LMFDB - Embedded newform 4029.2.a.l.1.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.23
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.33628 q^{2} -1.00000 q^{3} -0.214366 q^{4} -2.78532 q^{5} -1.33628 q^{6} +2.26746 q^{7} -2.95900 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.33628 q^{2} -1.00000 q^{3} -0.214366 q^{4} -2.78532 q^{5} -1.33628 q^{6} +2.26746 q^{7} -2.95900 q^{8} +1.00000 q^{9} -3.72196 q^{10} +2.19659 q^{11} +0.214366 q^{12} +4.11961 q^{13} +3.02995 q^{14} +2.78532 q^{15} -3.52532 q^{16} -1.00000 q^{17} +1.33628 q^{18} -5.10063 q^{19} +0.597077 q^{20} -2.26746 q^{21} +2.93524 q^{22} -4.60991 q^{23} +2.95900 q^{24} +2.75801 q^{25} +5.50494 q^{26} -1.00000 q^{27} -0.486066 q^{28} +1.32604 q^{29} +3.72196 q^{30} +6.45635 q^{31} +1.20721 q^{32} -2.19659 q^{33} -1.33628 q^{34} -6.31560 q^{35} -0.214366 q^{36} -6.29915 q^{37} -6.81585 q^{38} -4.11961 q^{39} +8.24177 q^{40} -2.12317 q^{41} -3.02995 q^{42} -1.24892 q^{43} -0.470872 q^{44} -2.78532 q^{45} -6.16011 q^{46} -8.03686 q^{47} +3.52532 q^{48} -1.85862 q^{49} +3.68546 q^{50} +1.00000 q^{51} -0.883103 q^{52} +9.17343 q^{53} -1.33628 q^{54} -6.11819 q^{55} -6.70942 q^{56} +5.10063 q^{57} +1.77196 q^{58} +2.78480 q^{59} -0.597077 q^{60} -1.20609 q^{61} +8.62747 q^{62} +2.26746 q^{63} +8.66380 q^{64} -11.4744 q^{65} -2.93524 q^{66} +11.1148 q^{67} +0.214366 q^{68} +4.60991 q^{69} -8.43939 q^{70} +6.75174 q^{71} -2.95900 q^{72} +9.54089 q^{73} -8.41740 q^{74} -2.75801 q^{75} +1.09340 q^{76} +4.98067 q^{77} -5.50494 q^{78} +1.00000 q^{79} +9.81913 q^{80} +1.00000 q^{81} -2.83714 q^{82} +17.9909 q^{83} +0.486066 q^{84} +2.78532 q^{85} -1.66890 q^{86} -1.32604 q^{87} -6.49971 q^{88} +5.07382 q^{89} -3.72196 q^{90} +9.34106 q^{91} +0.988206 q^{92} -6.45635 q^{93} -10.7395 q^{94} +14.2069 q^{95} -1.20721 q^{96} +17.3000 q^{97} -2.48364 q^{98} +2.19659 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9} + 17 q^{10} + 8 q^{11} - 41 q^{12} + 17 q^{13} + q^{14} + q^{15} + 55 q^{16} - 32 q^{17} - q^{18} + 48 q^{19} - 7 q^{20} - 4 q^{21} - 4 q^{22} - 19 q^{23} + 3 q^{24} + 63 q^{25} + 27 q^{26} - 32 q^{27} + 17 q^{28} - 15 q^{29} - 17 q^{30} + 20 q^{31} + 13 q^{32} - 8 q^{33} + q^{34} + 22 q^{35} + 41 q^{36} + 6 q^{37} + 11 q^{38} - 17 q^{39} + 47 q^{40} + q^{41} - q^{42} + 40 q^{43} + 22 q^{44} - q^{45} + 5 q^{46} - 5 q^{47} - 55 q^{48} + 88 q^{49} + 17 q^{50} + 32 q^{51} + 23 q^{52} - 34 q^{53} + q^{54} + 48 q^{55} - 48 q^{57} - 9 q^{58} + 41 q^{59} + 7 q^{60} + 20 q^{61} + 15 q^{62} + 4 q^{63} + 93 q^{64} - 58 q^{65} + 4 q^{66} + 52 q^{67} - 41 q^{68} + 19 q^{69} + 25 q^{70} + q^{71} - 3 q^{72} + 19 q^{73} + 12 q^{74} - 63 q^{75} + 128 q^{76} - 20 q^{77} - 27 q^{78} + 32 q^{79} - 16 q^{80} + 32 q^{81} - 5 q^{82} + 31 q^{83} - 17 q^{84} + q^{85} - 62 q^{86} + 15 q^{87} + 35 q^{88} + 18 q^{89} + 17 q^{90} + 48 q^{91} - 75 q^{92} - 20 q^{93} + 29 q^{94} + 5 q^{95} - 13 q^{96} + 17 q^{97} + 30 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9 + 17 * q^10 + 8 * q^11 - 41 * q^12 + 17 * q^13 + q^14 + q^15 + 55 * q^16 - 32 * q^17 - q^18 + 48 * q^19 - 7 * q^20 - 4 * q^21 - 4 * q^22 - 19 * q^23 + 3 * q^24 + 63 * q^25 + 27 * q^26 - 32 * q^27 + 17 * q^28 - 15 * q^29 - 17 * q^30 + 20 * q^31 + 13 * q^32 - 8 * q^33 + q^34 + 22 * q^35 + 41 * q^36 + 6 * q^37 + 11 * q^38 - 17 * q^39 + 47 * q^40 + q^41 - q^42 + 40 * q^43 + 22 * q^44 - q^45 + 5 * q^46 - 5 * q^47 - 55 * q^48 + 88 * q^49 + 17 * q^50 + 32 * q^51 + 23 * q^52 - 34 * q^53 + q^54 + 48 * q^55 - 48 * q^57 - 9 * q^58 + 41 * q^59 + 7 * q^60 + 20 * q^61 + 15 * q^62 + 4 * q^63 + 93 * q^64 - 58 * q^65 + 4 * q^66 + 52 * q^67 - 41 * q^68 + 19 * q^69 + 25 * q^70 + q^71 - 3 * q^72 + 19 * q^73 + 12 * q^74 - 63 * q^75 + 128 * q^76 - 20 * q^77 - 27 * q^78 + 32 * q^79 - 16 * q^80 + 32 * q^81 - 5 * q^82 + 31 * q^83 - 17 * q^84 + q^85 - 62 * q^86 + 15 * q^87 + 35 * q^88 + 18 * q^89 + 17 * q^90 + 48 * q^91 - 75 * q^92 - 20 * q^93 + 29 * q^94 + 5 * q^95 - 13 * q^96 + 17 * q^97 + 30 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.33628	0.944890	0.472445	−	0.881360i	$-0.343372\pi$
$2$	1.33628	0.944890	0.472445	+	0.881360i	$0.343372\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.214366	−0.107183
$5$	−2.78532	−1.24563	−0.622816	−	0.782368i	$-0.714012\pi$
$5$	−2.78532	−1.24563	−0.622816	+	0.782368i	$0.714012\pi$
$6$	−1.33628	−0.545533
$7$	2.26746	0.857019	0.428510	−	0.903537i	$-0.359039\pi$
$7$	2.26746	0.857019	0.428510	+	0.903537i	$0.359039\pi$
$8$	−2.95900	−1.04617
$9$	1.00000	0.333333
$10$	−3.72196	−1.17699
$11$	2.19659	0.662295	0.331148	−	0.943579i	$-0.392564\pi$
$11$	2.19659	0.662295	0.331148	+	0.943579i	$0.392564\pi$
$12$	0.214366	0.0618820
$13$	4.11961	1.14257	0.571287	−	0.820750i	$-0.306444\pi$
$13$	4.11961	1.14257	0.571287	+	0.820750i	$0.306444\pi$
$14$	3.02995	0.809789
$15$	2.78532	0.719167
$16$	−3.52532	−0.881329
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.33628	0.314963
$19$	−5.10063	−1.17016	−0.585082	−	0.810974i	$-0.698938\pi$
$19$	−5.10063	−1.17016	−0.585082	+	0.810974i	$0.698938\pi$
$20$	0.597077	0.133510
$21$	−2.26746	−0.494800
$22$	2.93524	0.625796
$23$	−4.60991	−0.961233	−0.480616	−	0.876931i	$-0.659587\pi$
$23$	−4.60991	−0.961233	−0.480616	+	0.876931i	$0.659587\pi$
$24$	2.95900	0.604004
$25$	2.75801	0.551602
$26$	5.50494	1.07961
$27$	−1.00000	−0.192450
$28$	−0.486066	−0.0918578
$29$	1.32604	0.246240	0.123120	−	0.992392i	$-0.460710\pi$
$29$	1.32604	0.246240	0.123120	+	0.992392i	$0.460710\pi$
$30$	3.72196	0.679533
$31$	6.45635	1.15960	0.579798	−	0.814761i	$-0.303132\pi$
$31$	6.45635	1.15960	0.579798	+	0.814761i	$0.303132\pi$
$32$	1.20721	0.213407
$33$	−2.19659	−0.382376
$34$	−1.33628	−0.229169
$35$	−6.31560	−1.06753
$36$	−0.214366	−0.0357276
$37$	−6.29915	−1.03557	−0.517787	−	0.855510i	$-0.673244\pi$
$37$	−6.29915	−1.03557	−0.517787	+	0.855510i	$0.673244\pi$
$38$	−6.81585	−1.10568
$39$	−4.11961	−0.659666
$40$	8.24177	1.30314
$41$	−2.12317	−0.331583	−0.165792	−	0.986161i	$-0.553018\pi$
$41$	−2.12317	−0.331583	−0.165792	+	0.986161i	$0.553018\pi$
