	0.636820	−	0.771013i	$-0.280250\pi$
$277$	21.1976	1.27364	0.636820	+	0.771013i	$0.280250\pi$
$278$	15.6320	0.937545
$279$	10.1334	0.606669
$280$	−0.0388116	−0.00231943
$281$	27.6676	1.65051	0.825254	−	0.564762i	$-0.191032\pi$
$281$	27.6676	1.65051	0.825254	+	0.564762i	$0.191032\pi$
$282$	0.598259	0.0356258
$283$	−13.1663	−0.782654	−0.391327	−	0.920252i	$-0.627984\pi$
$283$	−13.1663	−0.782654	−0.391327	+	0.920252i	$0.627984\pi$
$284$	9.06970	0.538188
$285$	−6.54325	−0.387589
$286$	−19.8473	−1.17360
$287$	−4.81368	−0.284142
$288$	7.97117	0.469706
$289$	1.00000	0.0588235
$290$	−1.14021	−0.0669556
$291$	4.43052	0.259722
$292$	−3.02971	−0.177301
$293$	2.40092	0.140263	0.0701315	−	0.997538i	$-0.477658\pi$
$293$	2.40092	0.140263	0.0701315	+	0.997538i	$0.477658\pi$
$294$	−13.3314	−0.777502
$295$	−11.7275	−0.682804
$296$	−0.513106	−0.0298237
$297$	−3.37317	−0.195731
$298$	37.5823	2.17708
$299$	12.9642	0.749742
$300$	6.64036	0.383382
$301$	−0.580832	−0.0334786
$302$	18.5947	1.07001
$303$	−19.8635	−1.14113
$304$	20.7516	1.19019
$305$	14.3873	0.823816
$306$	1.99316	0.113942
$307$	3.40577	0.194377	0.0971887	−	0.995266i	$-0.469015\pi$
$307$	3.40577	0.194377	0.0971887	+	0.995266i	$0.469015\pi$
$308$	3.71357	0.211600
$309$	6.43144	0.365872
$310$	25.8170	1.46631
$311$	−32.8697	−1.86387	−0.931935	−	0.362625i	$-0.881881\pi$
$311$	−32.8697	−1.86387	−0.931935	+	0.362625i	$0.881881\pi$
$312$	−0.160613	−0.00909291
$313$	−21.5982	−1.22080	−0.610402	−	0.792092i	$-0.708992\pi$
$313$	−21.5982	−1.22080	−0.610402	+	0.792092i	$0.708992\pi$
$314$	−49.6997	−2.80471
$315$	−0.713349	−0.0401926
$316$	−1.97270	−0.110973
$317$	11.6279	0.653086	0.326543	−	0.945182i	$-0.394116\pi$
$317$	11.6279	0.653086	0.326543	+	0.945182i	$0.394116\pi$
$318$	−21.8593	−1.22581
$319$	−1.50963	−0.0845232
$320$	9.94484	0.555933
$321$	−8.82922	−0.492799
$322$	−4.88497	−0.272229
$323$	5.11899	0.284828
$324$	1.97270	0.109595
$325$	−9.93691	−0.551200
$326$	17.6777	0.979075
$327$	16.0253	0.886199
$328$	−0.469293	−0.0259124
$329$	0.167509	0.00923507
$330$	−8.59390	−0.473079
$331$	−0.280446	−0.0154147	−0.00770736	−	0.999970i	$-0.502453\pi$
$331$	−0.280446	−0.0154147	−0.00770736	+	0.999970i	$0.502453\pi$
$332$	−16.2362	−0.891078
$333$	−9.43079	−0.516804
$334$	29.6677	1.62334
$335$	−13.2163	−0.722084
$336$	2.26235	0.123421
$337$	−11.2601	−0.613374	−0.306687	−	0.951810i	$-0.599221\pi$
$337$	−11.2601	−0.613374	−0.306687	+	0.951810i	$0.599221\pi$
$338$	8.54172	0.464608
$339$	−10.3479	−0.562023
$340$	2.52157	0.136751
$341$	34.1815	1.85103
$342$	10.2030	0.551714
$343$	−7.63923	−0.412480
$344$	−0.0566262	−0.00305308
$345$	5.61353	0.302222
$346$	−6.16661	−0.331519
$347$	−18.4030	−0.987926	−0.493963	−	0.869483i	$-0.664452\pi$
$347$	−18.4030	−0.987926	−0.493963	+	0.869483i	$0.664452\pi$
$348$	0.882867	0.0473266
$349$	−26.5979	−1.42375	−0.711876	−	0.702305i	$-0.752154\pi$
$349$	−26.5979	−1.42375	−0.711876	+	0.702305i	$0.752154\pi$
$350$	3.74426	0.200139
$351$	−2.95203	−0.157568
$352$	26.8881	1.43314
$353$	−28.0801	−1.49455	−0.747276	−	0.664514i	$-0.768639\pi$
$353$	−28.0801	−1.49455	−0.747276	+	0.664514i	$0.768639\pi$
$354$	18.2869	0.971939
$355$	−5.87680	−0.311908
$356$	25.7217	1.36325
$357$	0.558075	0.0295364
$358$	36.4503	1.92646
$359$	−9.97537	−0.526480	−0.263240	−	0.964730i	$-0.584791\pi$
$359$	−9.97537	−0.526480	−0.263240	+	0.964730i	$0.584791\pi$
$360$	−0.0695455	−0.00366537
$361$	7.20402	0.379159
$362$	1.52645	0.0802286
$363$	−0.378257	−0.0198534
$364$	3.24994	0.170343
$365$	1.96313	0.102755
$366$	−22.4344	−1.17266
$367$	−18.4903	−0.965184	−0.482592	−	0.875845i	$-0.660305\pi$
$367$	−18.4903	−0.965184	−0.482592	+	0.875845i	$0.660305\pi$
$368$	−17.8030	−0.928047
$369$	−8.62551	−0.449026
$370$	−24.0271	−1.24911
$371$	−6.12049	−0.317760
$372$	−19.9901	−1.03644
$373$	−1.21968	−0.0631528	−0.0315764	−	0.999501i	$-0.510053\pi$
$373$	−1.21968	−0.0631528	−0.0315764	+	0.999501i	$0.510053\pi$
$374$	6.72328	0.347652
$375$	−10.6938	−0.552228
$376$	0.0163307	0.000842193 0
$377$	−1.32116	−0.0680431
$378$	1.11233	0.0572123
