LMFDB - Embedded newform 4029.2.a.k.1.23

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:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.23
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)

$f(q)$	$=$	$q+1.66288 q^{2} +1.00000 q^{3} +0.765175 q^{4} +1.59112 q^{5} +1.66288 q^{6} -5.08770 q^{7} -2.05337 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.66288 q^{2} +1.00000 q^{3} +0.765175 q^{4} +1.59112 q^{5} +1.66288 q^{6} -5.08770 q^{7} -2.05337 q^{8} +1.00000 q^{9} +2.64585 q^{10} +4.95692 q^{11} +0.765175 q^{12} +0.606051 q^{13} -8.46024 q^{14} +1.59112 q^{15} -4.94486 q^{16} +1.00000 q^{17} +1.66288 q^{18} +3.54053 q^{19} +1.21749 q^{20} -5.08770 q^{21} +8.24277 q^{22} +4.44667 q^{23} -2.05337 q^{24} -2.46833 q^{25} +1.00779 q^{26} +1.00000 q^{27} -3.89298 q^{28} +8.26672 q^{29} +2.64585 q^{30} -5.27768 q^{31} -4.11598 q^{32} +4.95692 q^{33} +1.66288 q^{34} -8.09514 q^{35} +0.765175 q^{36} +7.77967 q^{37} +5.88748 q^{38} +0.606051 q^{39} -3.26715 q^{40} +1.05780 q^{41} -8.46024 q^{42} +7.52112 q^{43} +3.79291 q^{44} +1.59112 q^{45} +7.39428 q^{46} +3.93351 q^{47} -4.94486 q^{48} +18.8847 q^{49} -4.10455 q^{50} +1.00000 q^{51} +0.463736 q^{52} -5.66923 q^{53} +1.66288 q^{54} +7.88706 q^{55} +10.4469 q^{56} +3.54053 q^{57} +13.7466 q^{58} +1.55188 q^{59} +1.21749 q^{60} +7.07996 q^{61} -8.77615 q^{62} -5.08770 q^{63} +3.04533 q^{64} +0.964301 q^{65} +8.24277 q^{66} +7.72942 q^{67} +0.765175 q^{68} +4.44667 q^{69} -13.4613 q^{70} -10.7068 q^{71} -2.05337 q^{72} -14.8078 q^{73} +12.9367 q^{74} -2.46833 q^{75} +2.70912 q^{76} -25.2193 q^{77} +1.00779 q^{78} +1.00000 q^{79} -7.86787 q^{80} +1.00000 q^{81} +1.75899 q^{82} +0.297138 q^{83} -3.89298 q^{84} +1.59112 q^{85} +12.5067 q^{86} +8.26672 q^{87} -10.1784 q^{88} +3.46646 q^{89} +2.64585 q^{90} -3.08341 q^{91} +3.40248 q^{92} -5.27768 q^{93} +6.54096 q^{94} +5.63340 q^{95} -4.11598 q^{96} +0.671391 q^{97} +31.4030 q^{98} +4.95692 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * 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 $

$2$	1.66288	1.17583	0.587917	−	0.808921i	$-0.299948\pi$
$2$	1.66288	1.17583	0.587917	+	0.808921i	$0.299948\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.765175	0.382588
$5$	1.59112	0.711571	0.355785	−	0.934568i	$-0.384213\pi$
$5$	1.59112	0.711571	0.355785	+	0.934568i	$0.384213\pi$
$6$	1.66288	0.678869
$7$	−5.08770	−1.92297	−0.961485	−	0.274858i	$-0.911369\pi$
$7$	−5.08770	−1.92297	−0.961485	+	0.274858i	$0.911369\pi$
$8$	−2.05337	−0.725975
$9$	1.00000	0.333333
$10$	2.64585	0.836690
$11$	4.95692	1.49457	0.747284	−	0.664505i	$-0.231358\pi$
$11$	4.95692	1.49457	0.747284	+	0.664505i	$0.231358\pi$
$12$	0.765175	0.220887
$13$	0.606051	0.168088	0.0840442	−	0.996462i	$-0.473216\pi$
$13$	0.606051	0.168088	0.0840442	+	0.996462i	$0.473216\pi$
$14$	−8.46024	−2.26109
$15$	1.59112	0.410826
$16$	−4.94486	−1.23621
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.66288	0.391945
$19$	3.54053	0.812252	0.406126	−	0.913817i	$-0.366879\pi$
$19$	3.54053	0.812252	0.406126	+	0.913817i	$0.366879\pi$
$20$	1.21749	0.272238
$21$	−5.08770	−1.11023
$22$	8.24277	1.75736
$23$	4.44667	0.927195	0.463597	−	0.886046i	$-0.346558\pi$
$23$	4.44667	0.927195	0.463597	+	0.886046i	$0.346558\pi$
$24$	−2.05337	−0.419142
$25$	−2.46833	−0.493667
$26$	1.00779	0.197644
$27$	1.00000	0.192450
$28$	−3.89298	−0.735705
$29$	8.26672	1.53509	0.767546	−	0.640994i	$-0.221478\pi$
$29$	8.26672	1.53509	0.767546	+	0.640994i	$0.221478\pi$
$30$	2.64585	0.483063
$31$	−5.27768	−0.947899	−0.473949	−	0.880552i	$-0.657172\pi$
$31$	−5.27768	−0.947899	−0.473949	+	0.880552i	$0.657172\pi$
$32$	−4.11598	−0.727609
$33$	4.95692	0.862889
$34$	1.66288	0.285182
$35$	−8.09514	−1.36833
$36$	0.765175	0.127529
$37$	7.77967	1.27897	0.639485	−	0.768804i	$-0.279148\pi$
$37$	7.77967	1.27897	0.639485	+	0.768804i	$0.279148\pi$
$38$	5.88748	0.955075
$39$	0.606051	0.0970459
$40$	−3.26715	−0.516583
$41$	1.05780	0.165200	0.0826002	−	0.996583i	$-0.473678\pi$
$41$	1.05780	0.165200	0.0826002	+	0.996583i	$0.473678\pi$
$42$	−8.46024	−1.30544
$43$	7.52112	1.14696	0.573480	−	0.819219i	$-0.305593\pi$
$43$	7.52112	1.14696	0.573480	+	0.819219i	$0.305593\pi$
$44$	3.79291	0.571803
$45$	1.59112	0.237190
$46$	7.39428	1.09023
$47$	3.93351	0.573761	0.286880	−	0.957966i	$-0.407382\pi$
$47$	3.93351	0.573761	0.286880	+	0.957966i	$0.407382\pi$
$48$	−4.94486	−0.713729
$49$	18.8847	2.69781
$50$	−4.10455	−0.580471
$51$	1.00000	0.140028
$52$	0.463736	0.0643086
$53$	−5.66923	−0.778729	−0.389364	−	0.921084i	$-0.627305\pi$
$53$	−5.66923	−0.778729	−0.389364	+	0.921084i	$0.627305\pi$
$54$	1.66288	0.226290
$55$	7.88706	1.06349
$56$	10.4469	1.39603
$57$	3.54053	0.468954
$58$	13.7466	1.80501
$59$	1.55188	0.202038	0.101019	−	0.994885i	$-0.467790\pi$
$59$	1.55188	0.202038	0.101019	+	0.994885i	$0.467790\pi$
$60$	1.21749	0.157177
$61$	7.07996	0.906496	0.453248	−	0.891384i	$-0.350265\pi$
$61$	7.07996	0.906496	0.453248	+	0.891384i	$0.350265\pi$
$62$	−8.77615	−1.11457
$63$	−5.08770	−0.640990
$64$	3.04533	0.380666
$65$	0.964301	0.119607
$66$	8.24277	1.01461
$67$	7.72942	0.944299	0.472150	−	0.881518i	$-0.343478\pi$
$67$	7.72942	0.944299	0.472150	+	0.881518i	$0.343478\pi$
$68$	0.765175	0.0927912
$69$	4.44667	0.535316
$70$	−13.4613	−1.60893
$71$	−10.7068	−1.27066	−0.635330	−	0.772241i	$-0.719136\pi$
$71$	−10.7068	−1.27066	−0.635330	+	0.772241i	$0.719136\pi$
$72$	−2.05337	−0.241992
$73$	−14.8078	−1.73313	−0.866563	−	0.499068i	$-0.833676\pi$
