LMFDB - Embedded newform 4029.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-2.74441 q^{2} -1.00000 q^{3} +5.53180 q^{4} +1.03743 q^{5} +2.74441 q^{6} +3.45867 q^{7} -9.69270 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.74441 q^{2} -1.00000 q^{3} +5.53180 q^{4} +1.03743 q^{5} +2.74441 q^{6} +3.45867 q^{7} -9.69270 q^{8} +1.00000 q^{9} -2.84714 q^{10} -1.50542 q^{11} -5.53180 q^{12} +0.989935 q^{13} -9.49202 q^{14} -1.03743 q^{15} +15.5372 q^{16} +1.00000 q^{17} -2.74441 q^{18} +6.75726 q^{19} +5.73886 q^{20} -3.45867 q^{21} +4.13148 q^{22} -1.90814 q^{23} +9.69270 q^{24} -3.92374 q^{25} -2.71679 q^{26} -1.00000 q^{27} +19.1327 q^{28} -3.84976 q^{29} +2.84714 q^{30} -0.283183 q^{31} -23.2550 q^{32} +1.50542 q^{33} -2.74441 q^{34} +3.58813 q^{35} +5.53180 q^{36} +1.26811 q^{37} -18.5447 q^{38} -0.989935 q^{39} -10.0555 q^{40} +7.81884 q^{41} +9.49202 q^{42} -8.97058 q^{43} -8.32765 q^{44} +1.03743 q^{45} +5.23672 q^{46} +2.35233 q^{47} -15.5372 q^{48} +4.96240 q^{49} +10.7683 q^{50} -1.00000 q^{51} +5.47612 q^{52} -1.93970 q^{53} +2.74441 q^{54} -1.56177 q^{55} -33.5239 q^{56} -6.75726 q^{57} +10.5653 q^{58} +3.12511 q^{59} -5.73886 q^{60} -0.0662411 q^{61} +0.777170 q^{62} +3.45867 q^{63} +32.7470 q^{64} +1.02699 q^{65} -4.13148 q^{66} +12.6142 q^{67} +5.53180 q^{68} +1.90814 q^{69} -9.84732 q^{70} +8.14085 q^{71} -9.69270 q^{72} +1.16699 q^{73} -3.48021 q^{74} +3.92374 q^{75} +37.3798 q^{76} -5.20674 q^{77} +2.71679 q^{78} -1.00000 q^{79} +16.1188 q^{80} +1.00000 q^{81} -21.4581 q^{82} +4.09144 q^{83} -19.1327 q^{84} +1.03743 q^{85} +24.6190 q^{86} +3.84976 q^{87} +14.5915 q^{88} +16.5602 q^{89} -2.84714 q^{90} +3.42386 q^{91} -10.5554 q^{92} +0.283183 q^{93} -6.45577 q^{94} +7.01020 q^{95} +23.2550 q^{96} +6.24612 q^{97} -13.6189 q^{98} -1.50542 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9}+O(q^{10}) $ 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9} + 19 q^{10} + 19 q^{11} - 26 q^{12} + 4 q^{13} + 15 q^{14} + 2 q^{15} + 32 q^{16} + 25 q^{17} - 2 q^{18} + 29 q^{19} - 8 q^{20} - 12 q^{21} + 23 q^{22} + 6 q^{23} + 15 q^{25} - 8 q^{26} - 25 q^{27} + 23 q^{28} + 11 q^{29} - 19 q^{30} + 38 q^{31} - 27 q^{32} - 19 q^{33} - 2 q^{34} + 20 q^{35} + 26 q^{36} + 8 q^{37} - 25 q^{38} - 4 q^{39} + 48 q^{40} + 24 q^{41} - 15 q^{42} + 11 q^{43} + 6 q^{44} - 2 q^{45} + 25 q^{46} + 23 q^{47} - 32 q^{48} + 21 q^{49} - 21 q^{50} - 25 q^{51} + 31 q^{52} - 16 q^{53} + 2 q^{54} - 11 q^{55} + 18 q^{56} - 29 q^{57} - 5 q^{58} + 27 q^{59} + 8 q^{60} + 40 q^{61} - 34 q^{62} + 12 q^{63} + 46 q^{64} - 19 q^{65} - 23 q^{66} + 24 q^{67} + 26 q^{68} - 6 q^{69} + 17 q^{70} + 19 q^{71} + 13 q^{73} - 56 q^{74} - 15 q^{75} + 21 q^{76} - 30 q^{77} + 8 q^{78} - 25 q^{79} - 40 q^{80} + 25 q^{81} + 61 q^{82} + q^{83} - 23 q^{84} - 2 q^{85} + 62 q^{86} - 11 q^{87} - q^{88} - 10 q^{89} + 19 q^{90} + 50 q^{91} + 18 q^{92} - 38 q^{93} + 15 q^{94} + 14 q^{95} + 27 q^{96} + 19 q^{97} - 23 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9 + 19 * q^10 + 19 * q^11 - 26 * q^12 + 4 * q^13 + 15 * q^14 + 2 * q^15 + 32 * q^16 + 25 * q^17 - 2 * q^18 + 29 * q^19 - 8 * q^20 - 12 * q^21 + 23 * q^22 + 6 * q^23 + 15 * q^25 - 8 * q^26 - 25 * q^27 + 23 * q^28 + 11 * q^29 - 19 * q^30 + 38 * q^31 - 27 * q^32 - 19 * q^33 - 2 * q^34 + 20 * q^35 + 26 * q^36 + 8 * q^37 - 25 * q^38 - 4 * q^39 + 48 * q^40 + 24 * q^41 - 15 * q^42 + 11 * q^43 + 6 * q^44 - 2 * q^45 + 25 * q^46 + 23 * q^47 - 32 * q^48 + 21 * q^49 - 21 * q^50 - 25 * q^51 + 31 * q^52 - 16 * q^53 + 2 * q^54 - 11 * q^55 + 18 * q^56 - 29 * q^57 - 5 * q^58 + 27 * q^59 + 8 * q^60 + 40 * q^61 - 34 * q^62 + 12 * q^63 + 46 * q^64 - 19 * q^65 - 23 * q^66 + 24 * q^67 + 26 * q^68 - 6 * q^69 + 17 * q^70 + 19 * q^71 + 13 * q^73 - 56 * q^74 - 15 * q^75 + 21 * q^76 - 30 * q^77 + 8 * q^78 - 25 * q^79 - 40 * q^80 + 25 * q^81 + 61 * q^82 + q^83 - 23 * q^84 - 2 * q^85 + 62 * q^86 - 11 * q^87 - q^88 - 10 * q^89 + 19 * q^90 + 50 * q^91 + 18 * q^92 - 38 * q^93 + 15 * q^94 + 14 * q^95 + 27 * q^96 + 19 * q^97 - 23 * q^98 + 19 * 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 $

$2$	−2.74441	−1.94059	−0.970296	−	0.241920i	$-0.922223\pi$
$2$	−2.74441	−1.94059	−0.970296	+	0.241920i	$0.922223\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.53180	2.76590
$5$	1.03743	0.463954	0.231977	−	0.972721i	$-0.425481\pi$
$5$	1.03743	0.463954	0.231977	+	0.972721i	$0.425481\pi$
$6$	2.74441	1.12040
$7$	3.45867	1.30725	0.653627	−	0.756817i	$-0.273246\pi$
$7$	3.45867	1.30725	0.653627	+	0.756817i	$0.273246\pi$
$8$	−9.69270	−3.42689
$9$	1.00000	0.333333
$10$	−2.84714	−0.900345
$11$	−1.50542	−0.453900	−0.226950	−	0.973906i	$-0.572875\pi$
$11$	−1.50542	−0.453900	−0.226950	+	0.973906i	$0.572875\pi$
$12$	−5.53180	−1.59689
$13$	0.989935	0.274559	0.137279	−	0.990532i	$-0.456164\pi$
$13$	0.989935	0.274559	0.137279	+	0.990532i	$0.456164\pi$
$14$	−9.49202	−2.53685
$15$	−1.03743	−0.267864
$16$	15.5372	3.88430
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.74441	−0.646864
$19$	6.75726	1.55022	0.775111	−	0.631825i	$-0.217694\pi$
$19$	6.75726	1.55022	0.775111	+	0.631825i	$0.217694\pi$
$20$	5.73886	1.28325
$21$	−3.45867	−0.754744
$22$	4.13148	0.880834
$23$	−1.90814	−0.397874	−0.198937	−	0.980012i	$-0.563749\pi$
$23$	−1.90814	−0.397874	−0.198937	+	0.980012i	$0.563749\pi$
$24$	9.69270	1.97852
$25$	−3.92374	−0.784747
$26$	−2.71679	−0.532806
$27$	−1.00000	−0.192450
$28$	19.1327	3.61573
$29$	−3.84976	−0.714883	−0.357441	−	0.933936i	$-0.616351\pi$
$29$	−3.84976	−0.714883	−0.357441	+	0.933936i	$0.616351\pi$
$30$	2.84714	0.519814
$31$	−0.283183	−0.0508611	−0.0254306	−	0.999677i	$-0.508096\pi$
$31$	−0.283183	−0.0508611	−0.0254306	+	0.999677i	$0.508096\pi$
$32$	−23.2550	−4.11094
$33$	1.50542	0.262059
$34$	−2.74441	−0.470663
$35$	3.58813	0.606505
$36$	5.53180	0.921966
$37$	1.26811	0.208476	0.104238	−	0.994552i	$-0.466760\pi$
$37$	1.26811	0.208476	0.104238	+	0.994552i	$0.466760\pi$
$38$	−18.5447	−3.00835
$39$	−0.989935	−0.158516
$40$	−10.0555	−1.58992
$41$	7.81884	1.22110	0.610549	−	0.791979i	$-0.290949\pi$