$379$	−16.1943	−0.831846	−0.415923	−	0.909400i	$-0.636541\pi$
$379$	−16.1943	−0.831846	−0.415923	+	0.909400i	$0.636541\pi$
$380$	12.9079	0.662161
$381$	1.90483	0.0975875
$382$	−48.1711	−2.46465
$383$	−20.5434	−1.04972	−0.524859	−	0.851189i	$-0.675882\pi$
$383$	−20.5434	−1.04972	−0.524859	+	0.851189i	$0.675882\pi$
$384$	0.435220	0.0222097
$385$	−2.40624	−0.122634
$386$	−37.6047	−1.91403
$387$	−1.04078	−0.0529058
$388$	−8.74010	−0.443711
$389$	3.86275	0.195849	0.0979246	−	0.995194i	$-0.468780\pi$
$389$	3.86275	0.195849	0.0979246	+	0.995194i	$0.468780\pi$
$390$	−7.52096	−0.380839
$391$	−4.39164	−0.222095
$392$	−0.363908	−0.0183801
$393$	−4.06698	−0.205152
$394$	28.9331	1.45763
$395$	1.27823	0.0643148
$396$	6.65426	0.334389
$397$	−12.9618	−0.650534	−0.325267	−	0.945622i	$-0.605454\pi$
$397$	−12.9618	−0.650534	−0.325267	+	0.945622i	$0.605454\pi$
$398$	−4.94161	−0.247700
$399$	2.85678	0.143018
$400$	13.6458	0.682288
$401$	−5.64036	−0.281666	−0.140833	−	0.990033i	$-0.544978\pi$
$401$	−5.64036	−0.281666	−0.140833	+	0.990033i	$0.544978\pi$
$402$	20.6084	1.02785
$403$	29.9140	1.49012
$404$	39.1847	1.94951
$405$	−1.27823	−0.0635158
$406$	0.497816	0.0247062
$407$	−31.8116	−1.57684
$408$	0.0544076	0.00269358
$409$	−37.7460	−1.86642	−0.933211	−	0.359330i	$-0.883005\pi$
$409$	−37.7460	−1.86642	−0.933211	+	0.359330i	$0.883005\pi$
$410$	−21.9754	−1.08529
$411$	−4.60220	−0.227010
$412$	−12.6873	−0.625060
$413$	5.12024	0.251950
$414$	−8.75325	−0.430199
$415$	10.5204	0.516427
$416$	23.5311	1.15371
$417$	7.84280	0.384064
$418$	34.4164	1.68336
$419$	−25.7758	−1.25923	−0.629614	−	0.776908i	$-0.716787\pi$
$419$	−25.7758	−1.25923	−0.629614	+	0.776908i	$0.716787\pi$
$420$	1.40722	0.0686655
$421$	−24.1885	−1.17888	−0.589438	−	0.807814i	$-0.700651\pi$
$421$	−24.1885	−1.17888	−0.589438	+	0.807814i	$0.700651\pi$
$422$	16.5769	0.806953
$423$	0.300155	0.0145941
$424$	−0.596696	−0.0289781
$425$	3.36612	0.163281
$426$	9.16377	0.443986
$427$	−6.28150	−0.303983
$428$	17.4174	0.841903
$429$	−9.95770	−0.480762
$430$	−2.65162	−0.127872
$431$	−2.73554	−0.131766	−0.0658832	−	0.997827i	$-0.520986\pi$
$431$	−2.73554	−0.131766	−0.0658832	+	0.997827i	$0.520986\pi$
$432$	4.05385	0.195041
$433$	36.4097	1.74974	0.874869	−	0.484359i	$-0.160947\pi$
$433$	36.4097	1.74974	0.874869	+	0.484359i	$0.160947\pi$
$434$	−11.2717	−0.541059
$435$	−0.572062	−0.0274283
$436$	−31.6131	−1.51399
$437$	−22.4807	−1.07540
$438$	−3.06114	−0.146267
$439$	−28.2501	−1.34830	−0.674152	−	0.738593i	$-0.735491\pi$
$439$	−28.2501	−1.34830	−0.674152	+	0.738593i	$0.735491\pi$
$440$	−0.234588	−0.0111836
$441$	−6.68855	−0.318503
$442$	5.88388	0.279868
$443$	6.91331	0.328461	0.164231	−	0.986422i	$-0.447486\pi$
$443$	6.91331	0.328461	0.164231	+	0.986422i	$0.447486\pi$
$444$	18.6041	0.882914
$445$	−16.6666	−0.790073
$446$	−39.5133	−1.87101
$447$	18.8556	0.891838
$448$	−4.34191	−0.205136
$449$	−40.7678	−1.92395	−0.961977	−	0.273132i	$-0.911941\pi$
$449$	−40.7678	−1.92395	−0.961977	+	0.273132i	$0.911941\pi$
$450$	6.70924	0.316277
$451$	−29.0953	−1.37004
$452$	20.4134	0.960167
$453$	9.32924	0.438326
$454$	26.3267	1.23557
$455$	−2.10583	−0.0987227
$456$	0.278512	0.0130425
$457$	21.4665	1.00416	0.502079	−	0.864822i	$-0.332569\pi$
$457$	21.4665	1.00416	0.502079	+	0.864822i	$0.332569\pi$
$458$	31.9594	1.49337
$459$	1.00000	0.0466760
$460$	−11.0738	−0.516320
$461$	−24.1191	−1.12334	−0.561670	−	0.827361i	$-0.689841\pi$
$461$	−24.1191	−1.12334	−0.561670	+	0.827361i	$0.689841\pi$
$462$	3.75209	0.174563
$463$	−5.87226	−0.272907	−0.136453	−	0.990646i	$-0.543570\pi$
$463$	−5.87226	−0.272907	−0.136453	+	0.990646i	$0.543570\pi$
$464$	1.81427	0.0842252
$465$	12.9528	0.600671
$466$	−26.4244	−1.22409
$467$	13.5072	0.625040	0.312520	−	0.949911i	$-0.398827\pi$
$467$	13.5072	0.625040	0.312520	+	0.949911i	$0.398827\pi$
$468$	5.82348	0.269191
$469$	5.77023	0.266445
$470$	0.764713	0.0352736
$471$	−24.9351	−1.14895
$472$	0.499180	0.0229766
$473$	−3.51072	−0.161423
$474$	−1.99316	−0.0915491
$475$	17.2311	0.790619
$476$	−1.10092	−0.0504604
$477$	−10.9672	−0.502152
$478$	37.1163	1.69766