$73$	−14.8078	−1.73313	−0.866563	+	0.499068i	$0.833676\pi$
$74$	12.9367	1.50386
$75$	−2.46833	−0.285019
$76$	2.70912	0.310758
$77$	−25.2193	−2.87401
$78$	1.00779	0.114110
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	−7.86787	−0.879654
$81$	1.00000	0.111111
$82$	1.75899	0.194248
$83$	0.297138	0.0326152	0.0163076	−	0.999867i	$-0.494809\pi$
$83$	0.297138	0.0326152	0.0163076	+	0.999867i	$0.494809\pi$
$84$	−3.89298	−0.424759
$85$	1.59112	0.172581
$86$	12.5067	1.34864
$87$	8.26672	0.886286
$88$	−10.1784	−1.08502
$89$	3.46646	0.367444	0.183722	−	0.982978i	$-0.441185\pi$
$89$	3.46646	0.367444	0.183722	+	0.982978i	$0.441185\pi$
$90$	2.64585	0.278897
$91$	−3.08341	−0.323229
$92$	3.40248	0.354733
$93$	−5.27768	−0.547270
$94$	6.54096	0.674648
$95$	5.63340	0.577975
$96$	−4.11598	−0.420085
$97$	0.671391	0.0681694	0.0340847	−	0.999419i	$-0.489148\pi$
$97$	0.671391	0.0681694	0.0340847	+	0.999419i	$0.489148\pi$
$98$	31.4030	3.17218
$99$	4.95692	0.498189
$100$	−1.88871	−0.188871
$101$	12.8578	1.27940	0.639699	−	0.768625i	$-0.279059\pi$
$101$	12.8578	1.27940	0.639699	+	0.768625i	$0.279059\pi$
$102$	1.66288	0.164650
$103$	12.4592	1.22764	0.613819	−	0.789447i	$-0.289633\pi$
$103$	12.4592	1.22764	0.613819	+	0.789447i	$0.289633\pi$
$104$	−1.24445	−0.122028
$105$	−8.09514	−0.790005
$106$	−9.42726	−0.915656
$107$	11.7673	1.13759	0.568793	−	0.822481i	$-0.307411\pi$
$107$	11.7673	1.13759	0.568793	+	0.822481i	$0.307411\pi$
$108$	0.765175	0.0736290
$109$	−9.31503	−0.892218	−0.446109	−	0.894979i	$-0.647191\pi$
$109$	−9.31503	−0.892218	−0.446109	+	0.894979i	$0.647191\pi$
$110$	13.1152	1.25049
$111$	7.77967	0.738413
$112$	25.1579	2.37720
$113$	−11.1883	−1.05251	−0.526256	−	0.850326i	$-0.676404\pi$
$113$	−11.1883	−1.05251	−0.526256	+	0.850326i	$0.676404\pi$
$114$	5.88748	0.551413
$115$	7.07519	0.659765
$116$	6.32549	0.587307
$117$	0.606051	0.0560295
$118$	2.58059	0.237563
$119$	−5.08770	−0.466389
$120$	−3.26715	−0.298249
$121$	13.5710	1.23373
$122$	11.7731	1.06589
$123$	1.05780	0.0953785
$124$	−4.03835	−0.362654
$125$	−11.8830	−1.06285
$126$	−8.46024	−0.753698
$127$	−14.1331	−1.25411	−0.627053	−	0.778976i	$-0.715739\pi$
$127$	−14.1331	−1.25411	−0.627053	+	0.778976i	$0.715739\pi$
$128$	13.2960	1.17521
$129$	7.52112	0.662198
$130$	1.60352	0.140638
$131$	1.64814	0.143999	0.0719994	−	0.997405i	$-0.477062\pi$
$131$	1.64814	0.143999	0.0719994	+	0.997405i	$0.477062\pi$
$132$	3.79291	0.330131
$133$	−18.0131	−1.56194
$134$	12.8531	1.11034
$135$	1.59112	0.136942
$136$	−2.05337	−0.176075
$137$	−10.4714	−0.894629	−0.447314	−	0.894377i	$-0.647619\pi$
$137$	−10.4714	−0.894629	−0.447314	+	0.894377i	$0.647619\pi$
$138$	7.39428	0.629443
$139$	17.0977	1.45021	0.725104	−	0.688640i	$-0.241792\pi$
$139$	17.0977	1.45021	0.725104	+	0.688640i	$0.241792\pi$
$140$	−6.19421	−0.523506
$141$	3.93351	0.331261
$142$	−17.8041	−1.49409
$143$	3.00415	0.251219
$144$	−4.94486	−0.412071
$145$	13.1534	1.09233
$146$	−24.6237	−2.03787
$147$	18.8847	1.55758
$148$	5.95281	0.489318
$149$	−2.30424	−0.188770	−0.0943852	−	0.995536i	$-0.530089\pi$
$149$	−2.30424	−0.188770	−0.0943852	+	0.995536i	$0.530089\pi$
$150$	−4.10455	−0.335135
$151$	16.2878	1.32548	0.662741	−	0.748849i	$-0.269393\pi$
$151$	16.2878	1.32548	0.662741	+	0.748849i	$0.269393\pi$
$152$	−7.27000	−0.589675
$153$	1.00000	0.0808452
$154$	−41.9367	−3.37936
$155$	−8.39742	−0.674497
$156$	0.463736	0.0371286
$157$	−0.217354	−0.0173467	−0.00867337	−	0.999962i	$-0.502761\pi$
$157$	−0.217354	−0.0173467	−0.00867337	+	0.999962i	$0.502761\pi$
$158$	1.66288	0.132292
$159$	−5.66923	−0.449599
$160$	−6.54902	−0.517745
$161$	−22.6233	−1.78297
$162$	1.66288	0.130648
$163$	−0.257230	−0.0201478	−0.0100739	−	0.999949i	$-0.503207\pi$
$163$	−0.257230	−0.0201478	−0.0100739	+	0.999949i	$0.503207\pi$
$164$	0.809402	0.0632036
$165$	7.88706	0.614006
$166$	0.494106	0.0383501
$167$	−17.7368	−1.37251	−0.686257	−	0.727359i	$-0.740748\pi$
$167$	−17.7368	−1.37251	−0.686257	+	0.727359i	$0.740748\pi$
$168$	10.4469	0.805997
$169$	−12.6327	−0.971746
$170$	2.64585	0.202927
$171$	3.54053	0.270751
$172$	5.75498	0.438813
$173$	8.12880	0.618021	0.309011	−	0.951059i	$-0.400002\pi$
$173$	8.12880	0.618021	0.309011	+	0.951059i	$0.400002\pi$
$174$	13.7466	1.04213
$175$	12.5581	0.949307
$176$	−24.5113	−1.84761
$177$	1.55188	0.116646
$178$	5.76431	0.432053
$179$	19.7823	1.47860	0.739299	−	0.673377i	$-0.235157\pi$
$179$	19.7823	1.47860	0.739299	+	0.673377i	$0.235157\pi$
$180$	1.21749	0.0907461
$181$	6.48089	0.481721	0.240860	−	0.970560i	$-0.422570\pi$
$181$	6.48089	0.481721	0.240860	+	0.970560i	$0.422570\pi$
$182$	−5.12734	−0.380064
$183$	7.07996	0.523366
$184$	−9.13064	−0.673120
$185$	12.3784	0.910077
$186$	−8.77615	−0.643499
$187$	4.95692	0.362486
$188$	3.00982	0.219514
$189$	−5.08770	−0.370076
$190$	9.36768	0.679603
$191$	−12.7201	−0.920394	−0.460197	−	0.887817i	$-0.652221\pi$
$191$	−12.7201	−0.920394	−0.460197	+	0.887817i	$0.652221\pi$
$192$	3.04533	0.219778
$193$	−25.0419	−1.80255	−0.901276	−	0.433245i	$-0.857369\pi$
$193$	−25.0419	−1.80255	−0.901276	+	0.433245i	$0.857369\pi$
$194$	1.11644	0.0801560
$195$	0.964301	0.0690550
$196$	14.4501	1.03215
$197$	−21.0417	−1.49916	−0.749579	−	0.661915i	$-0.769744\pi$
$197$	−21.0417	−1.49916	−0.749579	+	0.661915i	$0.769744\pi$
$198$	8.24277	0.585788
$199$	10.5140	0.745317	0.372658	−	0.927969i	$-0.378446\pi$
$199$	10.5140	0.745317	0.372658	+	0.927969i	$0.378446\pi$
$200$	5.06840	0.358390
$201$	7.72942	0.545191
$202$	21.3810	1.50436
$203$	−42.0586	−2.95194
$204$	0.765175	0.0535730
