LMFDB - Embedded newform 4029.2.a.f.1.9

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			1.9
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)

$f(q)$	$=$	$q-0.891747 q^{2} -1.00000 q^{3} -1.20479 q^{4} +2.60961 q^{5} +0.891747 q^{6} -3.10366 q^{7} +2.85786 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.891747 q^{2} -1.00000 q^{3} -1.20479 q^{4} +2.60961 q^{5} +0.891747 q^{6} -3.10366 q^{7} +2.85786 q^{8} +1.00000 q^{9} -2.32711 q^{10} -1.58159 q^{11} +1.20479 q^{12} +2.28432 q^{13} +2.76768 q^{14} -2.60961 q^{15} -0.138917 q^{16} +1.00000 q^{17} -0.891747 q^{18} -0.262399 q^{19} -3.14402 q^{20} +3.10366 q^{21} +1.41038 q^{22} -1.11378 q^{23} -2.85786 q^{24} +1.81006 q^{25} -2.03704 q^{26} -1.00000 q^{27} +3.73925 q^{28} -0.856356 q^{29} +2.32711 q^{30} -6.88582 q^{31} -5.59184 q^{32} +1.58159 q^{33} -0.891747 q^{34} -8.09934 q^{35} -1.20479 q^{36} -2.50830 q^{37} +0.233993 q^{38} -2.28432 q^{39} +7.45790 q^{40} +12.4501 q^{41} -2.76768 q^{42} +12.3022 q^{43} +1.90548 q^{44} +2.60961 q^{45} +0.993215 q^{46} -7.14174 q^{47} +0.138917 q^{48} +2.63272 q^{49} -1.61412 q^{50} -1.00000 q^{51} -2.75212 q^{52} -10.2956 q^{53} +0.891747 q^{54} -4.12734 q^{55} -8.86983 q^{56} +0.262399 q^{57} +0.763653 q^{58} -3.35627 q^{59} +3.14402 q^{60} +6.55044 q^{61} +6.14042 q^{62} -3.10366 q^{63} +5.26434 q^{64} +5.96119 q^{65} -1.41038 q^{66} +1.81832 q^{67} -1.20479 q^{68} +1.11378 q^{69} +7.22257 q^{70} -0.585533 q^{71} +2.85786 q^{72} +12.8311 q^{73} +2.23677 q^{74} -1.81006 q^{75} +0.316134 q^{76} +4.90873 q^{77} +2.03704 q^{78} +1.00000 q^{79} -0.362518 q^{80} +1.00000 q^{81} -11.1024 q^{82} -5.86377 q^{83} -3.73925 q^{84} +2.60961 q^{85} -10.9705 q^{86} +0.856356 q^{87} -4.51997 q^{88} -13.3687 q^{89} -2.32711 q^{90} -7.08977 q^{91} +1.34187 q^{92} +6.88582 q^{93} +6.36863 q^{94} -0.684758 q^{95} +5.59184 q^{96} +3.31374 q^{97} -2.34772 q^{98} -1.58159 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.891747	−0.630561	−0.315280	−	0.948999i	$-0.602099\pi$
$2$	−0.891747	−0.630561	−0.315280	+	0.948999i	$0.602099\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.20479	−0.602393
$5$	2.60961	1.16705	0.583526	−	0.812094i	$-0.301672\pi$
$5$	2.60961	1.16705	0.583526	+	0.812094i	$0.301672\pi$
$6$	0.891747	0.364054
$7$	−3.10366	−1.17307	−0.586537	−	0.809922i	$-0.699509\pi$
$7$	−3.10366	−1.17307	−0.586537	+	0.809922i	$0.699509\pi$
$8$	2.85786	1.01041
$9$	1.00000	0.333333
$10$	−2.32711	−0.735898
$11$	−1.58159	−0.476868	−0.238434	−	0.971159i	$-0.576634\pi$
$11$	−1.58159	−0.476868	−0.238434	+	0.971159i	$0.576634\pi$
$12$	1.20479	0.347792
$13$	2.28432	0.633557	0.316779	−	0.948499i	$-0.397399\pi$
$13$	2.28432	0.633557	0.316779	+	0.948499i	$0.397399\pi$
$14$	2.76768	0.739694
$15$	−2.60961	−0.673798
$16$	−0.138917	−0.0347292
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.891747	−0.210187
$19$	−0.262399	−0.0601984	−0.0300992	−	0.999547i	$-0.509582\pi$
$19$	−0.262399	−0.0601984	−0.0300992	+	0.999547i	$0.509582\pi$
$20$	−3.14402	−0.703025
$21$	3.10366	0.677275
$22$	1.41038	0.300694
$23$	−1.11378	−0.232240	−0.116120	−	0.993235i	$-0.537046\pi$
$23$	−1.11378	−0.232240	−0.116120	+	0.993235i	$0.537046\pi$
$24$	−2.85786	−0.583358
$25$	1.81006	0.362012
$26$	−2.03704	−0.399496
$27$	−1.00000	−0.192450
$28$	3.73925	0.706652
$29$	−0.856356	−0.159021	−0.0795106	−	0.996834i	$-0.525336\pi$
$29$	−0.856356	−0.159021	−0.0795106	+	0.996834i	$0.525336\pi$
$30$	2.32711	0.424871
$31$	−6.88582	−1.23673	−0.618365	−	0.785891i	$-0.712205\pi$
$31$	−6.88582	−1.23673	−0.618365	+	0.785891i	$0.712205\pi$
$32$	−5.59184	−0.988507
$33$	1.58159	0.275320
$34$	−0.891747	−0.152933
$35$	−8.09934	−1.36904
$36$	−1.20479	−0.200798
$37$	−2.50830	−0.412362	−0.206181	−	0.978514i	$-0.566104\pi$
$37$	−2.50830	−0.412362	−0.206181	+	0.978514i	$0.566104\pi$
$38$	0.233993	0.0379587
$39$	−2.28432	−0.365785
$40$	7.45790	1.17920
$41$	12.4501	1.94438	0.972190	−	0.234193i	$-0.0752447\pi$
$41$	12.4501	1.94438	0.972190	+	0.234193i	$0.0752447\pi$
$42$	−2.76768	−0.427063
$43$	12.3022	1.87607	0.938034	−	0.346542i	$-0.112644\pi$
$43$	12.3022	1.87607	0.938034	+	0.346542i	$0.112644\pi$
$44$	1.90548	0.287262
$45$	2.60961	0.389018
$46$	0.993215	0.146442
$47$	−7.14174	−1.04173	−0.520865	−	0.853639i	$-0.674391\pi$
$47$	−7.14174	−1.04173	−0.520865	+	0.853639i	$0.674391\pi$
$48$	0.138917	0.0200509
$49$	2.63272	0.376102
$50$	−1.61412	−0.228271
$51$	−1.00000	−0.140028
$52$	−2.75212	−0.381651
$53$	−10.2956	−1.41421	−0.707106	−	0.707108i	$-0.750000\pi$
$53$	−10.2956	−1.41421	−0.707106	+	0.707108i	$0.750000\pi$
$54$	0.891747	0.121351
$55$	−4.12734	−0.556531
$56$	−8.86983	−1.18528
$57$	0.262399	0.0347555
$58$	0.763653	0.100273
$59$	−3.35627	−0.436950	−0.218475	−	0.975843i	$-0.570108\pi$
$59$	−3.35627	−0.436950	−0.218475	+	0.975843i	$0.570108\pi$
$60$	3.14402	0.405891
$61$	6.55044	0.838698	0.419349	−	0.907825i	$-0.362258\pi$
$61$	6.55044	0.838698	0.419349	+	0.907825i	$0.362258\pi$
$62$	6.14042	0.779834
$63$	−3.10366	−0.391025
$64$	5.26434	0.658043
$65$	5.96119	0.739395
$66$	−1.41038	−0.173606
$67$	1.81832	0.222143	0.111072	−	0.993812i	$-0.464572\pi$
$67$	1.81832	0.222143	0.111072	+	0.993812i	$0.464572\pi$
$68$	−1.20479	−0.146102
$69$	1.11378	0.134084
$70$	7.22257	0.863262
$71$	−0.585533	−0.0694899	−0.0347450	−	0.999396i	$-0.511062\pi$
$71$	−0.585533	−0.0694899	−0.0347450	+	0.999396i	$0.511062\pi$
$72$	2.85786	0.336802
$73$	12.8311	1.50176	0.750881	−	0.660438i	$-0.229629\pi$
$73$	12.8311	1.50176	0.750881	+	0.660438i	$0.229629\pi$
$74$	2.23677	0.260019