$479$	16.7309	0.764453	0.382226	−	0.924069i	$-0.375157\pi$
$479$	16.7309	0.764453	0.382226	+	0.924069i	$0.375157\pi$
$480$	10.1890	0.465062
$481$	−27.8400	−1.26939
$482$	2.44898	0.111548
$483$	−2.45086	−0.111518
$484$	0.746190	0.0339177
$485$	5.66323	0.257154
$486$	1.99316	0.0904118
$487$	32.3414	1.46553	0.732765	−	0.680482i	$-0.238229\pi$
$487$	32.3414	1.46553	0.732765	+	0.680482i	$0.238229\pi$
$488$	−0.612393	−0.0277217
$489$	8.86915	0.401077
$490$	−17.0406	−0.769816
$491$	−16.3056	−0.735862	−0.367931	−	0.929853i	$-0.619934\pi$
$491$	−16.3056	−0.735862	−0.367931	+	0.929853i	$0.619934\pi$
$492$	17.0156	0.767121
$493$	0.447542	0.0201563
$494$	30.1195	1.35514
$495$	−4.31169	−0.193796
$496$	−41.0791	−1.84451
$497$	2.56580	0.115092
$498$	−16.4046	−0.735109
$499$	32.1986	1.44141	0.720704	−	0.693243i	$-0.243819\pi$
$499$	32.1986	1.44141	0.720704	+	0.693243i	$0.243819\pi$
$500$	21.0958	0.943432
$501$	14.8847	0.665000
$502$	−19.1771	−0.855915
$503$	21.8361	0.973624	0.486812	−	0.873507i	$-0.338160\pi$
$503$	21.8361	0.973624	0.486812	+	0.873507i	$0.338160\pi$
$504$	0.0303635	0.00135250
$505$	−25.3901	−1.12984
$506$	−29.5262	−1.31260
$507$	4.28551	0.190326
$508$	−3.75767	−0.166720
$509$	37.3610	1.65600	0.827998	−	0.560731i	$-0.189480\pi$
$509$	37.3610	1.65600	0.827998	+	0.560731i	$0.189480\pi$
$510$	2.54772	0.112815
$511$	−0.857102	−0.0379159
$512$	−31.8728	−1.40859
$513$	5.11899	0.226009
$514$	9.17220	0.404568
$515$	8.22087	0.362255
$516$	2.05315	0.0903848
$517$	1.01247	0.0445286
$518$	10.4902	0.460913
$519$	−3.09388	−0.135806
$520$	−0.205300	−0.00900302
$521$	3.10318	0.135953	0.0679763	−	0.997687i	$-0.478346\pi$
$521$	3.10318	0.135953	0.0679763	+	0.997687i	$0.478346\pi$
$522$	0.892024	0.0390428
$523$	−31.3340	−1.37014	−0.685070	−	0.728477i	$-0.740229\pi$
$523$	−31.3340	−1.37014	−0.685070	+	0.728477i	$0.740229\pi$
$524$	8.02295	0.350484
$525$	1.87855	0.0819866
$526$	13.5169	0.589364
$527$	−10.1334	−0.441416
$528$	13.6743	0.595098
$529$	−3.71353	−0.161458
$530$	−27.9413	−1.21369
$531$	9.17482	0.398153
$532$	−5.63557	−0.244333
$533$	−25.4628	−1.10292
$534$	25.9885	1.12463
$535$	−11.2858	−0.487927
$536$	0.562549	0.0242984
$537$	18.2877	0.789172
$538$	−0.994178	−0.0428621
$539$	−22.5616	−0.971797
$540$	2.52157	0.108511
$541$	−6.54885	−0.281557	−0.140778	−	0.990041i	$-0.544961\pi$
$541$	−6.54885	−0.281557	−0.140778	+	0.990041i	$0.544961\pi$
$542$	10.4534	0.449010
$543$	0.765844	0.0328655
$544$	−7.97117	−0.341761
$545$	20.4840	0.877437
$546$	3.28365	0.140527
$547$	4.16495	0.178080	0.0890402	−	0.996028i	$-0.471620\pi$
$547$	4.16495	0.178080	0.0890402	+	0.996028i	$0.471620\pi$
$548$	9.07877	0.387826
$549$	−11.2557	−0.480380
$550$	22.6314	0.965005
$551$	2.29096	0.0975982
$552$	−0.238938	−0.0101699
$553$	−0.558075	−0.0237317
$554$	−42.2503	−1.79504
$555$	−12.0547	−0.511695
$556$	−15.4715	−0.656139
$557$	7.82527	0.331567	0.165784	−	0.986162i	$-0.446985\pi$
$557$	7.82527	0.331567	0.165784	+	0.986162i	$0.446985\pi$
$558$	−20.1975	−0.855027
$559$	−3.07241	−0.129949
$560$	2.89181	0.122201
$561$	3.37317	0.142415
$562$	−55.1460	−2.32619
$563$	−14.0670	−0.592852	−0.296426	−	0.955056i	$-0.595795\pi$
$563$	−14.0670	−0.592852	−0.296426	+	0.955056i	$0.595795\pi$
$564$	−0.592117	−0.0249326
$565$	−13.2271	−0.556467
$566$	26.2425	1.10306
$567$	0.558075	0.0234369
$568$	0.250144	0.0104958
$569$	−2.80111	−0.117429	−0.0587144	−	0.998275i	$-0.518700\pi$
$569$	−2.80111	−0.117429	−0.0587144	+	0.998275i	$0.518700\pi$
$570$	13.0418	0.546260
$571$	34.1846	1.43058	0.715291	−	0.698826i	$-0.246294\pi$
$571$	34.1846	1.43058	0.715291	+	0.698826i	$0.246294\pi$
$572$	19.6436	0.821339
$573$	−24.1682	−1.00964
$574$	9.59445	0.400465
$575$	−14.7828	−0.616485
$576$	−7.78015	−0.324173
$577$	−27.7965	−1.15718	−0.578591	−	0.815617i	$-0.696397\pi$
$577$	−27.7965	−1.15718	−0.578591	+	0.815617i	$0.696397\pi$
$578$	−1.99316	−0.0829047
$579$	−18.8668	−0.784079
$580$	1.12851	0.0468587
$581$	−4.59320	−0.190558
$582$	−8.83075	−0.366046
$583$	−36.9941	−1.53214
$584$	−0.0835602	−0.00345774
$585$	−3.77338	−0.156010
$586$	−4.78542	−0.197684