$41$	7.81884	1.22110	0.610549	+	0.791979i	$0.290949\pi$
$42$	9.49202	1.46465
$43$	−8.97058	−1.36800	−0.684001	−	0.729481i	$-0.739761\pi$
$43$	−8.97058	−1.36800	−0.684001	+	0.729481i	$0.739761\pi$
$44$	−8.32765	−1.25544
$45$	1.03743	0.154651
$46$	5.23672	0.772112
$47$	2.35233	0.343123	0.171561	−	0.985173i	$-0.445119\pi$
$47$	2.35233	0.343123	0.171561	+	0.985173i	$0.445119\pi$
$48$	−15.5372	−2.24260
$49$	4.96240	0.708915
$50$	10.7683	1.52287
$51$	−1.00000	−0.140028
$52$	5.47612	0.759401
$53$	−1.93970	−0.266438	−0.133219	−	0.991087i	$-0.542531\pi$
$53$	−1.93970	−0.266438	−0.133219	+	0.991087i	$0.542531\pi$
$54$	2.74441	0.373467
$55$	−1.56177	−0.210588
$56$	−33.5239	−4.47982
$57$	−6.75726	−0.895021
$58$	10.5653	1.38730
$59$	3.12511	0.406855	0.203428	−	0.979090i	$-0.434792\pi$
$59$	3.12511	0.406855	0.203428	+	0.979090i	$0.434792\pi$
$60$	−5.73886	−0.740884
$61$	−0.0662411	−0.00848130	−0.00424065	−	0.999991i	$-0.501350\pi$
$61$	−0.0662411	−0.00848130	−0.00424065	+	0.999991i	$0.501350\pi$
$62$	0.777170	0.0987007
$63$	3.45867	0.435752
$64$	32.7470	4.09337
$65$	1.02699	0.127382
$66$	−4.13148	−0.508550
$67$	12.6142	1.54106	0.770532	−	0.637401i	$-0.219991\pi$
$67$	12.6142	1.54106	0.770532	+	0.637401i	$0.219991\pi$
$68$	5.53180	0.670829
$69$	1.90814	0.229713
$70$	−9.84732	−1.17698
$71$	8.14085	0.966142	0.483071	−	0.875581i	$-0.339521\pi$
$71$	8.14085	0.966142	0.483071	+	0.875581i	$0.339521\pi$
$72$	−9.69270	−1.14230
$73$	1.16699	0.136586	0.0682930	−	0.997665i	$-0.478245\pi$
$73$	1.16699	0.136586	0.0682930	+	0.997665i	$0.478245\pi$
$74$	−3.48021	−0.404566
$75$	3.92374	0.453074
$76$	37.3798	4.28776
$77$	−5.20674	−0.593363
$78$	2.71679	0.307616
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	16.1188	1.80213
$81$	1.00000	0.111111
$82$	−21.4581	−2.36965
$83$	4.09144	0.449094	0.224547	−	0.974463i	$-0.427910\pi$
$83$	4.09144	0.449094	0.224547	+	0.974463i	$0.427910\pi$
$84$	−19.1327	−2.08754
$85$	1.03743	0.112525
$86$	24.6190	2.65473
$87$	3.84976	0.412738
$88$	14.5915	1.55546
$89$	16.5602	1.75537	0.877687	−	0.479234i	$-0.159086\pi$
$89$	16.5602	1.75537	0.877687	+	0.479234i	$0.159086\pi$
$90$	−2.84714	−0.300115
$91$	3.42386	0.358918
$92$	−10.5554	−1.10048
$93$	0.283183	0.0293647
$94$	−6.45577	−0.665861
$95$	7.01020	0.719231
$96$	23.2550	2.37345
$97$	6.24612	0.634197	0.317099	−	0.948393i	$-0.397291\pi$
$97$	6.24612	0.634197	0.317099	+	0.948393i	$0.397291\pi$
$98$	−13.6189	−1.37571
$99$	−1.50542	−0.151300
$100$	−21.7053	−2.17053
$101$	13.0395	1.29748	0.648738	−	0.761012i	$-0.275297\pi$
$101$	13.0395	1.29748	0.648738	+	0.761012i	$0.275297\pi$
$102$	2.74441	0.271737
$103$	−16.0181	−1.57831	−0.789155	−	0.614194i	$-0.789481\pi$
$103$	−16.0181	−1.57831	−0.789155	+	0.614194i	$0.789481\pi$
$104$	−9.59515	−0.940882
$105$	−3.58813	−0.350166
$106$	5.32333	0.517047
$107$	−0.832056	−0.0804379	−0.0402189	−	0.999191i	$-0.512806\pi$
$107$	−0.832056	−0.0804379	−0.0402189	+	0.999191i	$0.512806\pi$
$108$	−5.53180	−0.532297
$109$	15.6251	1.49661	0.748304	−	0.663356i	$-0.230868\pi$
$109$	15.6251	1.49661	0.748304	+	0.663356i	$0.230868\pi$
$110$	4.28613	0.408666
$111$	−1.26811	−0.120363
$112$	53.7380	5.07776
$113$	7.07867	0.665905	0.332953	−	0.942944i	$-0.391955\pi$
$113$	7.07867	0.665905	0.332953	+	0.942944i	$0.391955\pi$
$114$	18.5447	1.73687
$115$	−1.97956	−0.184595
$116$	−21.2961	−1.97729
$117$	0.989935	0.0915195
$118$	−8.57660	−0.789540
$119$	3.45867	0.317056
$120$	10.0555	0.917939
$121$	−8.73372	−0.793975
$122$	0.181793	0.0164587
$123$	−7.81884	−0.705001
$124$	−1.56651	−0.140677
$125$	−9.25777	−0.828040
$126$	−9.49202	−0.845616
$127$	2.89107	0.256541	0.128270	−	0.991739i	$-0.459057\pi$
$127$	2.89107	0.256541	0.128270	+	0.991739i	$0.459057\pi$
$128$	−43.3612	−3.83262
$129$	8.97058	0.789816
$130$	−2.81848	−0.247197
$131$	−14.3959	−1.25778	−0.628890	−	0.777495i	$-0.716490\pi$
$131$	−14.3959	−1.25778	−0.628890	+	0.777495i	$0.716490\pi$
$132$	8.32765	0.724829
$133$	23.3711	2.02653
$134$	−34.6184	−2.99058
$135$	−1.03743	−0.0892879
$136$	−9.69270	−0.831143
$137$	6.26194	0.534993	0.267497	−	0.963559i	$-0.413804\pi$
$137$	6.26194	0.534993	0.267497	+	0.963559i	$0.413804\pi$
$138$	−5.23672	−0.445779
$139$	−6.51856	−0.552897	−0.276448	−	0.961029i	$-0.589158\pi$
$139$	−6.51856	−0.552897	−0.276448	+	0.961029i	$0.589158\pi$
$140$	19.8488	1.67753
$141$	−2.35233	−0.198102
$142$	−22.3419	−1.87489
$143$	−1.49026	−0.124622
$144$	15.5372	1.29477
$145$	−3.99386	−0.331672
$146$	−3.20271	−0.265058
$147$	−4.96240	−0.409292
$148$	7.01491	0.576622
$149$	−16.9621	−1.38959	−0.694793	−	0.719209i	$-0.744504\pi$
$149$	−16.9621	−1.38959	−0.694793	+	0.719209i	$0.744504\pi$
$150$	−10.7683	−0.879232
$151$	11.2724	0.917332	0.458666	−	0.888609i	$-0.348327\pi$
$151$	11.2724	0.917332	0.458666	+	0.888609i	$0.348327\pi$
$152$	−65.4961	−5.31244
$153$	1.00000	0.0808452
$154$	14.2894	1.15147
$155$	−0.293783	−0.0235972
$156$	−5.47612	−0.438440
$157$	11.7942	0.941280	0.470640	−	0.882325i	$-0.344023\pi$
$157$	11.7942	0.941280	0.470640	+	0.882325i	$0.344023\pi$
$158$	2.74441	0.218334
$159$	1.93970	0.153828
$160$	−24.1255	−1.90729
$161$	−6.59962	−0.520123
$162$	−2.74441	−0.215621
$163$	16.0694	1.25865	0.629327	−	0.777140i	$-0.283331\pi$
$163$	16.0694	1.25865	0.629327	+	0.777140i	$0.283331\pi$
$164$	43.2522	3.37743
$165$	1.56177	0.121583
$166$	−11.2286	−0.871508
$167$	−8.84160	−0.684184	−0.342092	−	0.939666i	$-0.611135\pi$
$167$	−8.84160	−0.684184	−0.342092	+	0.939666i	$0.611135\pi$
$168$	33.5239	2.58642
$169$	−12.0200	−0.924618
$170$	−2.84714	−0.218366
$171$	6.75726	0.516741
$172$	−49.6234	−3.78375
$173$	−3.78457	−0.287736	−0.143868	−	0.989597i	$-0.545954\pi$
$173$	−3.78457	−0.287736	−0.143868	+	0.989597i	$0.545954\pi$
$174$	−10.5653	−0.800956
$175$	−13.5709	−1.02586
$176$	−23.3899	−1.76308
$177$	−3.12511	−0.234898
$178$	−45.4479	−3.40647
$179$	8.63407	0.645341	0.322670	−	0.946511i	$-0.395419\pi$
$179$	8.63407	0.645341	0.322670	+	0.946511i	$0.395419\pi$
$180$	5.73886	0.427749
$181$	−0.264653	−0.0196715	−0.00983576	−	0.999952i	$-0.503131\pi$