$75$	−1.81006	−0.209008
$76$	0.316134	0.0362631
$77$	4.90873	0.559402
$78$	2.03704	0.230649
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	−0.362518	−0.0405308
$81$	1.00000	0.111111
$82$	−11.1024	−1.22605
$83$	−5.86377	−0.643632	−0.321816	−	0.946802i	$-0.604293\pi$
$83$	−5.86377	−0.643632	−0.321816	+	0.946802i	$0.604293\pi$
$84$	−3.73925	−0.407986
$85$	2.60961	0.283052
$86$	−10.9705	−1.18298
$87$	0.856356	0.0918110
$88$	−4.51997	−0.481831
$89$	−13.3687	−1.41708	−0.708539	−	0.705671i	$-0.750646\pi$
$89$	−13.3687	−1.41708	−0.708539	+	0.705671i	$0.750646\pi$
$90$	−2.32711	−0.245299
$91$	−7.08977	−0.743210
$92$	1.34187	0.139900
$93$	6.88582	0.714027
$94$	6.36863	0.656874
$95$	−0.684758	−0.0702547
$96$	5.59184	0.570715
$97$	3.31374	0.336459	0.168229	−	0.985748i	$-0.446195\pi$
$97$	3.31374	0.336459	0.168229	+	0.985748i	$0.446195\pi$
$98$	−2.34772	−0.237155
$99$	−1.58159	−0.158956
$100$	−2.18074	−0.218074
$101$	12.1645	1.21041	0.605207	−	0.796069i	$-0.293091\pi$
$101$	12.1645	1.21041	0.605207	+	0.796069i	$0.293091\pi$
$102$	0.891747	0.0882962
$103$	−5.37495	−0.529610	−0.264805	−	0.964302i	$-0.585308\pi$
$103$	−5.37495	−0.529610	−0.264805	+	0.964302i	$0.585308\pi$
$104$	6.52828	0.640150
$105$	8.09934	0.790415
$106$	9.18109	0.891746
$107$	1.72034	0.166311	0.0831556	−	0.996537i	$-0.473500\pi$
$107$	1.72034	0.166311	0.0831556	+	0.996537i	$0.473500\pi$
$108$	1.20479	0.115931
$109$	−8.59261	−0.823023	−0.411511	−	0.911405i	$-0.634999\pi$
$109$	−8.59261	−0.823023	−0.411511	+	0.911405i	$0.634999\pi$
$110$	3.68055	0.350926
$111$	2.50830	0.238077
$112$	0.431151	0.0407399
$113$	−10.6633	−1.00312	−0.501558	−	0.865124i	$-0.667240\pi$
$113$	−10.6633	−1.00312	−0.501558	+	0.865124i	$0.667240\pi$
$114$	−0.233993	−0.0219155
$115$	−2.90654	−0.271037
$116$	1.03173	0.0957933
$117$	2.28432	0.211186
$118$	2.99295	0.275523
$119$	−3.10366	−0.284512
$120$	−7.45790	−0.680810
$121$	−8.49856	−0.772597
$122$	−5.84134	−0.528850
$123$	−12.4501	−1.12259
$124$	8.29595	0.744998
$125$	−8.32449	−0.744565
$126$	2.76768	0.246565
$127$	−2.11037	−0.187265	−0.0936324	−	0.995607i	$-0.529848\pi$
$127$	−2.11037	−0.187265	−0.0936324	+	0.995607i	$0.529848\pi$
$128$	6.48922	0.573571
$129$	−12.3022	−1.08315
$130$	−5.31588	−0.466233
$131$	16.5140	1.44284	0.721419	−	0.692499i	$-0.243490\pi$
$131$	16.5140	1.44284	0.721419	+	0.692499i	$0.243490\pi$
$132$	−1.90548	−0.165851
$133$	0.814396	0.0706171
$134$	−1.62148	−0.140075
$135$	−2.60961	−0.224599
$136$	2.85786	0.245059
$137$	20.2915	1.73362	0.866809	−	0.498641i	$-0.166167\pi$
$137$	20.2915	1.73362	0.866809	+	0.498641i	$0.166167\pi$
$138$	−0.993215	−0.0845481
$139$	−11.3107	−0.959357	−0.479679	−	0.877444i	$-0.659247\pi$
$139$	−11.3107	−0.959357	−0.479679	+	0.877444i	$0.659247\pi$
$140$	9.75798	0.824700
$141$	7.14174	0.601443
$142$	0.522147	0.0438176
$143$	−3.61287	−0.302123
$144$	−0.138917	−0.0115764
$145$	−2.23475	−0.185586
$146$	−11.4421	−0.946952
$147$	−2.63272	−0.217143
$148$	3.02197	0.248404
$149$	−19.4462	−1.59309	−0.796545	−	0.604579i	$-0.793341\pi$
$149$	−19.4462	−1.59309	−0.796545	+	0.604579i	$0.793341\pi$
$150$	1.61412	0.131792
$151$	11.3550	0.924060	0.462030	−	0.886864i	$-0.347121\pi$
$151$	11.3550	0.924060	0.462030	+	0.886864i	$0.347121\pi$
$152$	−0.749898	−0.0608248
$153$	1.00000	0.0808452
$154$	−4.37735	−0.352737
$155$	−17.9693	−1.44333
$156$	2.75212	0.220346
$157$	10.5710	0.843658	0.421829	−	0.906675i	$-0.361388\pi$
$157$	10.5710	0.843658	0.421829	+	0.906675i	$0.361388\pi$
$158$	−0.891747	−0.0709436
$159$	10.2956	0.816495
$160$	−14.5925	−1.15364
$161$	3.45681	0.272435
$162$	−0.891747	−0.0700623
$163$	−6.97449	−0.546284	−0.273142	−	0.961974i	$-0.588063\pi$
$163$	−6.97449	−0.546284	−0.273142	+	0.961974i	$0.588063\pi$
$164$	−14.9997	−1.17128
$165$	4.12734	0.321313
$166$	5.22900	0.405849
$167$	−13.2106	−1.02227	−0.511134	−	0.859501i	$-0.670774\pi$
$167$	−13.2106	−1.02227	−0.511134	+	0.859501i	$0.670774\pi$
$168$	8.86983	0.684322
$169$	−7.78186	−0.598605
$170$	−2.32711	−0.178481
$171$	−0.262399	−0.0200661
$172$	−14.8215	−1.13013
$173$	13.9821	1.06304	0.531519	−	0.847046i	$-0.321621\pi$
$173$	13.9821	1.06304	0.531519	+	0.847046i	$0.321621\pi$
$174$	−0.763653	−0.0578924
$175$	−5.61782	−0.424667
$176$	0.219710	0.0165613
$177$	3.35627	0.252273
$178$	11.9215	0.893554
$179$	−14.6714	−1.09659	−0.548297	−	0.836284i	$-0.684724\pi$
$179$	−14.6714	−1.09659	−0.548297	+	0.836284i	$0.684724\pi$
$180$	−3.14402	−0.234342
$181$	16.7588	1.24567	0.622835	−	0.782354i	$-0.285981\pi$
$181$	16.7588	1.24567	0.622835	+	0.782354i	$0.285981\pi$
$182$	6.32228	0.468639
$183$	−6.55044	−0.484223
$184$	−3.18304	−0.234657
$185$	−6.54569	−0.481248
$186$	−6.14042	−0.450237
$187$	−1.58159	−0.115658
$188$	8.60427	0.627531
$189$	3.10366	0.225758
$190$	0.610631	0.0442998
$191$	1.15257	0.0833967	0.0416983	−	0.999130i	$-0.486723\pi$
$191$	1.15257	0.0833967	0.0416983	+	0.999130i	$0.486723\pi$
$192$	−5.26434	−0.379921
$193$	−15.6096	−1.12360	−0.561801	−	0.827273i	$-0.689891\pi$
$193$	−15.6096	−1.12360	−0.561801	+	0.827273i	$0.689891\pi$
$194$	−2.95502	−0.212158
$195$	−5.96119	−0.426890
$196$	−3.17186	−0.226561
$197$	16.3906	1.16778	0.583889	−	0.811833i	$-0.301530\pi$
$197$	16.3906	1.16778	0.583889	+	0.811833i	$0.301530\pi$
$198$	1.41038	0.100231
$199$	−15.2383	−1.08021	−0.540107	−	0.841597i	$-0.681616\pi$
$199$	−15.2383	−1.08021	−0.540107	+	0.841597i	$0.681616\pi$
$200$	5.17290	0.365779
$201$	−1.81832	−0.128254
$202$	−10.8477	−0.763239
$203$	2.65784	0.186544
$204$	1.20479	0.0843519
$205$	32.4899	2.26919