$205$	1.68309	0.117552
$206$	20.7181	1.44350
$207$	4.44667	0.309065
$208$	−2.99684	−0.207793
$209$	17.5501	1.21397
$210$	−13.4613	−0.928916
$211$	20.7273	1.42693	0.713463	−	0.700693i	$-0.247126\pi$
$211$	20.7273	1.42693	0.713463	+	0.700693i	$0.247126\pi$
$212$	−4.33796	−0.297932
$213$	−10.7068	−0.733616
$214$	19.5676	1.33761
$215$	11.9670	0.816144
$216$	−2.05337	−0.139714
$217$	26.8512	1.82278
$218$	−15.4898	−1.04910
$219$	−14.8078	−1.00062
$220$	6.03498	0.406878
$221$	0.606051	0.0407674
$222$	12.9367	0.868252
$223$	9.06043	0.606731	0.303366	−	0.952874i	$-0.401890\pi$
$223$	9.06043	0.606731	0.303366	+	0.952874i	$0.401890\pi$
$224$	20.9409	1.39917
$225$	−2.46833	−0.164556
$226$	−18.6049	−1.23758
$227$	−26.7429	−1.77499	−0.887495	−	0.460818i	$-0.847556\pi$
$227$	−26.7429	−1.77499	−0.887495	+	0.460818i	$0.847556\pi$
$228$	2.70912	0.179416
$229$	−15.0923	−0.997329	−0.498664	−	0.866795i	$-0.666176\pi$
$229$	−15.0923	−0.997329	−0.498664	+	0.866795i	$0.666176\pi$
$230$	11.7652	0.775774
$231$	−25.2193	−1.65931
$232$	−16.9746	−1.11444
$233$	25.7987	1.69013	0.845063	−	0.534666i	$-0.179563\pi$
$233$	25.7987	1.69013	0.845063	+	0.534666i	$0.179563\pi$
$234$	1.00779	0.0658814
$235$	6.25868	0.408272
$236$	1.18746	0.0772971
$237$	1.00000	0.0649570
$238$	−8.46024	−0.548396
$239$	−12.9312	−0.836451	−0.418226	−	0.908343i	$-0.637348\pi$
$239$	−12.9312	−0.836451	−0.418226	+	0.908343i	$0.637348\pi$
$240$	−7.86787	−0.507869
$241$	16.4919	1.06234	0.531168	−	0.847267i	$-0.321753\pi$
$241$	16.4919	1.06234	0.531168	+	0.847267i	$0.321753\pi$
$242$	22.5670	1.45066
$243$	1.00000	0.0641500
$244$	5.41741	0.346814
$245$	30.0478	1.91968
$246$	1.75899	0.112149
$247$	2.14574	0.136530
$248$	10.8370	0.688151
$249$	0.297138	0.0188304
$250$	−19.7601	−1.24974
$251$	−18.0744	−1.14085	−0.570424	−	0.821350i	$-0.693221\pi$
$251$	−18.0744	−1.14085	−0.570424	+	0.821350i	$0.693221\pi$
$252$	−3.89298	−0.245235
$253$	22.0418	1.38575
$254$	−23.5016	−1.47462
$255$	1.59112	0.0996398
$256$	16.0190	1.00119
$257$	−1.09478	−0.0682903	−0.0341451	−	0.999417i	$-0.510871\pi$
$257$	−1.09478	−0.0682903	−0.0341451	+	0.999417i	$0.510871\pi$
$258$	12.5067	0.778635
$259$	−39.5806	−2.45942
$260$	0.737859	0.0457601
$261$	8.26672	0.511697
$262$	2.74066	0.169319
$263$	−30.3310	−1.87029	−0.935144	−	0.354268i	$-0.884730\pi$
$263$	−30.3310	−1.87029	−0.935144	+	0.354268i	$0.884730\pi$
$264$	−10.1784	−0.626436
$265$	−9.02043	−0.554121
$266$	−29.9537	−1.83658
$267$	3.46646	0.212144
$268$	5.91437	0.361277
$269$	5.00276	0.305024	0.152512	−	0.988302i	$-0.451264\pi$
$269$	5.00276	0.305024	0.152512	+	0.988302i	$0.451264\pi$
$270$	2.64585	0.161021
$271$	−19.1114	−1.16094	−0.580468	−	0.814283i	$-0.697130\pi$
$271$	−19.1114	−1.16094	−0.580468	+	0.814283i	$0.697130\pi$
$272$	−4.94486	−0.299826
$273$	−3.08341	−0.186616
$274$	−17.4126	−1.05194
$275$	−12.2353	−0.737818
$276$	3.40248	0.204805
$277$	−13.3579	−0.802597	−0.401298	−	0.915947i	$-0.631441\pi$
$277$	−13.3579	−0.802597	−0.401298	+	0.915947i	$0.631441\pi$
$278$	28.4314	1.70520
$279$	−5.27768	−0.315966
$280$	16.6223	0.993373
$281$	10.8122	0.645003	0.322502	−	0.946569i	$-0.395476\pi$
$281$	10.8122	0.645003	0.322502	+	0.946569i	$0.395476\pi$
$282$	6.54096	0.389508
$283$	−13.2510	−0.787690	−0.393845	−	0.919177i	$-0.628855\pi$
$283$	−13.2510	−0.787690	−0.393845	+	0.919177i	$0.628855\pi$
$284$	−8.19256	−0.486139
$285$	5.63340	0.333694
$286$	4.99554	0.295393
$287$	−5.38176	−0.317675
$288$	−4.11598	−0.242536
$289$	1.00000	0.0588235
$290$	21.8725	1.28440
$291$	0.671391	0.0393576
$292$	−11.3306	−0.663073
$293$	−17.1616	−1.00259	−0.501295	−	0.865276i	$-0.667143\pi$
$293$	−17.1616	−1.00259	−0.501295	+	0.865276i	$0.667143\pi$
$294$	31.4030	1.83146
$295$	2.46923	0.143764
$296$	−15.9745	−0.928500
$297$	4.95692	0.287630
$298$	−3.83167	−0.221963
$299$	2.69491	0.155851
$300$	−1.88871	−0.109045
$301$	−38.2652	−2.20557
$302$	27.0847	1.55855
$303$	12.8578	0.738661
$304$	−17.5074	−1.00412
$305$	11.2651	0.645036
$306$	1.66288	0.0950606
$307$	17.7631	1.01379	0.506897	−	0.862007i	$-0.330792\pi$
$307$	17.7631	1.01379	0.506897	+	0.862007i	$0.330792\pi$
$308$	−19.2972	−1.09956
$309$	12.4592	0.708777
$310$	−13.9639	−0.793097
$311$	11.8902	0.674233	0.337117	−	0.941463i	$-0.390548\pi$
$311$	11.8902	0.674233	0.337117	+	0.941463i	$0.390548\pi$
$312$	−1.24445	−0.0704529
$313$	10.7448	0.607333	0.303666	−	0.952778i	$-0.401789\pi$
$313$	10.7448	0.607333	0.303666	+	0.952778i	$0.401789\pi$
$314$	−0.361434	−0.0203969
$315$	−8.09514	−0.456110
$316$	0.765175	0.0430445
$317$	15.0540	0.845519	0.422759	−	0.906242i	$-0.361062\pi$
$317$	15.0540	0.845519	0.422759	+	0.906242i	$0.361062\pi$
$318$	−9.42726	−0.528654
$319$	40.9775	2.29430
$320$	4.84549	0.270871
$321$	11.7673	0.656785
$322$	−37.6199	−2.09648
$323$	3.54053	0.197000
$324$	0.765175	0.0425097
$325$	−1.49594	−0.0829797
$326$	−0.427744	−0.0236905
$327$	−9.31503	−0.515122
$328$	−2.17205	−0.119931
$329$	−20.0125	−1.10332
$330$	13.1152	0.721970
$331$	−9.68067	−0.532098	−0.266049	−	0.963960i	$-0.585718\pi$
$331$	−9.68067	−0.532098	−0.266049	+	0.963960i	$0.585718\pi$
$332$	0.227363	0.0124782
$333$	7.77967	0.426323
$334$	−29.4942	−1.61385
$335$	12.2984	0.671936
$336$	25.1579	1.37248
$337$	−21.5720	−1.17510	−0.587552	−	0.809187i	$-0.699908\pi$
$337$	−21.5720	−1.17510	−0.587552	+	0.809187i	$0.699908\pi$
$338$	−21.0067	−1.14261
$339$	−11.1883	−0.607668
$340$	1.21749	0.0660275
$341$	−26.1610	−1.41670
$342$	5.88748	0.318358
$343$	−60.4657	−3.26484
$344$	−15.4436	−0.832664
$345$	7.07519	0.380915
