LMFDB - Embedded newform 4029.2.a.h.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	$q-2.14934 q^{2} +1.00000 q^{3} +2.61967 q^{4} -2.01369 q^{5} -2.14934 q^{6} -1.06654 q^{7} -1.33187 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.14934 q^{2} +1.00000 q^{3} +2.61967 q^{4} -2.01369 q^{5} -2.14934 q^{6} -1.06654 q^{7} -1.33187 q^{8} +1.00000 q^{9} +4.32810 q^{10} -2.10525 q^{11} +2.61967 q^{12} +2.87507 q^{13} +2.29235 q^{14} -2.01369 q^{15} -2.37668 q^{16} -1.00000 q^{17} -2.14934 q^{18} +4.05585 q^{19} -5.27519 q^{20} -1.06654 q^{21} +4.52489 q^{22} -2.47517 q^{23} -1.33187 q^{24} -0.945058 q^{25} -6.17951 q^{26} +1.00000 q^{27} -2.79397 q^{28} +1.03673 q^{29} +4.32810 q^{30} +2.70392 q^{31} +7.77205 q^{32} -2.10525 q^{33} +2.14934 q^{34} +2.14767 q^{35} +2.61967 q^{36} -1.99531 q^{37} -8.71741 q^{38} +2.87507 q^{39} +2.68198 q^{40} +2.39437 q^{41} +2.29235 q^{42} +1.79385 q^{43} -5.51504 q^{44} -2.01369 q^{45} +5.31998 q^{46} -11.4237 q^{47} -2.37668 q^{48} -5.86250 q^{49} +2.03125 q^{50} -1.00000 q^{51} +7.53173 q^{52} +4.82974 q^{53} -2.14934 q^{54} +4.23931 q^{55} +1.42049 q^{56} +4.05585 q^{57} -2.22828 q^{58} -6.02702 q^{59} -5.27519 q^{60} +11.8915 q^{61} -5.81164 q^{62} -1.06654 q^{63} -11.9514 q^{64} -5.78950 q^{65} +4.52489 q^{66} +9.00042 q^{67} -2.61967 q^{68} -2.47517 q^{69} -4.61608 q^{70} -6.57695 q^{71} -1.33187 q^{72} +8.14705 q^{73} +4.28860 q^{74} -0.945058 q^{75} +10.6250 q^{76} +2.24532 q^{77} -6.17951 q^{78} +1.00000 q^{79} +4.78590 q^{80} +1.00000 q^{81} -5.14633 q^{82} +11.5168 q^{83} -2.79397 q^{84} +2.01369 q^{85} -3.85560 q^{86} +1.03673 q^{87} +2.80392 q^{88} -6.41893 q^{89} +4.32810 q^{90} -3.06637 q^{91} -6.48411 q^{92} +2.70392 q^{93} +24.5533 q^{94} -8.16722 q^{95} +7.77205 q^{96} -17.4166 q^{97} +12.6005 q^{98} -2.10525 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9	\( 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9} - 9 q^{10} - 19 q^{11} + 21 q^{12} - 12 q^{13} - 15 q^{14} - 12 q^{15} + q^{16} - 25 q^{17} - 7 q^{18} - 35 q^{19} - 11 q^{20} - 4 q^{21} - 2 q^{22} - 16 q^{23} - 21 q^{24} + 19 q^{25} - 5 q^{26} + 25 q^{27} + 3 q^{28} - 37 q^{29} - 9 q^{30} - 28 q^{31} - 19 q^{32} - 19 q^{33} + 7 q^{34} - 42 q^{35} + 21 q^{36} + 8 q^{37} - 35 q^{38} - 12 q^{39} - 9 q^{40} - 34 q^{41} - 15 q^{42} - 19 q^{43} - 56 q^{44} - 12 q^{45} + q^{46} - 25 q^{47} + q^{48} + 25 q^{49} - 7 q^{50} - 25 q^{51} - 37 q^{52} - 44 q^{53} - 7 q^{54} - 11 q^{55} - 18 q^{56} - 35 q^{57} - 3 q^{58} - 47 q^{59} - 11 q^{60} - 28 q^{61} + 11 q^{62} - 4 q^{63} - 9 q^{64} - 63 q^{65} - 2 q^{66} - 28 q^{67} - 21 q^{68} - 16 q^{69} + 5 q^{70} - 27 q^{71} - 21 q^{72} - 21 q^{73} - 18 q^{74} + 19 q^{75} - 50 q^{76} - 58 q^{77} - 5 q^{78} + 25 q^{79} - 56 q^{80} + 25 q^{81} - 5 q^{82} - 61 q^{83} + 3 q^{84} + 12 q^{85} - 28 q^{86} - 37 q^{87} + 15 q^{88} - 34 q^{89} - 9 q^{90} - 30 q^{91} - 31 q^{92} - 28 q^{93} + q^{94} - 32 q^{95} - 19 q^{96} - 11 q^{97} - 66 q^{98} - 19 q^{99}+O(q^{100}) \) 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9 - 9 * q^10 - 19 * q^11 + 21 * q^12 - 12 * q^13 - 15 * q^14 - 12 * q^15 + q^16 - 25 * q^17 - 7 * q^18 - 35 * q^19 - 11 * q^20 - 4 * q^21 - 2 * q^22 - 16 * q^23 - 21 * q^24 + 19 * q^25 - 5 * q^26 + 25 * q^27 + 3 * q^28 - 37 * q^29 - 9 * q^30 - 28 * q^31 - 19 * q^32 - 19 * q^33 + 7 * q^34 - 42 * q^35 + 21 * q^36 + 8 * q^37 - 35 * q^38 - 12 * q^39 - 9 * q^40 - 34 * q^41 - 15 * q^42 - 19 * q^43 - 56 * q^44 - 12 * q^45 + q^46 - 25 * q^47 + q^48 + 25 * q^49 - 7 * q^50 - 25 * q^51 - 37 * q^52 - 44 * q^53 - 7 * q^54 - 11 * q^55 - 18 * q^56 - 35 * q^57 - 3 * q^58 - 47 * q^59 - 11 * q^60 - 28 * q^61 + 11 * q^62 - 4 * q^63 - 9 * q^64 - 63 * q^65 - 2 * q^66 - 28 * q^67 - 21 * q^68 - 16 * q^69 + 5 * q^70 - 27 * q^71 - 21 * q^72 - 21 * q^73 - 18 * q^74 + 19 * q^75 - 50 * q^76 - 58 * q^77 - 5 * q^78 + 25 * q^79 - 56 * q^80 + 25 * q^81 - 5 * q^82 - 61 * q^83 + 3 * q^84 + 12 * q^85 - 28 * q^86 - 37 * q^87 + 15 * q^88 - 34 * q^89 - 9 * q^90 - 30 * q^91 - 31 * q^92 - 28 * q^93 + q^94 - 32 * q^95 - 19 * q^96 - 11 * q^97 - 66 * 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 $

$2$	−2.14934	−1.51981	−0.759907	−	0.650032i	$-0.774755\pi$
$2$	−2.14934	−1.51981	−0.759907	+	0.650032i	$0.774755\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.61967	1.30983
$5$	−2.01369	−0.900549	−0.450274	−	0.892890i	$-0.648674\pi$
$5$	−2.01369	−0.900549	−0.450274	+	0.892890i	$0.648674\pi$
$6$	−2.14934	−0.877465
$7$	−1.06654	−0.403113	−0.201557	−	0.979477i	$-0.564600\pi$
$7$	−1.06654	−0.403113	−0.201557	+	0.979477i	$0.564600\pi$