$206$	4.79310	0.333951
$207$	−1.11378	−0.0774134
$208$	−0.317331	−0.0220029
$209$	0.415008	0.0287067
$210$	−7.22257	−0.498405
$211$	−21.9622	−1.51194	−0.755969	−	0.654607i	$-0.772834\pi$
$211$	−21.9622	−1.51194	−0.755969	+	0.654607i	$0.772834\pi$
$212$	12.4040	0.851911
$213$	0.585533	0.0401200
$214$	−1.53411	−0.104869
$215$	32.1039	2.18947
$216$	−2.85786	−0.194453
$217$	21.3713	1.45078
$218$	7.66244	0.518966
$219$	−12.8311	−0.867042
$220$	4.97256	0.335250
$221$	2.28432	0.153660
$222$	−2.23677	−0.150122
$223$	−9.21811	−0.617290	−0.308645	−	0.951177i	$-0.599876\pi$
$223$	−9.21811	−0.617290	−0.308645	+	0.951177i	$0.599876\pi$
$224$	17.3552	1.15959
$225$	1.81006	0.120671
$226$	9.50895	0.632526
$227$	−17.2103	−1.14229	−0.571144	−	0.820850i	$-0.693500\pi$
$227$	−17.2103	−1.14229	−0.571144	+	0.820850i	$0.693500\pi$
$228$	−0.316134	−0.0209365
$229$	−14.8907	−0.984003	−0.492001	−	0.870594i	$-0.663735\pi$
$229$	−14.8907	−0.984003	−0.492001	+	0.870594i	$0.663735\pi$
$230$	2.59190	0.170905
$231$	−4.90873	−0.322971
$232$	−2.44735	−0.160676
$233$	−3.63924	−0.238414	−0.119207	−	0.992869i	$-0.538035\pi$
$233$	−3.63924	−0.238414	−0.119207	+	0.992869i	$0.538035\pi$
$234$	−2.03704	−0.133165
$235$	−18.6372	−1.21575
$236$	4.04359	0.263215
$237$	−1.00000	−0.0649570
$238$	2.76768	0.179402
$239$	22.5659	1.45967	0.729833	−	0.683625i	$-0.239598\pi$
$239$	22.5659	1.45967	0.729833	+	0.683625i	$0.239598\pi$
$240$	0.362518	0.0234005
$241$	4.92360	0.317157	0.158579	−	0.987346i	$-0.449309\pi$
$241$	4.92360	0.317157	0.158579	+	0.987346i	$0.449309\pi$
$242$	7.57857	0.487169
$243$	−1.00000	−0.0641500
$244$	−7.89189	−0.505226
$245$	6.87036	0.438931
$246$	11.1024	0.707860
$247$	−0.599403	−0.0381391
$248$	−19.6787	−1.24960
$249$	5.86377	0.371601
$250$	7.42335	0.469494
$251$	24.6154	1.55371	0.776854	−	0.629681i	$-0.216815\pi$
$251$	24.6154	1.55371	0.776854	+	0.629681i	$0.216815\pi$
$252$	3.73925	0.235551
$253$	1.76155	0.110748
$254$	1.88191	0.118082
$255$	−2.60961	−0.163420
$256$	−16.3154	−1.01971
$257$	−26.9740	−1.68259	−0.841294	−	0.540577i	$-0.818206\pi$
$257$	−26.9740	−1.68259	−0.841294	+	0.540577i	$0.818206\pi$
$258$	10.9705	0.682991
$259$	7.78492	0.483731
$260$	−7.18196	−0.445407
$261$	−0.856356	−0.0530071
$262$	−14.7263	−0.909797
$263$	−6.07245	−0.374444	−0.187222	−	0.982318i	$-0.559948\pi$
$263$	−6.07245	−0.374444	−0.187222	+	0.982318i	$0.559948\pi$
$264$	4.51997	0.278185
$265$	−26.8675	−1.65046
$266$	−0.726236	−0.0445284
$267$	13.3687	0.818151
$268$	−2.19069	−0.133818
$269$	−31.6073	−1.92713	−0.963565	−	0.267475i	$-0.913811\pi$
$269$	−31.6073	−1.92713	−0.963565	+	0.267475i	$0.913811\pi$
$270$	2.32711	0.141624
$271$	9.01245	0.547467	0.273734	−	0.961806i	$-0.411741\pi$
$271$	9.01245	0.547467	0.273734	+	0.961806i	$0.411741\pi$
$272$	−0.138917	−0.00842307
$273$	7.08977	0.429092
$274$	−18.0949	−1.09315
$275$	−2.86278	−0.172632
$276$	−1.34187	−0.0807713
$277$	−28.0940	−1.68801	−0.844003	−	0.536339i	$-0.819807\pi$
$277$	−28.0940	−1.68801	−0.844003	+	0.536339i	$0.819807\pi$
$278$	10.0862	0.604933
$279$	−6.88582	−0.412244
$280$	−23.1468	−1.38329
$281$	−24.3961	−1.45535	−0.727676	−	0.685921i	$-0.759400\pi$
$281$	−24.3961	−1.45535	−0.727676	+	0.685921i	$0.759400\pi$
$282$	−6.36863	−0.379246
$283$	−16.9647	−1.00844	−0.504222	−	0.863574i	$-0.668221\pi$
$283$	−16.9647	−1.00844	−0.504222	+	0.863574i	$0.668221\pi$
$284$	0.705442	0.0418603
$285$	0.684758	0.0405615
$286$	3.22177	0.190507
$287$	−38.6409	−2.28090
$288$	−5.59184	−0.329502
$289$	1.00000	0.0588235
$290$	1.99284	0.117023
$291$	−3.31374	−0.194255
$292$	−15.4587	−0.904651
$293$	8.20044	0.479075	0.239538	−	0.970887i	$-0.423004\pi$
$293$	8.20044	0.479075	0.239538	+	0.970887i	$0.423004\pi$
$294$	2.34772	0.136922
$295$	−8.75856	−0.509943
$296$	−7.16837	−0.416653
$297$	1.58159	0.0917734
$298$	17.3411	1.00454
$299$	−2.54425	−0.147138
$300$	2.18074	0.125905
$301$	−38.1819	−2.20077
$302$	−10.1258	−0.582676
$303$	−12.1645	−0.698832
$304$	0.0364516	0.00209064
$305$	17.0941	0.978805
$306$	−0.891747	−0.0509778
$307$	−23.6272	−1.34848	−0.674239	−	0.738514i	$-0.735528\pi$
$307$	−23.6272	−1.34848	−0.674239	+	0.738514i	$0.735528\pi$
$308$	−5.91397	−0.336980
$309$	5.37495	0.305770
$310$	16.0241	0.910107
$311$	−2.20387	−0.124970	−0.0624849	−	0.998046i	$-0.519903\pi$
$311$	−2.20387	−0.124970	−0.0624849	+	0.998046i	$0.519903\pi$
$312$	−6.52828	−0.369591
$313$	−10.8306	−0.612183	−0.306091	−	0.952002i	$-0.599021\pi$
$313$	−10.8306	−0.612183	−0.306091	+	0.952002i	$0.599021\pi$
$314$	−9.42666	−0.531977
$315$	−8.09934	−0.456346
$316$	−1.20479	−0.0677745
$317$	27.8924	1.56659	0.783296	−	0.621648i	$-0.213537\pi$
$317$	27.8924	1.56659	0.783296	+	0.621648i	$0.213537\pi$
$318$	−9.18109	−0.514850
$319$	1.35441	0.0758322
$320$	13.7379	0.767971
$321$	−1.72034	−0.0960198
$322$	−3.08260	−0.171787
$323$	−0.262399	−0.0146002
$324$	−1.20479	−0.0669326
$325$	4.13477	0.229356
$326$	6.21948	0.344465
$327$	8.59261	0.475172
$328$	35.5807	1.96461
$329$	22.1655	1.22203
$330$	−3.68055	−0.202607
$331$	−22.5132	−1.23744	−0.618720	−	0.785612i	$-0.712348\pi$
$331$	−22.5132	−1.23744	−0.618720	+	0.785612i	$0.712348\pi$
$332$	7.06459	0.387720
$333$	−2.50830	−0.137454
$334$	11.7805	0.644601
$335$	4.74510	0.259253
$336$	−0.431151	−0.0235212
$337$	−33.4072	−1.81981	−0.909904	−	0.414819i	$-0.863845\pi$
$337$	−33.4072	−1.81981	−0.909904	+	0.414819i	$0.863845\pi$
$338$	6.93946	0.377457
$339$	10.6633	0.579150
$340$	−3.14402	−0.170509
$341$	10.8906	0.589758
$342$	0.233993	0.0126529
$343$	13.5546	0.731878
$344$	35.1580	1.89559
