LMFDB - Embedded newform 4029.2.a.f.1.20

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			1.20
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)

$f(q)$	$=$	$q+2.37194 q^{2} -1.00000 q^{3} +3.62611 q^{4} -0.369639 q^{5} -2.37194 q^{6} -3.46859 q^{7} +3.85703 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.37194 q^{2} -1.00000 q^{3} +3.62611 q^{4} -0.369639 q^{5} -2.37194 q^{6} -3.46859 q^{7} +3.85703 q^{8} +1.00000 q^{9} -0.876762 q^{10} -0.755512 q^{11} -3.62611 q^{12} +1.48857 q^{13} -8.22730 q^{14} +0.369639 q^{15} +1.89644 q^{16} +1.00000 q^{17} +2.37194 q^{18} +5.19396 q^{19} -1.34035 q^{20} +3.46859 q^{21} -1.79203 q^{22} +0.713417 q^{23} -3.85703 q^{24} -4.86337 q^{25} +3.53081 q^{26} -1.00000 q^{27} -12.5775 q^{28} -8.05401 q^{29} +0.876762 q^{30} -10.2118 q^{31} -3.21581 q^{32} +0.755512 q^{33} +2.37194 q^{34} +1.28213 q^{35} +3.62611 q^{36} -1.46546 q^{37} +12.3198 q^{38} -1.48857 q^{39} -1.42571 q^{40} -2.84725 q^{41} +8.22730 q^{42} +5.46367 q^{43} -2.73957 q^{44} -0.369639 q^{45} +1.69218 q^{46} -7.61120 q^{47} -1.89644 q^{48} +5.03112 q^{49} -11.5356 q^{50} -1.00000 q^{51} +5.39773 q^{52} +5.87047 q^{53} -2.37194 q^{54} +0.279267 q^{55} -13.3785 q^{56} -5.19396 q^{57} -19.1036 q^{58} +6.49441 q^{59} +1.34035 q^{60} +1.86258 q^{61} -24.2219 q^{62} -3.46859 q^{63} -11.4206 q^{64} -0.550235 q^{65} +1.79203 q^{66} -12.6405 q^{67} +3.62611 q^{68} -0.713417 q^{69} +3.04113 q^{70} -6.02601 q^{71} +3.85703 q^{72} -9.49792 q^{73} -3.47597 q^{74} +4.86337 q^{75} +18.8338 q^{76} +2.62056 q^{77} -3.53081 q^{78} +1.00000 q^{79} -0.701000 q^{80} +1.00000 q^{81} -6.75352 q^{82} -4.39993 q^{83} +12.5775 q^{84} -0.369639 q^{85} +12.9595 q^{86} +8.05401 q^{87} -2.91403 q^{88} -8.97425 q^{89} -0.876762 q^{90} -5.16325 q^{91} +2.58693 q^{92} +10.2118 q^{93} -18.0533 q^{94} -1.91989 q^{95} +3.21581 q^{96} -10.6670 q^{97} +11.9335 q^{98} -0.755512 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9}+O(q^{10}) $ 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9	\( 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9} - 13 q^{10} - 23 q^{11} - 19 q^{12} - 18 q^{13} - 9 q^{14} - q^{15} + 21 q^{16} + 22 q^{17} + q^{18} - 30 q^{19} - 7 q^{20} + 15 q^{21} + 4 q^{22} - 3 q^{23} - 15 q^{24} + 19 q^{25} - 7 q^{26} - 22 q^{27} - 25 q^{28} - 7 q^{29} + 13 q^{30} - 10 q^{31} + 31 q^{32} + 23 q^{33} + q^{34} - 11 q^{35} + 19 q^{36} - q^{37} - 29 q^{38} + 18 q^{39} - 59 q^{40} + 9 q^{42} - 43 q^{43} - 80 q^{44} + q^{45} - 43 q^{46} + 2 q^{47} - 21 q^{48} + 43 q^{49} + 25 q^{50} - 22 q^{51} - 5 q^{52} - q^{53} - q^{54} - 19 q^{55} - 8 q^{56} + 30 q^{57} - 43 q^{58} - 28 q^{59} + 7 q^{60} - 29 q^{61} - 3 q^{62} - 15 q^{63} + 23 q^{64} + 19 q^{65} - 4 q^{66} - 16 q^{67} + 19 q^{68} + 3 q^{69} - 5 q^{70} - q^{71} + 15 q^{72} - 19 q^{73} - 24 q^{74} - 19 q^{75} - 72 q^{76} + 24 q^{77} + 7 q^{78} + 22 q^{79} - 82 q^{80} + 22 q^{81} - 81 q^{82} - 29 q^{83} + 25 q^{84} + q^{85} - 42 q^{86} + 7 q^{87} - 43 q^{88} - 28 q^{89} - 13 q^{90} - 96 q^{91} - 11 q^{92} + 10 q^{93} - 63 q^{94} - 23 q^{95} - 31 q^{96} - 51 q^{97} + 12 q^{98} - 23 q^{99}+O(q^{100}) \) 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9 - 13 * q^10 - 23 * q^11 - 19 * q^12 - 18 * q^13 - 9 * q^14 - q^15 + 21 * q^16 + 22 * q^17 + q^18 - 30 * q^19 - 7 * q^20 + 15 * q^21 + 4 * q^22 - 3 * q^23 - 15 * q^24 + 19 * q^25 - 7 * q^26 - 22 * q^27 - 25 * q^28 - 7 * q^29 + 13 * q^30 - 10 * q^31 + 31 * q^32 + 23 * q^33 + q^34 - 11 * q^35 + 19 * q^36 - q^37 - 29 * q^38 + 18 * q^39 - 59 * q^40 + 9 * q^42 - 43 * q^43 - 80 * q^44 + q^45 - 43 * q^46 + 2 * q^47 - 21 * q^48 + 43 * q^49 + 25 * q^50 - 22 * q^51 - 5 * q^52 - q^53 - q^54 - 19 * q^55 - 8 * q^56 + 30 * q^57 - 43 * q^58 - 28 * q^59 + 7 * q^60 - 29 * q^61 - 3 * q^62 - 15 * q^63 + 23 * q^64 + 19 * q^65 - 4 * q^66 - 16 * q^67 + 19 * q^68 + 3 * q^69 - 5 * q^70 - q^71 + 15 * q^72 - 19 * q^73 - 24 * q^74 - 19 * q^75 - 72 * q^76 + 24 * q^77 + 7 * q^78 + 22 * q^79 - 82 * q^80 + 22 * q^81 - 81 * q^82 - 29 * q^83 + 25 * q^84 + q^85 - 42 * q^86 + 7 * q^87 - 43 * q^88 - 28 * q^89 - 13 * q^90 - 96 * q^91 - 11 * q^92 + 10 * q^93 - 63 * q^94 - 23 * q^95 - 31 * q^96 - 51 * q^97 + 12 * q^98 - 23 * 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 $

$2$	2.37194	1.67722	0.838608	−	0.544735i	$-0.183370\pi$
$2$	2.37194	1.67722	0.838608	+	0.544735i	$0.183370\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.62611	1.81305
$5$	−0.369639	−0.165308	−0.0826538	−	0.996578i	$-0.526340\pi$
$5$	−0.369639	−0.165308	−0.0826538	+	0.996578i	$0.526340\pi$
$6$	−2.37194	−0.968341
$7$	−3.46859	−1.31100	−0.655502	−	0.755193i	$-0.727543\pi$
$7$	−3.46859	−1.31100	−0.655502	+	0.755193i	$0.727543\pi$
$8$	3.85703	1.36367
$9$	1.00000	0.333333
$10$	−0.876762	−0.277257
$11$	−0.755512	−0.227795	−0.113898	−	0.993492i	$-0.536334\pi$
$11$	−0.755512	−0.227795	−0.113898	+	0.993492i	$0.536334\pi$
$12$	−3.62611	−1.04677
$13$	1.48857	0.412856	0.206428	−	0.978462i	$-0.433816\pi$
$13$	1.48857	0.412856	0.206428	+	0.978462i	$0.433816\pi$
$14$	−8.22730	−2.19884
$15$	0.369639	0.0954404
$16$	1.89644	0.474111
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	2.37194	0.559072
$19$	5.19396	1.19158	0.595788	−	0.803142i	$-0.296840\pi$
$19$	5.19396	1.19158	0.595788	+	0.803142i	$0.296840\pi$
$20$	−1.34035	−0.299712
$21$	3.46859	0.756909
$22$	−1.79203	−0.382062
$23$	0.713417	0.148758	0.0743789	−	0.997230i	$-0.476303\pi$
$23$	0.713417	0.148758	0.0743789	+	0.997230i	$0.476303\pi$
$24$	−3.85703	−0.787314
$25$	−4.86337	−0.972673
$26$	3.53081	0.692449
$27$	−1.00000	−0.192450
$28$	−12.5775	−2.37692
$29$	−8.05401	−1.49559	−0.747796	−	0.663928i	$-0.768888\pi$
$29$	−8.05401	−1.49559	−0.747796	+	0.663928i	$0.768888\pi$
$30$	0.876762	0.160074
$31$	−10.2118	−1.83410	−0.917049	−	0.398773i	$-0.869436\pi$
$31$	−10.2118	−1.83410	−0.917049	+	0.398773i	$0.869436\pi$
$32$	−3.21581	−0.568481
$33$	0.755512	0.131518
$34$	2.37194	0.406785
$35$	1.28213	0.216719
$36$	3.62611	0.604351
$37$	−1.46546	−0.240919	−0.120460	−	0.992718i	$-0.538437\pi$
$37$	−1.46546	−0.240919	−0.120460	+	0.992718i	$0.538437\pi$