$42$	−3.02995	−0.467532
$43$	−1.24892	−0.190458	−0.0952290	−	0.995455i	$-0.530358\pi$
$43$	−1.24892	−0.190458	−0.0952290	+	0.995455i	$0.530358\pi$
$44$	−0.470872	−0.0709867
$45$	−2.78532	−0.415211
$46$	−6.16011	−0.908259
$47$	−8.03686	−1.17230	−0.586148	−	0.810204i	$-0.699356\pi$
$47$	−8.03686	−1.17230	−0.586148	+	0.810204i	$0.699356\pi$
$48$	3.52532	0.508836
$49$	−1.85862	−0.265518
$50$	3.68546	0.521203
$51$	1.00000	0.140028
$52$	−0.883103	−0.122464
$53$	9.17343	1.26007	0.630034	−	0.776568i	$-0.283041\pi$
$53$	9.17343	1.26007	0.630034	+	0.776568i	$0.283041\pi$
$54$	−1.33628	−0.181844
$55$	−6.11819	−0.824977
$56$	−6.70942	−0.896585
$57$	5.10063	0.675595
$58$	1.77196	0.232670
$59$	2.78480	0.362551	0.181275	−	0.983432i	$-0.441977\pi$
$59$	2.78480	0.362551	0.181275	+	0.983432i	$0.441977\pi$
$60$	−0.597077	−0.0770823
$61$	−1.20609	−0.154424	−0.0772118	−	0.997015i	$-0.524602\pi$
$61$	−1.20609	−0.154424	−0.0772118	+	0.997015i	$0.524602\pi$
$62$	8.62747	1.09569
$63$	2.26746	0.285673
$64$	8.66380	1.08298
$65$	−11.4744	−1.42323
$66$	−2.93524	−0.361304
$67$	11.1148	1.35789	0.678945	−	0.734189i	$-0.262437\pi$
$67$	11.1148	1.35789	0.678945	+	0.734189i	$0.262437\pi$
$68$	0.214366	0.0259957
$69$	4.60991	0.554968
$70$	−8.43939	−1.00870
$71$	6.75174	0.801284	0.400642	−	0.916235i	$-0.368787\pi$
$71$	6.75174	0.801284	0.400642	+	0.916235i	$0.368787\pi$
$72$	−2.95900	−0.348722
$73$	9.54089	1.11668	0.558338	−	0.829613i	$-0.311439\pi$
$73$	9.54089	1.11668	0.558338	+	0.829613i	$0.311439\pi$
$74$	−8.41740	−0.978503
$75$	−2.75801	−0.318467
$76$	1.09340	0.125422
$77$	4.98067	0.567600
$78$	−5.50494	−0.623312
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	9.81913	1.09781
$81$	1.00000	0.111111
$82$	−2.83714	−0.313310
$83$	17.9909	1.97476	0.987381	−	0.158364i	$-0.0506218\pi$
$83$	17.9909	1.97476	0.987381	+	0.158364i	$0.0506218\pi$
$84$	0.486066	0.0530341
$85$	2.78532	0.302110
$86$	−1.66890	−0.179962
$87$	−1.32604	−0.142167
$88$	−6.49971	−0.692871
$89$	5.07382	0.537824	0.268912	−	0.963165i	$-0.413336\pi$
$89$	5.07382	0.537824	0.268912	+	0.963165i	$0.413336\pi$
$90$	−3.72196	−0.392329
$91$	9.34106	0.979209
$92$	0.988206	0.103028
$93$	−6.45635	−0.669492
$94$	−10.7395	−1.10769
$95$	14.2069	1.45760
$96$	−1.20721	−0.123211
$97$	17.3000	1.75655	0.878276	−	0.478153i	$-0.158694\pi$
$97$	17.3000	1.75655	0.878276	+	0.478153i	$0.158694\pi$
$98$	−2.48364	−0.250885
$99$	2.19659	0.220765
$100$	−0.591222	−0.0591222
$101$	1.86268	0.185343	0.0926717	−	0.995697i	$-0.470459\pi$
$101$	1.86268	0.185343	0.0926717	+	0.995697i	$0.470459\pi$
$102$	1.33628	0.132311
$103$	15.4293	1.52030	0.760149	−	0.649748i	$-0.225126\pi$
$103$	15.4293	1.52030	0.760149	+	0.649748i	$0.225126\pi$
$104$	−12.1900	−1.19532
$105$	6.31560	0.616340
$106$	12.2582	1.19063
$107$	−2.07469	−0.200568	−0.100284	−	0.994959i	$-0.531975\pi$
$107$	−2.07469	−0.200568	−0.100284	+	0.994959i	$0.531975\pi$
$108$	0.214366	0.0206273
$109$	13.6369	1.30618	0.653089	−	0.757282i	$-0.273473\pi$
$109$	13.6369	1.30618	0.653089	+	0.757282i	$0.273473\pi$
$110$	−8.17560	−0.779512
$111$	6.29915	0.597888
$112$	−7.99351	−0.755316
$113$	−8.27909	−0.778831	−0.389416	−	0.921062i	$-0.627323\pi$
$113$	−8.27909	−0.778831	−0.389416	+	0.921062i	$0.627323\pi$
$114$	6.81585	0.638363
$115$	12.8401	1.19734
$116$	−0.284258	−0.0263927
$117$	4.11961	0.380858
$118$	3.72127	0.342570
$119$	−2.26746	−0.207858
$120$	−8.24177	−0.752368
$121$	−6.17501	−0.561365
$122$	−1.61167	−0.145913
$123$	2.12317	0.191440
$124$	−1.38402	−0.124289
$125$	6.24467	0.558540
$126$	3.02995	0.269930
$127$	−1.40432	−0.124613	−0.0623065	−	0.998057i	$-0.519846\pi$
$127$	−1.40432	−0.124613	−0.0623065	+	0.998057i	$0.519846\pi$
$128$	9.16281	0.809885
$129$	1.24892	0.109961
$130$	−15.3330	−1.34479
$131$	−9.02966	−0.788925	−0.394462	−	0.918912i	$-0.629069\pi$
$131$	−9.02966	−0.788925	−0.394462	+	0.918912i	$0.629069\pi$
$132$	0.470872	0.0409842
$133$	−11.5655	−1.00285
$134$	14.8525	1.28306
$135$	2.78532	0.239722
$136$	2.95900	0.253733
$137$	−10.1862	−0.870267	−0.435133	−	0.900366i	$-0.643299\pi$
$137$	−10.1862	−0.870267	−0.435133	+	0.900366i	$0.643299\pi$
$138$	6.16011	0.524384
$139$	−3.50767	−0.297516	−0.148758	−	0.988874i	$-0.547528\pi$
$139$	−3.50767	−0.297516	−0.148758	+	0.988874i	$0.547528\pi$
$140$	1.35385	0.114421
$141$	8.03686	0.676825
$142$	9.02219	0.757125
$143$	9.04908	0.756722
$144$	−3.52532	−0.293776
$145$	−3.69346	−0.306725
$146$	12.7493	1.05514
$147$	1.85862	0.153297
$148$	1.35032	0.110996
$149$	−6.04123	−0.494917	−0.247459	−	0.968898i	$-0.579595\pi$
$149$	−6.04123	−0.494917	−0.247459	+	0.968898i	$0.579595\pi$
$150$	−3.68546	−0.300917
$151$	18.1798	1.47945	0.739725	−	0.672909i	$-0.234956\pi$
$151$	18.1798	1.47945	0.739725	+	0.672909i	$0.234956\pi$
$152$	15.0928	1.22419
$153$	−1.00000	−0.0808452
$154$	6.65555	0.536320
$155$	−17.9830	−1.44443
$156$	0.883103	0.0707049
$157$	−5.76086	−0.459766	−0.229883	−	0.973218i	$-0.573834\pi$
$157$	−5.76086	−0.459766	−0.229883	+	0.973218i	$0.573834\pi$
$158$	1.33628	0.106308
$159$	−9.17343	−0.727501
$160$	−3.36247	−0.265827
$161$	−10.4528	−0.823795
$162$	1.33628	0.104988
$163$	10.2179	0.800324	0.400162	−	0.916444i	$-0.368954\pi$
$163$	10.2179	0.800324	0.400162	+	0.916444i	$0.368954\pi$
$164$	0.455135	0.0355400
$165$	6.11819	0.476301
$166$	24.0409	1.86593
$167$	−15.8040	−1.22295	−0.611474	−	0.791265i	$-0.709423\pi$
$167$	−15.8040	−1.22295	−0.611474	+	0.791265i	$0.709423\pi$
$168$	6.70942	0.517643
$169$	3.97121	0.305477
$170$	3.72196	0.285461
$171$	−5.10063	−0.390055
$172$	0.267725	0.0204138
$173$	−21.6086	−1.64287	−0.821436	−	0.570300i	$-0.806827\pi$
$173$	−21.6086	−1.64287	−0.821436	+	0.570300i	$0.806827\pi$
$174$	−1.77196	−0.134332
$175$	6.25367	0.472733
$176$	−7.74366	−0.583700
$177$	−2.78480	−0.209319
$178$	6.78003	0.508185
$179$	11.2015	0.837239	0.418619	−	0.908162i	$-0.362514\pi$
$179$	11.2015	0.837239	0.418619	+	0.908162i	$0.362514\pi$
$180$	0.597077	0.0445035
$181$	15.4594	1.14909	0.574544	−	0.818473i	$-0.305179\pi$