$345$	2.90654	0.156483
$346$	−12.4685	−0.670310
$347$	−13.9252	−0.747545	−0.373772	−	0.927521i	$-0.621936\pi$
$347$	−13.9252	−0.747545	−0.373772	+	0.927521i	$0.621936\pi$
$348$	−1.03173	−0.0553063
$349$	9.11472	0.487900	0.243950	−	0.969788i	$-0.421557\pi$
$349$	9.11472	0.487900	0.243950	+	0.969788i	$0.421557\pi$
$350$	5.00967	0.267778
$351$	−2.28432	−0.121928
$352$	8.84402	0.471388
$353$	−24.7388	−1.31671	−0.658357	−	0.752705i	$-0.728748\pi$
$353$	−24.7388	−1.31671	−0.658357	+	0.752705i	$0.728748\pi$
$354$	−2.99295	−0.159073
$355$	−1.52801	−0.0810984
$356$	16.1064	0.853639
$357$	3.10366	0.164263
$358$	13.0832	0.691469
$359$	31.1019	1.64149	0.820747	−	0.571292i	$-0.193557\pi$
$359$	31.1019	1.64149	0.820747	+	0.571292i	$0.193557\pi$
$360$	7.45790	0.393066
$361$	−18.9311	−0.996376
$362$	−14.9446	−0.785470
$363$	8.49856	0.446059
$364$	8.54166	0.447704
$365$	33.4840	1.75264
$366$	5.84134	0.305332
$367$	−7.01968	−0.366424	−0.183212	−	0.983073i	$-0.558649\pi$
$367$	−7.01968	−0.366424	−0.183212	+	0.983073i	$0.558649\pi$
$368$	0.154723	0.00806551
$369$	12.4501	0.648127
$370$	5.83710	0.303456
$371$	31.9541	1.65897
$372$	−8.29595	−0.430125
$373$	17.9398	0.928890	0.464445	−	0.885602i	$-0.346254\pi$
$373$	17.9398	0.928890	0.464445	+	0.885602i	$0.346254\pi$
$374$	1.41038	0.0729291
$375$	8.32449	0.429875
$376$	−20.4101	−1.05257
$377$	−1.95619	−0.100749
$378$	−2.76768	−0.142354
$379$	−25.2590	−1.29747	−0.648734	−	0.761016i	$-0.724701\pi$
$379$	−25.2590	−1.29747	−0.648734	+	0.761016i	$0.724701\pi$
$380$	0.824987	0.0423209
$381$	2.11037	0.108117
$382$	−1.02780	−0.0525867
$383$	−23.6411	−1.20800	−0.604002	−	0.796983i	$-0.706428\pi$
$383$	−23.6411	−1.20800	−0.604002	+	0.796983i	$0.706428\pi$
$384$	−6.48922	−0.331152
$385$	12.8099	0.652851
$386$	13.9198	0.708499
$387$	12.3022	0.625356
$388$	−3.99234	−0.202681
$389$	13.6297	0.691054	0.345527	−	0.938409i	$-0.387700\pi$
$389$	13.6297	0.691054	0.345527	+	0.938409i	$0.387700\pi$
$390$	5.31588	0.269180
$391$	−1.11378	−0.0563265
$392$	7.52393	0.380016
$393$	−16.5140	−0.833023
$394$	−14.6162	−0.736355
$395$	2.60961	0.131304
$396$	1.90548	0.0957541
$397$	−12.5637	−0.630556	−0.315278	−	0.948999i	$-0.602098\pi$
$397$	−12.5637	−0.630556	−0.315278	+	0.948999i	$0.602098\pi$
$398$	13.5887	0.681140
$399$	−0.814396	−0.0407708
$400$	−0.251448	−0.0125724
$401$	−26.9606	−1.34635	−0.673173	−	0.739485i	$-0.735069\pi$
$401$	−26.9606	−1.34635	−0.673173	+	0.739485i	$0.735069\pi$
$402$	1.62148	0.0808722
$403$	−15.7295	−0.783540
$404$	−14.6556	−0.729145
$405$	2.60961	0.129673
$406$	−2.37012	−0.117627
$407$	3.96711	0.196642
$408$	−2.85786	−0.141485
$409$	−29.5890	−1.46308	−0.731542	−	0.681796i	$-0.761199\pi$
$409$	−29.5890	−1.46308	−0.731542	+	0.681796i	$0.761199\pi$
$410$	−28.9728	−1.43086
$411$	−20.2915	−1.00090
$412$	6.47567	0.319033
$413$	10.4167	0.512574
$414$	0.993215	0.0488139
$415$	−15.3021	−0.751153
$416$	−12.7736	−0.626276
$417$	11.3107	0.553885
$418$	−0.370082	−0.0181013
$419$	−11.1108	−0.542796	−0.271398	−	0.962467i	$-0.587486\pi$
$419$	−11.1108	−0.542796	−0.271398	+	0.962467i	$0.587486\pi$
$420$	−9.75798	−0.476141
$421$	13.3984	0.652998	0.326499	−	0.945197i	$-0.394131\pi$
$421$	13.3984	0.652998	0.326499	+	0.945197i	$0.394131\pi$
$422$	19.5847	0.953369
$423$	−7.14174	−0.347243
$424$	−29.4234	−1.42893
$425$	1.81006	0.0878009
$426$	−0.522147	−0.0252981
$427$	−20.3304	−0.983855
$428$	−2.07264	−0.100185
$429$	3.61287	0.174431
$430$	−28.6286	−1.38059
$431$	−35.1772	−1.69443	−0.847214	−	0.531252i	$-0.821722\pi$
$431$	−35.1772	−1.69443	−0.847214	+	0.531252i	$0.821722\pi$
$432$	0.138917	0.00668364
$433$	17.1951	0.826343	0.413172	−	0.910653i	$-0.364421\pi$
$433$	17.1951	0.826343	0.413172	+	0.910653i	$0.364421\pi$
$434$	−19.0578	−0.914802
$435$	2.23475	0.107148
$436$	10.3523	0.495783
$437$	0.292256	0.0139805
$438$	11.4421	0.546723
$439$	−5.85192	−0.279297	−0.139649	−	0.990201i	$-0.544597\pi$
$439$	−5.85192	−0.279297	−0.139649	+	0.990201i	$0.544597\pi$
$440$	−11.7954	−0.562322
$441$	2.63272	0.125367
$442$	−2.03704	−0.0968921
$443$	3.35765	0.159527	0.0797634	−	0.996814i	$-0.474584\pi$
$443$	3.35765	0.159527	0.0797634	+	0.996814i	$0.474584\pi$
$444$	−3.02197	−0.143416
$445$	−34.8871	−1.65381
$446$	8.22022	0.389239
$447$	19.4462	0.919771
$448$	−16.3387	−0.771933
$449$	−33.9903	−1.60410	−0.802051	−	0.597255i	$-0.796258\pi$
$449$	−33.9903	−1.60410	−0.802051	+	0.597255i	$0.796258\pi$
$450$	−1.61412	−0.0760902
$451$	−19.6910	−0.927213
$452$	12.8470	0.604271
$453$	−11.3550	−0.533506
$454$	15.3472	0.720281
$455$	−18.5015	−0.867365
$456$	0.749898	0.0351172
$457$	28.1426	1.31645	0.658227	−	0.752819i	$-0.271307\pi$
$457$	28.1426	1.31645	0.658227	+	0.752819i	$0.271307\pi$
$458$	13.2787	0.620473
$459$	−1.00000	−0.0466760
$460$	3.50176	0.163271
$461$	10.3445	0.481794	0.240897	−	0.970551i	$-0.422558\pi$
$461$	10.3445	0.481794	0.240897	+	0.970551i	$0.422558\pi$
$462$	4.37735	0.203653
$463$	27.2511	1.26646	0.633232	−	0.773962i	$-0.281728\pi$
$463$	27.2511	1.26646	0.633232	+	0.773962i	$0.281728\pi$
$464$	0.118962	0.00552268
$465$	17.9693	0.833307
$466$	3.24528	0.150335
$467$	−13.1150	−0.606890	−0.303445	−	0.952849i	$-0.598137\pi$
$467$	−13.1150	−0.606890	−0.303445	+	0.952849i	$0.598137\pi$
$468$	−2.75212	−0.127217
$469$	−5.64345	−0.260590
$470$	16.6196	0.766607
$471$	−10.5710	−0.487086
$472$	−9.59176	−0.441497
$473$	−19.4571	−0.894638
$474$	0.891747	0.0409593
$475$	−0.474957	−0.0217925
$476$	3.73925	0.171388
$477$	−10.2956	−0.471404
$478$	−20.1231	−0.920408
$479$	13.7994	0.630512	0.315256	−	0.949007i	$-0.397910\pi$