$181$	−0.264653	−0.0196715	−0.00983576	+	0.999952i	$0.503131\pi$
$182$	−9.39648	−0.696513
$183$	0.0662411	0.00489668
$184$	18.4950	1.36347
$185$	1.31558	0.0967230
$186$	−0.777170	−0.0569849
$187$	−1.50542	−0.110087
$188$	13.0126	0.949043
$189$	−3.45867	−0.251581
$190$	−19.2389	−1.39573
$191$	8.74972	0.633108	0.316554	−	0.948575i	$-0.397474\pi$
$191$	8.74972	0.633108	0.316554	+	0.948575i	$0.397474\pi$
$192$	−32.7470	−2.36331
$193$	−20.8389	−1.50002	−0.750008	−	0.661429i	$-0.769950\pi$
$193$	−20.8389	−1.50002	−0.750008	+	0.661429i	$0.769950\pi$
$194$	−17.1419	−1.23072
$195$	−1.02699	−0.0735443
$196$	27.4510	1.96079
$197$	−3.53711	−0.252008	−0.126004	−	0.992030i	$-0.540215\pi$
$197$	−3.53711	−0.252008	−0.126004	+	0.992030i	$0.540215\pi$
$198$	4.13148	0.293611
$199$	−9.87158	−0.699777	−0.349889	−	0.936791i	$-0.613781\pi$
$199$	−9.87158	−0.699777	−0.349889	+	0.936791i	$0.613781\pi$
$200$	38.0316	2.68924
$201$	−12.6142	−0.889734
$202$	−35.7857	−2.51787
$203$	−13.3151	−0.934534
$204$	−5.53180	−0.387303
$205$	8.11151	0.566532
$206$	43.9603	3.06286
$207$	−1.90814	−0.132625
$208$	15.3808	1.06647
$209$	−10.1725	−0.703645
$210$	9.84732	0.679530
$211$	18.7497	1.29078	0.645391	−	0.763852i	$-0.276695\pi$
$211$	18.7497	1.29078	0.645391	+	0.763852i	$0.276695\pi$
$212$	−10.7300	−0.736940
$213$	−8.14085	−0.557802
$214$	2.28350	0.156097
$215$	−9.30637	−0.634689
$216$	9.69270	0.659505
$217$	−0.979436	−0.0664884
$218$	−42.8816	−2.90431
$219$	−1.16699	−0.0788580
$220$	−8.63937	−0.582466
$221$	0.989935	0.0665902
$222$	3.48021	0.233576
$223$	−23.0444	−1.54317	−0.771584	−	0.636128i	$-0.780535\pi$
$223$	−23.0444	−1.54317	−0.771584	+	0.636128i	$0.780535\pi$
$224$	−80.4314	−5.37405
$225$	−3.92374	−0.261582
$226$	−19.4268	−1.29225
$227$	20.0640	1.33169	0.665847	−	0.746088i	$-0.268070\pi$
$227$	20.0640	1.33169	0.665847	+	0.746088i	$0.268070\pi$
$228$	−37.3798	−2.47554
$229$	−12.7699	−0.843859	−0.421930	−	0.906629i	$-0.638647\pi$
$229$	−12.7699	−0.843859	−0.421930	+	0.906629i	$0.638647\pi$
$230$	5.43274	0.358224
$231$	5.20674	0.342578
$232$	37.3146	2.44982
$233$	13.6485	0.894140	0.447070	−	0.894499i	$-0.352467\pi$
$233$	13.6485	0.894140	0.447070	+	0.894499i	$0.352467\pi$
$234$	−2.71679	−0.177602
$235$	2.44038	0.159193
$236$	17.2875	1.12532
$237$	1.00000	0.0649570
$238$	−9.49202	−0.615276
$239$	−5.61322	−0.363089	−0.181545	−	0.983383i	$-0.558110\pi$
$239$	−5.61322	−0.363089	−0.181545	+	0.983383i	$0.558110\pi$
$240$	−16.1188	−1.04046
$241$	13.9223	0.896814	0.448407	−	0.893829i	$-0.351991\pi$
$241$	13.9223	0.896814	0.448407	+	0.893829i	$0.351991\pi$
$242$	23.9689	1.54078
$243$	−1.00000	−0.0641500
$244$	−0.366432	−0.0234584
$245$	5.14815	0.328904
$246$	21.4581	1.36812
$247$	6.68925	0.425627
$248$	2.74481	0.174295
$249$	−4.09144	−0.259285
$250$	25.4071	1.60689
$251$	−2.62991	−0.165998	−0.0829992	−	0.996550i	$-0.526450\pi$
$251$	−2.62991	−0.165998	−0.0829992	+	0.996550i	$0.526450\pi$
$252$	19.1327	1.20524
$253$	2.87254	0.180595
$254$	−7.93428	−0.497841
$255$	−1.03743	−0.0649665
$256$	53.5069	3.34418
$257$	−5.47439	−0.341483	−0.170741	−	0.985316i	$-0.554616\pi$
$257$	−5.47439	−0.341483	−0.170741	+	0.985316i	$0.554616\pi$
$258$	−24.6190	−1.53271
$259$	4.38597	0.272531
$260$	5.68110	0.352327
$261$	−3.84976	−0.238294
$262$	39.5084	2.44084
$263$	−9.30936	−0.574040	−0.287020	−	0.957925i	$-0.592665\pi$
$263$	−9.30936	−0.574040	−0.287020	+	0.957925i	$0.592665\pi$
$264$	−14.5915	−0.898048
$265$	−2.01230	−0.123615
$266$	−64.1400	−3.93268
$267$	−16.5602	−1.01347
$268$	69.7789	4.26243
$269$	−7.62253	−0.464754	−0.232377	−	0.972626i	$-0.574650\pi$
$269$	−7.62253	−0.464754	−0.232377	+	0.972626i	$0.574650\pi$
$270$	2.84714	0.173271
$271$	15.9941	0.971570	0.485785	−	0.874078i	$-0.338534\pi$
$271$	15.9941	0.971570	0.485785	+	0.874078i	$0.338534\pi$
$272$	15.5372	0.942080
$273$	−3.42386	−0.207221
$274$	−17.1853	−1.03820
$275$	5.90685	0.356197
$276$	10.5554	0.635363
$277$	7.96425	0.478526	0.239263	−	0.970955i	$-0.423094\pi$
$277$	7.96425	0.478526	0.239263	+	0.970955i	$0.423094\pi$
$278$	17.8896	1.07295
$279$	−0.283183	−0.0169537
$280$	−34.7787	−2.07843
$281$	20.2600	1.20861	0.604306	−	0.796752i	$-0.293450\pi$
$281$	20.2600	1.20861	0.604306	+	0.796752i	$0.293450\pi$
$282$	6.45577	0.384435
$283$	19.8327	1.17893	0.589467	−	0.807793i	$-0.299338\pi$
$283$	19.8327	1.17893	0.589467	+	0.807793i	$0.299338\pi$
$284$	45.0335	2.67225
$285$	−7.01020	−0.415248
$286$	4.08990	0.241841
$287$	27.0428	1.59629
$288$	−23.2550	−1.37031
$289$	1.00000	0.0588235
$290$	10.9608	0.643641
$291$	−6.24612	−0.366154
$292$	6.45556	0.377783
$293$	12.2217	0.714001	0.357000	−	0.934104i	$-0.383800\pi$
$293$	12.2217	0.714001	0.357000	+	0.934104i	$0.383800\pi$
$294$	13.6189	0.794269
$295$	3.24209	0.188762
$296$	−12.2914	−0.714423
$297$	1.50542	0.0873531
$298$	46.5509	2.69662
$299$	−1.88893	−0.109240
$300$	21.7053	1.25316
$301$	−31.0263	−1.78833
$302$	−30.9360	−1.78017
$303$	−13.0395	−0.749099
$304$	104.989	6.02152
$305$	−0.0687206	−0.00393493
$306$	−2.74441	−0.156888
$307$	9.11669	0.520317	0.260158	−	0.965566i	$-0.416225\pi$
$307$	9.11669	0.520317	0.260158	+	0.965566i	$0.416225\pi$
$308$	−28.8026	−1.64118
$309$	16.0181	0.911238
$310$	0.806261	0.0457925
$311$	−23.3277	−1.32279	−0.661397	−	0.750036i	$-0.730036\pi$
$311$	−23.3277	−1.32279	−0.661397	+	0.750036i	$0.730036\pi$
$312$	9.59515	0.543218
$313$	−27.8475	−1.57403	−0.787016	−	0.616932i	$-0.788375\pi$
$313$	−27.8475	−1.57403	−0.787016	+	0.616932i	$0.788375\pi$
$314$	−32.3682	−1.82664
$315$	3.58813	0.202168
$316$	−5.53180	−0.311188
$317$	7.95581	0.446843	0.223421	−	0.974722i	$-0.428277\pi$
$317$	7.95581	0.446843	0.223421	+	0.974722i	$0.428277\pi$
$318$	−5.32333	−0.298517
$319$	5.79549	0.324485
$320$	33.9727	1.89913
$321$	0.832056	0.0464408
$322$	18.1121	1.00935
$323$	6.75726	0.375984
$324$	5.53180	0.307322
$325$	−3.88424	−0.215459
$326$	−44.1011	−2.44254
$327$	−15.6251	−0.864067
$328$	−75.7857	−4.18456
$329$	8.13594	0.448549
$330$	−4.28613	−0.235944
$331$	31.4835	1.73049	0.865244	−	0.501350i	$-0.167163\pi$