$346$	13.5172	0.726691
$347$	29.2882	1.57227	0.786136	−	0.618054i	$-0.212079\pi$
$347$	29.2882	1.57227	0.786136	+	0.618054i	$0.212079\pi$
$348$	6.32549	0.339082
$349$	−22.0866	−1.18227	−0.591133	−	0.806574i	$-0.701319\pi$
$349$	−22.0866	−1.18227	−0.591133	+	0.806574i	$0.701319\pi$
$350$	20.8827	1.11623
$351$	0.606051	0.0323486
$352$	−20.4026	−1.08746
$353$	−18.3089	−0.974487	−0.487243	−	0.873266i	$-0.661998\pi$
$353$	−18.3089	−0.974487	−0.487243	+	0.873266i	$0.661998\pi$
$354$	2.58059	0.137157
$355$	−17.0358	−0.904164
$356$	2.65245	0.140579
$357$	−5.08770	−0.269270
$358$	32.8956	1.73859
$359$	−15.3075	−0.807900	−0.403950	−	0.914781i	$-0.632363\pi$
$359$	−15.3075	−0.807900	−0.403950	+	0.914781i	$0.632363\pi$
$360$	−3.26715	−0.172194
$361$	−6.46468	−0.340246
$362$	10.7770	0.566424
$363$	13.5710	0.712295
$364$	−2.35935	−0.123663
$365$	−23.5610	−1.23324
$366$	11.7731	0.615392
$367$	13.9951	0.730536	0.365268	−	0.930902i	$-0.380977\pi$
$367$	13.9951	0.730536	0.365268	+	0.930902i	$0.380977\pi$
$368$	−21.9881	−1.14621
$369$	1.05780	0.0550668
$370$	20.5838	1.07010
$371$	28.8433	1.49747
$372$	−4.03835	−0.209379
$373$	25.1406	1.30173	0.650865	−	0.759193i	$-0.274406\pi$
$373$	25.1406	1.30173	0.650865	+	0.759193i	$0.274406\pi$
$374$	8.24277	0.426223
$375$	−11.8830	−0.613637
$376$	−8.07693	−0.416536
$377$	5.01006	0.258031
$378$	−8.46024	−0.435148
$379$	−2.82623	−0.145174	−0.0725869	−	0.997362i	$-0.523125\pi$
$379$	−2.82623	−0.145174	−0.0725869	+	0.997362i	$0.523125\pi$
$380$	4.31054	0.221126
$381$	−14.1331	−0.724059
$382$	−21.1520	−1.08223
$383$	−6.86294	−0.350680	−0.175340	−	0.984508i	$-0.556102\pi$
$383$	−6.86294	−0.350680	−0.175340	+	0.984508i	$0.556102\pi$
$384$	13.2960	0.678508
$385$	−40.1270	−2.04506
$386$	−41.6417	−2.11950
$387$	7.52112	0.382320
$388$	0.513732	0.0260808
$389$	−22.7961	−1.15581	−0.577905	−	0.816104i	$-0.696129\pi$
$389$	−22.7961	−1.15581	−0.577905	+	0.816104i	$0.696129\pi$
$390$	1.60352	0.0811973
$391$	4.44667	0.224878
$392$	−38.7772	−1.95854
$393$	1.64814	0.0831377
$394$	−34.9898	−1.76276
$395$	1.59112	0.0800580
$396$	3.79291	0.190601
$397$	23.1038	1.15955	0.579773	−	0.814778i	$-0.303141\pi$
$397$	23.1038	1.15955	0.579773	+	0.814778i	$0.303141\pi$
$398$	17.4835	0.876370
$399$	−18.0131	−0.901785
$400$	12.2056	0.610278
$401$	−28.6880	−1.43261	−0.716305	−	0.697787i	$-0.754168\pi$
$401$	−28.6880	−1.43261	−0.716305	+	0.697787i	$0.754168\pi$
$402$	12.8531	0.641055
$403$	−3.19854	−0.159331
$404$	9.83847	0.489482
$405$	1.59112	0.0790634
$406$	−69.9385	−3.47099
$407$	38.5632	1.91151
$408$	−2.05337	−0.101657
$409$	−22.2441	−1.09990	−0.549950	−	0.835198i	$-0.685353\pi$
$409$	−22.2441	−1.09990	−0.549950	+	0.835198i	$0.685353\pi$
$410$	2.79877	0.138221
$411$	−10.4714	−0.516514
$412$	9.53345	0.469679
$413$	−7.89550	−0.388512
$414$	7.39428	0.363409
$415$	0.472783	0.0232080
$416$	−2.49449	−0.122303
$417$	17.0977	0.837278
$418$	29.1837	1.42742
$419$	13.1588	0.642849	0.321425	−	0.946935i	$-0.395838\pi$
$419$	13.1588	0.642849	0.321425	+	0.946935i	$0.395838\pi$
$420$	−6.19421	−0.302246
$421$	−16.9465	−0.825921	−0.412961	−	0.910749i	$-0.635505\pi$
$421$	−16.9465	−0.825921	−0.412961	+	0.910749i	$0.635505\pi$
$422$	34.4670	1.67783
$423$	3.93351	0.191254
$424$	11.6410	0.565338
$425$	−2.46833	−0.119732
$426$	−17.8041	−0.862611
$427$	−36.0207	−1.74316
$428$	9.00403	0.435226
$429$	3.00415	0.145042
$430$	19.8997	0.959650
$431$	−16.5172	−0.795607	−0.397804	−	0.917471i	$-0.630227\pi$
$431$	−16.5172	−0.795607	−0.397804	+	0.917471i	$0.630227\pi$
$432$	−4.94486	−0.237910
$433$	20.1704	0.969329	0.484665	−	0.874700i	$-0.338942\pi$
$433$	20.1704	0.969329	0.484665	+	0.874700i	$0.338942\pi$
$434$	44.6504	2.14329
$435$	13.1534	0.630655
$436$	−7.12763	−0.341352
$437$	15.7435	0.753116
$438$	−24.6237	−1.17656
$439$	−13.5294	−0.645722	−0.322861	−	0.946446i	$-0.604645\pi$
$439$	−13.5294	−0.645722	−0.322861	+	0.946446i	$0.604645\pi$
$440$	−16.1950	−0.772067
$441$	18.8847	0.899271
$442$	1.00779	0.0479358
$443$	−4.38924	−0.208539	−0.104270	−	0.994549i	$-0.533250\pi$
$443$	−4.38924	−0.208539	−0.104270	+	0.994549i	$0.533250\pi$
$444$	5.95281	0.282508
$445$	5.51555	0.261462
$446$	15.0664	0.713416
$447$	−2.30424	−0.108987
$448$	−15.4937	−0.732010
$449$	−7.05618	−0.333002	−0.166501	−	0.986041i	$-0.553247\pi$
$449$	−7.05618	−0.333002	−0.166501	+	0.986041i	$0.553247\pi$
$450$	−4.10455	−0.193490
$451$	5.24342	0.246903
$452$	−8.56105	−0.402678
$453$	16.2878	0.765267
$454$	−44.4703	−2.08709
$455$	−4.90607	−0.230000
$456$	−7.27000	−0.340449
$457$	1.84339	0.0862301	0.0431150	−	0.999070i	$-0.486272\pi$
$457$	1.84339	0.0862301	0.0431150	+	0.999070i	$0.486272\pi$
$458$	−25.0967	−1.17269
$459$	1.00000	0.0466760
$460$	5.41376	0.252418
$461$	7.03319	0.327568	0.163784	−	0.986496i	$-0.447630\pi$
$461$	7.03319	0.327568	0.163784	+	0.986496i	$0.447630\pi$
$462$	−41.9367	−1.95107
$463$	3.01753	0.140236	0.0701182	−	0.997539i	$-0.477662\pi$
$463$	3.01753	0.140236	0.0701182	+	0.997539i	$0.477662\pi$
$464$	−40.8778	−1.89770
$465$	−8.39742	−0.389421
$466$	42.9001	1.98731
$467$	41.5130	1.92099	0.960495	−	0.278297i	$-0.0897699\pi$
$467$	41.5130	1.92099	0.960495	+	0.278297i	$0.0897699\pi$
$468$	0.463736	0.0214362
$469$	−39.3250	−1.81586
$470$	10.4075	0.480060
$471$	−0.217354	−0.0100151
$472$	−3.18658	−0.146674
$473$	37.2816	1.71421
$474$	1.66288	0.0763787
$475$	−8.73920	−0.400982
$476$	−3.89298	−0.178435
$477$	−5.66923	−0.259576
$478$	−21.5031	−0.983529
$479$	13.2940	0.607420	0.303710	−	0.952764i	$-0.401775\pi$