$587$	−12.9563	−0.534764	−0.267382	−	0.963591i	$-0.586159\pi$
$587$	−12.9563	−0.534764	−0.267382	+	0.963591i	$0.586159\pi$
$588$	13.1945	0.544133
$589$	−51.8726	−2.13737
$590$	23.3749	0.962330
$591$	14.5162	0.597115
$592$	38.2310	1.57128
$593$	45.8121	1.88128	0.940638	−	0.339412i	$-0.110228\pi$
$593$	45.8121	1.88128	0.940638	+	0.339412i	$0.110228\pi$
$594$	6.72328	0.275859
$595$	0.713349	0.0292444
$596$	−37.1965	−1.52363
$597$	−2.47928	−0.101470
$598$	−25.8399	−1.05667
$599$	−33.4975	−1.36867	−0.684336	−	0.729167i	$-0.739908\pi$
$599$	−33.4975	−1.36867	−0.684336	+	0.729167i	$0.739908\pi$
$600$	0.183143	0.00747677
$601$	−8.46403	−0.345255	−0.172628	−	0.984987i	$-0.555226\pi$
$601$	−8.46403	−0.345255	−0.172628	+	0.984987i	$0.555226\pi$
$602$	1.15769	0.0471841
$603$	10.3395	0.421058
$604$	−18.4038	−0.748841
$605$	−0.483501	−0.0196571
$606$	39.5911	1.60828
$607$	31.7087	1.28702	0.643508	−	0.765440i	$-0.277478\pi$
$607$	31.7087	1.28702	0.643508	+	0.765440i	$0.277478\pi$
$608$	−40.8043	−1.65483
$609$	0.249762	0.0101209
$610$	−28.6763	−1.16107
$611$	0.886068	0.0358465
$612$	−1.97270	−0.0797418
$613$	−2.82202	−0.113980	−0.0569901	−	0.998375i	$-0.518150\pi$
$613$	−2.82202	−0.113980	−0.0569901	+	0.998375i	$0.518150\pi$
$614$	−6.78825	−0.273952
$615$	−11.0254	−0.444587
$616$	0.102421	0.00412666
$617$	25.8689	1.04144	0.520722	−	0.853727i	$-0.325663\pi$
$617$	25.8689	1.04144	0.520722	+	0.853727i	$0.325663\pi$
$618$	−12.8189	−0.515653
$619$	19.5822	0.787075	0.393537	−	0.919309i	$-0.371251\pi$
$619$	19.5822	0.787075	0.393537	+	0.919309i	$0.371251\pi$
$620$	−25.5520	−1.02619
$621$	−4.39164	−0.176230
$622$	65.5147	2.62690
$623$	7.27662	0.291532
$624$	11.9671	0.479067
$625$	3.16141	0.126457
$626$	43.0488	1.72058
$627$	17.2672	0.689585
$628$	49.1895	1.96287
$629$	9.43079	0.376030
$630$	1.42182	0.0566467
$631$	11.2666	0.448515	0.224257	−	0.974530i	$-0.428004\pi$
$631$	11.2666	0.448515	0.224257	+	0.974530i	$0.428004\pi$
$632$	−0.0544076	−0.00216422
$633$	8.31689	0.330567
$634$	−23.1762	−0.920446
$635$	2.43482	0.0966227
$636$	21.6349	0.857881
$637$	−19.7448	−0.782318
$638$	3.00895	0.119125
$639$	4.59760	0.181878
$640$	0.556312	0.0219902
$641$	37.9575	1.49923	0.749616	−	0.661873i	$-0.230238\pi$
$641$	37.9575	1.49923	0.749616	+	0.661873i	$0.230238\pi$
$642$	17.5981	0.694541
$643$	−1.57580	−0.0621434	−0.0310717	−	0.999517i	$-0.509892\pi$
$643$	−1.57580	−0.0621434	−0.0310717	+	0.999517i	$0.509892\pi$
$644$	4.83482	0.190519
$645$	−1.33036	−0.0523827
$646$	−10.2030	−0.401431
$647$	44.8230	1.76217	0.881087	−	0.472954i	$-0.156812\pi$
$647$	44.8230	1.76217	0.881087	+	0.472954i	$0.156812\pi$
$648$	0.0544076	0.00213733
$649$	30.9482	1.21482
$650$	19.8059	0.776851
$651$	−5.65518	−0.221644
$652$	−17.4962	−0.685204
$653$	15.9076	0.622514	0.311257	−	0.950326i	$-0.399250\pi$
$653$	15.9076	0.622514	0.311257	+	0.950326i	$0.399250\pi$
$654$	−31.9410	−1.24899
$655$	−5.19855	−0.203124
$656$	34.9665	1.36521
$657$	−1.53582	−0.0599180
$658$	−0.333873	−0.0130157
$659$	−21.0958	−0.821777	−0.410888	−	0.911686i	$-0.634781\pi$
$659$	−21.0958	−0.821777	−0.410888	+	0.911686i	$0.634781\pi$
$660$	8.50568	0.331083
$661$	−33.2101	−1.29172	−0.645861	−	0.763455i	$-0.723501\pi$
$661$	−33.2101	−1.29172	−0.645861	+	0.763455i	$0.723501\pi$
$662$	0.558975	0.0217252
$663$	2.95203	0.114647
$664$	−0.447798	−0.0173779
$665$	3.65162	0.141604
$666$	18.7971	0.728373
$667$	−1.96544	−0.0761022
$668$	−29.3631	−1.13609
$669$	−19.8244	−0.766455
$670$	26.3423	1.01769
$671$	−37.9672	−1.46571
$672$	−4.44851	−0.171605
$673$	25.2055	0.971599	0.485799	−	0.874070i	$-0.338529\pi$
$673$	25.2055	0.971599	0.485799	+	0.874070i	$0.338529\pi$
$674$	22.4431	0.864477
$675$	3.36612	0.129562
$676$	−8.45404	−0.325155
$677$	−6.33464	−0.243460	−0.121730	−	0.992563i	$-0.538844\pi$
$677$	−6.33464	−0.243460	−0.121730	+	0.992563i	$0.538844\pi$
$678$	20.6252	0.792104
$679$	−2.47256	−0.0948882
$680$	0.0695455	0.00266695
$681$	13.2085	0.506150
$682$	−68.1294	−2.60881
$683$	−13.2728	−0.507871	−0.253936	−	0.967221i	$-0.581725\pi$