$181$	15.4594	1.14909	0.574544	+	0.818473i	$0.305179\pi$
$182$	12.4822	0.925245
$183$	1.20609	0.0891565
$184$	13.6407	1.00561
$185$	17.5451	1.28994
$186$	−8.62747	−0.632597
$187$	−2.19659	−0.160630
$188$	1.72283	0.125650
$189$	−2.26746	−0.164933
$190$	18.9843	1.37727
$191$	−6.48816	−0.469467	−0.234733	−	0.972060i	$-0.575422\pi$
$191$	−6.48816	−0.469467	−0.234733	+	0.972060i	$0.575422\pi$
$192$	−8.66380	−0.625256
$193$	22.3328	1.60755	0.803775	−	0.594933i	$-0.202821\pi$
$193$	22.3328	1.60755	0.803775	+	0.594933i	$0.202821\pi$
$194$	23.1176	1.65975
$195$	11.4744	0.821702
$196$	0.398425	0.0284589
$197$	21.0790	1.50182	0.750909	−	0.660406i	$-0.229616\pi$
$197$	21.0790	1.50182	0.750909	+	0.660406i	$0.229616\pi$
$198$	2.93524	0.208599
$199$	−5.07083	−0.359461	−0.179731	−	0.983716i	$-0.557523\pi$
$199$	−5.07083	−0.359461	−0.179731	+	0.983716i	$0.557523\pi$
$200$	−8.16096	−0.577067
$201$	−11.1148	−0.783978
$202$	2.48905	0.175129
$203$	3.00675	0.211033
$204$	−0.214366	−0.0150086
$205$	5.91371	0.413031
$206$	20.6179	1.43652
$207$	−4.60991	−0.320411
$208$	−14.5229	−1.00698
$209$	−11.2040	−0.774994
$210$	8.43939	0.582373
$211$	9.52557	0.655768	0.327884	−	0.944718i	$-0.393665\pi$
$211$	9.52557	0.655768	0.327884	+	0.944718i	$0.393665\pi$
$212$	−1.96647	−0.135058
$213$	−6.75174	−0.462621
$214$	−2.77236	−0.189515
$215$	3.47863	0.237241
$216$	2.95900	0.201335
$217$	14.6395	0.993795
$218$	18.2227	1.23419
$219$	−9.54089	−0.644714
$220$	1.31153	0.0884234
$221$	−4.11961	−0.277115
$222$	8.41740	0.564939
$223$	3.56635	0.238821	0.119410	−	0.992845i	$-0.461900\pi$
$223$	3.56635	0.238821	0.119410	+	0.992845i	$0.461900\pi$
$224$	2.73731	0.182894
$225$	2.75801	0.183867
$226$	−11.0632	−0.735910
$227$	−11.4374	−0.759128	−0.379564	−	0.925165i	$-0.623926\pi$
$227$	−11.4374	−0.759128	−0.379564	+	0.925165i	$0.623926\pi$
$228$	−1.09340	−0.0724122
$229$	13.7612	0.909366	0.454683	−	0.890653i	$-0.349753\pi$
$229$	13.7612	0.909366	0.454683	+	0.890653i	$0.349753\pi$
$230$	17.1579	1.13136
$231$	−4.98067	−0.327704
$232$	−3.92377	−0.257608
$233$	3.90460	0.255799	0.127899	−	0.991787i	$-0.459177\pi$
$233$	3.90460	0.255799	0.127899	+	0.991787i	$0.459177\pi$
$234$	5.50494	0.359869
$235$	22.3852	1.46025
$236$	−0.596966	−0.0388592
$237$	−1.00000	−0.0649570
$238$	−3.02995	−0.196403
$239$	1.66241	0.107532	0.0537660	−	0.998554i	$-0.482877\pi$
$239$	1.66241	0.107532	0.0537660	+	0.998554i	$0.482877\pi$
$240$	−9.81913	−0.633822
$241$	16.5249	1.06446	0.532231	−	0.846599i	$-0.321354\pi$
$241$	16.5249	1.06446	0.532231	+	0.846599i	$0.321354\pi$
$242$	−8.25152	−0.530428
$243$	−1.00000	−0.0641500
$244$	0.258544	0.0165516
$245$	5.17686	0.330738
$246$	2.83714	0.180889
$247$	−21.0126	−1.33700
$248$	−19.1044	−1.21313
$249$	−17.9909	−1.14013
$250$	8.34460	0.527759
$251$	0.932074	0.0588320	0.0294160	−	0.999567i	$-0.490635\pi$
$251$	0.932074	0.0588320	0.0294160	+	0.999567i	$0.490635\pi$
$252$	−0.486066	−0.0306193
$253$	−10.1261	−0.636620
$254$	−1.87655	−0.117746
$255$	−2.78532	−0.174424
$256$	−5.08356	−0.317723
$257$	3.95359	0.246618	0.123309	−	0.992368i	$-0.460649\pi$
$257$	3.95359	0.246618	0.123309	+	0.992368i	$0.460649\pi$
$258$	1.66890	0.103901
$259$	−14.2831	−0.887506
$260$	2.45973	0.152546
$261$	1.32604	0.0820801
$262$	−12.0661	−0.745447
$263$	22.0404	1.35907	0.679533	−	0.733645i	$-0.262182\pi$
$263$	22.0404	1.35907	0.679533	+	0.733645i	$0.262182\pi$
$264$	6.49971	0.400029
$265$	−25.5509	−1.56958
$266$	−15.4547	−0.947586
$267$	−5.07382	−0.310513
$268$	−2.38263	−0.145543
$269$	10.0209	0.610983	0.305492	−	0.952195i	$-0.401179\pi$
$269$	10.0209	0.610983	0.305492	+	0.952195i	$0.401179\pi$
$270$	3.72196	0.226511
$271$	16.0716	0.976281	0.488140	−	0.872765i	$-0.337675\pi$
$271$	16.0716	0.976281	0.488140	+	0.872765i	$0.337675\pi$
$272$	3.52532	0.213754
$273$	−9.34106	−0.565347
$274$	−13.6116	−0.822306
$275$	6.05820	0.365323
$276$	−0.988206	−0.0594830
$277$	−19.1725	−1.15197	−0.575983	−	0.817462i	$-0.695380\pi$
$277$	−19.1725	−1.15197	−0.575983	+	0.817462i	$0.695380\pi$
$278$	−4.68721	−0.281120
$279$	6.45635	0.386532
$280$	18.6879	1.11682
$281$	−13.8331	−0.825212	−0.412606	−	0.910910i	$-0.635381\pi$
$281$	−13.8331	−0.825212	−0.412606	+	0.910910i	$0.635381\pi$
$282$	10.7395	0.639526
$283$	−28.5087	−1.69467	−0.847334	−	0.531060i	$-0.821794\pi$
$283$	−28.5087	−1.69467	−0.847334	+	0.531060i	$0.821794\pi$
$284$	−1.44734	−0.0858839
$285$	−14.2069	−0.841543
$286$	12.0921	0.715019
$287$	−4.81420	−0.284173
$288$	1.20721	0.0711357
$289$	1.00000	0.0588235
$290$	−4.93548	−0.289821
$291$	−17.3000	−1.01415
$292$	−2.04524	−0.119689
$293$	19.3802	1.13221	0.566103	−	0.824335i	$-0.308450\pi$
$293$	19.3802	1.13221	0.566103	+	0.824335i	$0.308450\pi$
$294$	2.48364	0.144849
$295$	−7.75657	−0.451605
$296$	18.6392	1.08338
$297$	−2.19659	−0.127459
$298$	−8.07276	−0.467642
$299$	−18.9910	−1.09828
$300$	0.591222	0.0341342
$301$	−2.83187	−0.163226
$302$	24.2932	1.39792
$303$	−1.86268	−0.107008
$304$	17.9813	1.03130
$305$	3.35934	0.192355
$306$	−1.33628	−0.0763898
$307$	6.99711	0.399346	0.199673	−	0.979863i	$-0.436012\pi$
$307$	6.99711	0.399346	0.199673	+	0.979863i	$0.436012\pi$
$308$	−1.06768	−0.0608370
$309$	−15.4293	−0.877745
$310$	−24.0303	−1.36483
$311$	−2.04512	−0.115968	−0.0579839	−	0.998318i	$-0.518467\pi$
$311$	−2.04512	−0.115968	−0.0579839	+	0.998318i	$0.518467\pi$
$312$	12.1900	0.690120
$313$	7.53797	0.426071	0.213036	−	0.977044i	$-0.431665\pi$
$313$	7.53797	0.426071	0.213036	+	0.977044i	$0.431665\pi$
$314$	−7.69809	−0.434429
$315$	−6.31560	−0.355844
$316$	−0.214366	−0.0120590
$317$	−33.3973	−1.87578	−0.937891	−	0.346930i	$-0.887224\pi$
$317$	−33.3973	−1.87578	−0.937891	+	0.346930i	$0.887224\pi$
$318$	−12.2582	−0.687408
$319$	2.91277	0.163084
$320$	−24.1315	−1.34899
$321$	2.07469	0.115798
$322$	−13.9678	−0.778396
$323$	5.10063	0.283807
$324$	−0.214366	−0.0119092
$325$	11.3619	0.630246
$326$	13.6539	0.756218
$327$	−13.6369	−0.754122
$328$	6.28247	0.346891
$329$	−18.2233	−1.00468
$330$	8.17560	0.450052
$331$	−10.1137	−0.555901	−0.277951	−	0.960595i	$-0.589655\pi$