$479$	13.2940	0.607420	0.303710	+	0.952764i	$0.401775\pi$
$480$	−6.54902	−0.298920
$481$	4.71488	0.214980
$482$	27.4240	1.24913
$483$	−22.6233	−1.02940
$484$	10.3842	0.472010
$485$	1.06826	0.0485074
$486$	1.66288	0.0754298
$487$	10.2560	0.464742	0.232371	−	0.972627i	$-0.425352\pi$
$487$	10.2560	0.464742	0.232371	+	0.972627i	$0.425352\pi$
$488$	−14.5378	−0.658093
$489$	−0.257230	−0.0116324
$490$	49.9660	2.25723
$491$	31.7420	1.43250	0.716248	−	0.697845i	$-0.245858\pi$
$491$	31.7420	1.43250	0.716248	+	0.697845i	$0.245858\pi$
$492$	0.809402	0.0364906
$493$	8.26672	0.372314
$494$	3.56811	0.160537
$495$	7.88706	0.354497
$496$	26.0974	1.17181
$497$	54.4728	2.44344
$498$	0.494106	0.0221414
$499$	3.51948	0.157554	0.0787769	−	0.996892i	$-0.474899\pi$
$499$	3.51948	0.157554	0.0787769	+	0.996892i	$0.474899\pi$
$500$	−9.09260	−0.406633
$501$	−17.7368	−0.792422
$502$	−30.0557	−1.34145
$503$	−3.53020	−0.157404	−0.0787018	−	0.996898i	$-0.525078\pi$
$503$	−3.53020	−0.157404	−0.0787018	+	0.996898i	$0.525078\pi$
$504$	10.4469	0.465343
$505$	20.4583	0.910383
$506$	36.6529	1.62942
$507$	−12.6327	−0.561038
$508$	−10.8143	−0.479806
$509$	−9.47027	−0.419762	−0.209881	−	0.977727i	$-0.567308\pi$
$509$	−9.47027	−0.419762	−0.209881	+	0.977727i	$0.567308\pi$
$510$	2.64585	0.117160
$511$	75.3378	3.33275
$512$	0.0457116	0.00202019
$513$	3.54053	0.156318
$514$	−1.82048	−0.0802981
$515$	19.8240	0.873551
$516$	5.75498	0.253349
$517$	19.4981	0.857524
$518$	−65.8179	−2.89187
$519$	8.12880	0.356815
$520$	−1.98006	−0.0868315
$521$	−6.02690	−0.264043	−0.132022	−	0.991247i	$-0.542147\pi$
$521$	−6.02690	−0.264043	−0.132022	+	0.991247i	$0.542147\pi$
$522$	13.7466	0.601672
$523$	7.16799	0.313434	0.156717	−	0.987644i	$-0.449909\pi$
$523$	7.16799	0.313434	0.156717	+	0.987644i	$0.449909\pi$
$524$	1.26112	0.0550922
$525$	12.5581	0.548082
$526$	−50.4368	−2.19915
$527$	−5.27768	−0.229899
$528$	−24.5113	−1.06672
$529$	−3.22713	−0.140310
$530$	−14.9999	−0.651554
$531$	1.55188	0.0673459
$532$	−13.7832	−0.597578
$533$	0.641080	0.0277683
$534$	5.76431	0.249446
$535$	18.7232	0.809473
$536$	−15.8713	−0.685538
$537$	19.7823	0.853669
$538$	8.31900	0.358657
$539$	93.6099	4.03206
$540$	1.21749	0.0523923
$541$	37.3149	1.60429	0.802147	−	0.597127i	$-0.203691\pi$
$541$	37.3149	1.60429	0.802147	+	0.597127i	$0.203691\pi$
$542$	−31.7800	−1.36507
$543$	6.48089	0.278122
$544$	−4.11598	−0.176471
$545$	−14.8213	−0.634877
$546$	−5.12734	−0.219430
$547$	−18.9889	−0.811907	−0.405953	−	0.913894i	$-0.633060\pi$
$547$	−18.9889	−0.811907	−0.405953	+	0.913894i	$0.633060\pi$
$548$	−8.01243	−0.342274
$549$	7.07996	0.302165
$550$	−20.3459	−0.867553
$551$	29.2685	1.24688
$552$	−9.13064	−0.388626
$553$	−5.08770	−0.216351
$554$	−22.2126	−0.943721
$555$	12.3784	0.525433
$556$	13.0827	0.554832
$557$	24.1703	1.02413	0.512064	−	0.858947i	$-0.328881\pi$
$557$	24.1703	1.02413	0.512064	+	0.858947i	$0.328881\pi$
$558$	−8.77615	−0.371524
$559$	4.55819	0.192791
$560$	40.0293	1.69155
$561$	4.95692	0.209281
$562$	17.9795	0.758417
$563$	−35.1250	−1.48034	−0.740171	−	0.672419i	$-0.765255\pi$
$563$	−35.1250	−1.48034	−0.740171	+	0.672419i	$0.765255\pi$
$564$	3.00982	0.126736
$565$	−17.8020	−0.748936
$566$	−22.0348	−0.926193
$567$	−5.08770	−0.213663
$568$	21.9849	0.922467
$569$	−4.38294	−0.183742	−0.0918712	−	0.995771i	$-0.529285\pi$
$569$	−4.38294	−0.183742	−0.0918712	+	0.995771i	$0.529285\pi$
$570$	9.36768	0.392369
$571$	28.2931	1.18403	0.592016	−	0.805927i	$-0.298332\pi$
$571$	28.2931	1.18403	0.592016	+	0.805927i	$0.298332\pi$
$572$	2.29870	0.0961135
$573$	−12.7201	−0.531390
$574$	−8.94923	−0.373534
$575$	−10.9759	−0.457725
$576$	3.04533	0.126889
$577$	−3.43189	−0.142872	−0.0714358	−	0.997445i	$-0.522758\pi$
$577$	−3.43189	−0.142872	−0.0714358	+	0.997445i	$0.522758\pi$
$578$	1.66288	0.0691668
$579$	−25.0419	−1.04070
$580$	10.0646	0.417911
$581$	−1.51175	−0.0627180
$582$	1.11644	0.0462781
$583$	−28.1019	−1.16386
$584$	30.4059	1.25821
$585$	0.964301	0.0398689
$586$	−28.5377	−1.17888
$587$	10.8010	0.445806	0.222903	−	0.974841i	$-0.428447\pi$
$587$	10.8010	0.445806	0.222903	+	0.974841i	$0.428447\pi$
$588$	14.4501	0.595912
$589$	−18.6857	−0.769933
$590$	4.10603	0.169043
$591$	−21.0417	−0.865539
$592$	−38.4693	−1.58108
$593$	6.74254	0.276883	0.138442	−	0.990371i	$-0.455791\pi$
$593$	6.74254	0.276883	0.138442	+	0.990371i	$0.455791\pi$
$594$	8.24277	0.338205
$595$	−8.09514	−0.331869
$596$	−1.76315	−0.0722212
$597$	10.5140	0.430309
$598$	4.48132	0.183255
$599$	11.6232	0.474910	0.237455	−	0.971398i	$-0.423687\pi$
$599$	11.6232	0.474910	0.237455	+	0.971398i	$0.423687\pi$
$600$	5.06840	0.206916
$601$	25.9422	1.05820	0.529101	−	0.848559i	$-0.322529\pi$
$601$	25.9422	1.05820	0.529101	+	0.848559i	$0.322529\pi$
$602$	−63.6305	−2.59339
$603$	7.72942	0.314766
$604$	12.4630	0.507113
$605$	21.5932	0.877887
$606$	21.3810	0.868544
$607$	3.62244	0.147030	0.0735151	−	0.997294i	$-0.476578\pi$
$607$	3.62244	0.147030	0.0735151	+	0.997294i	$0.476578\pi$
$608$	−14.5727	−0.591002
$609$	−42.0586	−1.70430
$610$	18.7325	0.758456
$611$	2.38391	0.0964426
$612$	0.765175	0.0309304
$613$	−8.49895	−0.343269	−0.171635	−	0.985161i	$-0.554905\pi$
$613$	−8.49895	−0.343269	−0.171635	+	0.985161i	$0.554905\pi$
$614$	29.5379	1.19205
$615$	1.68309	0.0678686
$616$	51.7845	2.08646
$617$	27.0735	1.08994	0.544970	−	0.838456i	$-0.316541\pi$
$617$	27.0735	1.08994	0.544970	+	0.838456i	$0.316541\pi$
$618$	20.7181	0.833405
$619$	−29.6565	−1.19199	−0.595997	−	0.802986i	$-0.703243\pi$