$8$	−1.33187	−0.470888
$9$	1.00000	0.333333
$10$	4.32810	1.36867
$11$	−2.10525	−0.634756	−0.317378	−	0.948299i	$-0.602802\pi$
$11$	−2.10525	−0.634756	−0.317378	+	0.948299i	$0.602802\pi$
$12$	2.61967	0.756232
$13$	2.87507	0.797402	0.398701	−	0.917081i	$-0.369461\pi$
$13$	2.87507	0.797402	0.398701	+	0.917081i	$0.369461\pi$
$14$	2.29235	0.612657
$15$	−2.01369	−0.519932
$16$	−2.37668	−0.594171
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.14934	−0.506604
$19$	4.05585	0.930476	0.465238	−	0.885186i	$-0.345969\pi$
$19$	4.05585	0.930476	0.465238	+	0.885186i	$0.345969\pi$
$20$	−5.27519	−1.17957
$21$	−1.06654	−0.232737
$22$	4.52489	0.964711
$23$	−2.47517	−0.516108	−0.258054	−	0.966130i	$-0.583081\pi$
$23$	−2.47517	−0.516108	−0.258054	+	0.966130i	$0.583081\pi$
$24$	−1.33187	−0.271867
$25$	−0.945058	−0.189012
$26$	−6.17951	−1.21190
$27$	1.00000	0.192450
$28$	−2.79397	−0.528011
$29$	1.03673	0.192515	0.0962577	−	0.995356i	$-0.469313\pi$
$29$	1.03673	0.192515	0.0962577	+	0.995356i	$0.469313\pi$
$30$	4.32810	0.790200
$31$	2.70392	0.485638	0.242819	−	0.970072i	$-0.421928\pi$
$31$	2.70392	0.485638	0.242819	+	0.970072i	$0.421928\pi$
$32$	7.77205	1.37392
$33$	−2.10525	−0.366476
$34$	2.14934	0.368609
$35$	2.14767	0.363023
$36$	2.61967	0.436611
$37$	−1.99531	−0.328027	−0.164013	−	0.986458i	$-0.552444\pi$
$37$	−1.99531	−0.328027	−0.164013	+	0.986458i	$0.552444\pi$
$38$	−8.71741	−1.41415
$39$	2.87507	0.460380
$40$	2.68198	0.424058
$41$	2.39437	0.373939	0.186969	−	0.982366i	$-0.440134\pi$
$41$	2.39437	0.373939	0.186969	+	0.982366i	$0.440134\pi$
$42$	2.29235	0.353717
$43$	1.79385	0.273560	0.136780	−	0.990601i	$-0.456325\pi$
$43$	1.79385	0.273560	0.136780	+	0.990601i	$0.456325\pi$
$44$	−5.51504	−0.831424
$45$	−2.01369	−0.300183
$46$	5.31998	0.784388
$47$	−11.4237	−1.66631	−0.833156	−	0.553038i	$-0.813468\pi$
$47$	−11.4237	−1.66631	−0.833156	+	0.553038i	$0.813468\pi$
$48$	−2.37668	−0.343045
$49$	−5.86250	−0.837500
$50$	2.03125	0.287262
$51$	−1.00000	−0.140028
$52$	7.53173	1.04446
$53$	4.82974	0.663415	0.331708	−	0.943382i	$-0.392375\pi$
$53$	4.82974	0.663415	0.331708	+	0.943382i	$0.392375\pi$
$54$	−2.14934	−0.292488
$55$	4.23931	0.571629
$56$	1.42049	0.189821
$57$	4.05585	0.537211
$58$	−2.22828	−0.292587
$59$	−6.02702	−0.784651	−0.392325	−	0.919826i	$-0.628329\pi$
$59$	−6.02702	−0.784651	−0.392325	+	0.919826i	$0.628329\pi$
$60$	−5.27519	−0.681024
$61$	11.8915	1.52256	0.761278	−	0.648426i	$-0.224572\pi$
$61$	11.8915	1.52256	0.761278	+	0.648426i	$0.224572\pi$
$62$	−5.81164	−0.738079
$63$	−1.06654	−0.134371
$64$	−11.9514	−1.49393
$65$	−5.78950	−0.718099
$66$	4.52489	0.556976
$67$	9.00042	1.09958	0.549788	−	0.835304i	$-0.314709\pi$
$67$	9.00042	1.09958	0.549788	+	0.835304i	$0.314709\pi$
$68$	−2.61967	−0.317681
$69$	−2.47517	−0.297975
$70$	−4.61608	−0.551727
$71$	−6.57695	−0.780540	−0.390270	−	0.920700i	$-0.627618\pi$
$71$	−6.57695	−0.780540	−0.390270	+	0.920700i	$0.627618\pi$
$72$	−1.33187	−0.156963
$73$	8.14705	0.953540	0.476770	−	0.879028i	$-0.341808\pi$
$73$	8.14705	0.953540	0.476770	+	0.879028i	$0.341808\pi$
$74$	4.28860	0.498540
$75$	−0.945058	−0.109126
$76$	10.6250	1.21877
$77$	2.24532	0.255878
$78$	−6.17951	−0.699692
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	4.78590	0.535080
$81$	1.00000	0.111111
$82$	−5.14633	−0.568317
$83$	11.5168	1.26414	0.632069	−	0.774912i	$-0.282206\pi$
$83$	11.5168	1.26414	0.632069	+	0.774912i	$0.282206\pi$
$84$	−2.79397	−0.304847
$85$	2.01369	0.218415
$86$	−3.85560	−0.415760
$87$	1.03673	0.111149
$88$	2.80392	0.298899
$89$	−6.41893	−0.680405	−0.340203	−	0.940352i	$-0.610496\pi$
$89$	−6.41893	−0.680405	−0.340203	+	0.940352i	$0.610496\pi$
$90$	4.32810	0.456222
$91$	−3.06637	−0.321443
$92$	−6.48411	−0.676016
$93$	2.70392	0.280383
$94$	24.5533	2.53248
$95$	−8.16722	−0.837940
$96$	7.77205	0.793231
$97$	−17.4166	−1.76839	−0.884195	−	0.467118i	$-0.845292\pi$
$97$	−17.4166	−1.76839	−0.884195	+	0.467118i	$0.845292\pi$
$98$	12.6005	1.27284
$99$	−2.10525	−0.211585
$100$	−2.47574	−0.247574
$101$	−14.9320	−1.48579	−0.742896	−	0.669406i	$-0.766549\pi$
$101$	−14.9320	−1.48579	−0.742896	+	0.669406i	$0.766549\pi$
$102$	2.14934	0.212816
$103$	−2.24085	−0.220798	−0.110399	−	0.993887i	$-0.535213\pi$
$103$	−2.24085	−0.220798	−0.110399	+	0.993887i	$0.535213\pi$
$104$	−3.82923	−0.375487
$105$	2.14767	0.209591
$106$	−10.3808	−1.00827
$107$	17.3618	1.67843	0.839216	−	0.543798i	$-0.183014\pi$
$107$	17.3618	1.67843	0.839216	+	0.543798i	$0.183014\pi$
$108$	2.61967	0.252077
$109$	19.1541	1.83463	0.917315	−	0.398162i	$-0.130352\pi$