$331$	31.4835	1.73049	0.865244	+	0.501350i	$0.167163\pi$
$332$	22.6330	1.24215
$333$	1.26811	0.0694919
$334$	24.2650	1.32772
$335$	13.0863	0.714982
$336$	−53.7380	−2.93165
$337$	−9.31573	−0.507460	−0.253730	−	0.967275i	$-0.581658\pi$
$337$	−9.31573	−0.507460	−0.253730	+	0.967275i	$0.581658\pi$
$338$	32.9879	1.79431
$339$	−7.07867	−0.384460
$340$	5.73886	0.311233
$341$	0.426308	0.0230859
$342$	−18.5447	−1.00278
$343$	−7.04737	−0.380522
$344$	86.9492	4.68799
$345$	1.97956	0.106576
$346$	10.3864	0.558378
$347$	−22.3926	−1.20210	−0.601049	−	0.799212i	$-0.705250\pi$
$347$	−22.3926	−1.20210	−0.601049	+	0.799212i	$0.705250\pi$
$348$	21.2961	1.14159
$349$	1.75464	0.0939237	0.0469619	−	0.998897i	$-0.485046\pi$
$349$	1.75464	0.0939237	0.0469619	+	0.998897i	$0.485046\pi$
$350$	37.2442	1.99078
$351$	−0.989935	−0.0528388
$352$	35.0085	1.86596
$353$	−24.2822	−1.29241	−0.646207	−	0.763162i	$-0.723646\pi$
$353$	−24.2822	−1.29241	−0.646207	+	0.763162i	$0.723646\pi$
$354$	8.57660	0.455841
$355$	8.44558	0.448245
$356$	91.6075	4.85519
$357$	−3.45867	−0.183052
$358$	−23.6955	−1.25234
$359$	22.0849	1.16559	0.582797	−	0.812618i	$-0.301958\pi$
$359$	22.0849	1.16559	0.582797	+	0.812618i	$0.301958\pi$
$360$	−10.0555	−0.529972
$361$	26.6606	1.40319
$362$	0.726317	0.0381744
$363$	8.73372	0.458402
$364$	18.9401	0.992731
$365$	1.21067	0.0633696
$366$	−0.181793	−0.00950246
$367$	36.4188	1.90105	0.950523	−	0.310655i	$-0.100548\pi$
$367$	36.4188	1.90105	0.950523	+	0.310655i	$0.100548\pi$
$368$	−29.6471	−1.54546
$369$	7.81884	0.407032
$370$	−3.61048	−0.187700
$371$	−6.70878	−0.348302
$372$	1.56651	0.0812197
$373$	−29.0099	−1.50208	−0.751038	−	0.660259i	$-0.770447\pi$
$373$	−29.0099	−1.50208	−0.751038	+	0.660259i	$0.770447\pi$
$374$	4.13148	0.213634
$375$	9.25777	0.478069
$376$	−22.8004	−1.17584
$377$	−3.81101	−0.196277
$378$	9.49202	0.488217
$379$	33.8283	1.73764	0.868821	−	0.495126i	$-0.164878\pi$
$379$	33.8283	1.73764	0.868821	+	0.495126i	$0.164878\pi$
$380$	38.7790	1.98932
$381$	−2.89107	−0.148114
$382$	−24.0128	−1.22860
$383$	−27.3909	−1.39961	−0.699805	−	0.714334i	$-0.746730\pi$
$383$	−27.3909	−1.39961	−0.699805	+	0.714334i	$0.746730\pi$
$384$	43.3612	2.21276
$385$	−5.40163	−0.275293
$386$	57.1905	2.91092
$387$	−8.97058	−0.456000
$388$	34.5523	1.75413
$389$	−26.6647	−1.35195	−0.675976	−	0.736924i	$-0.736278\pi$
$389$	−26.6647	−1.35195	−0.675976	+	0.736924i	$0.736278\pi$
$390$	2.81848	0.142719
$391$	−1.90814	−0.0964987
$392$	−48.0991	−2.42937
$393$	14.3959	0.726179
$394$	9.70728	0.489046
$395$	−1.03743	−0.0521989
$396$	−8.32765	−0.418480
$397$	−8.22925	−0.413014	−0.206507	−	0.978445i	$-0.566210\pi$
$397$	−8.22925	−0.413014	−0.206507	+	0.978445i	$0.566210\pi$
$398$	27.0917	1.35798
$399$	−23.3711	−1.17002
$400$	−60.9638	−3.04819
$401$	22.6042	1.12880	0.564400	−	0.825501i	$-0.309107\pi$
$401$	22.6042	1.12880	0.564400	+	0.825501i	$0.309107\pi$
$402$	34.6184	1.72661
$403$	−0.280333	−0.0139644
$404$	72.1317	3.58869
$405$	1.03743	0.0515504
$406$	36.5420	1.81355
$407$	−1.90903	−0.0946270
$408$	9.69270	0.479860
$409$	−12.0998	−0.598298	−0.299149	−	0.954206i	$-0.596703\pi$
$409$	−12.0998	−0.598298	−0.299149	+	0.954206i	$0.596703\pi$
$410$	−22.2613	−1.09941
$411$	−6.26194	−0.308879
$412$	−88.6089	−4.36544
$413$	10.8087	0.531863
$414$	5.23672	0.257371
$415$	4.24459	0.208359
$416$	−23.0210	−1.12869
$417$	6.51856	0.319215
$418$	27.9175	1.36549
$419$	24.7082	1.20708	0.603538	−	0.797334i	$-0.293757\pi$
$419$	24.7082	1.20708	0.603538	+	0.797334i	$0.293757\pi$
$420$	−19.8488	−0.968524
$421$	23.8251	1.16117	0.580583	−	0.814201i	$-0.302825\pi$
$421$	23.8251	1.16117	0.580583	+	0.814201i	$0.302825\pi$
$422$	−51.4569	−2.50488
$423$	2.35233	0.114374
$424$	18.8009	0.913053
$425$	−3.92374	−0.190329
$426$	22.3419	1.08247
$427$	−0.229106	−0.0110872
$428$	−4.60276	−0.222483
$429$	1.49026	0.0719506
$430$	25.5405	1.23167
$431$	−15.0636	−0.725587	−0.362793	−	0.931870i	$-0.618177\pi$
$431$	−15.0636	−0.725587	−0.362793	+	0.931870i	$0.618177\pi$
$432$	−15.5372	−0.747533
$433$	−33.1848	−1.59476	−0.797380	−	0.603477i	$-0.793782\pi$
$433$	−33.1848	−1.59476	−0.797380	+	0.603477i	$0.793782\pi$
$434$	2.68798	0.129027
$435$	3.99386	0.191491
$436$	86.4346	4.13947
$437$	−12.8938	−0.616794
$438$	3.20271	0.153031
$439$	−18.1507	−0.866285	−0.433142	−	0.901326i	$-0.642595\pi$
$439$	−18.1507	−0.866285	−0.433142	+	0.901326i	$0.642595\pi$
$440$	15.1377	0.721663
$441$	4.96240	0.236305
$442$	−2.71679	−0.129224
$443$	2.11212	0.100350	0.0501750	−	0.998740i	$-0.484022\pi$
$443$	2.11212	0.100350	0.0501750	+	0.998740i	$0.484022\pi$
$444$	−7.01491	−0.332913
$445$	17.1800	0.814412
$446$	63.2433	2.99466
$447$	16.9621	0.802278
$448$	113.261	5.35108
$449$	15.3368	0.723787	0.361894	−	0.932219i	$-0.382130\pi$
$449$	15.3368	0.723787	0.361894	+	0.932219i	$0.382130\pi$
$450$	10.7683	0.507625
$451$	−11.7706	−0.554256
$452$	39.1578	1.84183
$453$	−11.2724	−0.529622
$454$	−55.0639	−2.58428
$455$	3.55202	0.166521
$456$	65.4961	3.06714
$457$	9.80752	0.458777	0.229388	−	0.973335i	$-0.426327\pi$
$457$	9.80752	0.458777	0.229388	+	0.973335i	$0.426327\pi$
$458$	35.0459	1.63759
$459$	−1.00000	−0.0466760
$460$	−10.9505	−0.510572
$461$	27.7549	1.29267	0.646337	−	0.763052i	$-0.276300\pi$
$461$	27.7549	1.29267	0.646337	+	0.763052i	$0.276300\pi$
$462$	−14.2894	−0.664804
$463$	2.31565	0.107617	0.0538087	−	0.998551i	$-0.482864\pi$
$463$	2.31565	0.107617	0.0538087	+	0.998551i	$0.482864\pi$
$464$	−59.8144	−2.77682
$465$	0.293783	0.0136238
$466$	−37.4570	−1.73516
$467$	26.2949	1.21678	0.608391	−	0.793637i	$-0.291815\pi$
$467$	26.2949	1.21678	0.608391	+	0.793637i	$0.291815\pi$
$468$	5.47612	0.253134
$469$	43.6282	2.01456
$470$	−6.69742	−0.308929
$471$	−11.7942	−0.543448
$472$	−30.2908	−1.39425
$473$	13.5045	0.620935
$474$	−2.74441	−0.126055
$475$	−26.5137	−1.21653
$476$	19.1327	0.876944
$477$	−1.93970	−0.0888126
$478$	15.4050	0.704608
$479$	22.4199	1.02439	0.512196	−	0.858869i	$-0.328832\pi$
$479$	22.4199	1.02439	0.512196	+	0.858869i	$0.328832\pi$
$480$	24.1255	1.10117