$619$	−29.6565	−1.19199	−0.595997	+	0.802986i	$0.703243\pi$
$620$	−6.42550	−0.258054
$621$	4.44667	0.178439
$622$	19.7721	0.792787
$623$	−17.6363	−0.706583
$624$	−2.99684	−0.119970
$625$	−6.56565	−0.262626
$626$	17.8674	0.714123
$627$	17.5501	0.700883
$628$	−0.166314	−0.00663665
$629$	7.77967	0.310196
$630$	−13.4613	−0.536310
$631$	31.7839	1.26530	0.632649	−	0.774439i	$-0.281968\pi$
$631$	31.7839	1.26530	0.632649	+	0.774439i	$0.281968\pi$
$632$	−2.05337	−0.0816786
$633$	20.7273	0.823836
$634$	25.0331	0.994191
$635$	−22.4874	−0.892386
$636$	−4.33796	−0.172011
$637$	11.4451	0.453471
$638$	68.1407	2.69772
$639$	−10.7068	−0.423553
$640$	21.1555	0.836245
$641$	−2.43171	−0.0960469	−0.0480234	−	0.998846i	$-0.515292\pi$
$641$	−2.43171	−0.0960469	−0.0480234	+	0.998846i	$0.515292\pi$
$642$	19.5676	0.772271
$643$	−42.8242	−1.68882	−0.844412	−	0.535695i	$-0.820050\pi$
$643$	−42.8242	−1.68882	−0.844412	+	0.535695i	$0.820050\pi$
$644$	−17.3108	−0.682141
$645$	11.9670	0.471201
$646$	5.88748	0.231640
$647$	−4.67436	−0.183768	−0.0918840	−	0.995770i	$-0.529289\pi$
$647$	−4.67436	−0.183768	−0.0918840	+	0.995770i	$0.529289\pi$
$648$	−2.05337	−0.0806639
$649$	7.69254	0.301959
$650$	−2.48757	−0.0975704
$651$	26.8512	1.05238
$652$	−0.196826	−0.00770832
$653$	17.2752	0.676029	0.338015	−	0.941141i	$-0.390245\pi$
$653$	17.2752	0.676029	0.338015	+	0.941141i	$0.390245\pi$
$654$	−15.4898	−0.605699
$655$	2.62239	0.102465
$656$	−5.23066	−0.204223
$657$	−14.8078	−0.577709
$658$	−33.2784	−1.29733
$659$	1.62390	0.0632583	0.0316291	−	0.999500i	$-0.489930\pi$
$659$	1.62390	0.0632583	0.0316291	+	0.999500i	$0.489930\pi$
$660$	6.03498	0.234911
$661$	−25.1731	−0.979120	−0.489560	−	0.871969i	$-0.662843\pi$
$661$	−25.1731	−0.979120	−0.489560	+	0.871969i	$0.662843\pi$
$662$	−16.0978	−0.625659
$663$	0.606051	0.0235371
$664$	−0.610134	−0.0236778
$665$	−28.6611	−1.11143
$666$	12.9367	0.501286
$667$	36.7594	1.42333
$668$	−13.5718	−0.525107
$669$	9.06043	0.350297
$670$	20.4509	0.790086
$671$	35.0948	1.35482
$672$	20.9409	0.807811
$673$	−40.5297	−1.56230	−0.781152	−	0.624340i	$-0.785368\pi$
$673$	−40.5297	−1.56230	−0.781152	+	0.624340i	$0.785368\pi$
$674$	−35.8717	−1.38173
$675$	−2.46833	−0.0950063
$676$	−9.66623	−0.371778
$677$	26.2429	1.00860	0.504298	−	0.863529i	$-0.331751\pi$
$677$	26.2429	1.00860	0.504298	+	0.863529i	$0.331751\pi$
$678$	−18.6049	−0.714517
$679$	−3.41584	−0.131088
$680$	−3.26715	−0.125290
$681$	−26.7429	−1.02479
$682$	−43.5027	−1.66580
$683$	−3.49207	−0.133620	−0.0668102	−	0.997766i	$-0.521282\pi$
$683$	−3.49207	−0.133620	−0.0668102	+	0.997766i	$0.521282\pi$
$684$	2.70912	0.103586
$685$	−16.6612	−0.636592
$686$	−100.547	−3.83892
$687$	−15.0923	−0.575808
$688$	−37.1909	−1.41789
$689$	−3.43585	−0.130895
$690$	11.7652	0.447893
$691$	22.1758	0.843609	0.421804	−	0.906687i	$-0.361397\pi$
$691$	22.1758	0.843609	0.421804	+	0.906687i	$0.361397\pi$
$692$	6.21996	0.236447
$693$	−25.2193	−0.958003
$694$	48.7028	1.84873
$695$	27.2045	1.03193
$696$	−16.9746	−0.643421
$697$	1.05780	0.0400670
$698$	−36.7273	−1.39015
$699$	25.7987	0.975795
$700$	9.60919	0.363193
$701$	12.7567	0.481816	0.240908	−	0.970548i	$-0.422555\pi$
$701$	12.7567	0.481816	0.240908	+	0.970548i	$0.422555\pi$
$702$	1.00779	0.0380366
$703$	27.5441	1.03885
$704$	15.0955	0.568931
$705$	6.25868	0.235716
$706$	−30.4456	−1.14584
$707$	−65.4166	−2.46024
$708$	1.18746	0.0446275
$709$	−4.17730	−0.156882	−0.0784410	−	0.996919i	$-0.524994\pi$
$709$	−4.17730	−0.156882	−0.0784410	+	0.996919i	$0.524994\pi$
$710$	−28.3285	−1.06315
$711$	1.00000	0.0375029
$712$	−7.11791	−0.266755
$713$	−23.4681	−0.878886
$714$	−8.46024	−0.316617
$715$	4.77996	0.178760
$716$	15.1369	0.565694
$717$	−12.9312	−0.482925
$718$	−25.4546	−0.949958
$719$	−39.3963	−1.46924	−0.734618	−	0.678481i	$-0.762638\pi$
$719$	−39.3963	−1.46924	−0.734618	+	0.678481i	$0.762638\pi$
$720$	−7.86787	−0.293218
$721$	−63.3885	−2.36071
$722$	−10.7500	−0.400073
$723$	16.4919	0.613340
$724$	4.95902	0.184300
$725$	−20.4050	−0.757824
$726$	22.5670	0.837541
$727$	−6.38151	−0.236677	−0.118339	−	0.992973i	$-0.537757\pi$
$727$	−6.38151	−0.236677	−0.118339	+	0.992973i	$0.537757\pi$
$728$	6.33137	0.234656
$729$	1.00000	0.0370370
$730$	−39.1792	−1.45009
$731$	7.52112	0.278179
$732$	5.41741	0.200233
$733$	−28.1963	−1.04145	−0.520727	−	0.853723i	$-0.674339\pi$
$733$	−28.1963	−1.04145	−0.520727	+	0.853723i	$0.674339\pi$
$734$	23.2721	0.858990
$735$	30.0478	1.10833
$736$	−18.3024	−0.674635
$737$	38.3141	1.41132
$738$	1.75899	0.0647495
$739$	43.2845	1.59225	0.796123	−	0.605135i	$-0.206881\pi$
$739$	43.2845	1.59225	0.796123	+	0.605135i	$0.206881\pi$
$740$	9.47164	0.348184
$741$	2.14574	0.0788257
$742$	47.9631	1.76078
$743$	32.1611	1.17987	0.589937	−	0.807449i	$-0.299152\pi$
$743$	32.1611	1.17987	0.589937	+	0.807449i	$0.299152\pi$
$744$	10.8370	0.397304
$745$	−3.66632	−0.134324
$746$	41.8058	1.53062
$747$	0.297138	0.0108717
$748$	3.79291	0.138683
$749$	−59.8684	−2.18754
$750$	−19.7601	−0.721535
$751$	44.3318	1.61769	0.808845	−	0.588022i	$-0.200093\pi$
$751$	44.3318	1.61769	0.808845	+	0.588022i	$0.200093\pi$
$752$	−19.4506	−0.709292
$753$	−18.0744	−0.658669
$754$	8.33113	0.303402
$755$	25.9158	0.943174
$756$	−3.89298	−0.141586
$757$	−36.3644	−1.32169	−0.660843	−	0.750524i	$-0.729801\pi$
$757$	−36.3644	−1.32169	−0.660843	+	0.750524i	$0.729801\pi$
$758$	−4.69969	−0.170700
$759$	22.0418	0.800066
$760$	−11.5674	−0.419595
$761$	16.4643	0.596831	0.298415	−	0.954436i	$-0.403542\pi$
$761$	16.4643	0.596831	0.298415	+	0.954436i	$0.403542\pi$