$109$	19.1541	1.83463	0.917315	+	0.398162i	$0.130352\pi$
$110$	−9.11173	−0.868769
$111$	−1.99531	−0.189386
$112$	2.53482	0.239518
$113$	−12.8815	−1.21179	−0.605893	−	0.795546i	$-0.707184\pi$
$113$	−12.8815	−1.21179	−0.605893	+	0.795546i	$0.707184\pi$
$114$	−8.71741	−0.816460
$115$	4.98422	0.464781
$116$	2.71588	0.252163
$117$	2.87507	0.265801
$118$	12.9541	1.19252
$119$	1.06654	0.0977693
$120$	2.68198	0.244830
$121$	−6.56793	−0.597085
$122$	−25.5590	−2.31400
$123$	2.39437	0.215894
$124$	7.08336	0.636105
$125$	11.9715	1.07076
$126$	2.29235	0.204219
$127$	−5.74037	−0.509376	−0.254688	−	0.967023i	$-0.581973\pi$
$127$	−5.74037	−0.509376	−0.254688	+	0.967023i	$0.581973\pi$
$128$	10.1436	0.896572
$129$	1.79385	0.157940
$130$	12.4436	1.09138
$131$	2.11202	0.184528	0.0922639	−	0.995735i	$-0.470590\pi$
$131$	2.11202	0.184528	0.0922639	+	0.995735i	$0.470590\pi$
$132$	−5.51504	−0.480023
$133$	−4.32572	−0.375087
$134$	−19.3450	−1.67115
$135$	−2.01369	−0.173311
$136$	1.33187	0.114207
$137$	−0.983899	−0.0840601	−0.0420301	−	0.999116i	$-0.513383\pi$
$137$	−0.983899	−0.0840601	−0.0420301	+	0.999116i	$0.513383\pi$
$138$	5.31998	0.452867
$139$	0.912949	0.0774353	0.0387177	−	0.999250i	$-0.487673\pi$
$139$	0.912949	0.0774353	0.0387177	+	0.999250i	$0.487673\pi$
$140$	5.62619	0.475499
$141$	−11.4237	−0.962046
$142$	14.1361	1.18628
$143$	−6.05274	−0.506155
$144$	−2.37668	−0.198057
$145$	−2.08764	−0.173369
$146$	−17.5108	−1.44920
$147$	−5.86250	−0.483531
$148$	−5.22704	−0.429660
$149$	−0.245866	−0.0201422	−0.0100711	−	0.999949i	$-0.503206\pi$
$149$	−0.245866	−0.0201422	−0.0100711	+	0.999949i	$0.503206\pi$
$150$	2.03125	0.165851
$151$	−15.4267	−1.25541	−0.627703	−	0.778453i	$-0.716005\pi$
$151$	−15.4267	−1.25541	−0.627703	+	0.778453i	$0.716005\pi$
$152$	−5.40188	−0.438150
$153$	−1.00000	−0.0808452
$154$	−4.82597	−0.388887
$155$	−5.44485	−0.437341
$156$	7.53173	0.603021
$157$	17.3428	1.38411	0.692055	−	0.721845i	$-0.256706\pi$
$157$	17.3428	1.38411	0.692055	+	0.721845i	$0.256706\pi$
$158$	−2.14934	−0.170992
$159$	4.82974	0.383023
$160$	−15.6505	−1.23728
$161$	2.63986	0.208050
$162$	−2.14934	−0.168868
$163$	−14.5925	−1.14297	−0.571485	−	0.820612i	$-0.693633\pi$
$163$	−14.5925	−1.14297	−0.571485	+	0.820612i	$0.693633\pi$
$164$	6.27246	0.489797
$165$	4.23931	0.330030
$166$	−24.7536	−1.92125
$167$	−18.8859	−1.46144	−0.730718	−	0.682680i	$-0.760814\pi$
$167$	−18.8859	−1.46144	−0.730718	+	0.682680i	$0.760814\pi$
$168$	1.42049	0.109593
$169$	−4.73396	−0.364151
$170$	−4.32810	−0.331950
$171$	4.05585	0.310159
$172$	4.69929	0.358317
$173$	−22.0746	−1.67830	−0.839151	−	0.543899i	$-0.816947\pi$
$173$	−22.0746	−1.67830	−0.839151	+	0.543899i	$0.816947\pi$
$174$	−2.22828	−0.168925
$175$	1.00794	0.0761931
$176$	5.00351	0.377154
$177$	−6.02702	−0.453018
$178$	13.7965	1.03409
$179$	−13.5454	−1.01243	−0.506216	−	0.862407i	$-0.668956\pi$
$179$	−13.5454	−1.01243	−0.506216	+	0.862407i	$0.668956\pi$
$180$	−5.27519	−0.393189
$181$	16.6051	1.23425	0.617125	−	0.786865i	$-0.288297\pi$
$181$	16.6051	1.23425	0.617125	+	0.786865i	$0.288297\pi$
$182$	6.59068	0.488533
$183$	11.8915	0.879048
$184$	3.29661	0.243029
$185$	4.01793	0.295404
$186$	−5.81164	−0.426130
$187$	2.10525	0.153951
$188$	−29.9262	−2.18259
$189$	−1.06654	−0.0775792
$190$	17.5541	1.27351
$191$	−5.32476	−0.385286	−0.192643	−	0.981269i	$-0.561706\pi$
$191$	−5.32476	−0.385286	−0.192643	+	0.981269i	$0.561706\pi$
$192$	−11.9514	−0.862519
$193$	−19.3063	−1.38970	−0.694849	−	0.719156i	$-0.744529\pi$
$193$	−19.3063	−1.38970	−0.694849	+	0.719156i	$0.744529\pi$
$194$	37.4343	2.68762
$195$	−5.78950	−0.414595
$196$	−15.3578	−1.09698
$197$	18.9706	1.35160	0.675798	−	0.737087i	$-0.263799\pi$
$197$	18.9706	1.35160	0.675798	+	0.737087i	$0.263799\pi$
$198$	4.52489	0.321570
$199$	−2.51574	−0.178336	−0.0891681	−	0.996017i	$-0.528421\pi$
$199$	−2.51574	−0.178336	−0.0891681	+	0.996017i	$0.528421\pi$
$200$	1.25870	0.0890033
$201$	9.00042	0.634840
$202$	32.0940	2.25813
$203$	−1.10571	−0.0776054
$204$	−2.61967	−0.183413
$205$	−4.82153	−0.336750
$206$	4.81636	0.335572
$207$	−2.47517	−0.172036
$208$	−6.83314	−0.473793
$209$	−8.53857	−0.590625
$210$	−4.61608	−0.318540
$211$	−23.4342	−1.61328	−0.806639	−	0.591044i	$-0.798716\pi$
$211$	−23.4342	−1.61328	−0.806639	+	0.591044i	$0.798716\pi$
$212$	12.6523	0.868963
$213$	−6.57695	−0.450645
$214$	−37.3165	−2.55090
$215$	−3.61226	−0.246354
$216$	−1.33187	−0.0906224
$217$	−2.88383	−0.195767
$218$	−41.1687	−2.78830
$219$	8.14705	0.550526
$220$	11.1056	0.748738
$221$	−2.87507	−0.193398
$222$	4.28860	0.287832
$223$	0.720916	0.0482761	0.0241381	−	0.999709i	$-0.492316\pi$