$683$	−13.2728	−0.507871	−0.253936	+	0.967221i	$0.581725\pi$
$684$	−10.0982	−0.386116
$685$	−5.88267	−0.224765
$686$	15.2262	0.581341
$687$	16.0345	0.611755
$688$	4.21916	0.160854
$689$	−32.3754	−1.23340
$690$	−11.1887	−0.425946
$691$	−34.5799	−1.31548	−0.657741	−	0.753245i	$-0.728488\pi$
$691$	−34.5799	−1.31548	−0.657741	+	0.753245i	$0.728488\pi$
$692$	6.10330	0.232013
$693$	1.88248	0.0715095
$694$	36.6802	1.39236
$695$	10.0249	0.380267
$696$	0.0243497	0.000922971 0
$697$	8.62551	0.326714
$698$	53.0140	2.00661
$699$	−13.2575	−0.501446
$700$	−3.70582	−0.140067
$701$	−45.2520	−1.70915	−0.854573	−	0.519332i	$-0.826181\pi$
$701$	−45.2520	−1.70915	−0.854573	+	0.519332i	$0.826181\pi$
$702$	5.88388	0.222073
$703$	48.2761	1.82077
$704$	−26.2438	−0.989099
$705$	0.383668	0.0144498
$706$	55.9682	2.10639
$707$	11.0853	0.416905
$708$	−18.0992	−0.680210
$709$	−35.8767	−1.34738	−0.673689	−	0.739015i	$-0.735291\pi$
$709$	−35.8767	−1.34738	−0.673689	+	0.739015i	$0.735291\pi$
$710$	11.7134	0.439597
$711$	−1.00000	−0.0375029
$712$	0.709409	0.0265862
$713$	44.5021	1.66662
$714$	−1.11233	−0.0416281
$715$	−12.7282	−0.476009
$716$	−36.0762	−1.34823
$717$	18.6218	0.695443
$718$	19.8825	0.742010
$719$	−23.7693	−0.886447	−0.443223	−	0.896411i	$-0.646165\pi$
$719$	−23.7693	−0.886447	−0.443223	+	0.896411i	$0.646165\pi$
$720$	5.18176	0.193113
$721$	−3.58923	−0.133670
$722$	−14.3588	−0.534379
$723$	1.22869	0.0456955
$724$	−1.51078	−0.0561478
$725$	1.50648	0.0559493
$726$	0.753929	0.0279809
$727$	−31.0445	−1.15138	−0.575689	−	0.817669i	$-0.695266\pi$
$727$	−31.0445	−1.15138	−0.575689	+	0.817669i	$0.695266\pi$
$728$	0.0896340	0.00332206
$729$	1.00000	0.0370370
$730$	−3.91284	−0.144821
$731$	1.04078	0.0384946
$732$	22.2041	0.820686
$733$	17.5893	0.649677	0.324839	−	0.945769i	$-0.394690\pi$
$733$	17.5893	0.649677	0.324839	+	0.945769i	$0.394690\pi$
$734$	36.8541	1.36031
$735$	−8.54952	−0.315354
$736$	35.0065	1.29036
$737$	34.8770	1.28471
$738$	17.1921	0.632848
$739$	−29.8158	−1.09679	−0.548395	−	0.836219i	$-0.684761\pi$
$739$	−29.8158	−1.09679	−0.548395	+	0.836219i	$0.684761\pi$
$740$	23.7804	0.874185
$741$	15.1114	0.555132
$742$	12.1991	0.447845
$743$	−31.3659	−1.15070	−0.575351	−	0.817906i	$-0.695135\pi$
$743$	−31.3659	−1.15070	−0.575351	+	0.817906i	$0.695135\pi$
$744$	−0.551332	−0.0202128
$745$	24.1018	0.883021
$746$	2.43103	0.0890063
$747$	−8.23044	−0.301136
$748$	−6.65426	−0.243304
$749$	4.92737	0.180042
$750$	21.3146	0.778299
$751$	39.7117	1.44910	0.724550	−	0.689222i	$-0.242048\pi$
$751$	39.7117	1.44910	0.724550	+	0.689222i	$0.242048\pi$
$752$	−1.21678	−0.0443716
$753$	−9.62142	−0.350624
$754$	2.63328	0.0958985
$755$	11.9249	0.433993
$756$	−1.10092	−0.0400399
$757$	25.7628	0.936366	0.468183	−	0.883632i	$-0.344909\pi$
$757$	25.7628	0.936366	0.468183	+	0.883632i	$0.344909\pi$
$758$	32.2779	1.17239
$759$	−14.8137	−0.537704
$760$	0.356002	0.0129136
$761$	2.02249	0.0733154	0.0366577	−	0.999328i	$-0.488329\pi$
$761$	2.02249	0.0733154	0.0366577	+	0.999328i	$0.488329\pi$
$762$	−3.79664	−0.137538
$763$	−8.94329	−0.323769
$764$	47.6766	1.72488
$765$	1.27823	0.0462146
$766$	40.9464	1.47945
$767$	27.0844	0.977960
$768$	−16.4278	−0.592786
$769$	−25.4420	−0.917462	−0.458731	−	0.888575i	$-0.651696\pi$
$769$	−25.4420	−0.917462	−0.458731	+	0.888575i	$0.651696\pi$
$770$	4.79604	0.172837
$771$	4.60183	0.165731
$772$	37.2186	1.33953
$773$	−25.0336	−0.900395	−0.450197	−	0.892929i	$-0.648646\pi$
$773$	−25.0336	−0.900395	−0.450197	+	0.892929i	$0.648646\pi$
$774$	2.07444	0.0745643
$775$	−34.1102	−1.22527
$776$	−0.241054	−0.00865332
$777$	5.26308	0.188812
$778$	−7.69909	−0.276026
$779$	44.1539	1.58198
$780$	7.44376	0.266529
$781$	15.5085	0.554937
$782$	8.75325	0.313016
$783$	0.447542	0.0159938
$784$	27.1144	0.968371
$785$	−31.8728	−1.13759
$786$	8.10617	0.289137
$787$	32.2191	1.14849	0.574244	−	0.818684i	$-0.305296\pi$
$787$	32.2191	1.14849	0.574244	+	0.818684i	$0.305296\pi$
$788$	−28.6361	−1.02012
$789$	6.78162	0.241432
$790$	−2.54772	−0.0906440
$791$	5.77493	0.205333
$792$	0.183526	0.00652131
$793$	−33.2271	−1.17993
$794$	25.8350	0.916849