$481$	1.25534	0.0572388
$482$	−38.2085	−1.74035
$483$	6.59962	0.300293
$484$	−48.3132	−2.19605
$485$	6.47992	0.294238
$486$	2.74441	0.124489
$487$	−19.0981	−0.865417	−0.432709	−	0.901534i	$-0.642442\pi$
$487$	−19.0981	−0.865417	−0.432709	+	0.901534i	$0.642442\pi$
$488$	0.642055	0.0290645
$489$	−16.0694	−0.726685
$490$	−14.1287	−0.638268
$491$	6.59003	0.297404	0.148702	−	0.988882i	$-0.452491\pi$
$491$	6.59003	0.297404	0.148702	+	0.988882i	$0.452491\pi$
$492$	−43.2522	−1.94996
$493$	−3.84976	−0.173385
$494$	−18.3581	−0.825968
$495$	−1.56177	−0.0701961
$496$	−4.39986	−0.197560
$497$	28.1565	1.26299
$498$	11.2286	0.503165
$499$	19.7321	0.883329	0.441665	−	0.897180i	$-0.354388\pi$
$499$	19.7321	0.883329	0.441665	+	0.897180i	$0.354388\pi$
$500$	−51.2121	−2.29027
$501$	8.84160	0.395014
$502$	7.21756	0.322135
$503$	19.5375	0.871134	0.435567	−	0.900156i	$-0.356548\pi$
$503$	19.5375	0.871134	0.435567	+	0.900156i	$0.356548\pi$
$504$	−33.5239	−1.49327
$505$	13.5276	0.601969
$506$	−7.88344	−0.350462
$507$	12.0200	0.533828
$508$	15.9928	0.709566
$509$	−15.2618	−0.676466	−0.338233	−	0.941062i	$-0.609829\pi$
$509$	−15.2618	−0.676466	−0.338233	+	0.941062i	$0.609829\pi$
$510$	2.84714	0.126073
$511$	4.03624	0.178553
$512$	−60.1227	−2.65707
$513$	−6.75726	−0.298340
$514$	15.0240	0.662679
$515$	−16.6177	−0.732263
$516$	49.6234	2.18455
$517$	−3.54124	−0.155743
$518$	−12.0369	−0.528871
$519$	3.78457	0.166124
$520$	−9.95431	−0.436525
$521$	41.3256	1.81051	0.905253	−	0.424872i	$-0.139681\pi$
$521$	41.3256	1.81051	0.905253	+	0.424872i	$0.139681\pi$
$522$	10.5653	0.462432
$523$	0.0567138	0.00247992	0.00123996	−	0.999999i	$-0.499605\pi$
$523$	0.0567138	0.00247992	0.00123996	+	0.999999i	$0.499605\pi$
$524$	−79.6354	−3.47889
$525$	13.5709	0.592283
$526$	25.5487	1.11398
$527$	−0.283183	−0.0123356
$528$	23.3899	1.01792
$529$	−19.3590	−0.841696
$530$	5.52259	0.239886
$531$	3.12511	0.135618
$532$	129.284	5.60519
$533$	7.74014	0.335263
$534$	45.4479	1.96672
$535$	−0.863201	−0.0373194
$536$	−122.265	−5.28106
$537$	−8.63407	−0.372588
$538$	20.9194	0.901898
$539$	−7.47048	−0.321776
$540$	−5.73886	−0.246961
$541$	17.2774	0.742812	0.371406	−	0.928470i	$-0.378876\pi$
$541$	17.2774	0.742812	0.371406	+	0.928470i	$0.378876\pi$
$542$	−43.8943	−1.88542
$543$	0.264653	0.0113574
$544$	−23.2550	−0.997050
$545$	16.2099	0.694357
$546$	9.39648	0.402132
$547$	4.58847	0.196189	0.0980944	−	0.995177i	$-0.468725\pi$
$547$	4.58847	0.196189	0.0980944	+	0.995177i	$0.468725\pi$
$548$	34.6398	1.47974
$549$	−0.0662411	−0.00282710
$550$	−16.2108	−0.691232
$551$	−26.0138	−1.10823
$552$	−18.4950	−0.787201
$553$	−3.45867	−0.147078
$554$	−21.8572	−0.928623
$555$	−1.31558	−0.0558431
$556$	−36.0593	−1.52926
$557$	3.54085	0.150031	0.0750154	−	0.997182i	$-0.476099\pi$
$557$	3.54085	0.150031	0.0750154	+	0.997182i	$0.476099\pi$
$558$	0.777170	0.0329002
$559$	−8.88029	−0.375596
$560$	55.7495	2.35585
$561$	1.50542	0.0635587
$562$	−55.6019	−2.34542
$563$	−11.6126	−0.489413	−0.244707	−	0.969597i	$-0.578692\pi$
$563$	−11.6126	−0.489413	−0.244707	+	0.969597i	$0.578692\pi$
$564$	−13.0126	−0.547930
$565$	7.34363	0.308949
$566$	−54.4292	−2.28783
$567$	3.45867	0.145251
$568$	−78.9069	−3.31086
$569$	−9.32239	−0.390815	−0.195408	−	0.980722i	$-0.562603\pi$
$569$	−9.32239	−0.390815	−0.195408	+	0.980722i	$0.562603\pi$
$570$	19.2389	0.805827
$571$	−4.38602	−0.183549	−0.0917746	−	0.995780i	$-0.529254\pi$
$571$	−4.38602	−0.183549	−0.0917746	+	0.995780i	$0.529254\pi$
$572$	−8.24383	−0.344692
$573$	−8.74972	−0.365525
$574$	−74.2165	−3.09774
$575$	7.48703	0.312231
$576$	32.7470	1.36446
$577$	4.30122	0.179062	0.0895310	−	0.995984i	$-0.471463\pi$
$577$	4.30122	0.179062	0.0895310	+	0.995984i	$0.471463\pi$
$578$	−2.74441	−0.114152
$579$	20.8389	0.866035
$580$	−22.0932	−0.917372
$581$	14.1509	0.587080
$582$	17.1419	0.710556
$583$	2.92005	0.120936
$584$	−11.3113	−0.468065
$585$	1.02699	0.0424608
$586$	−33.5414	−1.38558
$587$	14.2864	0.589664	0.294832	−	0.955549i	$-0.404736\pi$
$587$	14.2864	0.589664	0.294832	+	0.955549i	$0.404736\pi$
$588$	−27.4510	−1.13206
$589$	−1.91354	−0.0788460
$590$	−8.89764	−0.366310
$591$	3.53711	0.145497
$592$	19.7028	0.809781
$593$	−5.41825	−0.222501	−0.111251	−	0.993792i	$-0.535486\pi$
$593$	−5.41825	−0.222501	−0.111251	+	0.993792i	$0.535486\pi$
$594$	−4.13148	−0.169517
$595$	3.58813	0.147099
$596$	−93.8307	−3.84346
$597$	9.87158	0.404017
$598$	5.18401	0.211990
$599$	19.7514	0.807019	0.403510	−	0.914975i	$-0.367790\pi$
$599$	19.7514	0.807019	0.403510	+	0.914975i	$0.367790\pi$
$600$	−38.0316	−1.55263
$601$	41.4188	1.68951	0.844753	−	0.535156i	$-0.179747\pi$
$601$	41.4188	1.68951	0.844753	+	0.535156i	$0.179747\pi$
$602$	85.1489	3.47041
$603$	12.6142	0.513688
$604$	62.3564	2.53725
$605$	−9.06064	−0.368368
$606$	35.7857	1.45369
$607$	27.5416	1.11788	0.558940	−	0.829208i	$-0.311208\pi$
$607$	27.5416	1.11788	0.558940	+	0.829208i	$0.311208\pi$
$608$	−157.140	−6.37288
$609$	13.3151	0.539553
$610$	0.188598	0.00763609
$611$	2.32865	0.0942073
$612$	5.53180	0.223610
$613$	−32.3127	−1.30510	−0.652548	−	0.757747i	$-0.726300\pi$
$613$	−32.3127	−1.30510	−0.652548	+	0.757747i	$0.726300\pi$
$614$	−25.0200	−1.00972
$615$	−8.11151	−0.327088
$616$	50.4674	2.03339
$617$	−5.04182	−0.202976	−0.101488	−	0.994837i	$-0.532360\pi$
$617$	−5.04182	−0.202976	−0.101488	+	0.994837i	$0.532360\pi$
$618$	−43.9603	−1.76834
$619$	1.14048	0.0458398	0.0229199	−	0.999737i	$-0.492704\pi$
$619$	1.14048	0.0458398	0.0229199	+	0.999737i	$0.492704\pi$
$620$	−1.62515	−0.0652675
$621$	1.90814	0.0765710
$622$	64.0209	2.56700
$623$	57.2762	2.29472
$624$	−15.3808	−0.615725
$625$	10.0144	0.400575
$626$	76.4249	3.05455
$627$	10.1725	0.406250
$628$	65.2431	2.60348
$629$	1.26811	0.0505628
$630$	−9.84732	−0.392327
$631$	41.6123	1.65656	0.828280	−	0.560315i	$-0.189320\pi$
$631$	41.6123	1.65656	0.828280	+	0.560315i	$0.189320\pi$
$632$	9.69270	0.385555
$633$	−18.7497	−0.745233
$634$	−21.8340	−0.867139
$635$	2.99929	0.119023
$636$	10.7300	0.425473
$637$	4.91246	0.194639
$638$	−15.9052	−0.629693