$38$	12.3198	1.99853
$39$	−1.48857	−0.238362
$40$	−1.42571	−0.225425
$41$	−2.84725	−0.444666	−0.222333	−	0.974971i	$-0.571367\pi$
$41$	−2.84725	−0.444666	−0.222333	+	0.974971i	$0.571367\pi$
$42$	8.22730	1.26950
$43$	5.46367	0.833202	0.416601	−	0.909089i	$-0.363221\pi$
$43$	5.46367	0.833202	0.416601	+	0.909089i	$0.363221\pi$
$44$	−2.73957	−0.413005
$45$	−0.369639	−0.0551025
$46$	1.69218	0.249499
$47$	−7.61120	−1.11021	−0.555104	−	0.831781i	$-0.687321\pi$
$47$	−7.61120	−1.11021	−0.555104	+	0.831781i	$0.687321\pi$
$48$	−1.89644	−0.273728
$49$	5.03112	0.718732
$50$	−11.5356	−1.63138
$51$	−1.00000	−0.140028
$52$	5.39773	0.748530
$53$	5.87047	0.806372	0.403186	−	0.915118i	$-0.367903\pi$
$53$	5.87047	0.806372	0.403186	+	0.915118i	$0.367903\pi$
$54$	−2.37194	−0.322780
$55$	0.279267	0.0376563
$56$	−13.3785	−1.78777
$57$	−5.19396	−0.687956
$58$	−19.1036	−2.50843
$59$	6.49441	0.845501	0.422750	−	0.906246i	$-0.361065\pi$
$59$	6.49441	0.845501	0.422750	+	0.906246i	$0.361065\pi$
$60$	1.34035	0.173039
$61$	1.86258	0.238479	0.119240	−	0.992865i	$-0.461954\pi$
$61$	1.86258	0.238479	0.119240	+	0.992865i	$0.461954\pi$
$62$	−24.2219	−3.07618
$63$	−3.46859	−0.437001
$64$	−11.4206	−1.42758
$65$	−0.550235	−0.0682482
$66$	1.79203	0.220584
$67$	−12.6405	−1.54428	−0.772142	−	0.635450i	$-0.780815\pi$
$67$	−12.6405	−1.54428	−0.772142	+	0.635450i	$0.780815\pi$
$68$	3.62611	0.439730
$69$	−0.713417	−0.0858854
$70$	3.04113	0.363485
$71$	−6.02601	−0.715156	−0.357578	−	0.933883i	$-0.616397\pi$
$71$	−6.02601	−0.715156	−0.357578	+	0.933883i	$0.616397\pi$
$72$	3.85703	0.454556
$73$	−9.49792	−1.11165	−0.555824	−	0.831300i	$-0.687597\pi$
$73$	−9.49792	−1.11165	−0.555824	+	0.831300i	$0.687597\pi$
$74$	−3.47597	−0.404074
$75$	4.86337	0.561573
$76$	18.8338	2.16039
$77$	2.62056	0.298641
$78$	−3.53081	−0.399785
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	−0.701000	−0.0783742
$81$	1.00000	0.111111
$82$	−6.75352	−0.745801
$83$	−4.39993	−0.482955	−0.241478	−	0.970406i	$-0.577632\pi$
$83$	−4.39993	−0.482955	−0.241478	+	0.970406i	$0.577632\pi$
$84$	12.5775	1.37232
$85$	−0.369639	−0.0400930
$86$	12.9595	1.39746
$87$	8.05401	0.863481
$88$	−2.91403	−0.310637
$89$	−8.97425	−0.951269	−0.475634	−	0.879643i	$-0.657781\pi$
$89$	−8.97425	−0.951269	−0.475634	+	0.879643i	$0.657781\pi$
$90$	−0.876762	−0.0924189
$91$	−5.16325	−0.541256
$92$	2.58693	0.269706
$93$	10.2118	1.05892
$94$	−18.0533	−1.86206
$95$	−1.91989	−0.196976
$96$	3.21581	0.328212
$97$	−10.6670	−1.08307	−0.541535	−	0.840678i	$-0.682157\pi$
$97$	−10.6670	−1.08307	−0.541535	+	0.840678i	$0.682157\pi$
$98$	11.9335	1.20547
$99$	−0.755512	−0.0759318
$100$	−17.6351	−1.76351
$101$	1.60306	0.159511	0.0797555	−	0.996814i	$-0.474586\pi$
$101$	1.60306	0.159511	0.0797555	+	0.996814i	$0.474586\pi$
$102$	−2.37194	−0.234857
$103$	2.79440	0.275340	0.137670	−	0.990478i	$-0.456039\pi$
$103$	2.79440	0.275340	0.137670	+	0.990478i	$0.456039\pi$
$104$	5.74148	0.562998
$105$	−1.28213	−0.125123
$106$	13.9244	1.35246
$107$	−3.68051	−0.355808	−0.177904	−	0.984048i	$-0.556932\pi$
$107$	−3.68051	−0.355808	−0.177904	+	0.984048i	$0.556932\pi$
$108$	−3.62611	−0.348922
$109$	17.6799	1.69342	0.846711	−	0.532053i	$-0.178579\pi$
$109$	17.6799	1.69342	0.846711	+	0.532053i	$0.178579\pi$
$110$	0.662404	0.0631578
$111$	1.46546	0.139095
$112$	−6.57799	−0.621562
$113$	8.08882	0.760932	0.380466	−	0.924795i	$-0.375764\pi$
$113$	8.08882	0.760932	0.380466	+	0.924795i	$0.375764\pi$
$114$	−12.3198	−1.15385
$115$	−0.263707	−0.0245908
$116$	−29.2047	−2.71159
$117$	1.48857	0.137619
$118$	15.4044	1.41809
$119$	−3.46859	−0.317965
$120$	1.42571	0.130149
$121$	−10.4292	−0.948109
$122$	4.41794	0.399982
$123$	2.84725	0.256728
$124$	−37.0292	−3.32532
$125$	3.64589	0.326098
$126$	−8.22730	−0.732946
$127$	−2.50366	−0.222164	−0.111082	−	0.993811i	$-0.535432\pi$
$127$	−2.50366	−0.222164	−0.111082	+	0.993811i	$0.535432\pi$
$128$	−20.6574	−1.82587
$129$	−5.46367	−0.481050
$130$	−1.30512	−0.114467
$131$	−8.01358	−0.700150	−0.350075	−	0.936722i	$-0.613844\pi$
$131$	−8.01358	−0.700150	−0.350075	+	0.936722i	$0.613844\pi$
$132$	2.73957	0.238449
$133$	−18.0157	−1.56216
$134$	−29.9826	−2.59010
$135$	0.369639	0.0318135
$136$	3.85703	0.330738
$137$	−0.126993	−0.0108498	−0.00542488	−	0.999985i	$-0.501727\pi$
$137$	−0.126993	−0.0108498	−0.00542488	+	0.999985i	$0.501727\pi$
$138$	−1.69218	−0.144048
$139$	−2.79374	−0.236962	−0.118481	−	0.992956i	$-0.537802\pi$
$139$	−2.79374	−0.236962	−0.118481	+	0.992956i	$0.537802\pi$
$140$	4.64913	0.392923
$141$	7.61120	0.640979
$142$	−14.2934	−1.19947
$143$	−1.12463	−0.0940466
$144$	1.89644	0.158037
$145$	2.97708	0.247233
$146$	−22.5285	−1.86447
$147$	−5.03112	−0.414960
$148$	−5.31390	−0.436800
$149$	2.99315	0.245209	0.122604	−	0.992456i	$-0.460875\pi$
$149$	2.99315	0.245209	0.122604	+	0.992456i	$0.460875\pi$
$150$	11.5356	0.941880
$151$	−16.7472	−1.36287	−0.681434	−	0.731879i	$-0.738643\pi$
$151$	−16.7472	−1.36287	−0.681434	+	0.731879i	$0.738643\pi$
$152$	20.0333	1.62491
$153$	1.00000	0.0808452
$154$	6.21582	0.500885
$155$	3.77469	0.303191
$156$	−5.39773	−0.432164
$157$	2.68783	0.214513	0.107256	−	0.994231i	$-0.465793\pi$
$157$	2.68783	0.214513	0.107256	+	0.994231i	$0.465793\pi$
$158$	2.37194	0.188702
$159$	−5.87047	−0.465559
$160$	1.18869	0.0939742
$161$	−2.47455	−0.195022
$162$	2.37194	0.186357
$163$	16.5535	1.29657	0.648284	−	0.761398i	$-0.275487\pi$
$163$	16.5535	1.29657	0.648284	+	0.761398i	$0.275487\pi$
$164$	−10.3244	−0.806204
$165$	−0.279267	−0.0217409
$166$	−10.4364	−0.810021
$167$	−6.77946	−0.524610	−0.262305	−	0.964985i	$-0.584483\pi$
$167$	−6.77946	−0.524610	−0.262305	+	0.964985i	$0.584483\pi$
$168$	13.3785	1.03217
$169$	−10.7842	−0.829550
$170$	−0.876762	−0.0672446
$171$	5.19396	0.397192
$172$	19.8119	1.51064
$173$	−2.85516	−0.217074	−0.108537	−	0.994092i	$-0.534617\pi$
$173$	−2.85516	−0.217074	−0.108537	+	0.994092i	$0.534617\pi$
$174$	19.1036	1.44824
$175$	16.8690	1.27518
$176$	−1.43279	−0.108000
$177$	−6.49441	−0.488150
$178$	−21.2864	−1.59548
$179$	14.6644	1.09607	0.548035	−	0.836456i	$-0.315376\pi$