$331$	−10.1137	−0.555901	−0.277951	+	0.960595i	$0.589655\pi$
$332$	−3.85664	−0.211661
$333$	−6.29915	−0.345191
$334$	−21.1185	−1.15555
$335$	−30.9583	−1.69143
$336$	7.99351	0.436082
$337$	15.7827	0.859736	0.429868	−	0.902892i	$-0.358560\pi$
$337$	15.7827	0.859736	0.429868	+	0.902892i	$0.358560\pi$
$338$	5.30663	0.288643
$339$	8.27909	0.449658
$340$	−0.597077	−0.0323810
$341$	14.1819	0.767994
$342$	−6.81585	−0.368559
$343$	−20.0866	−1.08457
$344$	3.69555	0.199251
$345$	−12.8401	−0.691286
$346$	−28.8751	−1.55233
$347$	−26.4449	−1.41964	−0.709819	−	0.704384i	$-0.751223\pi$
$347$	−26.4449	−1.41964	−0.709819	+	0.704384i	$0.751223\pi$
$348$	0.284258	0.0152378
$349$	24.0418	1.28693	0.643464	−	0.765477i	$-0.277497\pi$
$349$	24.0418	1.28693	0.643464	+	0.765477i	$0.277497\pi$
$350$	8.35663	0.446681
$351$	−4.11961	−0.219889
$352$	2.65174	0.141338
$353$	18.9687	1.00960	0.504800	−	0.863236i	$-0.331566\pi$
$353$	18.9687	1.00960	0.504800	+	0.863236i	$0.331566\pi$
$354$	−3.72127	−0.197783
$355$	−18.8057	−0.998105
$356$	−1.08765	−0.0576455
$357$	2.26746	0.120007
$358$	14.9683	0.791099
$359$	−19.0498	−1.00541	−0.502705	−	0.864458i	$-0.667662\pi$
$359$	−19.0498	−1.00541	−0.502705	+	0.864458i	$0.667662\pi$
$360$	8.24177	0.434380
$361$	7.01641	0.369285
$362$	20.6580	1.08576
$363$	6.17501	0.324104
$364$	−2.00240	−0.104954
$365$	−26.5744	−1.39097
$366$	1.61167	0.0842431
$367$	−3.21799	−0.167978	−0.0839889	−	0.996467i	$-0.526766\pi$
$367$	−3.21799	−0.167978	−0.0839889	+	0.996467i	$0.526766\pi$
$368$	16.2514	0.847162
$369$	−2.12317	−0.110528
$370$	23.4451	1.21886
$371$	20.8004	1.07990
$372$	1.38402	0.0717581
$373$	−35.7616	−1.85166	−0.925832	−	0.377934i	$-0.876635\pi$
$373$	−35.7616	−1.85166	−0.925832	+	0.377934i	$0.876635\pi$
$374$	−2.93524	−0.151778
$375$	−6.24467	−0.322473
$376$	23.7811	1.22642
$377$	5.46279	0.281348
$378$	−3.02995	−0.155844
$379$	−9.65711	−0.496053	−0.248026	−	0.968753i	$-0.579782\pi$
$379$	−9.65711	−0.496053	−0.248026	+	0.968753i	$0.579782\pi$
$380$	−3.04547	−0.156229
$381$	1.40432	0.0719453
$382$	−8.66998	−0.443595
$383$	8.08973	0.413366	0.206683	−	0.978408i	$-0.433733\pi$
$383$	8.08973	0.413366	0.206683	+	0.978408i	$0.433733\pi$
$384$	−9.16281	−0.467588
$385$	−13.8728	−0.707021
$386$	29.8428	1.51896
$387$	−1.24892	−0.0634860
$388$	−3.70853	−0.188272
$389$	21.7710	1.10383	0.551916	−	0.833900i	$-0.313897\pi$
$389$	21.7710	1.10383	0.551916	+	0.833900i	$0.313897\pi$
$390$	15.3330	0.776418
$391$	4.60991	0.233133
$392$	5.49968	0.277776
$393$	9.02966	0.455486
$394$	28.1674	1.41905
$395$	−2.78532	−0.140145
$396$	−0.470872	−0.0236622
$397$	16.7730	0.841814	0.420907	−	0.907104i	$-0.361712\pi$
$397$	16.7730	0.841814	0.420907	+	0.907104i	$0.361712\pi$
$398$	−6.77603	−0.339652
$399$	11.5655	0.578998
$400$	−9.72285	−0.486142
$401$	6.73862	0.336511	0.168255	−	0.985743i	$-0.446187\pi$
$401$	6.73862	0.336511	0.168255	+	0.985743i	$0.446187\pi$
$402$	−14.8525	−0.740773
$403$	26.5977	1.32492
$404$	−0.399294	−0.0198656
$405$	−2.78532	−0.138404
$406$	4.01785	0.199403
$407$	−13.8366	−0.685855
$408$	−2.95900	−0.146493
$409$	26.3447	1.30266	0.651331	−	0.758794i	$-0.274211\pi$
$409$	26.3447	1.30266	0.651331	+	0.758794i	$0.274211\pi$
$410$	7.90234	0.390269
$411$	10.1862	0.502449
$412$	−3.30752	−0.162950
$413$	6.31443	0.310713
$414$	−6.16011	−0.302753
$415$	−50.1105	−2.45983
$416$	4.97325	0.243834
$417$	3.50767	0.171771
$418$	−14.9716	−0.732285
$419$	−17.6718	−0.863324	−0.431662	−	0.902035i	$-0.642073\pi$
$419$	−17.6718	−0.863324	−0.431662	+	0.902035i	$0.642073\pi$
$420$	−1.35385	−0.0660610
$421$	−9.63483	−0.469573	−0.234786	−	0.972047i	$-0.575439\pi$
$421$	−9.63483	−0.469573	−0.234786	+	0.972047i	$0.575439\pi$
$422$	12.7288	0.619628
$423$	−8.03686	−0.390765
$424$	−27.1442	−1.31824
$425$	−2.75801	−0.133783
$426$	−9.02219	−0.437126
$427$	−2.73475	−0.132344
$428$	0.444742	0.0214974
$429$	−9.04908	−0.436894
$430$	4.64841	0.224166
$431$	22.4104	1.07947	0.539735	−	0.841835i	$-0.318524\pi$
$431$	22.4104	1.07947	0.539735	+	0.841835i	$0.318524\pi$
$432$	3.52532	0.169612
$433$	−17.3979	−0.836088	−0.418044	−	0.908427i	$-0.637284\pi$
$433$	−17.3979	−0.836088	−0.418044	+	0.908427i	$0.637284\pi$
$434$	19.5624	0.939027
$435$	3.69346	0.177088
$436$	−2.92328	−0.140000
$437$	23.5134	1.12480
$438$	−12.7493	−0.609184
$439$	−5.34693	−0.255195	−0.127598	−	0.991826i	$-0.540727\pi$
$439$	−5.34693	−0.255195	−0.127598	+	0.991826i	$0.540727\pi$
$440$	18.1038	0.863063
$441$	−1.85862	−0.0885059
$442$	−5.50494	−0.261843
$443$	31.9488	1.51793	0.758966	−	0.651130i	$-0.225705\pi$
$443$	31.9488	1.51793	0.758966	+	0.651130i	$0.225705\pi$
$444$	−1.35032	−0.0640834
$445$	−14.1322	−0.669932
$446$	4.76563	0.225659
$447$	6.04123	0.285741
$448$	19.6448	0.928131
$449$	−37.9986	−1.79326	−0.896632	−	0.442776i	$-0.853994\pi$
$449$	−37.9986	−1.79326	−0.896632	+	0.442776i	$0.853994\pi$
$450$	3.68546	0.173734
$451$	−4.66372	−0.219606
$452$	1.77475	0.0834773
$453$	−18.1798	−0.854161
$454$	−15.2836	−0.717293
$455$	−26.0178	−1.21973
$456$	−15.0928	−0.706784
$457$	3.79790	0.177658	0.0888292	−	0.996047i	$-0.471687\pi$
$457$	3.79790	0.177658	0.0888292	+	0.996047i	$0.471687\pi$
$458$	18.3888	0.859251
$459$	1.00000	0.0466760
$460$	−2.75247	−0.128335
$461$	35.3448	1.64617	0.823085	−	0.567919i	$-0.192251\pi$
$461$	35.3448	1.64617	0.823085	+	0.567919i	$0.192251\pi$
$462$	−6.65555	−0.309644
$463$	−23.5845	−1.09606	−0.548032	−	0.836457i	$-0.684623\pi$
$463$	−23.5845	−1.09606	−0.548032	+	0.836457i	$0.684623\pi$
$464$	−4.67473	−0.217019
$465$	17.9830	0.833942
$466$	5.21762	0.241702
$467$	15.1585	0.701450	0.350725	−	0.936478i	$-0.385935\pi$
$467$	15.1585	0.701450	0.350725	+	0.936478i	$0.385935\pi$
$468$	−0.883103	−0.0408215
$469$	25.2024	1.16374
$470$	29.9128	1.37978
$471$	5.76086	0.265446
$472$	−8.24025	−0.379288
$473$	−2.74335	−0.126139
$474$	−1.33628	−0.0613772
$475$	−14.0676	−0.645465
$476$	0.486066	0.0222788
$477$	9.17343	0.420023
$478$	2.22143	0.101606
$479$	13.7272	0.627212	0.313606	−	0.949553i	$-0.398463\pi$