$639$	8.14085	0.322047
$640$	−44.9842	−1.77816
$641$	39.7578	1.57034	0.785168	−	0.619282i	$-0.212576\pi$
$641$	39.7578	1.57034	0.785168	+	0.619282i	$0.212576\pi$
$642$	−2.28350	−0.0901227
$643$	−18.3743	−0.724612	−0.362306	−	0.932059i	$-0.618010\pi$
$643$	−18.3743	−0.724612	−0.362306	+	0.932059i	$0.618010\pi$
$644$	−36.5078	−1.43861
$645$	9.30637	0.366438
$646$	−18.5447	−0.729632
$647$	−45.5302	−1.78998	−0.894988	−	0.446091i	$-0.852816\pi$
$647$	−45.5302	−1.78998	−0.894988	+	0.446091i	$0.852816\pi$
$648$	−9.69270	−0.380765
$649$	−4.70459	−0.184671
$650$	10.6600	0.418118
$651$	0.979436	0.0383871
$652$	88.8928	3.48131
$653$	−6.90366	−0.270161	−0.135081	−	0.990835i	$-0.543129\pi$
$653$	−6.90366	−0.270161	−0.135081	+	0.990835i	$0.543129\pi$
$654$	42.8816	1.67680
$655$	−14.9348	−0.583551
$656$	121.483	4.74310
$657$	1.16699	0.0455287
$658$	−22.3284	−0.870450
$659$	33.8502	1.31862	0.659308	−	0.751873i	$-0.270849\pi$
$659$	33.8502	1.31862	0.659308	+	0.751873i	$0.270849\pi$
$660$	8.63937	0.336287
$661$	9.50646	0.369758	0.184879	−	0.982761i	$-0.440811\pi$
$661$	9.50646	0.369758	0.184879	+	0.982761i	$0.440811\pi$
$662$	−86.4037	−3.35817
$663$	−0.989935	−0.0384459
$664$	−39.6571	−1.53899
$665$	24.2460	0.940218
$666$	−3.48021	−0.134855
$667$	7.34588	0.284434
$668$	−48.9100	−1.89238
$669$	23.0444	0.890948
$670$	−35.9143	−1.38749
$671$	0.0997203	0.00384966
$672$	80.4314	3.10271
$673$	−4.57288	−0.176271	−0.0881357	−	0.996108i	$-0.528091\pi$
$673$	−4.57288	−0.176271	−0.0881357	+	0.996108i	$0.528091\pi$
$674$	25.5662	0.984774
$675$	3.92374	0.151025
$676$	−66.4924	−2.55740
$677$	−21.7902	−0.837464	−0.418732	−	0.908110i	$-0.637525\pi$
$677$	−21.7902	−0.837464	−0.418732	+	0.908110i	$0.637525\pi$
$678$	19.4268	0.746081
$679$	21.6033	0.829058
$680$	−10.0555	−0.385612
$681$	−20.0640	−0.768854
$682$	−1.16996	−0.0448002
$683$	27.3481	1.04644	0.523222	−	0.852196i	$-0.324730\pi$
$683$	27.3481	1.04644	0.523222	+	0.852196i	$0.324730\pi$
$684$	37.3798	1.42925
$685$	6.49633	0.248212
$686$	19.3409	0.738439
$687$	12.7699	0.487202
$688$	−139.378	−5.31372
$689$	−1.92017	−0.0731528
$690$	−5.43274	−0.206821
$691$	−15.3185	−0.582743	−0.291372	−	0.956610i	$-0.594112\pi$
$691$	−15.3185	−0.582743	−0.291372	+	0.956610i	$0.594112\pi$
$692$	−20.9355	−0.795848
$693$	−5.20674	−0.197788
$694$	61.4545	2.33278
$695$	−6.76256	−0.256519
$696$	−37.3146	−1.41441
$697$	7.81884	0.296160
$698$	−4.81545	−0.182268
$699$	−13.6485	−0.516232
$700$	−75.0715	−2.83744
$701$	27.1067	1.02381	0.511903	−	0.859043i	$-0.328941\pi$
$701$	27.1067	1.02381	0.511903	+	0.859043i	$0.328941\pi$
$702$	2.71679	0.102539
$703$	8.56893	0.323183
$704$	−49.2978	−1.85798
$705$	−2.44038	−0.0919101
$706$	66.6405	2.50805
$707$	45.0993	1.69613
$708$	−17.2875	−0.649704
$709$	−46.3437	−1.74048	−0.870238	−	0.492632i	$-0.836035\pi$
$709$	−46.3437	−1.74048	−0.870238	+	0.492632i	$0.836035\pi$
$710$	−23.1781	−0.869860
$711$	−1.00000	−0.0375029
$712$	−160.513	−6.01547
$713$	0.540352	0.0202363
$714$	9.49202	0.355230
$715$	−1.54605	−0.0578189
$716$	47.7619	1.78495
$717$	5.61322	0.209630
$718$	−60.6100	−2.26194
$719$	47.2911	1.76366	0.881830	−	0.471568i	$-0.156312\pi$
$719$	47.2911	1.76366	0.881830	+	0.471568i	$0.156312\pi$
$720$	16.1188	0.600711
$721$	−55.4013	−2.06325
$722$	−73.1676	−2.72301
$723$	−13.9223	−0.517776
$724$	−1.46401	−0.0544094
$725$	15.1054	0.561002
$726$	−23.9689	−0.889571
$727$	22.9937	0.852790	0.426395	−	0.904537i	$-0.359783\pi$
$727$	22.9937	0.852790	0.426395	+	0.904537i	$0.359783\pi$
$728$	−33.1865	−1.22997
$729$	1.00000	0.0370370
$730$	−3.32259	−0.122974
$731$	−8.97058	−0.331789
$732$	0.366432	0.0135437
$733$	−18.7188	−0.691393	−0.345696	−	0.938346i	$-0.612357\pi$
$733$	−18.7188	−0.691393	−0.345696	+	0.938346i	$0.612357\pi$
$734$	−99.9482	−3.68915
$735$	−5.14815	−0.189893
$736$	44.3738	1.63564
$737$	−18.9895	−0.699489
$738$	−21.4581	−0.789884
$739$	5.27375	0.193998	0.0969990	−	0.995284i	$-0.469076\pi$
$739$	5.27375	0.193998	0.0969990	+	0.995284i	$0.469076\pi$
$740$	7.27749	0.267526
$741$	−6.68925	−0.245736
$742$	18.4116	0.675913
$743$	−13.9477	−0.511690	−0.255845	−	0.966718i	$-0.582354\pi$
$743$	−13.9477	−0.511690	−0.255845	+	0.966718i	$0.582354\pi$
$744$	−2.74481	−0.100630
$745$	−17.5970	−0.644704
$746$	79.6152	2.91492
$747$	4.09144	0.149698
$748$	−8.32765	−0.304489
$749$	−2.87781	−0.105153
$750$	−25.4071	−0.927737
$751$	44.7817	1.63411	0.817053	−	0.576563i	$-0.195606\pi$
$751$	44.7817	1.63411	0.817053	+	0.576563i	$0.195606\pi$
$752$	36.5486	1.33279
$753$	2.62991	0.0958393
$754$	10.4590	0.380894
$755$	11.6943	0.425599
$756$	−19.1327	−0.695848
$757$	−23.2964	−0.846722	−0.423361	−	0.905961i	$-0.639150\pi$
$757$	−23.2964	−0.846722	−0.423361	+	0.905961i	$0.639150\pi$
$758$	−92.8387	−3.37205
$759$	−2.87254	−0.104267
$760$	−67.9478	−2.46472
$761$	−1.09196	−0.0395834	−0.0197917	−	0.999804i	$-0.506300\pi$
$761$	−1.09196	−0.0395834	−0.0197917	+	0.999804i	$0.506300\pi$
$762$	7.93428	0.287429
$763$	54.0419	1.95645
$764$	48.4017	1.75111
$765$	1.03743	0.0375084
$766$	75.1719	2.71607
$767$	3.09366	0.111706
$768$	−53.5069	−1.93077
$769$	5.97715	0.215541	0.107771	−	0.994176i	$-0.465629\pi$
$769$	5.97715	0.215541	0.107771	+	0.994176i	$0.465629\pi$
$770$	14.8243	0.534231
$771$	5.47439	0.197155
$772$	−115.277	−4.14889
$773$	5.60615	0.201639	0.100820	−	0.994905i	$-0.467853\pi$
$773$	5.60615	0.201639	0.100820	+	0.994905i	$0.467853\pi$
$774$	24.6190	0.884911
$775$	1.11113	0.0399131
$776$	−60.5418	−2.17332
$777$	−4.38597	−0.157346
$778$	73.1788	2.62359
$779$	52.8339	1.89297
$780$	−5.68110	−0.203416
$781$	−12.2554	−0.438531
$782$	5.23672	0.187265
$783$	3.84976	0.137579
$784$	77.1018	2.75363
$785$	12.2357	0.436710
$786$	−39.5084	−1.40922
$787$	−8.69054	−0.309784	−0.154892	−	0.987931i	$-0.549503\pi$
$787$	−8.69054	−0.309784	−0.154892	+	0.987931i	$0.549503\pi$
$788$	−19.5666	−0.697030
$789$	9.30936	0.331422
$790$	2.84714	0.101297
$791$	24.4828	0.870508
$792$	14.5915	0.518488
$793$	−0.0655744	−0.00232861
$794$	22.5844	0.801492
$795$	2.01230	0.0713691
$796$	−54.6075	−1.93551