$179$	14.6644	1.09607	0.548035	+	0.836456i	$0.315376\pi$
$180$	−1.34035	−0.0999039
$181$	13.9649	1.03800	0.519001	−	0.854773i	$-0.326304\pi$
$181$	13.9649	1.03800	0.519001	+	0.854773i	$0.326304\pi$
$182$	−12.2469	−0.907803
$183$	−1.86258	−0.137686
$184$	2.75168	0.202856
$185$	0.541690	0.0398258
$186$	24.2219	1.77603
$187$	−0.755512	−0.0552485
$188$	−27.5990	−2.01287
$189$	3.46859	0.252303
$190$	−4.55387	−0.330372
$191$	−13.3166	−0.963553	−0.481776	−	0.876294i	$-0.660008\pi$
$191$	−13.3166	−0.963553	−0.481776	+	0.876294i	$0.660008\pi$
$192$	11.4206	0.824211
$193$	16.8828	1.21525	0.607625	−	0.794224i	$-0.292122\pi$
$193$	16.8828	1.21525	0.607625	+	0.794224i	$0.292122\pi$
$194$	−25.3015	−1.81654
$195$	0.550235	0.0394031
$196$	18.2434	1.30310
$197$	9.38723	0.668813	0.334406	−	0.942429i	$-0.391464\pi$
$197$	9.38723	0.668813	0.334406	+	0.942429i	$0.391464\pi$
$198$	−1.79203	−0.127354
$199$	−0.0383157	−0.00271613	−0.00135806	−	0.999999i	$-0.500432\pi$
$199$	−0.0383157	−0.00271613	−0.00135806	+	0.999999i	$0.500432\pi$
$200$	−18.7582	−1.32640
$201$	12.6405	0.891593
$202$	3.80238	0.267534
$203$	27.9361	1.96073
$204$	−3.62611	−0.253878
$205$	1.05246	0.0735067
$206$	6.62814	0.461805
$207$	0.713417	0.0495859
$208$	2.82300	0.195740
$209$	−3.92409	−0.271435
$210$	−3.04113	−0.209858
$211$	21.4990	1.48005	0.740026	−	0.672578i	$-0.234813\pi$
$211$	21.4990	1.48005	0.740026	+	0.672578i	$0.234813\pi$
$212$	21.2870	1.46200
$213$	6.02601	0.412896
$214$	−8.72996	−0.596768
$215$	−2.01959	−0.137735
$216$	−3.85703	−0.262438
$217$	35.4207	2.40451
$218$	41.9356	2.84024
$219$	9.49792	0.641810
$220$	1.01265	0.0682729
$221$	1.48857	0.100132
$222$	3.47597	0.233292
$223$	4.58184	0.306823	0.153411	−	0.988162i	$-0.450974\pi$
$223$	4.58184	0.306823	0.153411	+	0.988162i	$0.450974\pi$
$224$	11.1543	0.745280
$225$	−4.86337	−0.324224
$226$	19.1862	1.27625
$227$	0.451367	0.0299583	0.0149791	−	0.999888i	$-0.495232\pi$
$227$	0.451367	0.0299583	0.0149791	+	0.999888i	$0.495232\pi$
$228$	−18.8338	−1.24730
$229$	20.5876	1.36047	0.680233	−	0.732996i	$-0.261879\pi$
$229$	20.5876	1.36047	0.680233	+	0.732996i	$0.261879\pi$
$230$	−0.625498	−0.0412441
$231$	−2.62056	−0.172420
$232$	−31.0646	−2.03949
$233$	6.83379	0.447697	0.223848	−	0.974624i	$-0.428138\pi$
$233$	6.83379	0.447697	0.223848	+	0.974624i	$0.428138\pi$
$234$	3.53081	0.230816
$235$	2.81340	0.183526
$236$	23.5494	1.53294
$237$	−1.00000	−0.0649570
$238$	−8.22730	−0.533296
$239$	−13.3033	−0.860519	−0.430259	−	0.902705i	$-0.641578\pi$
$239$	−13.3033	−0.860519	−0.430259	+	0.902705i	$0.641578\pi$
$240$	0.701000	0.0452494
$241$	14.1490	0.911420	0.455710	−	0.890128i	$-0.349385\pi$
$241$	14.1490	0.911420	0.455710	+	0.890128i	$0.349385\pi$
$242$	−24.7375	−1.59018
$243$	−1.00000	−0.0641500
$244$	6.75393	0.432376
$245$	−1.85970	−0.118812
$246$	6.75352	0.430589
$247$	7.73158	0.491949
$248$	−39.3874	−2.50110
$249$	4.39993	0.278834
$250$	8.64783	0.546937
$251$	−26.5654	−1.67679	−0.838397	−	0.545060i	$-0.816507\pi$
$251$	−26.5654	−1.67679	−0.838397	+	0.545060i	$0.816507\pi$
$252$	−12.5775	−0.792307
$253$	−0.538995	−0.0338863
$254$	−5.93854	−0.372617
$255$	0.369639	0.0231477
$256$	−26.1569	−1.63481
$257$	−14.9247	−0.930975	−0.465487	−	0.885055i	$-0.654121\pi$
$257$	−14.9247	−0.930975	−0.465487	+	0.885055i	$0.654121\pi$
$258$	−12.9595	−0.806824
$259$	5.08306	0.315846
$260$	−1.99521	−0.123738
$261$	−8.05401	−0.498531
$262$	−19.0078	−1.17430
$263$	28.3348	1.74720	0.873600	−	0.486645i	$-0.161780\pi$
$263$	28.3348	1.74720	0.873600	+	0.486645i	$0.161780\pi$
$264$	2.91403	0.179346
$265$	−2.16996	−0.133299
$266$	−42.7322	−2.62008
$267$	8.97425	0.549215
$268$	−45.8359	−2.79987
$269$	23.2724	1.41894	0.709472	−	0.704733i	$-0.248933\pi$
$269$	23.2724	1.41894	0.709472	+	0.704733i	$0.248933\pi$
$270$	0.876762	0.0533581
$271$	0.483650	0.0293796	0.0146898	−	0.999892i	$-0.495324\pi$
$271$	0.483650	0.0293796	0.0146898	+	0.999892i	$0.495324\pi$
$272$	1.89644	0.114989
$273$	5.16325	0.312494
$274$	−0.301220	−0.0181974
$275$	3.67433	0.221570
$276$	−2.58693	−0.155715
$277$	−0.741564	−0.0445563	−0.0222781	−	0.999752i	$-0.507092\pi$
$277$	−0.741564	−0.0445563	−0.0222781	+	0.999752i	$0.507092\pi$
$278$	−6.62658	−0.397436
$279$	−10.2118	−0.611366
$280$	4.94521	0.295533
$281$	13.9761	0.833744	0.416872	−	0.908965i	$-0.363126\pi$
$281$	13.9761	0.833744	0.416872	+	0.908965i	$0.363126\pi$
$282$	18.0533	1.07506
$283$	−31.7158	−1.88531	−0.942653	−	0.333774i	$-0.891678\pi$
$283$	−31.7158	−1.88531	−0.942653	+	0.333774i	$0.891678\pi$
$284$	−21.8510	−1.29662
$285$	1.91989	0.113724
$286$	−2.66757	−0.157737
$287$	9.87596	0.582959
$288$	−3.21581	−0.189494
$289$	1.00000	0.0588235
$290$	7.06146	0.414663
$291$	10.6670	0.625311
$292$	−34.4405	−2.01548
$293$	31.8911	1.86310	0.931548	−	0.363618i	$-0.118459\pi$
$293$	31.8911	1.86310	0.931548	+	0.363618i	$0.118459\pi$
$294$	−11.9335	−0.695977
$295$	−2.40059	−0.139768
$296$	−5.65231	−0.328534
$297$	0.755512	0.0438392
$298$	7.09959	0.411268
$299$	1.06197	0.0614155
$300$	17.6351	1.01816
$301$	−18.9512	−1.09233
$302$	−39.7234	−2.28583
$303$	−1.60306	−0.0920937
$304$	9.85005	0.564939
$305$	−0.688484	−0.0394225
$306$	2.37194	0.135595
$307$	12.8965	0.736041	0.368021	−	0.929818i	$-0.380036\pi$
$307$	12.8965	0.736041	0.368021	+	0.929818i	$0.380036\pi$
$308$	9.50244	0.541452
$309$	−2.79440	−0.158968
$310$	8.95335	0.508516
$311$	19.5494	1.10854	0.554271	−	0.832336i	$-0.312997\pi$
$311$	19.5494	1.10854	0.554271	+	0.832336i	$0.312997\pi$
$312$	−5.74148	−0.325047
$313$	−26.0101	−1.47018	−0.735090	−	0.677970i	$-0.762860\pi$
$313$	−26.0101	−1.47018	−0.735090	+	0.677970i	$0.762860\pi$
$314$	6.37539	0.359784
$315$	1.28213	0.0722397
$316$	3.62611	0.203985
$317$	7.76092	0.435896	0.217948	−	0.975960i	$-0.430064\pi$
$317$	7.76092	0.435896	0.217948	+	0.975960i	$0.430064\pi$
$318$	−13.9244	−0.780843
$319$	6.08490	0.340689
$320$	4.22150	0.235989
$321$	3.68051	0.205426
$322$	−5.86950	−0.327094
$323$	5.19396	0.288999
$324$	3.62611	0.201450
$325$	−7.23948	−0.401574
$326$	39.2639	2.17463
$327$	−17.6799	−0.977698
$328$	−10.9820	−0.606377
$329$	26.4001	1.45549
$330$	−0.662404	−0.0364641