$223$	0.720916	0.0482761	0.0241381	+	0.999709i	$0.492316\pi$
$224$	−8.28918	−0.553844
$225$	−0.945058	−0.0630039
$226$	27.6867	1.84169
$227$	19.4260	1.28935	0.644675	−	0.764457i	$-0.276993\pi$
$227$	19.4260	1.28935	0.644675	+	0.764457i	$0.276993\pi$
$228$	10.6250	0.703656
$229$	−13.8529	−0.915427	−0.457713	−	0.889100i	$-0.651331\pi$
$229$	−13.8529	−0.915427	−0.457713	+	0.889100i	$0.651331\pi$
$230$	−10.7128	−0.706380
$231$	2.24532	0.147731
$232$	−1.38079	−0.0906531
$233$	−23.0227	−1.50827	−0.754135	−	0.656720i	$-0.771944\pi$
$233$	−23.0227	−1.50827	−0.754135	+	0.656720i	$0.771944\pi$
$234$	−6.17951	−0.403967
$235$	23.0037	1.50060
$236$	−15.7888	−1.02776
$237$	1.00000	0.0649570
$238$	−2.29235	−0.148591
$239$	19.8575	1.28447	0.642237	−	0.766506i	$-0.278006\pi$
$239$	19.8575	1.28447	0.642237	+	0.766506i	$0.278006\pi$
$240$	4.78590	0.308929
$241$	−3.42407	−0.220564	−0.110282	−	0.993900i	$-0.535175\pi$
$241$	−3.42407	−0.220564	−0.110282	+	0.993900i	$0.535175\pi$
$242$	14.1167	0.907458
$243$	1.00000	0.0641500
$244$	31.1518	1.99429
$245$	11.8052	0.754210
$246$	−5.14633	−0.328118
$247$	11.6609	0.741963
$248$	−3.60127	−0.228681
$249$	11.5168	0.729851
$250$	−25.7308	−1.62736
$251$	−28.2049	−1.78028	−0.890140	−	0.455687i	$-0.849393\pi$
$251$	−28.2049	−1.78028	−0.890140	+	0.455687i	$0.849393\pi$
$252$	−2.79397	−0.176004
$253$	5.21084	0.327603
$254$	12.3380	0.774156
$255$	2.01369	0.126102
$256$	2.10086	0.131304
$257$	14.7020	0.917085	0.458542	−	0.888673i	$-0.348372\pi$
$257$	14.7020	0.917085	0.458542	+	0.888673i	$0.348372\pi$
$258$	−3.85560	−0.240039
$259$	2.12807	0.132232
$260$	−15.1666	−0.940590
$261$	1.03673	0.0641718
$262$	−4.53944	−0.280448
$263$	−17.3394	−1.06919	−0.534596	−	0.845108i	$-0.679536\pi$
$263$	−17.3394	−1.06919	−0.534596	+	0.845108i	$0.679536\pi$
$264$	2.80392	0.172569
$265$	−9.72559	−0.597438
$266$	9.29744	0.570063
$267$	−6.41893	−0.392832
$268$	23.5781	1.44026
$269$	11.2856	0.688098	0.344049	−	0.938952i	$-0.388201\pi$
$269$	11.2856	0.688098	0.344049	+	0.938952i	$0.388201\pi$
$270$	4.32810	0.263400
$271$	3.34472	0.203177	0.101589	−	0.994826i	$-0.467607\pi$
$271$	3.34472	0.203177	0.101589	+	0.994826i	$0.467607\pi$
$272$	2.37668	0.144108
$273$	−3.06637	−0.185585
$274$	2.11473	0.127756
$275$	1.98958	0.119976
$276$	−6.48411	−0.390298
$277$	18.1585	1.09104	0.545519	−	0.838098i	$-0.316333\pi$
$277$	18.1585	1.09104	0.545519	+	0.838098i	$0.316333\pi$
$278$	−1.96224	−0.117687
$279$	2.70392	0.161879
$280$	−2.86043	−0.170943
$281$	30.2152	1.80249	0.901243	−	0.433315i	$-0.142656\pi$
$281$	30.2152	1.80249	0.901243	+	0.433315i	$0.142656\pi$
$282$	24.5533	1.46213
$283$	19.9956	1.18861	0.594306	−	0.804239i	$-0.297427\pi$
$283$	19.9956	1.18861	0.594306	+	0.804239i	$0.297427\pi$
$284$	−17.2294	−1.02238
$285$	−8.16722	−0.483785
$286$	13.0094	0.769262
$287$	−2.55369	−0.150740
$288$	7.77205	0.457972
$289$	1.00000	0.0588235
$290$	4.48706	0.263489
$291$	−17.4166	−1.02098
$292$	21.3425	1.24898
$293$	−11.8017	−0.689464	−0.344732	−	0.938701i	$-0.612030\pi$
$293$	−11.8017	−0.689464	−0.344732	+	0.938701i	$0.612030\pi$
$294$	12.6005	0.734877
$295$	12.1365	0.706616
$296$	2.65750	0.154464
$297$	−2.10525	−0.122159
$298$	0.528451	0.0306123
$299$	−7.11629	−0.411546
$300$	−2.47574	−0.142937
$301$	−1.91321	−0.110275
$302$	33.1572	1.90798
$303$	−14.9320	−0.857823
$304$	−9.63948	−0.552862
$305$	−23.9459	−1.37114
$306$	2.14934	0.122870
$307$	14.6021	0.833385	0.416692	−	0.909048i	$-0.363189\pi$
$307$	14.6021	0.833385	0.416692	+	0.909048i	$0.363189\pi$
$308$	5.88200	0.335158
$309$	−2.24085	−0.127478
$310$	11.7028	0.664677
$311$	−23.1875	−1.31484	−0.657420	−	0.753524i	$-0.728352\pi$
$311$	−23.1875	−1.31484	−0.657420	+	0.753524i	$0.728352\pi$
$312$	−3.82923	−0.216787
$313$	−16.6169	−0.939244	−0.469622	−	0.882868i	$-0.655610\pi$
$313$	−16.6169	−0.939244	−0.469622	+	0.882868i	$0.655610\pi$
$314$	−37.2757	−2.10359
$315$	2.14767	0.121008
$316$	2.61967	0.147368
$317$	−2.40848	−0.135274	−0.0676369	−	0.997710i	$-0.521546\pi$
$317$	−2.40848	−0.135274	−0.0676369	+	0.997710i	$0.521546\pi$
$318$	−10.3808	−0.582124
$319$	−2.18257	−0.122200
$320$	24.0664	1.34535
$321$	17.3618	0.969043
$322$	−5.67396	−0.316197
$323$	−4.05585	−0.225674
$324$	2.61967	0.145537
$325$	−2.71711	−0.150718
$326$	31.3642	1.73710
$327$	19.1541	1.05922
$328$	−3.18900	−0.176083
$329$	12.1838	0.671712
$330$	−9.11173	−0.501584
$331$	−15.7714	−0.866876	−0.433438	−	0.901183i	$-0.642700\pi$
$331$	−15.7714	−0.866876	−0.433438	+	0.901183i	$0.642700\pi$
$332$	30.1703	1.65581
$333$	−1.99531	−0.109342