$797$	−9.66247	−0.342262	−0.171131	−	0.985248i	$-0.554742\pi$
$797$	−9.66247	−0.342262	−0.171131	+	0.985248i	$0.554742\pi$
$798$	64.1400	2.27053
$799$	2.35233	0.0832195
$800$	91.2465	3.22605
$801$	16.5602	0.585125
$802$	−62.0353	−2.19054
$803$	−1.75681	−0.0619964
$804$	−69.7789	−2.46091
$805$	−6.84666	−0.241313
$806$	0.769348	0.0270991
$807$	7.62253	0.268326
$808$	−126.388	−4.44631
$809$	−48.4006	−1.70168	−0.850838	−	0.525429i	$-0.823905\pi$
$809$	−48.4006	−1.70168	−0.850838	+	0.525429i	$0.823905\pi$
$810$	−2.84714	−0.100038
$811$	−18.2318	−0.640206	−0.320103	−	0.947383i	$-0.603718\pi$
$811$	−18.2318	−0.640206	−0.320103	+	0.947383i	$0.603718\pi$
$812$	−73.6562	−2.58483
$813$	−15.9941	−0.560936
$814$	5.23916	0.183633
$815$	16.6709	0.583957
$816$	−15.5372	−0.543910
$817$	−60.6166	−2.12071
$818$	33.2069	1.16105
$819$	3.42386	0.119639
$820$	44.8712	1.56697
$821$	33.8398	1.18102	0.590508	−	0.807032i	$-0.298927\pi$
$821$	33.8398	1.18102	0.590508	+	0.807032i	$0.298927\pi$
$822$	17.1853	0.599407
$823$	43.8647	1.52903	0.764513	−	0.644608i	$-0.222979\pi$
$823$	43.8647	1.52903	0.764513	+	0.644608i	$0.222979\pi$
$824$	155.259	5.40869
$825$	−5.90685	−0.205650
$826$	−29.6636	−1.03213
$827$	−29.2596	−1.01745	−0.508727	−	0.860928i	$-0.669884\pi$
$827$	−29.2596	−1.01745	−0.508727	+	0.860928i	$0.669884\pi$
$828$	−10.5554	−0.366827
$829$	−20.2841	−0.704496	−0.352248	−	0.935907i	$-0.614583\pi$
$829$	−20.2841	−0.704496	−0.352248	+	0.935907i	$0.614583\pi$
$830$	−11.6489	−0.404339
$831$	−7.96425	−0.276277
$832$	32.4174	1.12387
$833$	4.96240	0.171937
$834$	−17.8896	−0.619467
$835$	−9.17256	−0.317430
$836$	−56.2721	−1.94621
$837$	0.283183	0.00978823
$838$	−67.8095	−2.34244
$839$	−16.9476	−0.585097	−0.292548	−	0.956251i	$-0.594503\pi$
$839$	−16.9476	−0.585097	−0.292548	+	0.956251i	$0.594503\pi$
$840$	34.7787	1.19998
$841$	−14.1793	−0.488943
$842$	−65.3860	−2.25335
$843$	−20.2600	−0.697793
$844$	103.719	3.57017
$845$	−12.4700	−0.428980
$846$	−6.45577	−0.221954
$847$	−30.2071	−1.03793
$848$	−30.1374	−1.03492
$849$	−19.8327	−0.680657
$850$	10.7683	0.369351
$851$	−2.41973	−0.0829471
$852$	−45.0335	−1.54282
$853$	−21.6025	−0.739654	−0.369827	−	0.929101i	$-0.620583\pi$
$853$	−21.6025	−0.739654	−0.369827	+	0.929101i	$0.620583\pi$
$854$	0.628762	0.0215158
$855$	7.01020	0.239744
$856$	8.06487	0.275652
$857$	20.5104	0.700621	0.350310	−	0.936634i	$-0.386076\pi$
$857$	20.5104	0.700621	0.350310	+	0.936634i	$0.386076\pi$
$858$	−4.08990	−0.139627
$859$	−37.6556	−1.28479	−0.642397	−	0.766372i	$-0.722060\pi$
$859$	−37.6556	−1.28479	−0.642397	+	0.766372i	$0.722060\pi$
$860$	−51.4809	−1.75549
$861$	−27.0428	−0.921616
$862$	41.3406	1.40807
$863$	41.6966	1.41937	0.709684	−	0.704520i	$-0.248838\pi$
$863$	41.6966	1.41937	0.709684	+	0.704520i	$0.248838\pi$
$864$	23.2550	0.791152
$865$	−3.92624	−0.133496
$866$	91.0728	3.09478
$867$	−1.00000	−0.0339618
$868$	−5.41804	−0.183900
$869$	1.50542	0.0510677
$870$	−10.9608	−0.371606
$871$	12.4872	0.423112
$872$	−151.449	−5.12871
$873$	6.24612	0.211399
$874$	35.3859	1.19695
$875$	−32.0196	−1.08246
$876$	−6.45556	−0.218113
$877$	30.5436	1.03138	0.515692	−	0.856774i	$-0.327535\pi$
$877$	30.5436	1.03138	0.515692	+	0.856774i	$0.327535\pi$
$878$	49.8129	1.68111
$879$	−12.2217	−0.412228
$880$	−24.2654	−0.817988
$881$	−17.4408	−0.587596	−0.293798	−	0.955868i	$-0.594919\pi$
$881$	−17.4408	−0.587596	−0.293798	+	0.955868i	$0.594919\pi$
$882$	−13.6189	−0.458572
$883$	35.6861	1.20093	0.600467	−	0.799650i	$-0.294981\pi$
$883$	35.6861	1.20093	0.600467	+	0.799650i	$0.294981\pi$
$884$	5.47612	0.184182
$885$	−3.24209	−0.108982
$886$	−5.79654	−0.194739
$887$	−6.45519	−0.216744	−0.108372	−	0.994110i	$-0.534564\pi$
$887$	−6.45519	−0.216744	−0.108372	+	0.994110i	$0.534564\pi$
$888$	12.2914	0.412472
$889$	9.99925	0.335364
$890$	−47.1491	−1.58044
$891$	−1.50542	−0.0504333
$892$	−127.477	−4.26824
$893$	15.8953	0.531916
$894$	−46.5509	−1.55690
$895$	8.95726	0.299408
$896$	−149.972	−5.01021
$897$	1.88893	0.0630697
$898$	−42.0904	−1.40458
$899$	1.09019	0.0363597
$900$	−21.7053	−0.723510
$901$	−1.93970	−0.0646207
$902$	32.3034	1.07558
$903$	31.0263	1.03249
$904$	−68.6114	−2.28198
$905$	−0.274560	−0.00912667
$906$	30.9360	1.02778
$907$	−9.37722	−0.311365	−0.155683	−	0.987807i	$-0.549758\pi$
$907$	−9.37722	−0.311365	−0.155683	+	0.987807i	$0.549758\pi$
$908$	110.990	3.68333
$909$	13.0395	0.432492
$910$	−9.74821	−0.323150
$911$	−47.1550	−1.56231	−0.781157	−	0.624334i	$-0.785370\pi$
$911$	−47.1550	−1.56231	−0.781157	+	0.624334i	$0.785370\pi$
$912$	−104.989	−3.47653
$913$	−6.15932	−0.203844
$914$	−26.9159	−0.890298
$915$	0.0687206	0.00227183
$916$	−70.6405	−2.33403
$917$	−49.7908	−1.64424
$918$	2.74441	0.0905791
$919$	2.64984	0.0874103	0.0437052	−	0.999044i	$-0.486084\pi$
$919$	2.64984	0.0874103	0.0437052	+	0.999044i	$0.486084\pi$
$920$	19.1873	0.632587
$921$	−9.11669	−0.300405
$922$	−76.1708	−2.50855
$923$	8.05892	0.265262
$924$	28.8026	0.947536
$925$	−4.97572	−0.163601
$926$	−6.35510	−0.208842
$927$	−16.0181	−0.526103
$928$	89.5263	2.93884
$929$	−13.6274	−0.447100	−0.223550	−	0.974693i	$-0.571765\pi$
$929$	−13.6274	−0.447100	−0.223550	+	0.974693i	$0.571765\pi$
$930$	−0.806261	−0.0264383
$931$	33.5323	1.09898
$932$	75.5005	2.47310
$933$	23.3277	0.763716
$934$	−72.1640	−2.36128
$935$	−1.56177	−0.0510752
$936$	−9.59515	−0.313627
$937$	−15.6112	−0.509995	−0.254998	−	0.966942i	$-0.582075\pi$
$937$	−15.6112	−0.509995	−0.254998	+	0.966942i	$0.582075\pi$
$938$	−119.734	−3.90945
$939$	27.8475	0.908768
$940$	13.4997	0.440312
$941$	−27.5337	−0.897572	−0.448786	−	0.893639i	$-0.648143\pi$
$941$	−27.5337	−0.897572	−0.448786	+	0.893639i	$0.648143\pi$
$942$	32.3682	1.05461
$943$	−14.9194	−0.485843
$944$	48.5555	1.58035
$945$	−3.58813	−0.116722
$946$	−37.0618	−1.20498
$947$	−9.98355	−0.324422	−0.162211	−	0.986756i	$-0.551862\pi$
$947$	−9.98355	−0.324422	−0.162211	+	0.986756i	$0.551862\pi$
$948$	5.53180	0.179664
$949$	1.15525	0.0375009
$950$	72.7645	2.36079
$951$	−7.95581	−0.257985
$952$	−33.5239	−1.08652