$331$	−22.4514	−1.23404	−0.617019	−	0.786948i	$-0.711660\pi$
$331$	−22.4514	−1.23404	−0.617019	+	0.786948i	$0.711660\pi$
$332$	−15.9546	−0.875624
$333$	−1.46546	−0.0803065
$334$	−16.0805	−0.879885
$335$	4.67243	0.255282
$336$	6.57799	0.358859
$337$	−1.38798	−0.0756081	−0.0378041	−	0.999285i	$-0.512036\pi$
$337$	−1.38798	−0.0756081	−0.0378041	+	0.999285i	$0.512036\pi$
$338$	−25.5794	−1.39133
$339$	−8.08882	−0.439324
$340$	−1.34035	−0.0726908
$341$	7.71516	0.417799
$342$	12.3198	0.666176
$343$	6.82924	0.368744
$344$	21.0736	1.13621
$345$	0.263707	0.0141975
$346$	−6.77228	−0.364080
$347$	−29.3150	−1.57371	−0.786855	−	0.617138i	$-0.788292\pi$
$347$	−29.3150	−1.57371	−0.786855	+	0.617138i	$0.788292\pi$
$348$	29.2047	1.56554
$349$	−0.625116	−0.0334617	−0.0167308	−	0.999860i	$-0.505326\pi$
$349$	−0.625116	−0.0334617	−0.0167308	+	0.999860i	$0.505326\pi$
$350$	40.0124	2.13875
$351$	−1.48857	−0.0794541
$352$	2.42958	0.129497
$353$	10.3059	0.548528	0.274264	−	0.961654i	$-0.411566\pi$
$353$	10.3059	0.548528	0.274264	+	0.961654i	$0.411566\pi$
$354$	−15.4044	−0.818733
$355$	2.22745	0.118221
$356$	−32.5416	−1.72470
$357$	3.46859	0.183577
$358$	34.7831	1.83835
$359$	−0.148045	−0.00781353	−0.00390676	−	0.999992i	$-0.501244\pi$
$359$	−0.148045	−0.00781353	−0.00390676	+	0.999992i	$0.501244\pi$
$360$	−1.42571	−0.0751415
$361$	7.97718	0.419851
$362$	33.1239	1.74095
$363$	10.4292	0.547391
$364$	−18.7225	−0.981326
$365$	3.51080	0.183764
$366$	−4.41794	−0.230929
$367$	−12.1765	−0.635608	−0.317804	−	0.948156i	$-0.602945\pi$
$367$	−12.1765	−0.635608	−0.317804	+	0.948156i	$0.602945\pi$
$368$	1.35296	0.0705277
$369$	−2.84725	−0.148222
$370$	1.28486	0.0667965
$371$	−20.3623	−1.05716
$372$	37.0292	1.91987
$373$	−8.55829	−0.443131	−0.221566	−	0.975145i	$-0.571117\pi$
$373$	−8.55829	−0.443131	−0.221566	+	0.975145i	$0.571117\pi$
$374$	−1.79203	−0.0926636
$375$	−3.64589	−0.188273
$376$	−29.3567	−1.51395
$377$	−11.9890	−0.617464
$378$	8.22730	0.423166
$379$	8.62047	0.442804	0.221402	−	0.975183i	$-0.428937\pi$
$379$	8.62047	0.442804	0.221402	+	0.975183i	$0.428937\pi$
$380$	−6.96173	−0.357129
$381$	2.50366	0.128266
$382$	−31.5861	−1.61609
$383$	4.48680	0.229265	0.114632	−	0.993408i	$-0.463431\pi$
$383$	4.48680	0.229265	0.114632	+	0.993408i	$0.463431\pi$
$384$	20.6574	1.05417
$385$	−0.968662	−0.0493676
$386$	40.0450	2.03824
$387$	5.46367	0.277734
$388$	−38.6797	−1.96366
$389$	16.4811	0.835623	0.417812	−	0.908534i	$-0.362797\pi$
$389$	16.4811	0.835623	0.417812	+	0.908534i	$0.362797\pi$
$390$	1.30512	0.0660876
$391$	0.713417	0.0360791
$392$	19.4052	0.980111
$393$	8.01358	0.404232
$394$	22.2660	1.12174
$395$	−0.369639	−0.0185986
$396$	−2.73957	−0.137668
$397$	−35.7952	−1.79651	−0.898255	−	0.439474i	$-0.855165\pi$
$397$	−35.7952	−1.79651	−0.898255	+	0.439474i	$0.855165\pi$
$398$	−0.0908826	−0.00455553
$399$	18.0157	0.901913
$400$	−9.22311	−0.461155
$401$	3.02493	0.151058	0.0755288	−	0.997144i	$-0.475936\pi$
$401$	3.02493	0.151058	0.0755288	+	0.997144i	$0.475936\pi$
$402$	29.9826	1.49539
$403$	−15.2011	−0.757219
$404$	5.81289	0.289202
$405$	−0.369639	−0.0183675
$406$	66.2627	3.28856
$407$	1.10717	0.0548803
$408$	−3.85703	−0.190952
$409$	−13.9542	−0.689991	−0.344995	−	0.938604i	$-0.612119\pi$
$409$	−13.9542	−0.689991	−0.344995	+	0.938604i	$0.612119\pi$
$410$	2.49636	0.123287
$411$	0.126993	0.00626411
$412$	10.1328	0.499206
$413$	−22.5265	−1.10845
$414$	1.69218	0.0831663
$415$	1.62639	0.0798362
$416$	−4.78697	−0.234701
$417$	2.79374	0.136810
$418$	−9.30772	−0.455256
$419$	−35.7416	−1.74609	−0.873047	−	0.487636i	$-0.837859\pi$
$419$	−35.7416	−1.74609	−0.873047	+	0.487636i	$0.837859\pi$
$420$	−4.64913	−0.226854
$421$	38.6373	1.88307	0.941533	−	0.336920i	$-0.109385\pi$
$421$	38.6373	1.88307	0.941533	+	0.336920i	$0.109385\pi$
$422$	50.9944	2.48237
$423$	−7.61120	−0.370069
$424$	22.6426	1.09962
$425$	−4.86337	−0.235908
$426$	14.2934	0.692515
$427$	−6.46054	−0.312648
$428$	−13.3459	−0.645100
$429$	1.12463	0.0542978
$430$	−4.79034	−0.231011
$431$	−6.82805	−0.328895	−0.164448	−	0.986386i	$-0.552584\pi$
$431$	−6.82805	−0.328895	−0.164448	+	0.986386i	$0.552584\pi$
$432$	−1.89644	−0.0912427
$433$	6.50288	0.312509	0.156254	−	0.987717i	$-0.450058\pi$
$433$	6.50288	0.312509	0.156254	+	0.987717i	$0.450058\pi$
$434$	84.0157	4.03288
$435$	−2.97708	−0.142740
$436$	64.1091	3.07027
$437$	3.70546	0.177256
$438$	22.5285	1.07645
$439$	−30.9032	−1.47493	−0.737465	−	0.675385i	$-0.763977\pi$
$439$	−30.9032	−1.47493	−0.737465	+	0.675385i	$0.763977\pi$
$440$	1.07714	0.0513507
$441$	5.03112	0.239577
$442$	3.53081	0.167943
$443$	−18.6835	−0.887680	−0.443840	−	0.896106i	$-0.646384\pi$
$443$	−18.6835	−0.887680	−0.443840	+	0.896106i	$0.646384\pi$
$444$	5.31390	0.252187
$445$	3.31723	0.157252
$446$	10.8679	0.514608
$447$	−2.99315	−0.141571
$448$	39.6134	1.87156
$449$	−0.959349	−0.0452745	−0.0226372	−	0.999744i	$-0.507206\pi$
$449$	−0.959349	−0.0452745	−0.0226372	+	0.999744i	$0.507206\pi$
$450$	−11.5356	−0.543795
$451$	2.15113	0.101293
$452$	29.3309	1.37961
$453$	16.7472	0.786853
$454$	1.07062	0.0502465
$455$	1.90854	0.0894737
$456$	−20.0333	−0.938144
$457$	−11.1137	−0.519875	−0.259937	−	0.965625i	$-0.583702\pi$
$457$	−11.1137	−0.519875	−0.259937	+	0.965625i	$0.583702\pi$
$458$	48.8326	2.28180
$459$	−1.00000	−0.0466760
$460$	−0.956230	−0.0445845
$461$	18.2904	0.851867	0.425933	−	0.904754i	$-0.359946\pi$
$461$	18.2904	0.851867	0.425933	+	0.904754i	$0.359946\pi$
$462$	−6.21582	−0.289186
$463$	−1.20461	−0.0559830	−0.0279915	−	0.999608i	$-0.508911\pi$
$463$	−1.20461	−0.0559830	−0.0279915	+	0.999608i	$0.508911\pi$
$464$	−15.2740	−0.709077
$465$	−3.77469	−0.175047
$466$	16.2094	0.750884
$467$	7.20752	0.333524	0.166762	−	0.985997i	$-0.446669\pi$
$467$	7.20752	0.333524	0.166762	+	0.985997i	$0.446669\pi$
$468$	5.39773	0.249510
$469$	43.8448	2.02456
$470$	6.67321	0.307812
$471$	−2.68783	−0.123849
$472$	25.0492	1.15298
$473$	−4.12787	−0.189800
$474$	−2.37194	−0.108947
$475$	−25.2601	−1.15901
$476$	−12.5775	−0.576488
$477$	5.87047	0.268791
$478$	−31.5546	−1.44328
$479$	−1.51802	−0.0693603	−0.0346801	−	0.999398i	$-0.511041\pi$