$795$	−14.0186	−0.497187
$796$	4.89088	0.173353
$797$	−51.9188	−1.83906	−0.919529	−	0.393021i	$-0.871430\pi$
$797$	−51.9188	−1.83906	−0.919529	+	0.393021i	$0.871430\pi$
$798$	−5.69402	−0.201566
$799$	−0.300155	−0.0106187
$800$	−26.8320	−0.948653
$801$	13.0388	0.460703
$802$	11.2422	0.396974
$803$	−5.18057	−0.182818
$804$	−20.3968	−0.719341
$805$	−3.13277	−0.110416
$806$	−59.6236	−2.10015
$807$	−0.498794	−0.0175584
$808$	1.08072	0.0380197
$809$	−28.1727	−0.990500	−0.495250	−	0.868751i	$-0.664923\pi$
$809$	−28.1727	−0.990500	−0.495250	+	0.868751i	$0.664923\pi$
$810$	2.54772	0.0895179
$811$	39.4474	1.38519	0.692594	−	0.721328i	$-0.256468\pi$
$811$	39.4474	1.38519	0.692594	+	0.721328i	$0.256468\pi$
$812$	−0.492706	−0.0172906
$813$	5.24460	0.183936
$814$	63.4058	2.22237
$815$	11.3368	0.397112
$816$	−4.05385	−0.141913
$817$	5.32773	0.186394
$818$	75.2340	2.63050
$819$	1.64745	0.0575667
$820$	21.7498	0.759537
$821$	−41.3738	−1.44396	−0.721978	−	0.691916i	$-0.756767\pi$
$821$	−41.3738	−1.44396	−0.721978	+	0.691916i	$0.756767\pi$
$822$	9.17294	0.319943
$823$	−5.48624	−0.191238	−0.0956192	−	0.995418i	$-0.530483\pi$
$823$	−5.48624	−0.191238	−0.0956192	+	0.995418i	$0.530483\pi$
$824$	−0.349919	−0.0121900
$825$	11.3545	0.395313
$826$	−10.2055	−0.355094
$827$	25.6302	0.891251	0.445625	−	0.895220i	$-0.352981\pi$
$827$	25.6302	0.891251	0.445625	+	0.895220i	$0.352981\pi$
$828$	8.66339	0.301074
$829$	2.25423	0.0782928	0.0391464	−	0.999233i	$-0.487536\pi$
$829$	2.25423	0.0782928	0.0391464	+	0.999233i	$0.487536\pi$
$830$	−20.9689	−0.727841
$831$	−21.1976	−0.735336
$832$	−22.9673	−0.796246
$833$	6.68855	0.231745
$834$	−15.6320	−0.541292
$835$	19.0261	0.658425
$836$	−34.0631	−1.17810
$837$	−10.1334	−0.350260
$838$	51.3753	1.77473
$839$	4.40155	0.151958	0.0759792	−	0.997109i	$-0.475792\pi$
$839$	4.40155	0.151958	0.0759792	+	0.997109i	$0.475792\pi$
$840$	0.0388116	0.00133913
$841$	−28.7997	−0.993093
$842$	48.2117	1.66148
$843$	−27.6676	−0.952921
$844$	−16.4068	−0.564744
$845$	5.47787	0.188445
$846$	−0.598259	−0.0205686
$847$	0.211096	0.00725334
$848$	44.4592	1.52674
$849$	13.1663	0.451865
$850$	−6.70924	−0.230125
$851$	−41.4166	−1.41974
$852$	−9.06970	−0.310723
$853$	22.7060	0.777438	0.388719	−	0.921356i	$-0.372918\pi$
$853$	22.7060	0.777438	0.388719	+	0.921356i	$0.372918\pi$
$854$	12.5201	0.428427
$855$	6.54325	0.223774
$856$	0.480376	0.0164189
$857$	9.81791	0.335374	0.167687	−	0.985840i	$-0.446370\pi$
$857$	9.81791	0.335374	0.167687	+	0.985840i	$0.446370\pi$
$858$	19.8473	0.677576
$859$	2.61154	0.0891044	0.0445522	−	0.999007i	$-0.485814\pi$
$859$	2.61154	0.0891044	0.0445522	+	0.999007i	$0.485814\pi$
$860$	2.62440	0.0894912
$861$	4.81368	0.164050
$862$	5.45239	0.185709
$863$	−22.3906	−0.762184	−0.381092	−	0.924537i	$-0.624452\pi$
$863$	−22.3906	−0.762184	−0.381092	+	0.924537i	$0.624452\pi$
$864$	−7.97117	−0.271185
$865$	−3.95469	−0.134464
$866$	−72.5705	−2.46605
$867$	−1.00000	−0.0339618
$868$	11.1560	0.378659
$869$	−3.37317	−0.114427
$870$	1.14021	0.0386568
$871$	30.5226	1.03422
$872$	−0.871895	−0.0295261
$873$	−4.43052	−0.149950
$874$	44.8078	1.51565
$875$	5.96796	0.201754
$876$	3.02971	0.102365
$877$	−15.0386	−0.507819	−0.253909	−	0.967228i	$-0.581717\pi$
$877$	−15.0386	−0.507819	−0.253909	+	0.967228i	$0.581717\pi$
$878$	56.3071	1.90027
$879$	−2.40092	−0.0809809
$880$	17.4789	0.589215
$881$	−4.26775	−0.143784	−0.0718921	−	0.997412i	$-0.522904\pi$
$881$	−4.26775	−0.143784	−0.0718921	+	0.997412i	$0.522904\pi$
$882$	13.3314	0.448891
$883$	15.4500	0.519933	0.259967	−	0.965618i	$-0.416288\pi$
$883$	15.4500	0.519933	0.259967	+	0.965618i	$0.416288\pi$
$884$	−5.82348	−0.195865
$885$	11.7275	0.394217
$886$	−13.7794	−0.462926
$887$	−51.4585	−1.72781	−0.863904	−	0.503656i	$-0.831988\pi$
$887$	−51.4585	−1.72781	−0.863904	+	0.503656i	$0.831988\pi$
$888$	0.513106	0.0172187
$889$	−1.06304	−0.0356532
$890$	33.2193	1.11351
$891$	3.37317	0.113005
$892$	39.1076	1.30942
$893$	−1.53649	−0.0514167
$894$	−37.5823	−1.25694
$895$	23.3759	0.781370
$896$	−0.242885	−0.00811423
$897$	−12.9642	−0.432864