$334$	40.5922	2.22111
$335$	−18.1240	−0.990222
$336$	2.53482	0.138286
$337$	−29.3255	−1.59746	−0.798730	−	0.601689i	$-0.794495\pi$
$337$	−29.3255	−1.59746	−0.798730	+	0.601689i	$0.794495\pi$
$338$	10.1749	0.553441
$339$	−12.8815	−0.699625
$340$	5.27519	0.286087
$341$	−5.69242	−0.308262
$342$	−8.71741	−0.471384
$343$	13.7183	0.740720
$344$	−2.38918	−0.128816
$345$	4.98422	0.268341
$346$	47.4459	2.55070
$347$	−24.8720	−1.33520	−0.667598	−	0.744522i	$-0.732678\pi$
$347$	−24.8720	−1.33520	−0.667598	+	0.744522i	$0.732678\pi$
$348$	2.71588	0.145586
$349$	−20.5020	−1.09745	−0.548724	−	0.836004i	$-0.684886\pi$
$349$	−20.5020	−1.09745	−0.548724	+	0.836004i	$0.684886\pi$
$350$	−2.16641	−0.115799
$351$	2.87507	0.153460
$352$	−16.3621	−0.872102
$353$	−28.4256	−1.51294	−0.756472	−	0.654026i	$-0.773079\pi$
$353$	−28.4256	−1.51294	−0.756472	+	0.654026i	$0.773079\pi$
$354$	12.9541	0.688503
$355$	13.2439	0.702915
$356$	−16.8154	−0.891217
$357$	1.06654	0.0564471
$358$	29.1137	1.53871
$359$	−7.86044	−0.414858	−0.207429	−	0.978250i	$-0.566510\pi$
$359$	−7.86044	−0.414858	−0.207429	+	0.978250i	$0.566510\pi$
$360$	2.68198	0.141353
$361$	−2.55006	−0.134214
$362$	−35.6901	−1.87583
$363$	−6.56793	−0.344727
$364$	−8.03287	−0.421037
$365$	−16.4056	−0.858709
$366$	−25.5590	−1.33599
$367$	11.6601	0.608653	0.304326	−	0.952568i	$-0.401569\pi$
$367$	11.6601	0.608653	0.304326	+	0.952568i	$0.401569\pi$
$368$	5.88269	0.306657
$369$	2.39437	0.124646
$370$	−8.63591	−0.448959
$371$	−5.15109	−0.267431
$372$	7.08336	0.367255
$373$	1.63289	0.0845478	0.0422739	−	0.999106i	$-0.486540\pi$
$373$	1.63289	0.0845478	0.0422739	+	0.999106i	$0.486540\pi$
$374$	−4.52489	−0.233977
$375$	11.9715	0.618205
$376$	15.2149	0.784646
$377$	2.98066	0.153512
$378$	2.29235	0.117906
$379$	−22.3479	−1.14793	−0.573966	−	0.818879i	$-0.694596\pi$
$379$	−22.3479	−1.14793	−0.573966	+	0.818879i	$0.694596\pi$
$380$	−21.3954	−1.09756
$381$	−5.74037	−0.294088
$382$	11.4447	0.585563
$383$	−11.3203	−0.578441	−0.289221	−	0.957262i	$-0.593396\pi$
$383$	−11.3203	−0.578441	−0.289221	+	0.957262i	$0.593396\pi$
$384$	10.1436	0.517636
$385$	−4.52138	−0.230431
$386$	41.4958	2.11208
$387$	1.79385	0.0911866
$388$	−45.6257	−2.31630
$389$	−35.4459	−1.79718	−0.898590	−	0.438789i	$-0.855408\pi$
$389$	−35.4459	−1.79718	−0.898590	+	0.438789i	$0.855408\pi$
$390$	12.4436	0.630107
$391$	2.47517	0.125175
$392$	7.80810	0.394368
$393$	2.11202	0.106537
$394$	−40.7742	−2.05417
$395$	−2.01369	−0.101320
$396$	−5.51504	−0.277141
$397$	5.46768	0.274415	0.137207	−	0.990542i	$-0.456187\pi$
$397$	5.46768	0.274415	0.137207	+	0.990542i	$0.456187\pi$
$398$	5.40719	0.271038
$399$	−4.32572	−0.216557
$400$	2.24610	0.112305
$401$	30.3918	1.51769	0.758847	−	0.651269i	$-0.225763\pi$
$401$	30.3918	1.51769	0.758847	+	0.651269i	$0.225763\pi$
$402$	−19.3450	−0.964839
$403$	7.77396	0.387249
$404$	−39.1169	−1.94614
$405$	−2.01369	−0.100061
$406$	2.37654	0.117946
$407$	4.20062	0.208217
$408$	1.33187	0.0659375
$409$	2.68746	0.132886	0.0664431	−	0.997790i	$-0.478835\pi$
$409$	2.68746	0.132886	0.0664431	+	0.997790i	$0.478835\pi$
$410$	10.3631	0.511797
$411$	−0.983899	−0.0485321
$412$	−5.87029	−0.289208
$413$	6.42804	0.316303
$414$	5.31998	0.261463
$415$	−23.1913	−1.13842
$416$	22.3452	1.09556
$417$	0.912949	0.0447073
$418$	18.3523	0.897640
$419$	6.87815	0.336020	0.168010	−	0.985785i	$-0.446266\pi$
$419$	6.87815	0.336020	0.168010	+	0.985785i	$0.446266\pi$
$420$	5.62619	0.274530
$421$	−5.75078	−0.280276	−0.140138	−	0.990132i	$-0.544755\pi$
$421$	−5.75078	−0.280276	−0.140138	+	0.990132i	$0.544755\pi$
$422$	50.3681	2.45188
$423$	−11.4237	−0.555437
$424$	−6.43259	−0.312394
$425$	0.945058	0.0458421
$426$	14.1361	0.684896
$427$	−12.6828	−0.613762
$428$	45.4822	2.19847
$429$	−6.05274	−0.292229
$430$	7.76397	0.374412
$431$	−4.30313	−0.207275	−0.103637	−	0.994615i	$-0.533048\pi$
$431$	−4.30313	−0.207275	−0.103637	+	0.994615i	$0.533048\pi$
$432$	−2.37668	−0.114348
$433$	−12.2968	−0.590946	−0.295473	−	0.955351i	$-0.595477\pi$
$433$	−12.2968	−0.590946	−0.295473	+	0.955351i	$0.595477\pi$
$434$	6.19833	0.297529
$435$	−2.08764	−0.100095
$436$	50.1773	2.40306
$437$	−10.0389	−0.480227
$438$	−17.5108	−0.836697
$439$	−4.40361	−0.210173	−0.105086	−	0.994463i	$-0.533512\pi$
$439$	−4.40361	−0.210173	−0.105086	+	0.994463i	$0.533512\pi$
$440$	−5.64622	−0.269173
$441$	−5.86250	−0.279167
$442$	6.17951	0.293929
$443$	−27.1364	−1.28929	−0.644644	−	0.764483i	$-0.722995\pi$
$443$	−27.1364	−1.28929	−0.644644	+	0.764483i	$0.722995\pi$
$444$	−5.22704	−0.248065
$445$	12.9257	0.612738
$446$	−1.54949	−0.0733707