$479$	−1.51802	−0.0693603	−0.0346801	+	0.999398i	$0.511041\pi$
$480$	−1.18869	−0.0542560
$481$	−2.18144	−0.0994650
$482$	33.5607	1.52865
$483$	2.47455	0.112596
$484$	−37.8174	−1.71897
$485$	3.94294	0.179040
$486$	−2.37194	−0.107593
$487$	2.71388	0.122977	0.0614887	−	0.998108i	$-0.480415\pi$
$487$	2.71388	0.122977	0.0614887	+	0.998108i	$0.480415\pi$
$488$	7.18405	0.325207
$489$	−16.5535	−0.748574
$490$	−4.41110	−0.199273
$491$	−24.9030	−1.12386	−0.561928	−	0.827186i	$-0.689940\pi$
$491$	−24.9030	−1.12386	−0.561928	+	0.827186i	$0.689940\pi$
$492$	10.3244	0.465462
$493$	−8.05401	−0.362734
$494$	18.3389	0.825104
$495$	0.279267	0.0125521
$496$	−19.3662	−0.869567
$497$	20.9018	0.937572
$498$	10.4364	0.467666
$499$	−17.0344	−0.762563	−0.381282	−	0.924459i	$-0.624517\pi$
$499$	−17.0344	−0.762563	−0.381282	+	0.924459i	$0.624517\pi$
$500$	13.2204	0.591233
$501$	6.77946	0.302884
$502$	−63.0116	−2.81235
$503$	28.4268	1.26749	0.633744	−	0.773543i	$-0.281517\pi$
$503$	28.4268	1.26749	0.633744	+	0.773543i	$0.281517\pi$
$504$	−13.3785	−0.595925
$505$	−0.592555	−0.0263684
$506$	−1.27846	−0.0568347
$507$	10.7842	0.478941
$508$	−9.07855	−0.402795
$509$	−6.98832	−0.309752	−0.154876	−	0.987934i	$-0.549498\pi$
$509$	−6.98832	−0.309752	−0.154876	+	0.987934i	$0.549498\pi$
$510$	0.876762	0.0388237
$511$	32.9444	1.45737
$512$	−20.7279	−0.916053
$513$	−5.19396	−0.229319
$514$	−35.4004	−1.56145
$515$	−1.03292	−0.0455158
$516$	−19.8119	−0.872169
$517$	5.75035	0.252900
$518$	12.0567	0.529742
$519$	2.85516	0.125328
$520$	−2.12227	−0.0930679
$521$	−13.4413	−0.588875	−0.294438	−	0.955671i	$-0.595132\pi$
$521$	−13.4413	−0.588875	−0.294438	+	0.955671i	$0.595132\pi$
$522$	−19.1036	−0.836144
$523$	6.33730	0.277111	0.138555	−	0.990355i	$-0.455754\pi$
$523$	6.33730	0.277111	0.138555	+	0.990355i	$0.455754\pi$
$524$	−29.0581	−1.26941
$525$	−16.8690	−0.736225
$526$	67.2085	2.93043
$527$	−10.2118	−0.444834
$528$	1.43279	0.0623540
$529$	−22.4910	−0.977871
$530$	−5.14701	−0.223572
$531$	6.49441	0.281834
$532$	−65.3269	−2.83228
$533$	−4.23834	−0.183583
$534$	21.2864	0.921153
$535$	1.36046	0.0588178
$536$	−48.7549	−2.10589
$537$	−14.6644	−0.632816
$538$	55.2008	2.37988
$539$	−3.80107	−0.163724
$540$	1.34035	0.0576795
$541$	17.4951	0.752172	0.376086	−	0.926585i	$-0.377270\pi$
$541$	17.4951	0.752172	0.376086	+	0.926585i	$0.377270\pi$
$542$	1.14719	0.0492760
$543$	−13.9649	−0.599291
$544$	−3.21581	−0.137877
$545$	−6.53516	−0.279936
$546$	12.2469	0.524120
$547$	23.4470	1.00252	0.501260	−	0.865297i	$-0.332870\pi$
$547$	23.4470	1.00252	0.501260	+	0.865297i	$0.332870\pi$
$548$	−0.460491	−0.0196712
$549$	1.86258	0.0794931
$550$	8.71530	0.371622
$551$	−41.8322	−1.78211
$552$	−2.75168	−0.117119
$553$	−3.46859	−0.147499
$554$	−1.75895	−0.0747305
$555$	−0.541690	−0.0229934
$556$	−10.1304	−0.429624
$557$	1.22667	0.0519756	0.0259878	−	0.999662i	$-0.491727\pi$
$557$	1.22667	0.0519756	0.0259878	+	0.999662i	$0.491727\pi$
$558$	−24.2219	−1.02539
$559$	8.13308	0.343993
$560$	2.43148	0.102749
$561$	0.755512	0.0318977
$562$	33.1505	1.39837
$563$	−16.3024	−0.687064	−0.343532	−	0.939141i	$-0.611623\pi$
$563$	−16.3024	−0.687064	−0.343532	+	0.939141i	$0.611623\pi$
$564$	27.5990	1.16213
$565$	−2.98994	−0.125788
$566$	−75.2279	−3.16207
$567$	−3.46859	−0.145667
$568$	−23.2425	−0.975235
$569$	23.7017	0.993627	0.496813	−	0.867857i	$-0.334503\pi$
$569$	23.7017	0.993627	0.496813	+	0.867857i	$0.334503\pi$
$570$	4.55387	0.190740
$571$	26.8950	1.12552	0.562760	−	0.826621i	$-0.309740\pi$
$571$	26.8950	1.12552	0.562760	+	0.826621i	$0.309740\pi$
$572$	−4.07805	−0.170512
$573$	13.3166	0.556307
$574$	23.4252	0.977749
$575$	−3.46961	−0.144693
$576$	−11.4206	−0.475859
$577$	25.5085	1.06193	0.530967	−	0.847392i	$-0.321829\pi$
$577$	25.5085	1.06193	0.530967	+	0.847392i	$0.321829\pi$
$578$	2.37194	0.0986598
$579$	−16.8828	−0.701625
$580$	10.7952	0.448247
$581$	15.2616	0.633156
$582$	25.3015	1.04878
$583$	−4.43521	−0.183688
$584$	−36.6338	−1.51592
$585$	−0.550235	−0.0227494
$586$	75.6438	3.12482
$587$	−35.6038	−1.46952	−0.734762	−	0.678325i	$-0.762706\pi$
$587$	−35.6038	−1.46952	−0.734762	+	0.678325i	$0.762706\pi$
$588$	−18.2434	−0.752345
$589$	−53.0398	−2.18547
$590$	−5.69406	−0.234421
$591$	−9.38723	−0.386139
$592$	−2.77915	−0.114223
$593$	−19.6116	−0.805351	−0.402676	−	0.915343i	$-0.631920\pi$
$593$	−19.6116	−0.805351	−0.402676	+	0.915343i	$0.631920\pi$
$594$	1.79203	0.0735279
$595$	1.28213	0.0525621
$596$	10.8535	0.444577
$597$	0.0383157	0.00156816
$598$	2.51894	0.103007
$599$	12.3182	0.503308	0.251654	−	0.967817i	$-0.419025\pi$
$599$	12.3182	0.503308	0.251654	+	0.967817i	$0.419025\pi$
$600$	18.7582	0.765799
$601$	−22.8106	−0.930464	−0.465232	−	0.885189i	$-0.654029\pi$
$601$	−22.8106	−0.930464	−0.465232	+	0.885189i	$0.654029\pi$
$602$	−44.9513	−1.83208
$603$	−12.6405	−0.514761
$604$	−60.7272	−2.47095
$605$	3.85504	0.156730
$606$	−3.80238	−0.154461
$607$	12.0275	0.488182	0.244091	−	0.969752i	$-0.421510\pi$
$607$	12.0275	0.488182	0.244091	+	0.969752i	$0.421510\pi$
$608$	−16.7028	−0.677387
$609$	−27.9361	−1.13203
$610$	−1.63304	−0.0661200
$611$	−11.3298	−0.458356
$612$	3.62611	0.146577
$613$	20.6782	0.835186	0.417593	−	0.908634i	$-0.362874\pi$
$613$	20.6782	0.835186	0.417593	+	0.908634i	$0.362874\pi$
$614$	30.5897	1.23450
$615$	−1.05246	−0.0424391
$616$	10.1076	0.407246
$617$	34.6512	1.39501	0.697503	−	0.716582i	$-0.254294\pi$
$617$	34.6512	1.39501	0.697503	+	0.716582i	$0.254294\pi$
$618$	−6.62814	−0.266623
$619$	−36.6924	−1.47479	−0.737395	−	0.675461i	$-0.763945\pi$
$619$	−36.6924	−1.47479	−0.737395	+	0.675461i	$0.763945\pi$
$620$	13.6874	0.549701
$621$	−0.713417	−0.0286285
$622$	46.3699	1.85926
$623$	31.1280	1.24712
$624$	−2.82300	−0.113010
$625$	22.9692	0.918767
$626$	−61.6945	−2.46581
$627$	3.92409	0.156713
$628$	9.74638	0.388923
$629$	−1.46546	−0.0584315
$630$	3.04113	0.121162
$631$	−8.35239	−0.332503	−0.166252	−	0.986083i	$-0.553166\pi$
$631$	−8.35239	−0.332503	−0.166252	+	0.986083i	$0.553166\pi$
$632$	3.85703	0.153425
$633$	−21.4990	−0.854509
$634$	18.4084	0.731093
$635$	0.925451	0.0367254