$898$	81.2570	2.71158
$899$	−4.53510	−0.151254
$900$	−6.64036	−0.221345
$901$	10.9672	0.365369
$902$	57.9917	1.93091
$903$	0.580832	0.0193289
$904$	0.563007	0.0187253
$905$	0.978926	0.0325406
$906$	−18.5947	−0.617768
$907$	32.2779	1.07177	0.535884	−	0.844291i	$-0.319978\pi$
$907$	32.2779	1.07177	0.535884	+	0.844291i	$0.319978\pi$
$908$	−26.0564	−0.864712
$909$	19.8635	0.658829
$910$	4.19726	0.139138
$911$	24.8005	0.821676	0.410838	−	0.911708i	$-0.365236\pi$
$911$	24.8005	0.821676	0.410838	+	0.911708i	$0.365236\pi$
$912$	−20.7516	−0.687154
$913$	−27.7627	−0.918810
$914$	−42.7862	−1.41524
$915$	−14.3873	−0.475631
$916$	−31.6313	−1.04513
$917$	2.26968	0.0749515
$918$	−1.99316	−0.0657842
$919$	−59.0162	−1.94676	−0.973382	−	0.229189i	$-0.926393\pi$
$919$	−59.0162	−1.94676	−0.973382	+	0.229189i	$0.926393\pi$
$920$	−0.305418	−0.0100693
$921$	−3.40577	−0.112224
$922$	48.0734	1.58321
$923$	13.5723	0.446736
$924$	−3.71357	−0.122168
$925$	31.7452	1.04378
$926$	11.7044	0.384630
$927$	−6.43144	−0.211236
$928$	−3.56743	−0.117107
$929$	29.0905	0.954430	0.477215	−	0.878787i	$-0.341646\pi$
$929$	29.0905	0.954430	0.477215	+	0.878787i	$0.341646\pi$
$930$	−25.8170	−0.846574
$931$	34.2386	1.12213
$932$	26.1532	0.856675
$933$	32.8697	1.07611
$934$	−26.9221	−0.880918
$935$	4.31169	0.141007
$936$	0.160613	0.00524979
$937$	−20.6465	−0.674492	−0.337246	−	0.941417i	$-0.609495\pi$
$937$	−20.6465	−0.674492	−0.337246	+	0.941417i	$0.609495\pi$
$938$	−11.5010	−0.375522
$939$	21.5982	0.704832
$940$	−0.756863	−0.0246861
$941$	−38.9673	−1.27030	−0.635149	−	0.772390i	$-0.719061\pi$
$941$	−38.9673	−1.27030	−0.635149	+	0.772390i	$0.719061\pi$
$942$	49.6997	1.61930
$943$	−37.8801	−1.23355
$944$	−37.1933	−1.21054
$945$	0.713349	0.0232052
$946$	6.99744	0.227506
$947$	1.46255	0.0475265	0.0237632	−	0.999718i	$-0.492435\pi$
$947$	1.46255	0.0475265	0.0237632	+	0.999718i	$0.492435\pi$
$948$	1.97270	0.0640704
$949$	−4.53379	−0.147173
$950$	−34.3445	−1.11428
$951$	−11.6279	−0.377059
$952$	−0.0303635	−0.000984086 0
$953$	39.5801	1.28213	0.641063	−	0.767488i	$-0.278494\pi$
$953$	39.5801	1.28213	0.641063	+	0.767488i	$0.278494\pi$
$954$	21.8593	0.707722
$955$	−30.8925	−0.999658
$956$	−36.7353	−1.18810
$957$	1.50963	0.0487995
$958$	−33.3474	−1.07740
$959$	2.56837	0.0829370
$960$	−9.94484	−0.320968
$961$	71.6851	2.31242
$962$	55.4897	1.78906
$963$	8.82922	0.284518
$964$	−2.42384	−0.0780667
$965$	−24.1162	−0.776327
$966$	4.88497	0.157171
$967$	11.9479	0.384220	0.192110	−	0.981373i	$-0.438467\pi$
$967$	11.9479	0.384220	0.192110	+	0.981373i	$0.438467\pi$
$968$	0.0205801	0.000661468 0
$969$	−5.11899	−0.164446
$970$	−11.2877	−0.362428
$971$	−41.6046	−1.33515	−0.667577	−	0.744541i	$-0.732668\pi$
$971$	−41.6046	−1.33515	−0.667577	+	0.744541i	$0.732668\pi$
$972$	−1.97270	−0.0632745
$973$	−4.37687	−0.140316
$974$	−64.4618	−2.06549
$975$	9.93691	0.318236
$976$	45.6287	1.46054
$977$	−11.1632	−0.357141	−0.178571	−	0.983927i	$-0.557147\pi$
$977$	−11.1632	−0.357141	−0.178571	+	0.983927i	$0.557147\pi$
$978$	−17.6777	−0.565269
$979$	43.9820	1.40567
$980$	16.8657	0.538754
$981$	−16.0253	−0.511647
$982$	32.4998	1.03711
$983$	35.3013	1.12594	0.562969	−	0.826478i	$-0.309659\pi$
$983$	35.3013	1.12594	0.562969	+	0.826478i	$0.309659\pi$
$984$	0.469293	0.0149605
$985$	18.5550	0.591212
$986$	−0.892024	−0.0284078
$987$	−0.167509	−0.00533187
$988$	−29.8103	−0.948393
$989$	−4.57072	−0.145340
$990$	8.59390	0.273132
$991$	−36.6469	−1.16413	−0.582063	−	0.813144i	$-0.697754\pi$
$991$	−36.6469	−1.16413	−0.582063	+	0.813144i	$0.697754\pi$
$992$	80.7748	2.56460
$993$	0.280446	0.00889969
$994$	−5.11407	−0.162208
$995$	−3.16909	−0.100467
$996$	16.2362	0.514464
$997$	−14.5445	−0.460629	−0.230315	−	0.973116i	$-0.573976\pi$
$997$	−14.5445	−0.460629	−0.230315	+	0.973116i	$0.573976\pi$
$998$	−64.1772	−2.03149
$999$	9.43079	0.298377