$447$	−0.245866	−0.0116291
$448$	12.7466	0.602221
$449$	−31.4496	−1.48420	−0.742098	−	0.670291i	$-0.766169\pi$
$449$	−31.4496	−1.48420	−0.742098	+	0.670291i	$0.766169\pi$
$450$	2.03125	0.0957541
$451$	−5.04075	−0.237360
$452$	−33.7451	−1.58724
$453$	−15.4267	−0.724808
$454$	−41.7531	−1.95957
$455$	6.17472	0.289475
$456$	−5.40188	−0.252966
$457$	14.0827	0.658761	0.329380	−	0.944197i	$-0.393160\pi$
$457$	14.0827	0.658761	0.329380	+	0.944197i	$0.393160\pi$
$458$	29.7747	1.39128
$459$	−1.00000	−0.0466760
$460$	13.0570	0.608785
$461$	−8.27182	−0.385257	−0.192628	−	0.981272i	$-0.561701\pi$
$461$	−8.27182	−0.385257	−0.192628	+	0.981272i	$0.561701\pi$
$462$	−4.82597	−0.224524
$463$	4.38083	0.203595	0.101797	−	0.994805i	$-0.467541\pi$
$463$	4.38083	0.203595	0.101797	+	0.994805i	$0.467541\pi$
$464$	−2.46397	−0.114387
$465$	−5.44485	−0.252499
$466$	49.4837	2.29229
$467$	−30.4506	−1.40909	−0.704543	−	0.709661i	$-0.748848\pi$
$467$	−30.4506	−1.40909	−0.704543	+	0.709661i	$0.748848\pi$
$468$	7.53173	0.348154
$469$	−9.59928	−0.443253
$470$	−49.4428	−2.28062
$471$	17.3428	0.799116
$472$	8.02722	0.369483
$473$	−3.77650	−0.173644
$474$	−2.14934	−0.0987225
$475$	−3.83302	−0.175871
$476$	2.79397	0.128061
$477$	4.82974	0.221138
$478$	−42.6805	−1.95216
$479$	1.54930	0.0707892	0.0353946	−	0.999373i	$-0.488731\pi$
$479$	1.54930	0.0707892	0.0353946	+	0.999373i	$0.488731\pi$
$480$	−15.6505	−0.714344
$481$	−5.73666	−0.261569
$482$	7.35949	0.335216
$483$	2.63986	0.120118
$484$	−17.2058	−0.782081
$485$	35.0717	1.59252
$486$	−2.14934	−0.0974961
$487$	18.1009	0.820228	0.410114	−	0.912034i	$-0.365489\pi$
$487$	18.1009	0.820228	0.410114	+	0.912034i	$0.365489\pi$
$488$	−15.8380	−0.716953
$489$	−14.5925	−0.659894
$490$	−25.3735	−1.14626
$491$	35.2261	1.58973	0.794867	−	0.606784i	$-0.207541\pi$
$491$	35.2261	1.58973	0.794867	+	0.606784i	$0.207541\pi$
$492$	6.27246	0.282784
$493$	−1.03673	−0.0466918
$494$	−25.0632	−1.12765
$495$	4.23931	0.190543
$496$	−6.42636	−0.288552
$497$	7.01456	0.314646
$498$	−24.7536	−1.10924
$499$	−7.80890	−0.349574	−0.174787	−	0.984606i	$-0.555924\pi$
$499$	−7.80890	−0.349574	−0.174787	+	0.984606i	$0.555924\pi$
$500$	31.3613	1.40252
$501$	−18.8859	−0.843760
$502$	60.6220	2.70569
$503$	−23.2347	−1.03598	−0.517991	−	0.855386i	$-0.673320\pi$
$503$	−23.2347	−1.03598	−0.517991	+	0.855386i	$0.673320\pi$
$504$	1.42049	0.0632737
$505$	30.0685	1.33803
$506$	−11.1999	−0.497895
$507$	−4.73396	−0.210242
$508$	−15.0379	−0.667197
$509$	35.6734	1.58120	0.790598	−	0.612335i	$-0.209770\pi$
$509$	35.6734	1.58120	0.790598	+	0.612335i	$0.209770\pi$
$510$	−4.32810	−0.191652
$511$	−8.68913	−0.384384
$512$	−24.8026	−1.09613
$513$	4.05585	0.179070
$514$	−31.5996	−1.39380
$515$	4.51238	0.198839
$516$	4.69929	0.206875
$517$	24.0496	1.05770
$518$	−4.57395	−0.200968
$519$	−22.0746	−0.968968
$520$	7.71087	0.338144
$521$	8.36025	0.366269	0.183135	−	0.983088i	$-0.441376\pi$
$521$	8.36025	0.366269	0.183135	+	0.983088i	$0.441376\pi$
$522$	−2.22828	−0.0975291
$523$	−44.7198	−1.95546	−0.977730	−	0.209868i	$-0.932697\pi$
$523$	−44.7198	−1.95546	−0.977730	+	0.209868i	$0.932697\pi$
$524$	5.53278	0.241700
$525$	1.00794	0.0439901
$526$	37.2683	1.62497
$527$	−2.70392	−0.117785
$528$	5.00351	0.217750
$529$	−16.8735	−0.733632
$530$	20.9036	0.907994
$531$	−6.02702	−0.261550
$532$	−11.3319	−0.491302
$533$	6.88400	0.298179
$534$	13.7965	0.597031
$535$	−34.9613	−1.51151
$536$	−11.9874	−0.517777
$537$	−13.5454	−0.584528
$538$	−24.2567	−1.04578
$539$	12.3420	0.531608
$540$	−5.27519	−0.227008
$541$	−40.3958	−1.73675	−0.868376	−	0.495906i	$-0.834836\pi$
$541$	−40.3958	−1.73675	−0.868376	+	0.495906i	$0.834836\pi$
$542$	−7.18894	−0.308792
$543$	16.6051	0.712594
$544$	−7.77205	−0.333224
$545$	−38.5704	−1.65217
$546$	6.59068	0.282055
$547$	−18.9547	−0.810444	−0.405222	−	0.914218i	$-0.632806\pi$
$547$	−18.9547	−0.810444	−0.405222	+	0.914218i	$0.632806\pi$
$548$	−2.57749	−0.110105
$549$	11.8915	0.507518
$550$	−4.27629	−0.182342
$551$	4.20481	0.179131
$552$	3.29661	0.140313
$553$	−1.06654	−0.0453538
$554$	−39.0288	−1.65817
$555$	4.01793	0.170552
$556$	2.39162	0.101427
$557$	−5.73106	−0.242833	−0.121416	−	0.992602i	$-0.538744\pi$
$557$	−5.73106	−0.242833	−0.121416	+	0.992602i	$0.538744\pi$
$558$	−5.81164	−0.246026
$559$	5.15745	0.218137
$560$	−5.10434	−0.215698
$561$	2.10525	0.0888836
$562$	−64.9427	−2.73944
$563$	−25.7894	−1.08689	−0.543446	−	0.839444i	$-0.682881\pi$
$563$	−25.7894	−1.08689	−0.543446	+	0.839444i	$0.682881\pi$
$564$	−29.9262	−1.26012
$565$	25.9393	1.09127
$566$	−42.9773	−1.80647
$567$	−1.06654	−0.0447903