$636$	−21.2870	−0.844084
$637$	7.48919	0.296733
$638$	14.4330	0.571409
$639$	−6.02601	−0.238385
$640$	7.63578	0.301831
$641$	−35.7095	−1.41044	−0.705220	−	0.708988i	$-0.749152\pi$
$641$	−35.7095	−1.41044	−0.705220	+	0.708988i	$0.749152\pi$
$642$	8.72996	0.344544
$643$	−16.6743	−0.657569	−0.328784	−	0.944405i	$-0.606639\pi$
$643$	−16.6743	−0.657569	−0.328784	+	0.944405i	$0.606639\pi$
$644$	−8.97300	−0.353586
$645$	2.01959	0.0795212
$646$	12.3198	0.484715
$647$	−7.67840	−0.301869	−0.150934	−	0.988544i	$-0.548228\pi$
$647$	−7.67840	−0.301869	−0.150934	+	0.988544i	$0.548228\pi$
$648$	3.85703	0.151519
$649$	−4.90660	−0.192601
$650$	−17.1716	−0.673526
$651$	−35.4207	−1.38825
$652$	60.0247	2.35075
$653$	31.9536	1.25044	0.625221	−	0.780448i	$-0.285009\pi$
$653$	31.9536	1.25044	0.625221	+	0.780448i	$0.285009\pi$
$654$	−41.9356	−1.63981
$655$	2.96213	0.115740
$656$	−5.39966	−0.210821
$657$	−9.49792	−0.370549
$658$	62.6196	2.44117
$659$	26.7295	1.04124	0.520618	−	0.853790i	$-0.325702\pi$
$659$	26.7295	1.04124	0.520618	+	0.853790i	$0.325702\pi$
$660$	−1.01265	−0.0394174
$661$	18.8061	0.731474	0.365737	−	0.930718i	$-0.380817\pi$
$661$	18.8061	0.731474	0.365737	+	0.930718i	$0.380817\pi$
$662$	−53.2533	−2.06975
$663$	−1.48857	−0.0578114
$664$	−16.9707	−0.658591
$665$	6.65931	0.258237
$666$	−3.47597	−0.134691
$667$	−5.74587	−0.222481
$668$	−24.5831	−0.951147
$669$	−4.58184	−0.177144
$670$	11.0827	0.428163
$671$	−1.40720	−0.0543245
$672$	−11.1543	−0.430288
$673$	9.94547	0.383370	0.191685	−	0.981457i	$-0.438605\pi$
$673$	9.94547	0.383370	0.191685	+	0.981457i	$0.438605\pi$
$674$	−3.29221	−0.126811
$675$	4.86337	0.187191
$676$	−39.1045	−1.50402
$677$	34.9834	1.34452	0.672260	−	0.740315i	$-0.265324\pi$
$677$	34.9834	1.34452	0.672260	+	0.740315i	$0.265324\pi$
$678$	−19.1862	−0.736842
$679$	36.9995	1.41991
$680$	−1.42571	−0.0546735
$681$	−0.451367	−0.0172964
$682$	18.2999	0.700739
$683$	41.2162	1.57709	0.788547	−	0.614974i	$-0.210834\pi$
$683$	41.2162	1.57709	0.788547	+	0.614974i	$0.210834\pi$
$684$	18.8338	0.720130
$685$	0.0469416	0.00179355
$686$	16.1986	0.618464
$687$	−20.5876	−0.785466
$688$	10.3616	0.395031
$689$	8.73863	0.332915
$690$	0.625498	0.0238123
$691$	−43.3188	−1.64793	−0.823963	−	0.566644i	$-0.808241\pi$
$691$	−43.3188	−1.64793	−0.823963	+	0.566644i	$0.808241\pi$
$692$	−10.3531	−0.393567
$693$	2.62056	0.0995469
$694$	−69.5334	−2.63945
$695$	1.03267	0.0391716
$696$	31.0646	1.17750
$697$	−2.84725	−0.107847
$698$	−1.48274	−0.0561225
$699$	−6.83379	−0.258478
$700$	61.1689	2.31197
$701$	−11.6000	−0.438127	−0.219063	−	0.975711i	$-0.570300\pi$
$701$	−11.6000	−0.438127	−0.219063	+	0.975711i	$0.570300\pi$
$702$	−3.53081	−0.133262
$703$	−7.61151	−0.287074
$704$	8.62840	0.325195
$705$	−2.81340	−0.105959
$706$	24.4450	0.920001
$707$	−5.56038	−0.209119
$708$	−23.5494	−0.885042
$709$	14.2493	0.535144	0.267572	−	0.963538i	$-0.413779\pi$
$709$	14.2493	0.535144	0.267572	+	0.963538i	$0.413779\pi$
$710$	5.28338	0.198282
$711$	1.00000	0.0375029
$712$	−34.6140	−1.29721
$713$	−7.28530	−0.272837
$714$	8.22730	0.307899
$715$	0.415709	0.0155466
$716$	53.1747	1.98723
$717$	13.3033	0.496821
$718$	−0.351155	−0.0131050
$719$	−20.2333	−0.754576	−0.377288	−	0.926096i	$-0.623143\pi$
$719$	−20.2333	−0.754576	−0.377288	+	0.926096i	$0.623143\pi$
$720$	−0.701000	−0.0261247
$721$	−9.69261	−0.360972
$722$	18.9214	0.704181
$723$	−14.1490	−0.526208
$724$	50.6382	1.88195
$725$	39.1696	1.45472
$726$	24.7375	0.918093
$727$	5.09231	0.188863	0.0944316	−	0.995531i	$-0.469897\pi$
$727$	5.09231	0.188863	0.0944316	+	0.995531i	$0.469897\pi$
$728$	−19.9148	−0.738093
$729$	1.00000	0.0370370
$730$	8.32742	0.308212
$731$	5.46367	0.202081
$732$	−6.75393	−0.249632
$733$	−2.90117	−0.107157	−0.0535786	−	0.998564i	$-0.517063\pi$
$733$	−2.90117	−0.107157	−0.0535786	+	0.998564i	$0.517063\pi$
$734$	−28.8820	−1.06605
$735$	1.85970	0.0685960
$736$	−2.29422	−0.0845659
$737$	9.55005	0.351781
$738$	−6.75352	−0.248600
$739$	23.7856	0.874966	0.437483	−	0.899227i	$-0.355870\pi$
$739$	23.7856	0.874966	0.437483	+	0.899227i	$0.355870\pi$
$740$	1.96423	0.0722064
$741$	−7.73158	−0.284027
$742$	−48.2981	−1.77308
$743$	5.87074	0.215377	0.107688	−	0.994185i	$-0.465655\pi$
$743$	5.87074	0.215377	0.107688	+	0.994185i	$0.465655\pi$
$744$	39.3874	1.44401
$745$	−1.10639	−0.0405349
$746$	−20.2998	−0.743227
$747$	−4.39993	−0.160985
$748$	−2.73957	−0.100168
$749$	12.7662	0.466466
$750$	−8.64783	−0.315774
$751$	−46.0094	−1.67891	−0.839454	−	0.543431i	$-0.817125\pi$
$751$	−46.0094	−1.67891	−0.839454	+	0.543431i	$0.817125\pi$
$752$	−14.4342	−0.526362
$753$	26.5654	0.968098
$754$	−28.4372	−1.03562
$755$	6.19042	0.225293
$756$	12.5775	0.457439
$757$	−5.65533	−0.205546	−0.102773	−	0.994705i	$-0.532772\pi$
$757$	−5.65533	−0.205546	−0.102773	+	0.994705i	$0.532772\pi$
$758$	20.4472	0.742677
$759$	0.538995	0.0195643
$760$	−7.40508	−0.268610
$761$	−34.8238	−1.26236	−0.631181	−	0.775636i	$-0.717429\pi$
$761$	−34.8238	−1.26236	−0.631181	+	0.775636i	$0.717429\pi$
$762$	5.93854	0.215131
$763$	−61.3242	−2.22008
$764$	−48.2873	−1.74697
$765$	−0.369639	−0.0133643
$766$	10.6424	0.384527
$767$	9.66741	0.349070
$768$	26.1569	0.943857
$769$	−30.3720	−1.09524	−0.547621	−	0.836727i	$-0.684466\pi$
$769$	−30.3720	−1.09524	−0.547621	+	0.836727i	$0.684466\pi$
$770$	−2.29761	−0.0828001
$771$	14.9247	0.537498
$772$	61.2188	2.20331
$773$	−2.39081	−0.0859914	−0.0429957	−	0.999075i	$-0.513690\pi$
$773$	−2.39081	−0.0859914	−0.0429957	+	0.999075i	$0.513690\pi$
$774$	12.9595	0.465820
$775$	49.6639	1.78398
$776$	−41.1430	−1.47695
$777$	−5.08306	−0.182354
$778$	39.0921	1.40152
$779$	−14.7885	−0.529853
$780$	1.99521	0.0714400
$781$	4.55272	0.162909
$782$	1.69218	0.0605124
$783$	8.05401	0.287827
$784$	9.54124	0.340759
$785$	−0.993529	−0.0354606
$786$	19.0078	0.677984
$787$	−49.5550	−1.76645	−0.883223	−	0.468953i	$-0.844631\pi$
$787$	−49.5550	−1.76645	−0.883223	+	0.468953i	$0.844631\pi$
$788$	34.0391	1.21259
$789$	−28.3348	−1.00875
$790$	−0.876762	−0.0311938
$791$	−28.0568	−0.997585
$792$	−2.91403	−0.103546
$793$	2.77259	0.0984576
$794$	−84.9042	−3.01314