$762$	−23.5016	−0.851374
$763$	47.3921	1.71571
$764$	−9.73311	−0.352132
$765$	1.59112	0.0575271
$766$	−11.4123	−0.412342
$767$	0.940519	0.0339602
$768$	16.0190	0.578035
$769$	−42.2499	−1.52357	−0.761786	−	0.647829i	$-0.775677\pi$
$769$	−42.2499	−1.52357	−0.761786	+	0.647829i	$0.775677\pi$
$770$	−66.7264	−2.40465
$771$	−1.09478	−0.0394274
$772$	−19.1614	−0.689634
$773$	−21.2901	−0.765752	−0.382876	−	0.923800i	$-0.625066\pi$
$773$	−21.2901	−0.765752	−0.382876	+	0.923800i	$0.625066\pi$
$774$	12.5067	0.449545
$775$	13.0271	0.467946
$776$	−1.37861	−0.0494893
$777$	−39.5806	−1.41995
$778$	−37.9073	−1.35904
$779$	3.74516	0.134184
$780$	0.737859	0.0264196
$781$	−53.0726	−1.89909
$782$	7.39428	0.264419
$783$	8.26672	0.295429
$784$	−93.3821	−3.33507
$785$	−0.345837	−0.0123434
$786$	2.74066	0.0977563
$787$	−11.8451	−0.422233	−0.211117	−	0.977461i	$-0.567710\pi$
$787$	−11.8451	−0.422233	−0.211117	+	0.977461i	$0.567710\pi$
$788$	−16.1006	−0.573559
$789$	−30.3310	−1.07981
$790$	2.64585	0.0941350
$791$	56.9230	2.02395
$792$	−10.1784	−0.361673
$793$	4.29082	0.152371
$794$	38.4189	1.36343
$795$	−9.02043	−0.319922
$796$	8.04505	0.285149
$797$	−16.7464	−0.593187	−0.296593	−	0.955004i	$-0.595851\pi$
$797$	−16.7464	−0.593187	−0.296593	+	0.955004i	$0.595851\pi$
$798$	−29.9537	−1.06035
$799$	3.93351	0.139157
$800$	10.1596	0.359197
$801$	3.46646	0.122481
$802$	−47.7047	−1.68451
$803$	−73.4012	−2.59027
$804$	5.91437	0.208584
$805$	−35.9964	−1.26871
$806$	−5.31880	−0.187347
$807$	5.00276	0.176105
$808$	−26.4018	−0.928811
$809$	29.0673	1.02195	0.510976	−	0.859595i	$-0.329284\pi$
$809$	29.0673	1.02195	0.510976	+	0.859595i	$0.329284\pi$
$810$	2.64585	0.0929655
$811$	27.9403	0.981116	0.490558	−	0.871409i	$-0.336793\pi$
$811$	27.9403	0.981116	0.490558	+	0.871409i	$0.336793\pi$
$812$	−32.1822	−1.12937
$813$	−19.1114	−0.670267
$814$	64.1260	2.24761
$815$	−0.409285	−0.0143366
$816$	−4.94486	−0.173105
$817$	26.6287	0.931621
$818$	−36.9893	−1.29330
$819$	−3.08341	−0.107743
$820$	1.28786	0.0449739
$821$	−32.2455	−1.12537	−0.562687	−	0.826670i	$-0.690232\pi$
$821$	−32.2455	−1.12537	−0.562687	+	0.826670i	$0.690232\pi$
$822$	−17.4126	−0.607335
$823$	−21.6304	−0.753988	−0.376994	−	0.926216i	$-0.623042\pi$
$823$	−21.6304	−0.753988	−0.376994	+	0.926216i	$0.623042\pi$
$824$	−25.5832	−0.891234
$825$	−12.2353	−0.425980
$826$	−13.1293	−0.456826
$827$	−24.5102	−0.852304	−0.426152	−	0.904652i	$-0.640131\pi$
$827$	−24.5102	−0.852304	−0.426152	+	0.904652i	$0.640131\pi$
$828$	3.40248	0.118244
$829$	−38.0015	−1.31985	−0.659923	−	0.751333i	$-0.729411\pi$
$829$	−38.0015	−1.31985	−0.659923	+	0.751333i	$0.729411\pi$
$830$	0.786182	0.0272888
$831$	−13.3579	−0.463379
$832$	1.84563	0.0639856
$833$	18.8847	0.654316
$834$	28.4314	0.984500
$835$	−28.2214	−0.976642
$836$	13.4289	0.464448
$837$	−5.27768	−0.182423
$838$	21.8815	0.755884
$839$	31.2249	1.07800	0.539001	−	0.842305i	$-0.318802\pi$
$839$	31.2249	1.07800	0.539001	+	0.842305i	$0.318802\pi$
$840$	16.6223	0.573524
$841$	39.3387	1.35651
$842$	−28.1800	−0.971147
$843$	10.8122	0.372393
$844$	15.8600	0.545924
$845$	−20.1002	−0.691466
$846$	6.54096	0.224883
$847$	−69.0454	−2.37243
$848$	28.0335	0.962676
$849$	−13.2510	−0.454773
$850$	−4.10455	−0.140785
$851$	34.5936	1.18585
$852$	−8.19256	−0.280672
$853$	−16.8970	−0.578543	−0.289271	−	0.957247i	$-0.593413\pi$
$853$	−16.8970	−0.578543	−0.289271	+	0.957247i	$0.593413\pi$
$854$	−59.8982	−2.04967
$855$	5.63340	0.192658
$856$	−24.1625	−0.825858
$857$	44.3593	1.51528	0.757642	−	0.652671i	$-0.226351\pi$
$857$	44.3593	1.51528	0.757642	+	0.652671i	$0.226351\pi$
$858$	4.99554	0.170545
$859$	4.39551	0.149973	0.0749864	−	0.997185i	$-0.476109\pi$
$859$	4.39551	0.149973	0.0749864	+	0.997185i	$0.476109\pi$
$860$	9.15686	0.312246
$861$	−5.38176	−0.183410
$862$	−27.4662	−0.935503
$863$	1.29184	0.0439748	0.0219874	−	0.999758i	$-0.493001\pi$
$863$	1.29184	0.0439748	0.0219874	+	0.999758i	$0.493001\pi$
$864$	−4.11598	−0.140028
$865$	12.9339	0.439766
$866$	33.5410	1.13977
$867$	1.00000	0.0339618
$868$	20.5459	0.697373
$869$	4.95692	0.168152
$870$	21.8725	0.741546
$871$	4.68443	0.158726
$872$	19.1272	0.647728
$873$	0.671391	0.0227231
$874$	26.1797	0.885540
$875$	60.4572	2.04383
$876$	−11.3306	−0.382825
$877$	−12.8797	−0.434916	−0.217458	−	0.976070i	$-0.569777\pi$
$877$	−12.8797	−0.434916	−0.217458	+	0.976070i	$0.569777\pi$
$878$	−22.4977	−0.759262
$879$	−17.1616	−0.578846
$880$	−39.0004	−1.31470
$881$	−25.9750	−0.875121	−0.437560	−	0.899189i	$-0.644157\pi$
$881$	−25.9750	−0.875121	−0.437560	+	0.899189i	$0.644157\pi$
$882$	31.4030	1.05739
$883$	−52.7633	−1.77563	−0.887813	−	0.460204i	$-0.847776\pi$
$883$	−52.7633	−1.77563	−0.887813	+	0.460204i	$0.847776\pi$
$884$	0.463736	0.0155971
$885$	2.46923	0.0830022
$886$	−7.29879	−0.245208
$887$	−43.2203	−1.45120	−0.725598	−	0.688119i	$-0.758437\pi$
$887$	−43.2203	−1.45120	−0.725598	+	0.688119i	$0.758437\pi$
$888$	−15.9745	−0.536069
$889$	71.9048	2.41161
$890$	9.17171	0.307436
$891$	4.95692	0.166063
$892$	6.93282	0.232128
$893$	13.9267	0.466039
$894$	−3.83167	−0.128150
$895$	31.4760	1.05213
$896$	−67.6460	−2.25989
$897$	2.69491	0.0899804
$898$	−11.7336	−0.391555
$899$	−43.6291	−1.45511
$900$	−1.88871	−0.0629570
$901$	−5.66923	−0.188869
$902$	8.71919	0.290317
$903$	−38.2652	−1.27339
$904$	22.9738	0.764097
$905$	10.3119	0.342778
$906$	27.0847	0.899828
$907$	−26.1662	−0.868834	−0.434417	−	0.900712i	$-0.643046\pi$
$907$	−26.1662	−0.868834	−0.434417	+	0.900712i	$0.643046\pi$
$908$	−20.4630	−0.679089