$479$	13.7994	0.630512	0.315256	+	0.949007i	$0.397910\pi$
$480$	14.5925	0.666054
$481$	−5.72977	−0.261255
$482$	−4.39061	−0.199987
$483$	−3.45681	−0.157290
$484$	10.2390	0.465407
$485$	8.64756	0.392665
$486$	0.891747	0.0404505
$487$	−24.7874	−1.12322	−0.561612	−	0.827401i	$-0.689818\pi$
$487$	−24.7874	−1.12322	−0.561612	+	0.827401i	$0.689818\pi$
$488$	18.7203	0.847426
$489$	6.97449	0.315397
$490$	−6.12663	−0.276773
$491$	33.4879	1.51129	0.755643	−	0.654983i	$-0.227324\pi$
$491$	33.4879	1.51129	0.755643	+	0.654983i	$0.227324\pi$
$492$	14.9997	0.676240
$493$	−0.856356	−0.0385683
$494$	0.534516	0.0240490
$495$	−4.12734	−0.185510
$496$	0.956556	0.0429506
$497$	1.81729	0.0815168
$498$	−5.22900	−0.234317
$499$	−31.2717	−1.39992	−0.699958	−	0.714184i	$-0.746798\pi$
$499$	−31.2717	−1.39992	−0.699958	+	0.714184i	$0.746798\pi$
$500$	10.0292	0.448521
$501$	13.2106	0.590206
$502$	−21.9507	−0.979707
$503$	−33.1923	−1.47997	−0.739986	−	0.672622i	$-0.765168\pi$
$503$	−33.1923	−1.47997	−0.739986	+	0.672622i	$0.765168\pi$
$504$	−8.86983	−0.395094
$505$	31.7446	1.41262
$506$	−1.57086	−0.0698333
$507$	7.78186	0.345605
$508$	2.54254	0.112807
$509$	−21.1578	−0.937805	−0.468902	−	0.883250i	$-0.655350\pi$
$509$	−21.1578	−0.937805	−0.468902	+	0.883250i	$0.655350\pi$
$510$	2.32711	0.103046
$511$	−39.8233	−1.76168
$512$	1.57081	0.0694206
$513$	0.262399	0.0115852
$514$	24.0540	1.06097
$515$	−14.0265	−0.618083
$516$	14.8215	0.652481
$517$	11.2953	0.496768
$518$	−6.94218	−0.305022
$519$	−13.9821	−0.613745
$520$	17.0363	0.747089
$521$	41.0921	1.80028	0.900140	−	0.435602i	$-0.143464\pi$
$521$	41.0921	1.80028	0.900140	+	0.435602i	$0.143464\pi$
$522$	0.763653	0.0334242
$523$	−20.7803	−0.908660	−0.454330	−	0.890834i	$-0.650121\pi$
$523$	−20.7803	−0.908660	−0.454330	+	0.890834i	$0.650121\pi$
$524$	−19.8959	−0.869156
$525$	5.61782	0.245182
$526$	5.41510	0.236109
$527$	−6.88582	−0.299951
$528$	−0.219710	−0.00956164
$529$	−21.7595	−0.946064
$530$	23.9591	1.04071
$531$	−3.35627	−0.145650
$532$	−0.981174	−0.0425393
$533$	28.4401	1.23188
$534$	−11.9215	−0.515894
$535$	4.48941	0.194094
$536$	5.19650	0.224455
$537$	14.6714	0.633119
$538$	28.1857	1.21517
$539$	−4.16389	−0.179351
$540$	3.14402	0.135297
$541$	−21.8378	−0.938880	−0.469440	−	0.882964i	$-0.655544\pi$
$541$	−21.8378	−0.938880	−0.469440	+	0.882964i	$0.655544\pi$
$542$	−8.03683	−0.345211
$543$	−16.7588	−0.719187
$544$	−5.59184	−0.239748
$545$	−22.4234	−0.960511
$546$	−6.32228	−0.270569
$547$	22.6613	0.968927	0.484464	−	0.874811i	$-0.339015\pi$
$547$	22.6613	0.968927	0.484464	+	0.874811i	$0.339015\pi$
$548$	−24.4469	−1.04432
$549$	6.55044	0.279566
$550$	2.55288	0.108855
$551$	0.224706	0.00957282
$552$	3.18304	0.135479
$553$	−3.10366	−0.131981
$554$	25.0528	1.06439
$555$	6.54569	0.277849
$556$	13.6269	0.577910
$557$	17.5032	0.741635	0.370818	−	0.928706i	$-0.379078\pi$
$557$	17.5032	0.741635	0.370818	+	0.928706i	$0.379078\pi$
$558$	6.14042	0.259945
$559$	28.1022	1.18860
$560$	1.12513	0.0475456
$561$	1.58159	0.0667749
$562$	21.7552	0.917688
$563$	34.7428	1.46423	0.732117	−	0.681179i	$-0.238532\pi$
$563$	34.7428	1.46423	0.732117	+	0.681179i	$0.238532\pi$
$564$	−8.60427	−0.362305
$565$	−27.8270	−1.17069
$566$	15.1282	0.635885
$567$	−3.10366	−0.130342
$568$	−1.67337	−0.0702130
$569$	27.7634	1.16390	0.581952	−	0.813223i	$-0.302289\pi$
$569$	27.7634	1.16390	0.581952	+	0.813223i	$0.302289\pi$
$570$	−0.610631	−0.0255765
$571$	−37.9853	−1.58963	−0.794817	−	0.606849i	$-0.792433\pi$
$571$	−37.9853	−1.58963	−0.794817	+	0.606849i	$0.792433\pi$
$572$	4.35274	0.181997
$573$	−1.15257	−0.0481491
$574$	34.4579	1.43825
$575$	−2.01602	−0.0840738
$576$	5.26434	0.219348
$577$	21.5041	0.895227	0.447613	−	0.894227i	$-0.352274\pi$
$577$	21.5041	0.895227	0.447613	+	0.894227i	$0.352274\pi$
$578$	−0.891747	−0.0370918
$579$	15.6096	0.648712
$580$	2.69240	0.111796
$581$	18.1991	0.755028
$582$	2.95502	0.122489
$583$	16.2835	0.674393
$584$	36.6694	1.51739
$585$	5.96119	0.246465
$586$	−7.31272	−0.302086
$587$	−38.4818	−1.58831	−0.794157	−	0.607713i	$-0.792087\pi$
$587$	−38.4818	−1.58831	−0.794157	+	0.607713i	$0.792087\pi$
$588$	3.17186	0.130805
$589$	1.80683	0.0744491
$590$	7.81043	0.321550
$591$	−16.3906	−0.674217
$592$	0.348445	0.0143210
$593$	43.5520	1.78847	0.894233	−	0.447601i	$-0.147722\pi$
$593$	43.5520	1.78847	0.894233	+	0.447601i	$0.147722\pi$
$594$	−1.41038	−0.0578687
$595$	−8.09934	−0.332041
$596$	23.4285	0.959667
$597$	15.2383	0.623661
$598$	2.26882	0.0927791
$599$	−16.5939	−0.678008	−0.339004	−	0.940785i	$-0.610090\pi$
$599$	−16.5939	−0.678008	−0.339004	+	0.940785i	$0.610090\pi$
$600$	−5.17290	−0.211183
$601$	13.6596	0.557186	0.278593	−	0.960409i	$-0.410132\pi$
$601$	13.6596	0.557186	0.278593	+	0.960409i	$0.410132\pi$
$602$	34.0486	1.38772
$603$	1.81832	0.0740477
$604$	−13.6804	−0.556647
$605$	−22.1779	−0.901661
$606$	10.8477	0.440656
$607$	36.0760	1.46428	0.732140	−	0.681154i	$-0.238522\pi$
$607$	36.0760	1.46428	0.732140	+	0.681154i	$0.238522\pi$
$608$	1.46729	0.0595065
$609$	−2.65784	−0.107701
$610$	−15.2436	−0.617196
$611$	−16.3141	−0.659996
$612$	−1.20479	−0.0487006
$613$	17.3919	0.702453	0.351226	−	0.936291i	$-0.385765\pi$
$613$	17.3919	0.702453	0.351226	+	0.936291i	$0.385765\pi$
$614$	21.0695	0.850297
$615$	−32.4899	−1.31012
$616$	14.0285	0.565223
$617$	−7.50008	−0.301942	−0.150971	−	0.988538i	$-0.548240\pi$
$617$	−7.50008	−0.301942	−0.150971	+	0.988538i	$0.548240\pi$
$618$	−4.79310	−0.192807
$619$	43.6061	1.75268	0.876338	−	0.481697i	$-0.159980\pi$