$568$	8.75965	0.367547
$569$	−5.50101	−0.230614	−0.115307	−	0.993330i	$-0.536785\pi$
$569$	−5.50101	−0.230614	−0.115307	+	0.993330i	$0.536785\pi$
$570$	17.5541	0.735262
$571$	−26.3341	−1.10205	−0.551023	−	0.834490i	$-0.685762\pi$
$571$	−26.3341	−1.10205	−0.551023	+	0.834490i	$0.685762\pi$
$572$	−15.8561	−0.662979
$573$	−5.32476	−0.222445
$574$	5.48875	0.229096
$575$	2.33918	0.0975505
$576$	−11.9514	−0.497975
$577$	2.60274	0.108353	0.0541766	−	0.998531i	$-0.482747\pi$
$577$	2.60274	0.108353	0.0541766	+	0.998531i	$0.482747\pi$
$578$	−2.14934	−0.0894008
$579$	−19.3063	−0.802342
$580$	−5.46893	−0.227085
$581$	−12.2831	−0.509591
$582$	37.4343	1.55170
$583$	−10.1678	−0.421107
$584$	−10.8508	−0.449010
$585$	−5.78950	−0.239366
$586$	25.3659	1.04786
$587$	20.5860	0.849674	0.424837	−	0.905270i	$-0.360331\pi$
$587$	20.5860	0.849674	0.424837	+	0.905270i	$0.360331\pi$
$588$	−15.3578	−0.633344
$589$	10.9667	0.451875
$590$	−26.0856	−1.07393
$591$	18.9706	0.780345
$592$	4.74222	0.194904
$593$	10.2383	0.420435	0.210218	−	0.977655i	$-0.432583\pi$
$593$	10.2383	0.420435	0.210218	+	0.977655i	$0.432583\pi$
$594$	4.52489	0.185659
$595$	−2.14767	−0.0880460
$596$	−0.644088	−0.0263829
$597$	−2.51574	−0.102962
$598$	15.2953	0.625473
$599$	30.2754	1.23702	0.618509	−	0.785778i	$-0.287737\pi$
$599$	30.2754	1.23702	0.618509	+	0.785778i	$0.287737\pi$
$600$	1.25870	0.0513861
$601$	21.5842	0.880436	0.440218	−	0.897891i	$-0.354901\pi$
$601$	21.5842	0.880436	0.440218	+	0.897891i	$0.354901\pi$
$602$	4.11214	0.167598
$603$	9.00042	0.366525
$604$	−40.4127	−1.64437
$605$	13.2258	0.537704
$606$	32.0940	1.30373
$607$	−26.6145	−1.08025	−0.540125	−	0.841585i	$-0.681623\pi$
$607$	−26.6145	−1.08025	−0.540125	+	0.841585i	$0.681623\pi$
$608$	31.5223	1.27840
$609$	−1.10571	−0.0448055
$610$	51.4678	2.08387
$611$	−32.8438	−1.32872
$612$	−2.61967	−0.105894
$613$	−36.6910	−1.48193	−0.740967	−	0.671541i	$-0.765633\pi$
$613$	−36.6910	−1.48193	−0.740967	+	0.671541i	$0.765633\pi$
$614$	−31.3849	−1.26659
$615$	−4.82153	−0.194423
$616$	−2.99048	−0.120490
$617$	20.0071	0.805455	0.402727	−	0.915320i	$-0.368062\pi$
$617$	20.0071	0.805455	0.402727	+	0.915320i	$0.368062\pi$
$618$	4.81636	0.193742
$619$	−33.5229	−1.34740	−0.673699	−	0.739006i	$-0.735296\pi$
$619$	−33.5229	−1.34740	−0.673699	+	0.739006i	$0.735296\pi$
$620$	−14.2637	−0.572843
$621$	−2.47517	−0.0993251
$622$	49.8377	1.99831
$623$	6.84602	0.274280
$624$	−6.83314	−0.273545
$625$	−19.3816	−0.775263
$626$	35.7154	1.42748
$627$	−8.53857	−0.340998
$628$	45.4325	1.81295
$629$	1.99531	0.0795582
$630$	−4.61608	−0.183909
$631$	−33.7238	−1.34252	−0.671262	−	0.741221i	$-0.734247\pi$
$631$	−33.7238	−1.34252	−0.671262	+	0.741221i	$0.734247\pi$
$632$	−1.33187	−0.0529790
$633$	−23.4342	−0.931427
$634$	5.17664	0.205591
$635$	11.5593	0.458718
$636$	12.6523	0.501696
$637$	−16.8551	−0.667824
$638$	4.69108	0.185722
$639$	−6.57695	−0.260180
$640$	−20.4260	−0.807407
$641$	0.949755	0.0375131	0.0187565	−	0.999824i	$-0.494029\pi$
$641$	0.949755	0.0375131	0.0187565	+	0.999824i	$0.494029\pi$
$642$	−37.3165	−1.47276
$643$	−33.0803	−1.30456	−0.652280	−	0.757978i	$-0.726187\pi$
$643$	−33.0803	−1.30456	−0.652280	+	0.757978i	$0.726187\pi$
$644$	6.91555	0.272511
$645$	−3.61226	−0.142232
$646$	8.71741	0.342982
$647$	34.6790	1.36337	0.681685	−	0.731646i	$-0.261247\pi$
$647$	34.6790	1.36337	0.681685	+	0.731646i	$0.261247\pi$
$648$	−1.33187	−0.0523209
$649$	12.6884	0.498062
$650$	5.84000	0.229064
$651$	−2.88383	−0.113026
$652$	−38.2274	−1.49710
$653$	32.4660	1.27049	0.635247	−	0.772309i	$-0.280898\pi$
$653$	32.4660	1.27049	0.635247	+	0.772309i	$0.280898\pi$
$654$	−41.1687	−1.60982
$655$	−4.25294	−0.166176
$656$	−5.69067	−0.222183
$657$	8.14705	0.317847
$658$	−26.1870	−1.02088
$659$	−8.06915	−0.314330	−0.157165	−	0.987572i	$-0.550235\pi$
$659$	−8.06915	−0.314330	−0.157165	+	0.987572i	$0.550235\pi$
$660$	11.1056	0.432284
$661$	27.7166	1.07805	0.539025	−	0.842290i	$-0.318793\pi$
$661$	27.7166	1.07805	0.539025	+	0.842290i	$0.318793\pi$
$662$	33.8982	1.31749
$663$	−2.87507	−0.111659
$664$	−15.3390	−0.595267
$665$	8.71065	0.337784
$666$	4.28860	0.166180
$667$	−2.56607	−0.0993588
$668$	−49.4748	−1.91424
$669$	0.720916	0.0278722
$670$	38.9547	1.50495
$671$	−25.0346	−0.966451
$672$	−8.28918	−0.319762
$673$	28.7482	1.10816	0.554082	−	0.832462i	$-0.313070\pi$
$673$	28.7482	1.10816	0.554082	+	0.832462i	$0.313070\pi$
$674$	63.0304	2.42784
$675$	−0.945058	−0.0363753
$676$	−12.4014	−0.476976
$677$	−36.4061	−1.39920	−0.699600	−	0.714535i	$-0.746638\pi$
$677$	−36.4061	−1.39920	−0.699600	+	0.714535i	$0.746638\pi$