$909$	12.8578	0.426466
$910$	−8.15822	−0.270442
$911$	−54.9617	−1.82096	−0.910482	−	0.413549i	$-0.864289\pi$
$911$	−54.9617	−1.82096	−0.910482	+	0.413549i	$0.864289\pi$
$912$	−17.5074	−0.579728
$913$	1.47289	0.0487456
$914$	3.06534	0.101392
$915$	11.2651	0.372412
$916$	−11.5483	−0.381566
$917$	−8.38525	−0.276905
$918$	1.66288	0.0548833
$919$	−18.0423	−0.595162	−0.297581	−	0.954697i	$-0.596180\pi$
$919$	−18.0423	−0.595162	−0.297581	+	0.954697i	$0.596180\pi$
$920$	−14.5280	−0.478973
$921$	17.7631	0.585314
$922$	11.6954	0.385166
$923$	−6.48885	−0.213583
$924$	−19.2972	−0.634831
$925$	−19.2028	−0.631385
$926$	5.01779	0.164895
$927$	12.4592	0.409213
$928$	−34.0257	−1.11695
$929$	41.4962	1.36145	0.680723	−	0.732541i	$-0.261666\pi$
$929$	41.4962	1.36145	0.680723	+	0.732541i	$0.261666\pi$
$930$	−13.9639	−0.457895
$931$	66.8617	2.19130
$932$	19.7405	0.646622
$933$	11.8902	0.389269
$934$	69.0311	2.25877
$935$	7.88706	0.257934
$936$	−1.24445	−0.0406760
$937$	18.0915	0.591022	0.295511	−	0.955339i	$-0.404510\pi$
$937$	18.0915	0.591022	0.295511	+	0.955339i	$0.404510\pi$
$938$	−65.3928	−2.13515
$939$	10.7448	0.350644
$940$	4.78899	0.156200
$941$	43.1717	1.40736	0.703679	−	0.710518i	$-0.251539\pi$
$941$	43.1717	1.40736	0.703679	+	0.710518i	$0.251539\pi$
$942$	−0.361434	−0.0117762
$943$	4.70368	0.153173
$944$	−7.67383	−0.249762
$945$	−8.09514	−0.263335
$946$	61.9949	2.01563
$947$	−12.3326	−0.400757	−0.200378	−	0.979719i	$-0.564217\pi$
$947$	−12.3326	−0.400757	−0.200378	+	0.979719i	$0.564217\pi$
$948$	0.765175	0.0248517
$949$	−8.97431	−0.291318
$950$	−14.5323	−0.471489
$951$	15.0540	0.488161
$952$	10.4469	0.338586
$953$	−37.1721	−1.20412	−0.602061	−	0.798450i	$-0.705653\pi$
$953$	−37.1721	−1.20412	−0.602061	+	0.798450i	$0.705653\pi$
$954$	−9.42726	−0.305219
$955$	−20.2392	−0.654926
$956$	−9.89465	−0.320016
$957$	40.9775	1.32461
$958$	22.1064	0.714226
$959$	53.2751	1.72034
$960$	4.84549	0.156387
$961$	−3.14614	−0.101488
$962$	7.84028	0.252781
$963$	11.7673	0.379195
$964$	12.6192	0.406436
$965$	−39.8446	−1.28264
$966$	−37.6199	−1.21040
$967$	25.9909	0.835811	0.417906	−	0.908490i	$-0.362764\pi$
$967$	25.9909	0.835811	0.417906	+	0.908490i	$0.362764\pi$
$968$	−27.8663	−0.895658
$969$	3.54053	0.113738
$970$	1.77640	0.0570367
$971$	53.4931	1.71667	0.858337	−	0.513086i	$-0.171498\pi$
$971$	53.4931	1.71667	0.858337	+	0.513086i	$0.171498\pi$
$972$	0.765175	0.0245430
$973$	−86.9879	−2.78871
$974$	17.0545	0.546460
$975$	−1.49594	−0.0479084
$976$	−35.0094	−1.12062
$977$	−44.7529	−1.43177	−0.715886	−	0.698217i	$-0.753977\pi$
$977$	−44.7529	−1.43177	−0.715886	+	0.698217i	$0.753977\pi$
$978$	−0.427744	−0.0136777
$979$	17.1829	0.549169
$980$	22.9919	0.734448
$981$	−9.31503	−0.297406
$982$	52.7832	1.68438
$983$	−36.0291	−1.14915	−0.574574	−	0.818453i	$-0.694832\pi$
$983$	−36.0291	−1.14915	−0.574574	+	0.818453i	$0.694832\pi$
$984$	−2.17205	−0.0692424
$985$	−33.4799	−1.06676
$986$	13.7466	0.437780
$987$	−20.0125	−0.637005
$988$	1.64187	0.0522348
$989$	33.4439	1.06346
$990$	13.1152	0.416830
$991$	−22.8116	−0.724635	−0.362318	−	0.932055i	$-0.618014\pi$
$991$	−22.8116	−0.724635	−0.362318	+	0.932055i	$0.618014\pi$
$992$	21.7228	0.689700
$993$	−9.68067	−0.307207
$994$	90.5819	2.87308
$995$	16.7290	0.530346
$996$	0.227363	0.00720427
$997$	16.4010	0.519426	0.259713	−	0.965686i	$-0.416372\pi$
$997$	16.4010	0.519426	0.259713	+	0.965686i	$0.416372\pi$
$998$	5.85248	0.185257
$999$	7.77967	0.246138

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.k.1.23	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.k.1.23	✓	31	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)

\(f(q)\)	\(=\)	\(q+1.66288 q^{2} +1.00000 q^{3} +0.765175 q^{4} +1.59112 q^{5} +1.66288 q^{6} -5.08770 q^{7} -2.05337 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.66288 q^{2} +1.00000 q^{3} +0.765175 q^{4} +1.59112 q^{5} +1.66288 q^{6} -5.08770 q^{7} -2.05337 q^{8} +1.00000 q^{9} +2.64585 q^{10} +4.95692 q^{11} +0.765175 q^{12} +0.606051 q^{13} -8.46024 q^{14} +1.59112 q^{15} -4.94486 q^{16} +1.00000 q^{17} +1.66288 q^{18} +3.54053 q^{19} +1.21749 q^{20} -5.08770 q^{21} +8.24277 q^{22} +4.44667 q^{23} -2.05337 q^{24} -2.46833 q^{25} +1.00779 q^{26} +1.00000 q^{27} -3.89298 q^{28} +8.26672 q^{29} +2.64585 q^{30} -5.27768 q^{31} -4.11598 q^{32} +4.95692 q^{33} +1.66288 q^{34} -8.09514 q^{35} +0.765175 q^{36} +7.77967 q^{37} +5.88748 q^{38} +0.606051 q^{39} -3.26715 q^{40} +1.05780 q^{41} -8.46024 q^{42} +7.52112 q^{43} +3.79291 q^{44} +1.59112 q^{45} +7.39428 q^{46} +3.93351 q^{47} -4.94486 q^{48} +18.8847 q^{49} -4.10455 q^{50} +1.00000 q^{51} +0.463736 q^{52} -5.66923 q^{53} +1.66288 q^{54} +7.88706 q^{55} +10.4469 q^{56} +3.54053 q^{57} +13.7466 q^{58} +1.55188 q^{59} +1.21749 q^{60} +7.07996 q^{61} -8.77615 q^{62} -5.08770 q^{63} +3.04533 q^{64} +0.964301 q^{65} +8.24277 q^{66} +7.72942 q^{67} +0.765175 q^{68} +4.44667 q^{69} -13.4613 q^{70} -10.7068 q^{71} -2.05337 q^{72} -14.8078 q^{73} +12.9367 q^{74} -2.46833 q^{75} +2.70912 q^{76} -25.2193 q^{77} +1.00779 q^{78} +1.00000 q^{79} -7.86787 q^{80} +1.00000 q^{81} +1.75899 q^{82} +0.297138 q^{83} -3.89298 q^{84} +1.59112 q^{85} +12.5067 q^{86} +8.26672 q^{87} -10.1784 q^{88} +3.46646 q^{89} +2.64585 q^{90} -3.08341 q^{91} +3.40248 q^{92} -5.27768 q^{93} +6.54096 q^{94} +5.63340 q^{95} -4.11598 q^{96} +0.671391 q^{97} +31.4030 q^{98} +4.95692 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * q^99

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