$479$	13.7272	0.627212	0.313606	+	0.949553i	$0.398463\pi$
$480$	3.36247	0.153475
$481$	−25.9500	−1.18322
$482$	22.0818	1.00580
$483$	10.4528	0.475618
$484$	1.32371	0.0601687
$485$	−48.1861	−2.18802
$486$	−1.33628	−0.0606147
$487$	20.5042	0.929136	0.464568	−	0.885537i	$-0.346210\pi$
$487$	20.5042	0.929136	0.464568	+	0.885537i	$0.346210\pi$
$488$	3.56882	0.161553
$489$	−10.2179	−0.462067
$490$	6.91772	0.312511
$491$	15.5218	0.700488	0.350244	−	0.936659i	$-0.386099\pi$
$491$	15.5218	0.700488	0.350244	+	0.936659i	$0.386099\pi$
$492$	−0.455135	−0.0205191
$493$	−1.32604	−0.0597220
$494$	−28.0787	−1.26332
$495$	−6.11819	−0.274992
$496$	−22.7607	−1.02198
$497$	15.3093	0.686716
$498$	−24.0409	−1.07730
$499$	41.3594	1.85150	0.925751	−	0.378133i	$-0.123434\pi$
$499$	41.3594	1.85150	0.925751	+	0.378133i	$0.123434\pi$
$500$	−1.33864	−0.0598659
$501$	15.8040	0.706069
$502$	1.24551	0.0555898
$503$	−10.1495	−0.452543	−0.226271	−	0.974064i	$-0.572654\pi$
$503$	−10.1495	−0.452543	−0.226271	+	0.974064i	$0.572654\pi$
$504$	−6.70942	−0.298862
$505$	−5.18815	−0.230870
$506$	−13.5312	−0.601536
$507$	−3.97121	−0.176368
$508$	0.301037	0.0133564
$509$	15.1781	0.672756	0.336378	−	0.941727i	$-0.390798\pi$
$509$	15.1781	0.672756	0.336378	+	0.941727i	$0.390798\pi$
$510$	−3.72196	−0.164811
$511$	21.6336	0.957014
$512$	−25.1187	−1.11010
$513$	5.10063	0.225198
$514$	5.28309	0.233027
$515$	−42.9757	−1.89373
$516$	−0.267725	−0.0117859
$517$	−17.6536	−0.776406
$518$	−19.0861	−0.838596
$519$	21.6086	0.948513
$520$	33.9529	1.48893
$521$	−37.5222	−1.64388	−0.821938	−	0.569577i	$-0.807107\pi$
$521$	−37.5222	−1.64388	−0.821938	+	0.569577i	$0.807107\pi$
$522$	1.77196	0.0775567
$523$	21.1749	0.925915	0.462957	−	0.886381i	$-0.346788\pi$
$523$	21.1749	0.925915	0.462957	+	0.886381i	$0.346788\pi$
$524$	1.93565	0.0845592
$525$	−6.25367	−0.272933
$526$	29.4520	1.28417
$527$	−6.45635	−0.281243
$528$	7.74366	0.336999
$529$	−1.74873	−0.0760318
$530$	−34.1431	−1.48308
$531$	2.78480	0.120850
$532$	2.47924	0.107489
$533$	−8.74663	−0.378859
$534$	−6.78003	−0.293401
$535$	5.77868	0.249834
$536$	−32.8888	−1.42058
$537$	−11.2015	−0.483380
$538$	13.3907	0.577312
$539$	−4.08263	−0.175851
$540$	−0.597077	−0.0256941
$541$	13.5491	0.582521	0.291261	−	0.956644i	$-0.405925\pi$
$541$	13.5491	0.582521	0.291261	+	0.956644i	$0.405925\pi$
$542$	21.4761	0.922478
$543$	−15.4594	−0.663427
$544$	−1.20721	−0.0517588
$545$	−37.9831	−1.62702
$546$	−12.4822	−0.534190
$547$	−24.0274	−1.02734	−0.513669	−	0.857988i	$-0.671714\pi$
$547$	−24.0274	−1.02734	−0.513669	+	0.857988i	$0.671714\pi$
$548$	2.18357	0.0932777
$549$	−1.20609	−0.0514746
$550$	8.09543	0.345190
$551$	−6.76366	−0.288142
$552$	−13.6407	−0.580589
$553$	2.26746	0.0964222
$554$	−25.6198	−1.08848
$555$	−17.5451	−0.744750
$556$	0.751923	0.0318886
$557$	−18.5087	−0.784240	−0.392120	−	0.919914i	$-0.628258\pi$
$557$	−18.5087	−0.784240	−0.392120	+	0.919914i	$0.628258\pi$
$558$	8.62747	0.365230
$559$	−5.14505	−0.217612
$560$	22.2645	0.940847
$561$	2.19659	0.0927399
$562$	−18.4848	−0.779734
$563$	34.2912	1.44520	0.722600	−	0.691266i	$-0.242947\pi$
$563$	34.2912	1.44520	0.722600	+	0.691266i	$0.242947\pi$
$564$	−1.72283	−0.0725441
$565$	23.0599	0.970138
$566$	−38.0955	−1.60128
$567$	2.26746	0.0952244
$568$	−19.9784	−0.838276
$569$	−21.8272	−0.915042	−0.457521	−	0.889199i	$-0.651263\pi$
$569$	−21.8272	−0.915042	−0.457521	+	0.889199i	$0.651263\pi$
$570$	−18.9843	−0.795166
$571$	−25.9546	−1.08617	−0.543083	−	0.839679i	$-0.682743\pi$
$571$	−25.9546	−1.08617	−0.543083	+	0.839679i	$0.682743\pi$
$572$	−1.93981	−0.0811076
$573$	6.48816	0.271047
$574$	−6.43310	−0.268513
$575$	−12.7142	−0.530217
$576$	8.66380	0.360992
$577$	12.6580	0.526958	0.263479	−	0.964665i	$-0.415130\pi$
$577$	12.6580	0.526958	0.263479	+	0.964665i	$0.415130\pi$
$578$	1.33628	0.0555818
$579$	−22.3328	−0.928120
$580$	0.791751	0.0328757
$581$	40.7937	1.69241
$582$	−23.1176	−0.958257
$583$	20.1502	0.834537
$584$	−28.2315	−1.16823
$585$	−11.4744	−0.474410
$586$	25.8974	1.06981
$587$	37.6048	1.55212	0.776059	−	0.630660i	$-0.217216\pi$
$587$	37.6048	1.55212	0.776059	+	0.630660i	$0.217216\pi$
$588$	−0.398425	−0.0164308
$589$	−32.9315	−1.35692
$590$	−10.3649	−0.426717
$591$	−21.0790	−0.867075
$592$	22.2065	0.912681
$593$	30.9710	1.27183	0.635914	−	0.771760i	$-0.280623\pi$
$593$	30.9710	1.27183	0.635914	+	0.771760i	$0.280623\pi$
$594$	−2.93524	−0.120435
$595$	6.31560	0.258914
$596$	1.29503	0.0530466
$597$	5.07083	0.207535
$598$	−25.3773	−1.03775
$599$	−24.6212	−1.00599	−0.502997	−	0.864288i	$-0.667769\pi$
$599$	−24.6212	−1.00599	−0.502997	+	0.864288i	$0.667769\pi$
$600$	8.16096	0.333170
$601$	9.17408	0.374219	0.187109	−	0.982339i	$-0.440088\pi$
$601$	9.17408	0.374219	0.187109	+	0.982339i	$0.440088\pi$
$602$	−3.78416	−0.154231
$603$	11.1148	0.452630
$604$	−3.89712	−0.158572
$605$	17.1994	0.699255
$606$	−2.48905	−0.101111
$607$	−44.2526	−1.79616	−0.898079	−	0.439833i	$-0.855037\pi$
$607$	−44.2526	−1.79616	−0.898079	+	0.439833i	$0.855037\pi$
$608$	−6.15754	−0.249721
$609$	−3.00675	−0.121840
$610$	4.48901	0.181755
$611$	−33.1087	−1.33944
$612$	0.214366	0.00866522
$613$	15.4683	0.624758	0.312379	−	0.949957i	$-0.398874\pi$
$613$	15.4683	0.624758	0.312379	+	0.949957i	$0.398874\pi$
$614$	9.35007	0.377338
$615$	−5.91371	−0.238464
$616$	−14.7378	−0.593804
$617$	−19.2166	−0.773632	−0.386816	−	0.922157i	$-0.626425\pi$
$617$	−19.2166	−0.773632	−0.386816	+	0.922157i	$0.626425\pi$
$618$	−20.6179	−0.829372
$619$	−36.8739	−1.48209	−0.741043	−	0.671458i	$-0.765668\pi$
$619$	−36.8739	−1.48209	−0.741043	+	0.671458i	$0.765668\pi$
$620$	3.85494	0.154818
$621$	4.60991	0.184989
$622$	−2.73284	−0.109577
$623$	11.5047	0.460926
$624$	14.5229	0.581383
$625$	−31.1834	−1.24734
$626$	10.0728	0.402591
$627$	11.2040	0.447443
$628$	1.23493	0.0492791
$629$	6.29915	0.251163
$630$	−8.43939	−0.336233
$631$	48.1522	1.91691	0.958454	−	0.285247i	$-0.0920755\pi$
$631$	48.1522	1.91691	0.958454	+	0.285247i	$0.0920755\pi$
$632$	−2.95900	−0.117703
$633$	−9.52557	−0.378608
$634$	−44.6281	−1.77241