$619$	43.6061	1.75268	0.876338	+	0.481697i	$0.159980\pi$
$620$	21.6492	0.869452
$621$	1.11378	0.0446947
$622$	1.96529	0.0788011
$623$	41.4919	1.66234
$624$	0.317331	0.0127034
$625$	−30.7740	−1.23096
$626$	9.65817	0.386018
$627$	−0.415008	−0.0165738
$628$	−12.7358	−0.508214
$629$	−2.50830	−0.100013
$630$	7.22257	0.287754
$631$	10.1221	0.402954	0.201477	−	0.979493i	$-0.435426\pi$
$631$	10.1221	0.402954	0.201477	+	0.979493i	$0.435426\pi$
$632$	2.85786	0.113680
$633$	21.9622	0.872918
$634$	−24.8730	−0.987832
$635$	−5.50723	−0.218548
$636$	−12.4040	−0.491851
$637$	6.01398	0.238282
$638$	−1.20779	−0.0478168
$639$	−0.585533	−0.0231633
$640$	16.9343	0.669388
$641$	−34.7802	−1.37373	−0.686867	−	0.726783i	$-0.741015\pi$
$641$	−34.7802	−1.37373	−0.686867	+	0.726783i	$0.741015\pi$
$642$	1.53411	0.0605463
$643$	31.9890	1.26152	0.630761	−	0.775977i	$-0.282743\pi$
$643$	31.9890	1.26152	0.630761	+	0.775977i	$0.282743\pi$
$644$	−4.16472	−0.164113
$645$	−32.1039	−1.26409
$646$	0.233993	0.00920634
$647$	−14.6906	−0.577549	−0.288774	−	0.957397i	$-0.593248\pi$
$647$	−14.6906	−0.577549	−0.288774	+	0.957397i	$0.593248\pi$
$648$	2.85786	0.112267
$649$	5.30826	0.208367
$650$	−3.68717	−0.144623
$651$	−21.3713	−0.837606
$652$	8.40277	0.329078
$653$	20.2671	0.793113	0.396556	−	0.918010i	$-0.370205\pi$
$653$	20.2671	0.793113	0.396556	+	0.918010i	$0.370205\pi$
$654$	−7.66244	−0.299625
$655$	43.0952	1.68387
$656$	−1.72953	−0.0675268
$657$	12.8311	0.500587
$658$	−19.7661	−0.770562
$659$	32.9843	1.28488	0.642442	−	0.766334i	$-0.277921\pi$
$659$	32.9843	1.28488	0.642442	+	0.766334i	$0.277921\pi$
$660$	−4.97256	−0.193557
$661$	−26.4354	−1.02822	−0.514108	−	0.857725i	$-0.671877\pi$
$661$	−26.4354	−1.02822	−0.514108	+	0.857725i	$0.671877\pi$
$662$	20.0761	0.780280
$663$	−2.28432	−0.0887158
$664$	−16.7578	−0.650330
$665$	2.12526	0.0824139
$666$	2.23677	0.0866731
$667$	0.953796	0.0369311
$668$	15.9160	0.615807
$669$	9.21811	0.356393
$670$	−4.23143	−0.163475
$671$	−10.3601	−0.399949
$672$	−17.3552	−0.669491
$673$	−39.0682	−1.50597	−0.752984	−	0.658039i	$-0.771386\pi$
$673$	−39.0682	−1.50597	−0.752984	+	0.658039i	$0.771386\pi$
$674$	29.7908	1.14750
$675$	−1.81006	−0.0696693
$676$	9.37548	0.360596
$677$	18.5486	0.712882	0.356441	−	0.934318i	$-0.383990\pi$
$677$	18.5486	0.712882	0.356441	+	0.934318i	$0.383990\pi$
$678$	−9.50895	−0.365189
$679$	−10.2847	−0.394691
$680$	7.45790	0.285997
$681$	17.2103	0.659500
$682$	−9.71164	−0.371878
$683$	24.6738	0.944118	0.472059	−	0.881567i	$-0.343511\pi$
$683$	24.6738	0.944118	0.472059	+	0.881567i	$0.343511\pi$
$684$	0.316134	0.0120877
$685$	52.9528	2.02322
$686$	−12.0873	−0.461494
$687$	14.8907	0.568114
$688$	−1.70898	−0.0651543
$689$	−23.5185	−0.895984
$690$	−2.59190	−0.0986721
$691$	−15.6287	−0.594544	−0.297272	−	0.954793i	$-0.596077\pi$
$691$	−15.6287	−0.594544	−0.297272	+	0.954793i	$0.596077\pi$
$692$	−16.8454	−0.640367
$693$	4.90873	0.186467
$694$	12.4178	0.471372
$695$	−29.5164	−1.11962
$696$	2.44735	0.0927664
$697$	12.4501	0.471581
$698$	−8.12803	−0.307650
$699$	3.63924	0.137649
$700$	6.76827	0.255817
$701$	−29.3919	−1.11012	−0.555058	−	0.831812i	$-0.687304\pi$
$701$	−29.3919	−1.11012	−0.555058	+	0.831812i	$0.687304\pi$
$702$	2.03704	0.0768831
$703$	0.658174	0.0248235
$704$	−8.32605	−0.313800
$705$	18.6372	0.701916
$706$	22.0608	0.830269
$707$	−37.7545	−1.41990
$708$	−4.04359	−0.151968
$709$	34.1620	1.28298	0.641490	−	0.767132i	$-0.278317\pi$
$709$	34.1620	1.28298	0.641490	+	0.767132i	$0.278317\pi$
$710$	1.36260	0.0511375
$711$	1.00000	0.0375029
$712$	−38.2059	−1.43183
$713$	7.66933	0.287219
$714$	−2.76768	−0.103578
$715$	−9.42818	−0.352594
$716$	17.6759	0.660581
$717$	−22.5659	−0.842739
$718$	−27.7350	−1.03506
$719$	18.3745	0.685252	0.342626	−	0.939472i	$-0.388684\pi$
$719$	18.3745	0.685252	0.342626	+	0.939472i	$0.388684\pi$
$720$	−0.362518	−0.0135103
$721$	16.6820	0.621272
$722$	16.8818	0.628276
$723$	−4.92360	−0.183111
$724$	−20.1907	−0.750383
$725$	−1.55006	−0.0575676
$726$	−7.57857	−0.281267
$727$	23.8499	0.884545	0.442273	−	0.896881i	$-0.354172\pi$
$727$	23.8499	0.884545	0.442273	+	0.896881i	$0.354172\pi$
$728$	−20.2616	−0.750944
$729$	1.00000	0.0370370
$730$	−29.8593	−1.10514
$731$	12.3022	0.455013
$732$	7.89189	0.291692
$733$	−1.99610	−0.0737278	−0.0368639	−	0.999320i	$-0.511737\pi$
$733$	−1.99610	−0.0737278	−0.0368639	+	0.999320i	$0.511737\pi$
$734$	6.25978	0.231053
$735$	−6.87036	−0.253417
$736$	6.22811	0.229571
$737$	−2.87584	−0.105933
$738$	−11.1024	−0.408683
$739$	3.70795	0.136399	0.0681996	−	0.997672i	$-0.478275\pi$
$739$	3.70795	0.136399	0.0681996	+	0.997672i	$0.478275\pi$
$740$	7.88615	0.289901
$741$	0.599403	0.0220196
$742$	−28.4950	−1.04608
$743$	26.8342	0.984450	0.492225	−	0.870468i	$-0.336184\pi$
$743$	26.8342	0.984450	0.492225	+	0.870468i	$0.336184\pi$
$744$	19.6787	0.721457
$745$	−50.7469	−1.85922
$746$	−15.9978	−0.585721
$747$	−5.86377	−0.214544
$748$	1.90548	0.0696713
$749$	−5.33934	−0.195095
$750$	−7.42335	−0.271062
$751$	7.62221	0.278139	0.139069	−	0.990283i	$-0.455589\pi$
$751$	7.62221	0.278139	0.139069	+	0.990283i	$0.455589\pi$
$752$	0.992107	0.0361784
$753$	−24.6154	−0.897033
$754$	1.74443	0.0635284
$755$	29.6322	1.07843
$756$	−3.73925	−0.135995
$757$	−8.31582	−0.302244	−0.151122	−	0.988515i	$-0.548289\pi$
$757$	−8.31582	−0.302244	−0.151122	+	0.988515i	$0.548289\pi$
$758$	22.5246	0.818132
$759$	−1.76155	−0.0639404
$760$	−1.95694	−0.0709857
$761$	46.4001	1.68200	0.841002	−	0.541033i	$-0.181966\pi$
$761$	46.4001	1.68200	0.841002	+	0.541033i	$0.181966\pi$