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.g.1.4	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.g.1.4	✓	22	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-1.99316 q^{2} -1.00000 q^{3} +1.97270 q^{4} -1.27823 q^{5} +1.99316 q^{6} +0.558075 q^{7} +0.0544076 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.99316 q^{2} -1.00000 q^{3} +1.97270 q^{4} -1.27823 q^{5} +1.99316 q^{6} +0.558075 q^{7} +0.0544076 q^{8} +1.00000 q^{9} +2.54772 q^{10} +3.37317 q^{11} -1.97270 q^{12} +2.95203 q^{13} -1.11233 q^{14} +1.27823 q^{15} -4.05385 q^{16} -1.00000 q^{17} -1.99316 q^{18} -5.11899 q^{19} -2.52157 q^{20} -0.558075 q^{21} -6.72328 q^{22} +4.39164 q^{23} -0.0544076 q^{24} -3.36612 q^{25} -5.88388 q^{26} -1.00000 q^{27} +1.10092 q^{28} -0.447542 q^{29} -2.54772 q^{30} +10.1334 q^{31} +7.97117 q^{32} -3.37317 q^{33} +1.99316 q^{34} -0.713349 q^{35} +1.97270 q^{36} -9.43079 q^{37} +10.2030 q^{38} -2.95203 q^{39} -0.0695455 q^{40} -8.62551 q^{41} +1.11233 q^{42} -1.04078 q^{43} +6.65426 q^{44} -1.27823 q^{45} -8.75325 q^{46} +0.300155 q^{47} +4.05385 q^{48} -6.68855 q^{49} +6.70924 q^{50} +1.00000 q^{51} +5.82348 q^{52} -10.9672 q^{53} +1.99316 q^{54} -4.31169 q^{55} +0.0303635 q^{56} +5.11899 q^{57} +0.892024 q^{58} +9.17482 q^{59} +2.52157 q^{60} -11.2557 q^{61} -20.1975 q^{62} +0.558075 q^{63} -7.78015 q^{64} -3.77338 q^{65} +6.72328 q^{66} +10.3395 q^{67} -1.97270 q^{68} -4.39164 q^{69} +1.42182 q^{70} +4.59760 q^{71} +0.0544076 q^{72} -1.53582 q^{73} +18.7971 q^{74} +3.36612 q^{75} -10.0982 q^{76} +1.88248 q^{77} +5.88388 q^{78} -1.00000 q^{79} +5.18176 q^{80} +1.00000 q^{81} +17.1921 q^{82} -8.23044 q^{83} -1.10092 q^{84} +1.27823 q^{85} +2.07444 q^{86} +0.447542 q^{87} +0.183526 q^{88} +13.0388 q^{89} +2.54772 q^{90} +1.64745 q^{91} +8.66339 q^{92} -10.1334 q^{93} -0.598259 q^{94} +6.54325 q^{95} -7.97117 q^{96} -4.43052 q^{97} +13.3314 q^{98} +3.37317 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9}+O(q^{10}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9	\( 22 q + 2 q^{2} - 22 q^{3} + 16 q^{4} + 5 q^{5} - 2 q^{6} - 4 q^{7} + 6 q^{8} + 22 q^{9} - 5 q^{10} - 2 q^{11} - 16 q^{12} - 11 q^{13} - 7 q^{14} - 5 q^{15} - 22 q^{17} + 2 q^{18} - 36 q^{19} + 4 q^{21} - 9 q^{22} + 21 q^{23} - 6 q^{24} + 9 q^{25} - 16 q^{26} - 22 q^{27} - 17 q^{28} - q^{29} + 5 q^{30} - 12 q^{31} - 11 q^{32} + 2 q^{33} - 2 q^{34} - 14 q^{35} + 16 q^{36} - 6 q^{37} + q^{38} + 11 q^{39} - 24 q^{40} - 17 q^{41} + 7 q^{42} - 36 q^{43} + 16 q^{44} + 5 q^{45} - 23 q^{46} - 17 q^{47} - 6 q^{49} - 33 q^{50} + 22 q^{51} - 57 q^{52} - 2 q^{53} - 2 q^{54} - 24 q^{55} - 64 q^{56} + 36 q^{57} - 7 q^{58} - 59 q^{59} - 30 q^{61} - 4 q^{62} - 4 q^{63} - 22 q^{64} + 36 q^{65} + 9 q^{66} - 16 q^{67} - 16 q^{68} - 21 q^{69} - 39 q^{70} - 11 q^{71} + 6 q^{72} - 19 q^{73} - 28 q^{74} - 9 q^{75} - 77 q^{76} + 2 q^{77} + 16 q^{78} - 22 q^{79} - 2 q^{80} + 22 q^{81} + 33 q^{82} - 23 q^{83} + 17 q^{84} - 5 q^{85} + 6 q^{86} + q^{87} - 23 q^{88} + 12 q^{89} - 5 q^{90} - 24 q^{91} + 66 q^{92} + 12 q^{93} - 61 q^{94} - 11 q^{95} + 11 q^{96} - 9 q^{97} + 17 q^{98} - 2 q^{99}+O(q^{100}) \) 22 * q + 2 * q^2 - 22 * q^3 + 16 * q^4 + 5 * q^5 - 2 * q^6 - 4 * q^7 + 6 * q^8 + 22 * q^9 - 5 * q^10 - 2 * q^11 - 16 * q^12 - 11 * q^13 - 7 * q^14 - 5 * q^15 - 22 * q^17 + 2 * q^18 - 36 * q^19 + 4 * q^21 - 9 * q^22 + 21 * q^23 - 6 * q^24 + 9 * q^25 - 16 * q^26 - 22 * q^27 - 17 * q^28 - q^29 + 5 * q^30 - 12 * q^31 - 11 * q^32 + 2 * q^33 - 2 * q^34 - 14 * q^35 + 16 * q^36 - 6 * q^37 + q^38 + 11 * q^39 - 24 * q^40 - 17 * q^41 + 7 * q^42 - 36 * q^43 + 16 * q^44 + 5 * q^45 - 23 * q^46 - 17 * q^47 - 6 * q^49 - 33 * q^50 + 22 * q^51 - 57 * q^52 - 2 * q^53 - 2 * q^54 - 24 * q^55 - 64 * q^56 + 36 * q^57 - 7 * q^58 - 59 * q^59 - 30 * q^61 - 4 * q^62 - 4 * q^63 - 22 * q^64 + 36 * q^65 + 9 * q^66 - 16 * q^67 - 16 * q^68 - 21 * q^69 - 39 * q^70 - 11 * q^71 + 6 * q^72 - 19 * q^73 - 28 * q^74 - 9 * q^75 - 77 * q^76 + 2 * q^77 + 16 * q^78 - 22 * q^79 - 2 * q^80 + 22 * q^81 + 33 * q^82 - 23 * q^83 + 17 * q^84 - 5 * q^85 + 6 * q^86 + q^87 - 23 * q^88 + 12 * q^89 - 5 * q^90 - 24 * q^91 + 66 * q^92 + 12 * q^93 - 61 * q^94 - 11 * q^95 + 11 * q^96 - 9 * q^97 + 17 * q^98 - 2 * q^99

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