$635$	3.91147	0.155222
$636$	1.96647	0.0779756
$637$	−7.65681	−0.303374
$638$	3.89226	0.154096
$639$	6.75174	0.267095
$640$	−25.5214	−1.00882
$641$	−39.3186	−1.55299	−0.776496	−	0.630122i	$-0.783005\pi$
$641$	−39.3186	−1.55299	−0.776496	+	0.630122i	$0.783005\pi$
$642$	2.77236	0.109416
$643$	0.804326	0.0317195	0.0158598	−	0.999874i	$-0.494951\pi$
$643$	0.804326	0.0317195	0.0158598	+	0.999874i	$0.494951\pi$
$644$	2.24072	0.0882967
$645$	−3.47863	−0.136971
$646$	6.81585	0.268166
$647$	−13.5056	−0.530962	−0.265481	−	0.964116i	$-0.585531\pi$
$647$	−13.5056	−0.530962	−0.265481	+	0.964116i	$0.585531\pi$
$648$	−2.95900	−0.116241
$649$	6.11706	0.240116
$650$	15.1827	0.595513
$651$	−14.6395	−0.573768
$652$	−2.19036	−0.0857810
$653$	33.5863	1.31433	0.657166	−	0.753746i	$-0.271755\pi$
$653$	33.5863	1.31433	0.657166	+	0.753746i	$0.271755\pi$
$654$	−18.2227	−0.712562
$655$	25.1505	0.982711
$656$	7.48484	0.292234
$657$	9.54089	0.372226
$658$	−24.3513	−0.949313
$659$	10.9914	0.428164	0.214082	−	0.976816i	$-0.431324\pi$
$659$	10.9914	0.428164	0.214082	+	0.976816i	$0.431324\pi$
$660$	−1.31153	−0.0510513
$661$	23.2591	0.904676	0.452338	−	0.891847i	$-0.350590\pi$
$661$	23.2591	0.904676	0.452338	+	0.891847i	$0.350590\pi$
$662$	−13.5148	−0.525266
$663$	4.11961	0.159992
$664$	−53.2353	−2.06593
$665$	32.2135	1.24919
$666$	−8.41740	−0.326168
$667$	−6.11295	−0.236694
$668$	3.38783	0.131079
$669$	−3.56635	−0.137883
$670$	−41.3688	−1.59822
$671$	−2.64927	−0.102274
$672$	−2.73731	−0.105594
$673$	−21.6816	−0.835765	−0.417882	−	0.908501i	$-0.637228\pi$
$673$	−21.6816	−0.835765	−0.417882	+	0.908501i	$0.637228\pi$
$674$	21.0900	0.812356
$675$	−2.75801	−0.106156
$676$	−0.851291	−0.0327419
$677$	−41.0522	−1.57777	−0.788883	−	0.614543i	$-0.789340\pi$
$677$	−41.0522	−1.57777	−0.788883	+	0.614543i	$0.789340\pi$
$678$	11.0632	0.424878
$679$	39.2271	1.50540
$680$	−8.24177	−0.316058
$681$	11.4374	0.438283
$682$	18.9510	0.725670
$683$	35.3403	1.35226	0.676129	−	0.736784i	$-0.263656\pi$
$683$	35.3403	1.35226	0.676129	+	0.736784i	$0.263656\pi$
$684$	1.09340	0.0418072
$685$	28.3719	1.08403
$686$	−26.8412	−1.02480
$687$	−13.7612	−0.525023
$688$	4.40282	0.167856
$689$	37.7910	1.43972
$690$	−17.1579	−0.653190
$691$	18.0953	0.688376	0.344188	−	0.938901i	$-0.388154\pi$
$691$	18.0953	0.688376	0.344188	+	0.938901i	$0.388154\pi$
$692$	4.63215	0.176088
$693$	4.98067	0.189200
$694$	−35.3377	−1.34140
$695$	9.76997	0.370596
$696$	3.92377	0.148730
$697$	2.12317	0.0804208
$698$	32.1265	1.21600
$699$	−3.90460	−0.147686
$700$	−1.34057	−0.0506689
$701$	5.24967	0.198277	0.0991386	−	0.995074i	$-0.468391\pi$
$701$	5.24967	0.198277	0.0991386	+	0.995074i	$0.468391\pi$
$702$	−5.50494	−0.207771
$703$	32.1296	1.21179
$704$	19.0308	0.717249
$705$	−22.3852	−0.843076
$706$	25.3474	0.953961
$707$	4.22355	0.158843
$708$	0.596966	0.0224354
$709$	−7.48220	−0.281000	−0.140500	−	0.990081i	$-0.544871\pi$
$709$	−7.48220	−0.281000	−0.140500	+	0.990081i	$0.544871\pi$
$710$	−25.1297	−0.943100
$711$	1.00000	0.0375029
$712$	−15.0135	−0.562654
$713$	−29.7632	−1.11464
$714$	3.02995	0.113393
$715$	−25.2046	−0.942598
$716$	−2.40122	−0.0897376
$717$	−1.66241	−0.0620837
$718$	−25.4558	−0.950002
$719$	22.4727	0.838090	0.419045	−	0.907966i	$-0.362365\pi$
$719$	22.4727	0.838090	0.419045	+	0.907966i	$0.362365\pi$
$720$	9.81913	0.365937
$721$	34.9854	1.30293
$722$	9.37587	0.348934
$723$	−16.5249	−0.614568
$724$	−3.31397	−0.123163
$725$	3.65724	0.135827
$726$	8.25152	0.306243
$727$	−31.0573	−1.15185	−0.575927	−	0.817501i	$-0.695359\pi$
$727$	−31.0573	−1.15185	−0.575927	+	0.817501i	$0.695359\pi$
$728$	−27.6402	−1.02442
$729$	1.00000	0.0370370
$730$	−35.5108	−1.31431
$731$	1.24892	0.0461928
$732$	−0.258544	−0.00955605
$733$	53.1730	1.96399	0.981995	−	0.188907i	$-0.0604945\pi$
$733$	53.1730	1.96399	0.981995	+	0.188907i	$0.0604945\pi$
$734$	−4.30013	−0.158721
$735$	−5.17686	−0.190952
$736$	−5.56514	−0.205134
$737$	24.4146	0.899324
$738$	−2.83714	−0.104437
$739$	−44.8612	−1.65025	−0.825123	−	0.564953i	$-0.808894\pi$
$739$	−44.8612	−1.65025	−0.825123	+	0.564953i	$0.808894\pi$
$740$	−3.76107	−0.138260
$741$	21.0126	0.771918
$742$	27.7951	1.02039
$743$	2.05770	0.0754898	0.0377449	−	0.999287i	$-0.487983\pi$
$743$	2.05770	0.0754898	0.0377449	+	0.999287i	$0.487983\pi$
$744$	19.1044	0.700400
$745$	16.8268	0.616485
$746$	−47.7874	−1.74962
$747$	17.9909	0.658254
$748$	0.470872	0.0172168
$749$	−4.70428	−0.171891
$750$	−8.34460	−0.304702
$751$	−17.2117	−0.628064	−0.314032	−	0.949412i	$-0.601680\pi$
$751$	−17.2117	−0.628064	−0.314032	+	0.949412i	$0.601680\pi$
$752$	28.3325	1.03318
$753$	−0.932074	−0.0339667
$754$	7.29980	0.265843
$755$	−50.6365	−1.84285
$756$	0.486066	0.0176780
$757$	25.9556	0.943373	0.471687	−	0.881766i	$-0.343645\pi$
$757$	25.9556	0.943373	0.471687	+	0.881766i	$0.343645\pi$
$758$	−12.9046	−0.468715
$759$	10.1261	0.367553
$760$	−42.0382	−1.52489
$761$	−45.7700	−1.65916	−0.829581	−	0.558386i	$-0.811421\pi$
$761$	−45.7700	−1.65916	−0.829581	+	0.558386i	$0.811421\pi$
$762$	1.87655	0.0679804
$763$	30.9211	1.11942
$764$	1.39084	0.0503188
$765$	2.78532	0.100703
$766$	10.8101	0.390585
$767$	11.4723	0.414241
$768$	5.08356	0.183437
$769$	22.7727	0.821204	0.410602	−	0.911815i	$-0.365318\pi$
$769$	22.7727	0.821204	0.410602	+	0.911815i	$0.365318\pi$
$770$	−18.5378	−0.668057
$771$	−3.95359	−0.142385
$772$	−4.78739	−0.172302
$773$	1.85446	0.0667002	0.0333501	−	0.999444i	$-0.489382\pi$
$773$	1.85446	0.0667002	0.0333501	+	0.999444i	$0.489382\pi$
$774$	−1.66890	−0.0599873
$775$	17.8067	0.639634
$776$	−51.1909	−1.83765
$777$	14.2831	0.512402
$778$	29.0920	1.04300
$779$	10.8295	0.388007
$780$	−2.45973	−0.0880723
$781$	14.8308	0.530686
$782$	6.16011	0.220285
$783$	−1.32604	−0.0473890
$784$	6.55224	0.234009
$785$	16.0458	0.572700
$786$	12.0661	0.430384
$787$	−17.2661	−0.615471	−0.307735	−	0.951472i	$-0.599571\pi$
$787$	−17.2661	−0.615471	−0.307735	+	0.951472i	$0.599571\pi$
$788$	−4.51862	−0.160969
$789$	−22.0404	−0.784658
$790$	−3.72196	−0.132421
$791$	−18.7725	−0.667474