$762$	−1.88191	−0.0681745
$763$	26.6686	0.965467
$764$	−1.38859	−0.0502376
$765$	2.60961	0.0943506
$766$	21.0819	0.761720
$767$	−7.66682	−0.276833
$768$	16.3154	0.588732
$769$	5.40007	0.194732	0.0973658	−	0.995249i	$-0.468958\pi$
$769$	5.40007	0.194732	0.0973658	+	0.995249i	$0.468958\pi$
$770$	−11.4232	−0.411662
$771$	26.9740	0.971443
$772$	18.8062	0.676850
$773$	−9.23570	−0.332185	−0.166093	−	0.986110i	$-0.553115\pi$
$773$	−9.23570	−0.332185	−0.166093	+	0.986110i	$0.553115\pi$
$774$	−10.9705	−0.394325
$775$	−12.4638	−0.447712
$776$	9.47019	0.339960
$777$	−7.78492	−0.279282
$778$	−12.1543	−0.435751
$779$	−3.26689	−0.117048
$780$	7.18196	0.257156
$781$	0.926074	0.0331375
$782$	0.993215	0.0355173
$783$	0.856356	0.0306037
$784$	−0.365728	−0.0130617
$785$	27.5862	0.984593
$786$	14.7263	0.525271
$787$	30.4855	1.08669	0.543346	−	0.839509i	$-0.317157\pi$
$787$	30.4855	1.08669	0.543346	+	0.839509i	$0.317157\pi$
$788$	−19.7471	−0.703462
$789$	6.07245	0.216185
$790$	−2.32711	−0.0827950
$791$	33.0952	1.17673
$792$	−4.51997	−0.160610
$793$	14.9633	0.531364
$794$	11.2037	0.397604
$795$	26.8675	0.952893
$796$	18.3589	0.650713
$797$	47.6054	1.68627	0.843134	−	0.537703i	$-0.180708\pi$
$797$	47.6054	1.68627	0.843134	+	0.537703i	$0.180708\pi$
$798$	0.726236	0.0257085
$799$	−7.14174	−0.252657
$800$	−10.1216	−0.357852
$801$	−13.3687	−0.472360
$802$	24.0420	0.848953
$803$	−20.2935	−0.716143
$804$	2.19069	0.0772596
$805$	9.02093	0.317946
$806$	14.0267	0.494069
$807$	31.6073	1.11263
$808$	34.7644	1.22301
$809$	−41.5359	−1.46033	−0.730163	−	0.683273i	$-0.760556\pi$
$809$	−41.5359	−1.46033	−0.730163	+	0.683273i	$0.760556\pi$
$810$	−2.32711	−0.0817664
$811$	27.7414	0.974133	0.487067	−	0.873365i	$-0.338067\pi$
$811$	27.7414	0.974133	0.487067	+	0.873365i	$0.338067\pi$
$812$	−3.20213	−0.112373
$813$	−9.01245	−0.316080
$814$	−3.53766	−0.123995
$815$	−18.2007	−0.637542
$816$	0.138917	0.00486306
$817$	−3.22808	−0.112936
$818$	26.3860	0.922563
$819$	−7.08977	−0.247737
$820$	−39.1434	−1.36695
$821$	−32.8116	−1.14513	−0.572567	−	0.819858i	$-0.694052\pi$
$821$	−32.8116	−1.14513	−0.572567	+	0.819858i	$0.694052\pi$
$822$	18.0949	0.631131
$823$	−34.6002	−1.20609	−0.603043	−	0.797709i	$-0.706045\pi$
$823$	−34.6002	−1.20609	−0.603043	+	0.797709i	$0.706045\pi$
$824$	−15.3609	−0.535121
$825$	2.86278	0.0996692
$826$	−9.28910	−0.323209
$827$	18.8742	0.656319	0.328160	−	0.944622i	$-0.393572\pi$
$827$	18.8742	0.656319	0.328160	+	0.944622i	$0.393572\pi$
$828$	1.34187	0.0466333
$829$	34.6967	1.20507	0.602533	−	0.798094i	$-0.294158\pi$
$829$	34.6967	1.20507	0.602533	+	0.798094i	$0.294158\pi$
$830$	13.6456	0.473647
$831$	28.0940	0.974571
$832$	12.0255	0.416908
$833$	2.63272	0.0912182
$834$	−10.0862	−0.349258
$835$	−34.4745	−1.19304
$836$	−0.499996	−0.0172927
$837$	6.88582	0.238009
$838$	9.90799	0.342266
$839$	5.27312	0.182048	0.0910242	−	0.995849i	$-0.470986\pi$
$839$	5.27312	0.182048	0.0910242	+	0.995849i	$0.470986\pi$
$840$	23.1468	0.798640
$841$	−28.2667	−0.974712
$842$	−11.9480	−0.411755
$843$	24.3961	0.840248
$844$	26.4597	0.910782
$845$	−20.3076	−0.698604
$846$	6.36863	0.218958
$847$	26.3767	0.906313
$848$	1.43023	0.0491144
$849$	16.9647	0.582226
$850$	−1.61412	−0.0553638
$851$	2.79371	0.0957671
$852$	−0.705442	−0.0241680
$853$	−12.3053	−0.421326	−0.210663	−	0.977559i	$-0.567562\pi$
$853$	−12.3053	−0.421326	−0.210663	+	0.977559i	$0.567562\pi$
$854$	18.1295	0.620380
$855$	−0.684758	−0.0234182
$856$	4.91648	0.168042
$857$	−9.47038	−0.323502	−0.161751	−	0.986832i	$-0.551714\pi$
$857$	−9.47038	−0.323502	−0.161751	+	0.986832i	$0.551714\pi$
$858$	−3.22177	−0.109989
$859$	−30.0777	−1.02624	−0.513119	−	0.858317i	$-0.671510\pi$
$859$	−30.0777	−1.02624	−0.513119	+	0.858317i	$0.671510\pi$
$860$	−38.6784	−1.31892
$861$	38.6409	1.31688
$862$	31.3692	1.06844
$863$	21.7773	0.741309	0.370654	−	0.928771i	$-0.379133\pi$
$863$	21.7773	0.741309	0.370654	+	0.928771i	$0.379133\pi$
$864$	5.59184	0.190238
$865$	36.4878	1.24062
$866$	−15.3337	−0.521060
$867$	−1.00000	−0.0339618
$868$	−25.7478	−0.873938
$869$	−1.58159	−0.0536519
$870$	−1.99284	−0.0675635
$871$	4.15363	0.140740
$872$	−24.5565	−0.831587
$873$	3.31374	0.112153
$874$	−0.260618	−0.00881554
$875$	25.8364	0.873430
$876$	15.4587	0.522300
$877$	17.1298	0.578432	0.289216	−	0.957264i	$-0.406605\pi$
$877$	17.1298	0.578432	0.289216	+	0.957264i	$0.406605\pi$
$878$	5.21844	0.176114
$879$	−8.20044	−0.276594
$880$	0.573357	0.0193279
$881$	6.90571	0.232659	0.116330	−	0.993211i	$-0.462887\pi$
$881$	6.90571	0.232659	0.116330	+	0.993211i	$0.462887\pi$
$882$	−2.34772	−0.0790518
$883$	5.17915	0.174292	0.0871462	−	0.996196i	$-0.472225\pi$
$883$	5.17915	0.174292	0.0871462	+	0.996196i	$0.472225\pi$
$884$	−2.75212	−0.0925639
$885$	8.75856	0.294416
$886$	−2.99418	−0.100591
$887$	−57.9714	−1.94649	−0.973245	−	0.229772i	$-0.926202\pi$
$887$	−57.9714	−1.94649	−0.973245	+	0.229772i	$0.926202\pi$
$888$	7.16837	0.240555
$889$	6.54986	0.219675
$890$	31.1105	1.04283
$891$	−1.58159	−0.0529854
$892$	11.1059	0.371851
$893$	1.87398	0.0627104
$894$	−17.3411	−0.579972
$895$	−38.2867	−1.27978
$896$	−20.1403	−0.672841
$897$	2.54425	0.0849499
$898$	30.3108	1.01148
$899$	5.89672	0.196666
$900$	−2.18074	−0.0726912
$901$	−10.2956	−0.342997
$902$	17.5594	0.584664
$903$	38.1819	1.27061
$904$	−30.4742	−1.01356
$905$	43.7338	1.45376
$906$	10.1258	0.336408
$907$	32.1389	1.06715	0.533577	−	0.845752i	$-0.320848\pi$
$907$	32.1389	1.06715	0.533577	+	0.845752i	$0.320848\pi$
$908$	20.7347	0.688106
$909$	12.1645	0.403471
$910$	16.4987	0.546926