$795$	2.16996	0.0769604
$796$	−0.138937	−0.00492448
$797$	33.0345	1.17014	0.585071	−	0.810982i	$-0.301067\pi$
$797$	33.0345	1.17014	0.585071	+	0.810982i	$0.301067\pi$
$798$	42.7322	1.51270
$799$	−7.61120	−0.269265
$800$	15.6397	0.552946
$801$	−8.97425	−0.317090
$802$	7.17495	0.253356
$803$	7.17579	0.253228
$804$	45.8359	1.61651
$805$	0.914691	0.0322386
$806$	−36.0560	−1.27002
$807$	−23.2724	−0.819228
$808$	6.18308	0.217520
$809$	−17.8355	−0.627062	−0.313531	−	0.949578i	$-0.601512\pi$
$809$	−17.8355	−0.627062	−0.313531	+	0.949578i	$0.601512\pi$
$810$	−0.876762	−0.0308063
$811$	46.6002	1.63635	0.818176	−	0.574967i	$-0.194985\pi$
$811$	46.6002	1.63635	0.818176	+	0.574967i	$0.194985\pi$
$812$	101.299	3.55491
$813$	−0.483650	−0.0169623
$814$	2.62614	0.0920461
$815$	−6.11881	−0.214333
$816$	−1.89644	−0.0663888
$817$	28.3781	0.992823
$818$	−33.0985	−1.15726
$819$	−5.16325	−0.180419
$820$	3.81632	0.133272
$821$	35.1269	1.22594	0.612969	−	0.790107i	$-0.289975\pi$
$821$	35.1269	1.22594	0.612969	+	0.790107i	$0.289975\pi$
$822$	0.301220	0.0105063
$823$	−29.0284	−1.01187	−0.505934	−	0.862572i	$-0.668852\pi$
$823$	−29.0284	−1.01187	−0.505934	+	0.862572i	$0.668852\pi$
$824$	10.7781	0.375472
$825$	−3.67433	−0.127924
$826$	−53.4315	−1.85912
$827$	−10.7233	−0.372886	−0.186443	−	0.982466i	$-0.559696\pi$
$827$	−10.7233	−0.372886	−0.186443	+	0.982466i	$0.559696\pi$
$828$	2.58693	0.0899020
$829$	−10.5882	−0.367744	−0.183872	−	0.982950i	$-0.558863\pi$
$829$	−10.5882	−0.367744	−0.183872	+	0.982950i	$0.558863\pi$
$830$	3.85770	0.133903
$831$	0.741564	0.0257246
$832$	−17.0004	−0.589383
$833$	5.03112	0.174318
$834$	6.62658	0.229460
$835$	2.50595	0.0867221
$836$	−14.2292	−0.492127
$837$	10.2118	0.352973
$838$	−84.7771	−2.92858
$839$	−2.47921	−0.0855920	−0.0427960	−	0.999084i	$-0.513627\pi$
$839$	−2.47921	−0.0855920	−0.0427960	+	0.999084i	$0.513627\pi$
$840$	−4.94521	−0.170626
$841$	35.8671	1.23680
$842$	91.6454	3.15831
$843$	−13.9761	−0.481362
$844$	77.9577	2.68341
$845$	3.98624	0.137131
$846$	−18.0533	−0.620686
$847$	36.1746	1.24298
$848$	11.1330	0.382310
$849$	31.7158	1.08848
$850$	−11.5356	−0.395669
$851$	−1.04548	−0.0358386
$852$	21.8510	0.748602
$853$	−32.7861	−1.12257	−0.561287	−	0.827621i	$-0.689693\pi$
$853$	−32.7861	−1.12257	−0.561287	+	0.827621i	$0.689693\pi$
$854$	−15.3240	−0.524377
$855$	−1.91989	−0.0656588
$856$	−14.1959	−0.485204
$857$	−19.5985	−0.669472	−0.334736	−	0.942312i	$-0.608647\pi$
$857$	−19.5985	−0.669472	−0.334736	+	0.942312i	$0.608647\pi$
$858$	2.66757	0.0910692
$859$	−40.0630	−1.36693	−0.683465	−	0.729983i	$-0.739528\pi$
$859$	−40.0630	−1.36693	−0.683465	+	0.729983i	$0.739528\pi$
$860$	−7.32324	−0.249721
$861$	−9.87596	−0.336572
$862$	−16.1957	−0.551629
$863$	−34.9501	−1.18972	−0.594858	−	0.803831i	$-0.702792\pi$
$863$	−34.9501	−1.18972	−0.594858	+	0.803831i	$0.702792\pi$
$864$	3.21581	0.109404
$865$	1.05538	0.0358840
$866$	15.4245	0.524144
$867$	−1.00000	−0.0339618
$868$	128.439	4.35951
$869$	−0.755512	−0.0256290
$870$	−7.06146	−0.239406
$871$	−18.8163	−0.637567
$872$	68.1918	2.30927
$873$	−10.6670	−0.361023
$874$	8.78913	0.297297
$875$	−12.6461	−0.427516
$876$	34.4405	1.16364
$877$	19.4312	0.656146	0.328073	−	0.944652i	$-0.393601\pi$
$877$	19.4312	0.656146	0.328073	+	0.944652i	$0.393601\pi$
$878$	−73.3007	−2.47378
$879$	−31.8911	−1.07566
$880$	0.529614	0.0178533
$881$	−25.2555	−0.850878	−0.425439	−	0.904987i	$-0.639880\pi$
$881$	−25.2555	−0.850878	−0.425439	+	0.904987i	$0.639880\pi$
$882$	11.9335	0.401823
$883$	4.16941	0.140312	0.0701560	−	0.997536i	$-0.477650\pi$
$883$	4.16941	0.140312	0.0701560	+	0.997536i	$0.477650\pi$
$884$	5.39773	0.181545
$885$	2.40059	0.0806949
$886$	−44.3162	−1.48883
$887$	0.274458	0.00921540	0.00460770	−	0.999989i	$-0.498533\pi$
$887$	0.274458	0.00921540	0.00460770	+	0.999989i	$0.498533\pi$
$888$	5.65231	0.189679
$889$	8.68418	0.291258
$890$	7.86829	0.263746
$891$	−0.755512	−0.0253106
$892$	16.6143	0.556287
$893$	−39.5322	−1.32290
$894$	−7.09959	−0.237446
$895$	−5.42054	−0.181189
$896$	71.6520	2.39373
$897$	−1.06197	−0.0354583
$898$	−2.27552	−0.0759351
$899$	82.2462	2.74306
$900$	−17.6351	−0.587836
$901$	5.87047	0.195574
$902$	5.10236	0.169890
$903$	18.9512	0.630658
$904$	31.1988	1.03766
$905$	−5.16197	−0.171590
$906$	39.7234	1.31972
$907$	−35.4982	−1.17870	−0.589348	−	0.807879i	$-0.700615\pi$
$907$	−35.4982	−1.17870	−0.589348	+	0.807879i	$0.700615\pi$
$908$	1.63670	0.0543160
$909$	1.60306	0.0531703
$910$	4.52694	0.150067
$911$	48.2607	1.59895	0.799475	−	0.600700i	$-0.205111\pi$
$911$	48.2607	1.59895	0.799475	+	0.600700i	$0.205111\pi$
$912$	−9.85005	−0.326168
$913$	3.32420	0.110015
$914$	−26.3609	−0.871942
$915$	0.688484	0.0227606
$916$	74.6528	2.46660
$917$	27.7958	0.917899
$918$	−2.37194	−0.0782857
$919$	19.7116	0.650225	0.325113	−	0.945675i	$-0.394598\pi$
$919$	19.7116	0.650225	0.325113	+	0.945675i	$0.394598\pi$
$920$	−1.01713	−0.0335337
$921$	−12.8965	−0.424954
$922$	43.3837	1.42876
$923$	−8.97016	−0.295256
$924$	−9.50244	−0.312607
$925$	7.12705	0.234336
$926$	−2.85726	−0.0938956
$927$	2.79440	0.0917800
$928$	25.9002	0.850215
$929$	−10.0842	−0.330853	−0.165427	−	0.986222i	$-0.552900\pi$
$929$	−10.0842	−0.330853	−0.165427	+	0.986222i	$0.552900\pi$
$930$	−8.95335	−0.293592
$931$	26.1314	0.856423
$932$	24.7801	0.811698
$933$	−19.5494	−0.640017
$934$	17.0958	0.559392
$935$	0.279267	0.00913299
$936$	5.74148	0.187666
$937$	−21.2449	−0.694040	−0.347020	−	0.937858i	$-0.612806\pi$
$937$	−21.2449	−0.694040	−0.347020	+	0.937858i	$0.612806\pi$
$938$	103.997	3.39563
$939$	26.0101	0.848809
$940$	10.2017	0.332742
$941$	41.9359	1.36707	0.683535	−	0.729918i	$-0.260442\pi$
$941$	41.9359	1.36707	0.683535	+	0.729918i	$0.260442\pi$
$942$	−6.37539	−0.207721
$943$	−2.03128	−0.0661476
$944$	12.3163	0.400861
$945$	−1.28213	−0.0417076
$946$	−9.79107	−0.318335
$947$	29.7573	0.966982	0.483491	−	0.875349i	$-0.339369\pi$
$947$	29.7573	0.966982	0.483491	+	0.875349i	$0.339369\pi$
$948$	−3.62611	−0.117771
$949$	−14.1384	−0.458950
$950$	−59.9155	−1.94392
$951$	−7.76092	−0.251665
$952$	−13.3785	−0.433599