$792$	−6.49971	−0.230957
$793$	−4.96861	−0.176441
$794$	22.4134	0.795422
$795$	25.5509	0.906199
$796$	1.08701	0.0385281
$797$	−13.8414	−0.490289	−0.245145	−	0.969487i	$-0.578835\pi$
$797$	−13.8414	−0.490289	−0.245145	+	0.969487i	$0.578835\pi$
$798$	15.4547	0.547089
$799$	8.03686	0.284324
$800$	3.32950	0.117716
$801$	5.07382	0.179275
$802$	9.00466	0.317966
$803$	20.9574	0.739570
$804$	2.38263	0.0840290
$805$	29.1144	1.02615
$806$	35.5418	1.25191
$807$	−10.0209	−0.352751
$808$	−5.51167	−0.193900
$809$	−16.2566	−0.571550	−0.285775	−	0.958297i	$-0.592251\pi$
$809$	−16.2566	−0.571550	−0.285775	+	0.958297i	$0.592251\pi$
$810$	−3.72196	−0.130776
$811$	13.3128	0.467475	0.233737	−	0.972300i	$-0.424904\pi$
$811$	13.3128	0.467475	0.233737	+	0.972300i	$0.424904\pi$
$812$	−0.644545	−0.0226191
$813$	−16.0716	−0.563656
$814$	−18.4895	−0.648058
$815$	−28.4600	−0.996910
$816$	−3.52532	−0.123411
$817$	6.37026	0.222867
$818$	35.2038	1.23087
$819$	9.34106	0.326403
$820$	−1.26770	−0.0442698
$821$	−30.5854	−1.06744	−0.533719	−	0.845662i	$-0.679206\pi$
$821$	−30.5854	−1.06744	−0.533719	+	0.845662i	$0.679206\pi$
$822$	13.6116	0.474759
$823$	33.2163	1.15785	0.578924	−	0.815382i	$-0.303473\pi$
$823$	33.2163	1.15785	0.578924	+	0.815382i	$0.303473\pi$
$824$	−45.6555	−1.59049
$825$	−6.05820	−0.210919
$826$	8.43783	0.293590
$827$	22.9495	0.798033	0.399016	−	0.916944i	$-0.369352\pi$
$827$	22.9495	0.798033	0.399016	+	0.916944i	$0.369352\pi$
$828$	0.988206	0.0343425
$829$	−29.8434	−1.03650	−0.518252	−	0.855228i	$-0.673417\pi$
$829$	−29.8434	−1.03650	−0.518252	+	0.855228i	$0.673417\pi$
$830$	−66.9615	−2.32427
$831$	19.1725	0.665087
$832$	35.6915	1.23738
$833$	1.85862	0.0643975
$834$	4.68721	0.162305
$835$	44.0191	1.52334
$836$	2.40175	0.0830661
$837$	−6.45635	−0.223164
$838$	−23.6144	−0.815746
$839$	−32.8570	−1.13435	−0.567175	−	0.823597i	$-0.691964\pi$
$839$	−32.8570	−1.13435	−0.567175	+	0.823597i	$0.691964\pi$
$840$	−18.6879	−0.644794
$841$	−27.2416	−0.939366
$842$	−12.8748	−0.443695
$843$	13.8331	0.476436
$844$	−2.04196	−0.0702870
$845$	−11.0611	−0.380513
$846$	−10.7395	−0.369230
$847$	−14.0016	−0.481101
$848$	−32.3393	−1.11053
$849$	28.5087	0.978417
$850$	−3.68546	−0.126410
$851$	29.0385	0.995427
$852$	1.44734	0.0495851
$853$	−2.02771	−0.0694275	−0.0347138	−	0.999397i	$-0.511052\pi$
$853$	−2.02771	−0.0694275	−0.0347138	+	0.999397i	$0.511052\pi$
$854$	−3.65439	−0.125051
$855$	14.2069	0.485865
$856$	6.13902	0.209827
$857$	−5.39801	−0.184393	−0.0921963	−	0.995741i	$-0.529389\pi$
$857$	−5.39801	−0.184393	−0.0921963	+	0.995741i	$0.529389\pi$
$858$	−12.0921	−0.412816
$859$	32.8560	1.12103	0.560516	−	0.828144i	$-0.310603\pi$
$859$	32.8560	1.12103	0.560516	+	0.828144i	$0.310603\pi$
$860$	−0.745699	−0.0254281
$861$	4.81420	0.164068
$862$	29.9465	1.01998
$863$	7.85416	0.267359	0.133679	−	0.991025i	$-0.457321\pi$
$863$	7.85416	0.267359	0.133679	+	0.991025i	$0.457321\pi$
$864$	−1.20721	−0.0410702
$865$	60.1869	2.04642
$866$	−23.2484	−0.790011
$867$	−1.00000	−0.0339618
$868$	−3.13821	−0.106518
$869$	2.19659	0.0745140
$870$	4.93548	0.167328
$871$	45.7887	1.55149
$872$	−40.3516	−1.36648
$873$	17.3000	0.585518
$874$	31.4205	1.06281
$875$	14.1595	0.478680
$876$	2.04524	0.0691022
$877$	9.41495	0.317920	0.158960	−	0.987285i	$-0.449186\pi$
$877$	9.41495	0.317920	0.158960	+	0.987285i	$0.449186\pi$
$878$	−7.14498	−0.241131
$879$	−19.3802	−0.653679
$880$	21.5686	0.727076
$881$	−1.94645	−0.0655775	−0.0327888	−	0.999462i	$-0.510439\pi$
$881$	−1.94645	−0.0655775	−0.0327888	+	0.999462i	$0.510439\pi$
$882$	−2.48364	−0.0836284
$883$	−0.0280441	−0.000943759 0	−0.000471880	−	1.00000i	$-0.500150\pi$
$883$	−0.0280441	−0.000943759 0	−0.000471880		1.00000i	$0.500150\pi$
$884$	0.883103	0.0297020
$885$	7.75657	0.260734
$886$	42.6924	1.43428
$887$	24.1514	0.810926	0.405463	−	0.914111i	$-0.367110\pi$
$887$	24.1514	0.810926	0.405463	+	0.914111i	$0.367110\pi$
$888$	−18.6392	−0.625491
$889$	−3.18423	−0.106796
$890$	−18.8846	−0.633012
$891$	2.19659	0.0735884
$892$	−0.764503	−0.0255975
$893$	40.9930	1.37178
$894$	8.07276	0.269993
$895$	−31.1997	−1.04289
$896$	20.7763	0.694088
$897$	18.9910	0.634092
$898$	−50.7766	−1.69444
$899$	8.56141	0.285539
$900$	−0.591222	−0.0197074
$901$	−9.17343	−0.305611
$902$	−6.23202	−0.207504
$903$	2.83187	0.0942387
$904$	24.4979	0.814787
$905$	−43.0594	−1.43134
$906$	−24.2932	−0.807088
$907$	1.84053	0.0611138	0.0305569	−	0.999533i	$-0.490272\pi$
$907$	1.84053	0.0611138	0.0305569	+	0.999533i	$0.490272\pi$
$908$	2.45179	0.0813655
$909$	1.86268	0.0617811
$910$	−34.7670	−1.15252
$911$	48.2294	1.59791	0.798955	−	0.601391i	$-0.205386\pi$
$911$	48.2294	1.59791	0.798955	+	0.601391i	$0.205386\pi$
$912$	−17.9813	−0.595421
$913$	39.5186	1.30788
$914$	5.07505	0.167868
$915$	−3.35934	−0.111056
$916$	−2.94993	−0.0974684
$917$	−20.4744	−0.676124
$918$	1.33628	0.0441037
$919$	6.61348	0.218159	0.109079	−	0.994033i	$-0.465210\pi$
$919$	6.61348	0.218159	0.109079	+	0.994033i	$0.465210\pi$
$920$	−37.9938	−1.25262
$921$	−6.99711	−0.230562
$922$	47.2304	1.55545
$923$	27.8145	0.915527
$924$	1.06768	0.0351242
$925$	−17.3731	−0.571224
$926$	−31.5154	−1.03566
$927$	15.4293	0.506766
$928$	1.60082	0.0525494
$929$	−27.3702	−0.897988	−0.448994	−	0.893535i	$-0.648218\pi$
$929$	−27.3702	−0.897988	−0.448994	+	0.893535i	$0.648218\pi$
$930$	24.0303	0.787983
$931$	9.48015	0.310699
$932$	−0.837012	−0.0274172
$933$	2.04512	0.0669541
$934$	20.2559	0.662793
$935$	6.11819	0.200086
$936$	−12.1900	−0.398441
$937$	3.51577	0.114855	0.0574276	−	0.998350i	$-0.481710\pi$
$937$	3.51577	0.114855	0.0574276	+	0.998350i	$0.481710\pi$
$938$	33.6774	1.09960
$939$	−7.53797	−0.245992
$940$	−4.79862	−0.156514
$941$	7.46588	0.243381	0.121690	−	0.992568i	$-0.461168\pi$
$941$	7.46588	0.243381	0.121690	+	0.992568i	$0.461168\pi$
$942$	7.69809	0.250817
$943$	9.78762	0.318729
$944$	−9.81731	−0.319526
$945$	6.31560	0.205447
$946$	−3.66587	−0.119188
$947$	27.3343	0.888244	0.444122	−	0.895966i	$-0.353516\pi$
$947$	27.3343	0.888244	0.444122	+	0.895966i	$0.353516\pi$