$911$	−13.6838	−0.453364	−0.226682	−	0.973969i	$-0.572788\pi$
$911$	−13.6838	−0.453364	−0.226682	+	0.973969i	$0.572788\pi$
$912$	−0.0364516	−0.00120703
$913$	9.27409	0.306928
$914$	−25.0961	−0.830105
$915$	−17.0941	−0.565113
$916$	17.9401	0.592757
$917$	−51.2540	−1.69256
$918$	0.891747	0.0294321
$919$	−33.5660	−1.10724	−0.553620	−	0.832769i	$-0.686754\pi$
$919$	−33.5660	−1.10724	−0.553620	+	0.832769i	$0.686754\pi$
$920$	−8.30650	−0.273857
$921$	23.6272	0.778544
$922$	−9.22472	−0.303800
$923$	−1.33755	−0.0440259
$924$	5.91397	0.194555
$925$	−4.54018	−0.149280
$926$	−24.3011	−0.798583
$927$	−5.37495	−0.176537
$928$	4.78861	0.157194
$929$	−0.121711	−0.00399319	−0.00199660	−	0.999998i	$-0.500636\pi$
$929$	−0.121711	−0.00399319	−0.00199660	+	0.999998i	$0.500636\pi$
$930$	−16.0241	−0.525451
$931$	−0.690821	−0.0226407
$932$	4.38451	0.143619
$933$	2.20387	0.0721514
$934$	11.6953	0.382681
$935$	−4.12734	−0.134978
$936$	6.52828	0.213383
$937$	8.26454	0.269991	0.134995	−	0.990846i	$-0.456898\pi$
$937$	8.26454	0.269991	0.134995	+	0.990846i	$0.456898\pi$
$938$	5.03253	0.164318
$939$	10.8306	0.353444
$940$	22.4538	0.732362
$941$	−10.7750	−0.351255	−0.175627	−	0.984457i	$-0.556195\pi$
$941$	−10.7750	−0.351255	−0.175627	+	0.984457i	$0.556195\pi$
$942$	9.42666	0.307137
$943$	−13.8667	−0.451563
$944$	0.466243	0.0151749
$945$	8.09934	0.263472
$946$	17.3508	0.564123
$947$	−20.2148	−0.656892	−0.328446	−	0.944523i	$-0.606525\pi$
$947$	−20.2148	−0.656892	−0.328446	+	0.944523i	$0.606525\pi$
$948$	1.20479	0.0391296
$949$	29.3103	0.951452
$950$	0.423542	0.0137415
$951$	−27.8924	−0.904473
$952$	−8.86983	−0.287473
$953$	11.4423	0.370654	0.185327	−	0.982677i	$-0.440666\pi$
$953$	11.4423	0.370654	0.185327	+	0.982677i	$0.440666\pi$
$954$	9.18109	0.297249
$955$	3.00775	0.0973283
$956$	−27.1871	−0.879293
$957$	−1.35441	−0.0437817
$958$	−12.3056	−0.397576
$959$	−62.9779	−2.03366
$960$	−13.7379	−0.443388
$961$	16.4146	0.529502
$962$	5.10951	0.164737
$963$	1.72034	0.0554371
$964$	−5.93189	−0.191053
$965$	−40.7349	−1.31130
$966$	3.08260	0.0991811
$967$	−30.6153	−0.984522	−0.492261	−	0.870448i	$-0.663829\pi$
$967$	−30.6153	−0.984522	−0.492261	+	0.870448i	$0.663829\pi$
$968$	−24.2877	−0.780636
$969$	0.262399	0.00842946
$970$	−7.71144	−0.247599
$971$	−48.9357	−1.57042	−0.785211	−	0.619228i	$-0.787446\pi$
$971$	−48.9357	−1.57042	−0.785211	+	0.619228i	$0.787446\pi$
$972$	1.20479	0.0386435
$973$	35.1044	1.12540
$974$	22.1041	0.708260
$975$	−4.13477	−0.132418
$976$	−0.909966	−0.0291273
$977$	32.3270	1.03423	0.517116	−	0.855915i	$-0.327005\pi$
$977$	32.3270	1.03423	0.517116	+	0.855915i	$0.327005\pi$
$978$	−6.21948	−0.198877
$979$	21.1438	0.675760
$980$	−8.27732	−0.264409
$981$	−8.59261	−0.274341
$982$	−29.8627	−0.952958
$983$	25.7878	0.822504	0.411252	−	0.911522i	$-0.365092\pi$
$983$	25.7878	0.822504	0.411252	+	0.911522i	$0.365092\pi$
$984$	−35.5807	−1.13427
$985$	42.7729	1.36286
$986$	0.763653	0.0243197
$987$	−22.1655	−0.705537
$988$	0.722153	0.0229747
$989$	−13.7020	−0.435699
$990$	3.68055	0.116975
$991$	−45.5023	−1.44543	−0.722715	−	0.691147i	$-0.757106\pi$
$991$	−45.5023	−1.44543	−0.722715	+	0.691147i	$0.757106\pi$
$992$	38.5044	1.22252
$993$	22.5132	0.714436
$994$	−1.62057	−0.0514013
$995$	−39.7660	−1.26067
$996$	−7.06459	−0.223850
$997$	13.1803	0.417425	0.208712	−	0.977977i	$-0.433073\pi$
$997$	13.1803	0.417425	0.208712	+	0.977977i	$0.433073\pi$
$998$	27.8865	0.882732
$999$	2.50830	0.0793591

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.f.1.9	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.f.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-0.891747 q^{2} -1.00000 q^{3} -1.20479 q^{4} +2.60961 q^{5} +0.891747 q^{6} -3.10366 q^{7} +2.85786 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.891747 q^{2} -1.00000 q^{3} -1.20479 q^{4} +2.60961 q^{5} +0.891747 q^{6} -3.10366 q^{7} +2.85786 q^{8} +1.00000 q^{9} -2.32711 q^{10} -1.58159 q^{11} +1.20479 q^{12} +2.28432 q^{13} +2.76768 q^{14} -2.60961 q^{15} -0.138917 q^{16} +1.00000 q^{17} -0.891747 q^{18} -0.262399 q^{19} -3.14402 q^{20} +3.10366 q^{21} +1.41038 q^{22} -1.11378 q^{23} -2.85786 q^{24} +1.81006 q^{25} -2.03704 q^{26} -1.00000 q^{27} +3.73925 q^{28} -0.856356 q^{29} +2.32711 q^{30} -6.88582 q^{31} -5.59184 q^{32} +1.58159 q^{33} -0.891747 q^{34} -8.09934 q^{35} -1.20479 q^{36} -2.50830 q^{37} +0.233993 q^{38} -2.28432 q^{39} +7.45790 q^{40} +12.4501 q^{41} -2.76768 q^{42} +12.3022 q^{43} +1.90548 q^{44} +2.60961 q^{45} +0.993215 q^{46} -7.14174 q^{47} +0.138917 q^{48} +2.63272 q^{49} -1.61412 q^{50} -1.00000 q^{51} -2.75212 q^{52} -10.2956 q^{53} +0.891747 q^{54} -4.12734 q^{55} -8.86983 q^{56} +0.262399 q^{57} +0.763653 q^{58} -3.35627 q^{59} +3.14402 q^{60} +6.55044 q^{61} +6.14042 q^{62} -3.10366 q^{63} +5.26434 q^{64} +5.96119 q^{65} -1.41038 q^{66} +1.81832 q^{67} -1.20479 q^{68} +1.11378 q^{69} +7.22257 q^{70} -0.585533 q^{71} +2.85786 q^{72} +12.8311 q^{73} +2.23677 q^{74} -1.81006 q^{75} +0.316134 q^{76} +4.90873 q^{77} +2.03704 q^{78} +1.00000 q^{79} -0.362518 q^{80} +1.00000 q^{81} -11.1024 q^{82} -5.86377 q^{83} -3.73925 q^{84} +2.60961 q^{85} -10.9705 q^{86} +0.856356 q^{87} -4.51997 q^{88} -13.3687 q^{89} -2.32711 q^{90} -7.08977 q^{91} +1.34187 q^{92} +6.88582 q^{93} +6.36863 q^{94} -0.684758 q^{95} +5.59184 q^{96} +3.31374 q^{97} -2.34772 q^{98} -1.58159 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9}+O(q^{10}) \) 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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