$953$	−14.2337	−0.461076	−0.230538	−	0.973063i	$-0.574049\pi$
$953$	−14.2337	−0.461076	−0.230538	+	0.973063i	$0.574049\pi$
$954$	13.9244	0.450820
$955$	4.92232	0.159283
$956$	−48.2392	−1.56017
$957$	−6.08490	−0.196697
$958$	−3.60067	−0.116332
$959$	0.440487	0.0142241
$960$	−4.22150	−0.136248
$961$	73.2815	2.36392
$962$	−5.17424	−0.166824
$963$	−3.68051	−0.118603
$964$	51.3059	1.65245
$965$	−6.24054	−0.200890
$966$	5.86950	0.188848
$967$	−16.4728	−0.529730	−0.264865	−	0.964285i	$-0.585327\pi$
$967$	−16.4728	−0.529730	−0.264865	+	0.964285i	$0.585327\pi$
$968$	−40.2258	−1.29291
$969$	−5.19396	−0.166854
$970$	9.35242	0.300288
$971$	−15.5577	−0.499271	−0.249636	−	0.968340i	$-0.580311\pi$
$971$	−15.5577	−0.499271	−0.249636	+	0.968340i	$0.580311\pi$
$972$	−3.62611	−0.116307
$973$	9.69033	0.310658
$974$	6.43716	0.206260
$975$	7.23948	0.231849
$976$	3.53229	0.113066
$977$	−14.9750	−0.479091	−0.239546	−	0.970885i	$-0.576998\pi$
$977$	−14.9750	−0.479091	−0.239546	+	0.970885i	$0.576998\pi$
$978$	−39.2639	−1.25552
$979$	6.78015	0.216695
$980$	−6.74347	−0.215412
$981$	17.6799	0.564474
$982$	−59.0685	−1.88495
$983$	31.2279	0.996014	0.498007	−	0.867173i	$-0.334065\pi$
$983$	31.2279	0.996014	0.498007	+	0.867173i	$0.334065\pi$
$984$	10.9820	0.350092
$985$	−3.46989	−0.110560
$986$	−19.1036	−0.608384
$987$	−26.4001	−0.840326
$988$	28.0356	0.891930
$989$	3.89788	0.123945
$990$	0.662404	0.0210526
$991$	5.46820	0.173703	0.0868516	−	0.996221i	$-0.472319\pi$
$991$	5.46820	0.173703	0.0868516	+	0.996221i	$0.472319\pi$
$992$	32.8393	1.04265
$993$	22.4514	0.712472
$994$	49.5778	1.57251
$995$	0.0141630	0.000448996 0
$996$	15.9546	0.505542
$997$	−20.3637	−0.644925	−0.322462	−	0.946582i	$-0.604511\pi$
$997$	−20.3637	−0.644925	−0.322462	+	0.946582i	$0.604511\pi$
$998$	−40.4046	−1.27898
$999$	1.46546	0.0463650

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.f.1.20	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.f.1.20	✓	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)

\(f(q)\)	\(=\)	\(q+2.37194 q^{2} -1.00000 q^{3} +3.62611 q^{4} -0.369639 q^{5} -2.37194 q^{6} -3.46859 q^{7} +3.85703 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.37194 q^{2} -1.00000 q^{3} +3.62611 q^{4} -0.369639 q^{5} -2.37194 q^{6} -3.46859 q^{7} +3.85703 q^{8} +1.00000 q^{9} -0.876762 q^{10} -0.755512 q^{11} -3.62611 q^{12} +1.48857 q^{13} -8.22730 q^{14} +0.369639 q^{15} +1.89644 q^{16} +1.00000 q^{17} +2.37194 q^{18} +5.19396 q^{19} -1.34035 q^{20} +3.46859 q^{21} -1.79203 q^{22} +0.713417 q^{23} -3.85703 q^{24} -4.86337 q^{25} +3.53081 q^{26} -1.00000 q^{27} -12.5775 q^{28} -8.05401 q^{29} +0.876762 q^{30} -10.2118 q^{31} -3.21581 q^{32} +0.755512 q^{33} +2.37194 q^{34} +1.28213 q^{35} +3.62611 q^{36} -1.46546 q^{37} +12.3198 q^{38} -1.48857 q^{39} -1.42571 q^{40} -2.84725 q^{41} +8.22730 q^{42} +5.46367 q^{43} -2.73957 q^{44} -0.369639 q^{45} +1.69218 q^{46} -7.61120 q^{47} -1.89644 q^{48} +5.03112 q^{49} -11.5356 q^{50} -1.00000 q^{51} +5.39773 q^{52} +5.87047 q^{53} -2.37194 q^{54} +0.279267 q^{55} -13.3785 q^{56} -5.19396 q^{57} -19.1036 q^{58} +6.49441 q^{59} +1.34035 q^{60} +1.86258 q^{61} -24.2219 q^{62} -3.46859 q^{63} -11.4206 q^{64} -0.550235 q^{65} +1.79203 q^{66} -12.6405 q^{67} +3.62611 q^{68} -0.713417 q^{69} +3.04113 q^{70} -6.02601 q^{71} +3.85703 q^{72} -9.49792 q^{73} -3.47597 q^{74} +4.86337 q^{75} +18.8338 q^{76} +2.62056 q^{77} -3.53081 q^{78} +1.00000 q^{79} -0.701000 q^{80} +1.00000 q^{81} -6.75352 q^{82} -4.39993 q^{83} +12.5775 q^{84} -0.369639 q^{85} +12.9595 q^{86} +8.05401 q^{87} -2.91403 q^{88} -8.97425 q^{89} -0.876762 q^{90} -5.16325 q^{91} +2.58693 q^{92} +10.2118 q^{93} -18.0533 q^{94} -1.91989 q^{95} +3.21581 q^{96} -10.6670 q^{97} +11.9335 q^{98} -0.755512 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9}+O(q^{10}) \) 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9	\( 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9} - 13 q^{10} - 23 q^{11} - 19 q^{12} - 18 q^{13} - 9 q^{14} - q^{15} + 21 q^{16} + 22 q^{17} + q^{18} - 30 q^{19} - 7 q^{20} + 15 q^{21} + 4 q^{22} - 3 q^{23} - 15 q^{24} + 19 q^{25} - 7 q^{26} - 22 q^{27} - 25 q^{28} - 7 q^{29} + 13 q^{30} - 10 q^{31} + 31 q^{32} + 23 q^{33} + q^{34} - 11 q^{35} + 19 q^{36} - q^{37} - 29 q^{38} + 18 q^{39} - 59 q^{40} + 9 q^{42} - 43 q^{43} - 80 q^{44} + q^{45} - 43 q^{46} + 2 q^{47} - 21 q^{48} + 43 q^{49} + 25 q^{50} - 22 q^{51} - 5 q^{52} - q^{53} - q^{54} - 19 q^{55} - 8 q^{56} + 30 q^{57} - 43 q^{58} - 28 q^{59} + 7 q^{60} - 29 q^{61} - 3 q^{62} - 15 q^{63} + 23 q^{64} + 19 q^{65} - 4 q^{66} - 16 q^{67} + 19 q^{68} + 3 q^{69} - 5 q^{70} - q^{71} + 15 q^{72} - 19 q^{73} - 24 q^{74} - 19 q^{75} - 72 q^{76} + 24 q^{77} + 7 q^{78} + 22 q^{79} - 82 q^{80} + 22 q^{81} - 81 q^{82} - 29 q^{83} + 25 q^{84} + q^{85} - 42 q^{86} + 7 q^{87} - 43 q^{88} - 28 q^{89} - 13 q^{90} - 96 q^{91} - 11 q^{92} + 10 q^{93} - 63 q^{94} - 23 q^{95} - 31 q^{96} - 51 q^{97} + 12 q^{98} - 23 q^{99}+O(q^{100}) \) 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9 - 13 * q^10 - 23 * q^11 - 19 * q^12 - 18 * q^13 - 9 * q^14 - q^15 + 21 * q^16 + 22 * q^17 + q^18 - 30 * q^19 - 7 * q^20 + 15 * q^21 + 4 * q^22 - 3 * q^23 - 15 * q^24 + 19 * q^25 - 7 * q^26 - 22 * q^27 - 25 * q^28 - 7 * q^29 + 13 * q^30 - 10 * q^31 + 31 * q^32 + 23 * q^33 + q^34 - 11 * q^35 + 19 * q^36 - q^37 - 29 * q^38 + 18 * q^39 - 59 * q^40 + 9 * q^42 - 43 * q^43 - 80 * q^44 + q^45 - 43 * q^46 + 2 * q^47 - 21 * q^48 + 43 * q^49 + 25 * q^50 - 22 * q^51 - 5 * q^52 - q^53 - q^54 - 19 * q^55 - 8 * q^56 + 30 * q^57 - 43 * q^58 - 28 * q^59 + 7 * q^60 - 29 * q^61 - 3 * q^62 - 15 * q^63 + 23 * q^64 + 19 * q^65 - 4 * q^66 - 16 * q^67 + 19 * q^68 + 3 * q^69 - 5 * q^70 - q^71 + 15 * q^72 - 19 * q^73 - 24 * q^74 - 19 * q^75 - 72 * q^76 + 24 * q^77 + 7 * q^78 + 22 * q^79 - 82 * q^80 + 22 * q^81 - 81 * q^82 - 29 * q^83 + 25 * q^84 + q^85 - 42 * q^86 + 7 * q^87 - 43 * q^88 - 28 * q^89 - 13 * q^90 - 96 * q^91 - 11 * q^92 + 10 * q^93 - 63 * q^94 - 23 * q^95 - 31 * q^96 - 51 * q^97 + 12 * q^98 - 23 * q^99

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