$948$	0.214366	0.00696227
$949$	39.3048	1.27589
$950$	−18.7982	−0.609893
$951$	33.3973	1.08298
$952$	6.70942	0.217454
$953$	6.23873	0.202092	0.101046	−	0.994882i	$-0.467781\pi$
$953$	6.23873	0.202092	0.101046	+	0.994882i	$0.467781\pi$
$954$	12.2582	0.396875
$955$	18.0716	0.584784
$956$	−0.356363	−0.0115256
$957$	−2.91277	−0.0941565
$958$	18.3433	0.592646
$959$	−23.0968	−0.745835
$960$	24.1315	0.778840
$961$	10.6845	0.344661
$962$	−34.6764	−1.11801
$963$	−2.07469	−0.0668559
$964$	−3.54237	−0.114092
$965$	−62.2040	−2.00242
$966$	13.9678	0.449407
$967$	−27.1149	−0.871957	−0.435978	−	0.899957i	$-0.643598\pi$
$967$	−27.1149	−0.871957	−0.435978	+	0.899957i	$0.643598\pi$
$968$	18.2719	0.587281
$969$	−5.10063	−0.163856
$970$	−64.3900	−2.06744
$971$	−14.0278	−0.450174	−0.225087	−	0.974339i	$-0.572267\pi$
$971$	−14.0278	−0.450174	−0.225087	+	0.974339i	$0.572267\pi$
$972$	0.214366	0.00687578
$973$	−7.95349	−0.254977
$974$	27.3993	0.877931
$975$	−11.3619	−0.363873
$976$	4.25184	0.136098
$977$	−46.6084	−1.49113	−0.745567	−	0.666431i	$-0.767821\pi$
$977$	−46.6084	−1.49113	−0.745567	+	0.666431i	$0.767821\pi$
$978$	−13.6539	−0.436603
$979$	11.1451	0.356199
$980$	−1.10974	−0.0354494
$981$	13.6369	0.435392
$982$	20.7414	0.661884
$983$	−20.9707	−0.668861	−0.334431	−	0.942420i	$-0.608544\pi$
$983$	−20.9707	−0.668861	−0.334431	+	0.942420i	$0.608544\pi$
$984$	−6.28247	−0.200278
$985$	−58.7118	−1.87071
$986$	−1.77196	−0.0564308
$987$	18.2233	0.580053
$988$	4.50438	0.143304
$989$	5.75739	0.183074
$990$	−8.17560	−0.259837
$991$	−52.1868	−1.65777	−0.828885	−	0.559420i	$-0.811024\pi$
$991$	−52.1868	−1.65777	−0.828885	+	0.559420i	$0.811024\pi$
$992$	7.79419	0.247466
$993$	10.1137	0.320950
$994$	20.4574	0.648871
$995$	14.1239	0.447757
$996$	3.85664	0.122202
$997$	41.1262	1.30248	0.651240	−	0.758872i	$-0.274249\pi$
$997$	41.1262	1.30248	0.651240	+	0.758872i	$0.274249\pi$
$998$	55.2676	1.74947
$999$	6.29915	0.199296

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.l.1.23	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.l.1.23	✓	32	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.33628 q^{2} -1.00000 q^{3} -0.214366 q^{4} -2.78532 q^{5} -1.33628 q^{6} +2.26746 q^{7} -2.95900 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.33628 q^{2} -1.00000 q^{3} -0.214366 q^{4} -2.78532 q^{5} -1.33628 q^{6} +2.26746 q^{7} -2.95900 q^{8} +1.00000 q^{9} -3.72196 q^{10} +2.19659 q^{11} +0.214366 q^{12} +4.11961 q^{13} +3.02995 q^{14} +2.78532 q^{15} -3.52532 q^{16} -1.00000 q^{17} +1.33628 q^{18} -5.10063 q^{19} +0.597077 q^{20} -2.26746 q^{21} +2.93524 q^{22} -4.60991 q^{23} +2.95900 q^{24} +2.75801 q^{25} +5.50494 q^{26} -1.00000 q^{27} -0.486066 q^{28} +1.32604 q^{29} +3.72196 q^{30} +6.45635 q^{31} +1.20721 q^{32} -2.19659 q^{33} -1.33628 q^{34} -6.31560 q^{35} -0.214366 q^{36} -6.29915 q^{37} -6.81585 q^{38} -4.11961 q^{39} +8.24177 q^{40} -2.12317 q^{41} -3.02995 q^{42} -1.24892 q^{43} -0.470872 q^{44} -2.78532 q^{45} -6.16011 q^{46} -8.03686 q^{47} +3.52532 q^{48} -1.85862 q^{49} +3.68546 q^{50} +1.00000 q^{51} -0.883103 q^{52} +9.17343 q^{53} -1.33628 q^{54} -6.11819 q^{55} -6.70942 q^{56} +5.10063 q^{57} +1.77196 q^{58} +2.78480 q^{59} -0.597077 q^{60} -1.20609 q^{61} +8.62747 q^{62} +2.26746 q^{63} +8.66380 q^{64} -11.4744 q^{65} -2.93524 q^{66} +11.1148 q^{67} +0.214366 q^{68} +4.60991 q^{69} -8.43939 q^{70} +6.75174 q^{71} -2.95900 q^{72} +9.54089 q^{73} -8.41740 q^{74} -2.75801 q^{75} +1.09340 q^{76} +4.98067 q^{77} -5.50494 q^{78} +1.00000 q^{79} +9.81913 q^{80} +1.00000 q^{81} -2.83714 q^{82} +17.9909 q^{83} +0.486066 q^{84} +2.78532 q^{85} -1.66890 q^{86} -1.32604 q^{87} -6.49971 q^{88} +5.07382 q^{89} -3.72196 q^{90} +9.34106 q^{91} +0.988206 q^{92} -6.45635 q^{93} -10.7395 q^{94} +14.2069 q^{95} -1.20721 q^{96} +17.3000 q^{97} -2.48364 q^{98} +2.19659 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9} + 17 q^{10} + 8 q^{11} - 41 q^{12} + 17 q^{13} + q^{14} + q^{15} + 55 q^{16} - 32 q^{17} - q^{18} + 48 q^{19} - 7 q^{20} - 4 q^{21} - 4 q^{22} - 19 q^{23} + 3 q^{24} + 63 q^{25} + 27 q^{26} - 32 q^{27} + 17 q^{28} - 15 q^{29} - 17 q^{30} + 20 q^{31} + 13 q^{32} - 8 q^{33} + q^{34} + 22 q^{35} + 41 q^{36} + 6 q^{37} + 11 q^{38} - 17 q^{39} + 47 q^{40} + q^{41} - q^{42} + 40 q^{43} + 22 q^{44} - q^{45} + 5 q^{46} - 5 q^{47} - 55 q^{48} + 88 q^{49} + 17 q^{50} + 32 q^{51} + 23 q^{52} - 34 q^{53} + q^{54} + 48 q^{55} - 48 q^{57} - 9 q^{58} + 41 q^{59} + 7 q^{60} + 20 q^{61} + 15 q^{62} + 4 q^{63} + 93 q^{64} - 58 q^{65} + 4 q^{66} + 52 q^{67} - 41 q^{68} + 19 q^{69} + 25 q^{70} + q^{71} - 3 q^{72} + 19 q^{73} + 12 q^{74} - 63 q^{75} + 128 q^{76} - 20 q^{77} - 27 q^{78} + 32 q^{79} - 16 q^{80} + 32 q^{81} - 5 q^{82} + 31 q^{83} - 17 q^{84} + q^{85} - 62 q^{86} + 15 q^{87} + 35 q^{88} + 18 q^{89} + 17 q^{90} + 48 q^{91} - 75 q^{92} - 20 q^{93} + 29 q^{94} + 5 q^{95} - 13 q^{96} + 17 q^{97} + 30 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9 + 17 * q^10 + 8 * q^11 - 41 * q^12 + 17 * q^13 + q^14 + q^15 + 55 * q^16 - 32 * q^17 - q^18 + 48 * q^19 - 7 * q^20 - 4 * q^21 - 4 * q^22 - 19 * q^23 + 3 * q^24 + 63 * q^25 + 27 * q^26 - 32 * q^27 + 17 * q^28 - 15 * q^29 - 17 * q^30 + 20 * q^31 + 13 * q^32 - 8 * q^33 + q^34 + 22 * q^35 + 41 * q^36 + 6 * q^37 + 11 * q^38 - 17 * q^39 + 47 * q^40 + q^41 - q^42 + 40 * q^43 + 22 * q^44 - q^45 + 5 * q^46 - 5 * q^47 - 55 * q^48 + 88 * q^49 + 17 * q^50 + 32 * q^51 + 23 * q^52 - 34 * q^53 + q^54 + 48 * q^55 - 48 * q^57 - 9 * q^58 + 41 * q^59 + 7 * q^60 + 20 * q^61 + 15 * q^62 + 4 * q^63 + 93 * q^64 - 58 * q^65 + 4 * q^66 + 52 * q^67 - 41 * q^68 + 19 * q^69 + 25 * q^70 + q^71 - 3 * q^72 + 19 * q^73 + 12 * q^74 - 63 * q^75 + 128 * q^76 - 20 * q^77 - 27 * q^78 + 32 * q^79 - 16 * q^80 + 32 * q^81 - 5 * q^82 + 31 * q^83 - 17 * q^84 + q^85 - 62 * q^86 + 15 * q^87 + 35 * q^88 + 18 * q^89 + 17 * q^90 + 48 * q^91 - 75 * q^92 - 20 * q^93 + 29 * q^94 + 5 * q^95 - 13 * q^96 + 17 * q^97 + 30 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more