$953$	33.7631	1.09370	0.546848	−	0.837232i	$-0.315828\pi$
$953$	33.7631	1.09370	0.546848	+	0.837232i	$0.315828\pi$
$954$	5.32333	0.172349
$955$	9.07724	0.293733
$956$	−31.0512	−1.00427
$957$	−5.79549	−0.187342
$958$	−61.5295	−1.98793
$959$	21.6580	0.699373
$960$	−33.9727	−1.09647
$961$	−30.9198	−0.997413
$962$	−3.44518	−0.111077
$963$	−0.832056	−0.0268126
$964$	77.0153	2.48050
$965$	−21.6189	−0.695938
$966$	−18.1121	−0.582747
$967$	45.4144	1.46043	0.730214	−	0.683219i	$-0.239421\pi$
$967$	45.4144	1.46043	0.730214	+	0.683219i	$0.239421\pi$
$968$	84.6534	2.72086
$969$	−6.75726	−0.217074
$970$	−17.7836	−0.570996
$971$	−13.0893	−0.420055	−0.210028	−	0.977695i	$-0.567355\pi$
$971$	−13.0893	−0.420055	−0.210028	+	0.977695i	$0.567355\pi$
$972$	−5.53180	−0.177432
$973$	−22.5456	−0.722777
$974$	52.4130	1.67942
$975$	3.88424	0.124395
$976$	−1.02920	−0.0329439
$977$	−27.7816	−0.888813	−0.444407	−	0.895825i	$-0.646585\pi$
$977$	−27.7816	−0.888813	−0.444407	+	0.895825i	$0.646585\pi$
$978$	44.1011	1.41020
$979$	−24.9299	−0.796764
$980$	28.4785	0.909714
$981$	15.6251	0.498870
$982$	−18.0858	−0.577140
$983$	−16.5206	−0.526927	−0.263463	−	0.964669i	$-0.584865\pi$
$983$	−16.5206	−0.526927	−0.263463	+	0.964669i	$0.584865\pi$
$984$	75.7857	2.41596
$985$	−3.66951	−0.116920
$986$	10.5653	0.336469
$987$	−8.13594	−0.258970
$988$	37.0036	1.17724
$989$	17.1171	0.544293
$990$	4.28613	0.136222
$991$	−10.1446	−0.322253	−0.161126	−	0.986934i	$-0.551513\pi$
$991$	−10.1446	−0.322253	−0.161126	+	0.986934i	$0.551513\pi$
$992$	6.58542	0.209087
$993$	−31.4835	−0.999098
$994$	−77.2731	−2.45095
$995$	−10.2411	−0.324664
$996$	−22.6330	−0.717155
$997$	−59.1381	−1.87292	−0.936461	−	0.350771i	$-0.885920\pi$
$997$	−59.1381	−1.87292	−0.936461	+	0.350771i	$0.885920\pi$
$998$	−54.1530	−1.71418
$999$	−1.26811	−0.0401212

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.i.1.1	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.i.1.1	✓	25	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)

\(f(q)\)	\(=\)	\(q-2.74441 q^{2} -1.00000 q^{3} +5.53180 q^{4} +1.03743 q^{5} +2.74441 q^{6} +3.45867 q^{7} -9.69270 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.74441 q^{2} -1.00000 q^{3} +5.53180 q^{4} +1.03743 q^{5} +2.74441 q^{6} +3.45867 q^{7} -9.69270 q^{8} +1.00000 q^{9} -2.84714 q^{10} -1.50542 q^{11} -5.53180 q^{12} +0.989935 q^{13} -9.49202 q^{14} -1.03743 q^{15} +15.5372 q^{16} +1.00000 q^{17} -2.74441 q^{18} +6.75726 q^{19} +5.73886 q^{20} -3.45867 q^{21} +4.13148 q^{22} -1.90814 q^{23} +9.69270 q^{24} -3.92374 q^{25} -2.71679 q^{26} -1.00000 q^{27} +19.1327 q^{28} -3.84976 q^{29} +2.84714 q^{30} -0.283183 q^{31} -23.2550 q^{32} +1.50542 q^{33} -2.74441 q^{34} +3.58813 q^{35} +5.53180 q^{36} +1.26811 q^{37} -18.5447 q^{38} -0.989935 q^{39} -10.0555 q^{40} +7.81884 q^{41} +9.49202 q^{42} -8.97058 q^{43} -8.32765 q^{44} +1.03743 q^{45} +5.23672 q^{46} +2.35233 q^{47} -15.5372 q^{48} +4.96240 q^{49} +10.7683 q^{50} -1.00000 q^{51} +5.47612 q^{52} -1.93970 q^{53} +2.74441 q^{54} -1.56177 q^{55} -33.5239 q^{56} -6.75726 q^{57} +10.5653 q^{58} +3.12511 q^{59} -5.73886 q^{60} -0.0662411 q^{61} +0.777170 q^{62} +3.45867 q^{63} +32.7470 q^{64} +1.02699 q^{65} -4.13148 q^{66} +12.6142 q^{67} +5.53180 q^{68} +1.90814 q^{69} -9.84732 q^{70} +8.14085 q^{71} -9.69270 q^{72} +1.16699 q^{73} -3.48021 q^{74} +3.92374 q^{75} +37.3798 q^{76} -5.20674 q^{77} +2.71679 q^{78} -1.00000 q^{79} +16.1188 q^{80} +1.00000 q^{81} -21.4581 q^{82} +4.09144 q^{83} -19.1327 q^{84} +1.03743 q^{85} +24.6190 q^{86} +3.84976 q^{87} +14.5915 q^{88} +16.5602 q^{89} -2.84714 q^{90} +3.42386 q^{91} -10.5554 q^{92} +0.283183 q^{93} -6.45577 q^{94} +7.01020 q^{95} +23.2550 q^{96} +6.24612 q^{97} -13.6189 q^{98} -1.50542 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9}+O(q^{10}) \) 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9} + 19 q^{10} + 19 q^{11} - 26 q^{12} + 4 q^{13} + 15 q^{14} + 2 q^{15} + 32 q^{16} + 25 q^{17} - 2 q^{18} + 29 q^{19} - 8 q^{20} - 12 q^{21} + 23 q^{22} + 6 q^{23} + 15 q^{25} - 8 q^{26} - 25 q^{27} + 23 q^{28} + 11 q^{29} - 19 q^{30} + 38 q^{31} - 27 q^{32} - 19 q^{33} - 2 q^{34} + 20 q^{35} + 26 q^{36} + 8 q^{37} - 25 q^{38} - 4 q^{39} + 48 q^{40} + 24 q^{41} - 15 q^{42} + 11 q^{43} + 6 q^{44} - 2 q^{45} + 25 q^{46} + 23 q^{47} - 32 q^{48} + 21 q^{49} - 21 q^{50} - 25 q^{51} + 31 q^{52} - 16 q^{53} + 2 q^{54} - 11 q^{55} + 18 q^{56} - 29 q^{57} - 5 q^{58} + 27 q^{59} + 8 q^{60} + 40 q^{61} - 34 q^{62} + 12 q^{63} + 46 q^{64} - 19 q^{65} - 23 q^{66} + 24 q^{67} + 26 q^{68} - 6 q^{69} + 17 q^{70} + 19 q^{71} + 13 q^{73} - 56 q^{74} - 15 q^{75} + 21 q^{76} - 30 q^{77} + 8 q^{78} - 25 q^{79} - 40 q^{80} + 25 q^{81} + 61 q^{82} + q^{83} - 23 q^{84} - 2 q^{85} + 62 q^{86} - 11 q^{87} - q^{88} - 10 q^{89} + 19 q^{90} + 50 q^{91} + 18 q^{92} - 38 q^{93} + 15 q^{94} + 14 q^{95} + 27 q^{96} + 19 q^{97} - 23 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9 + 19 * q^10 + 19 * q^11 - 26 * q^12 + 4 * q^13 + 15 * q^14 + 2 * q^15 + 32 * q^16 + 25 * q^17 - 2 * q^18 + 29 * q^19 - 8 * q^20 - 12 * q^21 + 23 * q^22 + 6 * q^23 + 15 * q^25 - 8 * q^26 - 25 * q^27 + 23 * q^28 + 11 * q^29 - 19 * q^30 + 38 * q^31 - 27 * q^32 - 19 * q^33 - 2 * q^34 + 20 * q^35 + 26 * q^36 + 8 * q^37 - 25 * q^38 - 4 * q^39 + 48 * q^40 + 24 * q^41 - 15 * q^42 + 11 * q^43 + 6 * q^44 - 2 * q^45 + 25 * q^46 + 23 * q^47 - 32 * q^48 + 21 * q^49 - 21 * q^50 - 25 * q^51 + 31 * q^52 - 16 * q^53 + 2 * q^54 - 11 * q^55 + 18 * q^56 - 29 * q^57 - 5 * q^58 + 27 * q^59 + 8 * q^60 + 40 * q^61 - 34 * q^62 + 12 * q^63 + 46 * q^64 - 19 * q^65 - 23 * q^66 + 24 * q^67 + 26 * q^68 - 6 * q^69 + 17 * q^70 + 19 * q^71 + 13 * q^73 - 56 * q^74 - 15 * q^75 + 21 * q^76 - 30 * q^77 + 8 * q^78 - 25 * q^79 - 40 * q^80 + 25 * q^81 + 61 * q^82 + q^83 - 23 * q^84 - 2 * q^85 + 62 * q^86 - 11 * q^87 - q^88 - 10 * q^89 + 19 * q^90 + 50 * q^91 + 18 * q^92 - 38 * q^93 + 15 * q^94 + 14 * q^95 + 27 * q^96 + 19 * q^97 - 23 * q^98 + 19 * q^99

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