$678$	27.6867	1.06330
$679$	18.5755	0.712861
$680$	−2.68198	−0.102849
$681$	19.4260	0.744407
$682$	12.2349	0.468500
$683$	49.2402	1.88412	0.942062	−	0.335440i	$-0.108885\pi$
$683$	49.2402	1.88412	0.942062	+	0.335440i	$0.108885\pi$
$684$	10.6250	0.406256
$685$	1.98127	0.0757003
$686$	−29.4854	−1.12576
$687$	−13.8529	−0.528522
$688$	−4.26342	−0.162541
$689$	13.8858	0.529009
$690$	−10.7128	−0.407829
$691$	5.81168	0.221087	0.110543	−	0.993871i	$-0.464741\pi$
$691$	5.81168	0.221087	0.110543	+	0.993871i	$0.464741\pi$
$692$	−57.8281	−2.19829
$693$	2.24532	0.0852928
$694$	53.4583	2.02925
$695$	−1.83839	−0.0697343
$696$	−1.38079	−0.0523386
$697$	−2.39437	−0.0906934
$698$	44.0658	1.66792
$699$	−23.0227	−0.870800
$700$	2.64046	0.0998002
$701$	−21.6088	−0.816153	−0.408076	−	0.912948i	$-0.633800\pi$
$701$	−21.6088	−0.816153	−0.408076	+	0.912948i	$0.633800\pi$
$702$	−6.17951	−0.233231
$703$	−8.09268	−0.305221
$704$	25.1607	0.948279
$705$	23.0037	0.866369
$706$	61.0964	2.29939
$707$	15.9256	0.598943
$708$	−15.7888	−0.593378
$709$	−44.6326	−1.67621	−0.838107	−	0.545506i	$-0.816338\pi$
$709$	−44.6326	−1.67621	−0.838107	+	0.545506i	$0.816338\pi$
$710$	−28.4657	−1.06830
$711$	1.00000	0.0375029
$712$	8.54919	0.320394
$713$	−6.69265	−0.250642
$714$	−2.29235	−0.0857891
$715$	12.1883	0.455818
$716$	−35.4845	−1.32612
$717$	19.8575	0.741592
$718$	16.8948	0.630507
$719$	−49.3086	−1.83890	−0.919450	−	0.393206i	$-0.871366\pi$
$719$	−49.3086	−1.83890	−0.919450	+	0.393206i	$0.871366\pi$
$720$	4.78590	0.178360
$721$	2.38995	0.0890065
$722$	5.48094	0.203980
$723$	−3.42407	−0.127342
$724$	43.4999	1.61666
$725$	−0.979767	−0.0363876
$726$	14.1167	0.523921
$727$	−36.1192	−1.33959	−0.669793	−	0.742548i	$-0.733617\pi$
$727$	−36.1192	−1.33959	−0.669793	+	0.742548i	$0.733617\pi$
$728$	4.08401	0.151364
$729$	1.00000	0.0370370
$730$	35.2613	1.30508
$731$	−1.79385	−0.0663480
$732$	31.1518	1.15141
$733$	−19.0067	−0.702030	−0.351015	−	0.936370i	$-0.614163\pi$
$733$	−19.0067	−0.702030	−0.351015	+	0.936370i	$0.614163\pi$
$734$	−25.0615	−0.925038
$735$	11.8052	0.435443
$736$	−19.2371	−0.709090
$737$	−18.9481	−0.697962
$738$	−5.14633	−0.189439
$739$	4.73271	0.174096	0.0870478	−	0.996204i	$-0.472257\pi$
$739$	4.73271	0.174096	0.0870478	+	0.996204i	$0.472257\pi$
$740$	10.5256	0.386930
$741$	11.6609	0.428373
$742$	11.0715	0.406446
$743$	13.0082	0.477224	0.238612	−	0.971115i	$-0.423308\pi$
$743$	13.0082	0.477224	0.238612	+	0.971115i	$0.423308\pi$
$744$	−3.60127	−0.132029
$745$	0.495098	0.0181390
$746$	−3.50964	−0.128497
$747$	11.5168	0.421379
$748$	5.51504	0.201650
$749$	−18.5170	−0.676598
$750$	−25.7308	−0.939557
$751$	−11.5496	−0.421452	−0.210726	−	0.977545i	$-0.567583\pi$
$751$	−11.5496	−0.421452	−0.210726	+	0.977545i	$0.567583\pi$
$752$	27.1504	0.990074
$753$	−28.2049	−1.02784
$754$	−6.40646	−0.233310
$755$	31.0645	1.13055
$756$	−2.79397	−0.101616
$757$	28.5624	1.03812	0.519059	−	0.854738i	$-0.326282\pi$
$757$	28.5624	1.03812	0.519059	+	0.854738i	$0.326282\pi$
$758$	48.0331	1.74464
$759$	5.21084	0.189142
$760$	10.8777	0.394576
$761$	−12.0492	−0.436785	−0.218392	−	0.975861i	$-0.570081\pi$
$761$	−12.0492	−0.436785	−0.218392	+	0.975861i	$0.570081\pi$
$762$	12.3380	0.446959
$763$	−20.4286	−0.739563
$764$	−13.9491	−0.504661
$765$	2.01369	0.0728051
$766$	24.3312	0.879123
$767$	−17.3281	−0.625682
$768$	2.10086	0.0758083
$769$	−3.28799	−0.118568	−0.0592840	−	0.998241i	$-0.518882\pi$
$769$	−3.28799	−0.118568	−0.0592840	+	0.998241i	$0.518882\pi$
$770$	9.71799	0.350212
$771$	14.7020	0.529479
$772$	−50.5760	−1.82027
$773$	39.4146	1.41764	0.708822	−	0.705387i	$-0.249227\pi$
$773$	39.4146	1.41764	0.708822	+	0.705387i	$0.249227\pi$
$774$	−3.85560	−0.138587
$775$	−2.55536	−0.0917913
$776$	23.1967	0.832713
$777$	2.12807	0.0763442
$778$	76.1854	2.73138
$779$	9.71123	0.347941
$780$	−15.1666	−0.543050
$781$	13.8461	0.495452
$782$	−5.31998	−0.190242
$783$	1.03673	0.0370496
$784$	13.9333	0.497618
$785$	−34.9231	−1.24646
$786$	−4.53944	−0.161917
$787$	34.8136	1.24097	0.620486	−	0.784218i	$-0.286935\pi$
$787$	34.8136	1.24097	0.620486	+	0.784218i	$0.286935\pi$
$788$	49.6965	1.77037
$789$	−17.3394	−0.617299
$790$	4.32810	0.153987
$791$	13.7386	0.488487
$792$	2.80392	0.0996329
$793$	34.1890	1.21409
$794$	−11.7519	−0.417059
$795$	−9.72559	−0.344931
$796$	−6.59040	−0.233591
$797$	−34.4533	−1.22040	−0.610199	−	0.792248i	$-0.708911\pi$
$797$	−34.4533	−1.22040	−0.610199	+	0.792248i	$0.708911\pi$
$798$	9.29744	0.329126
$799$	11.4237	0.404140
$800$	−7.34504	−0.259686
$801$	−6.41893	−0.226802
$802$	−65.3223	−2.30661
$803$	−17.1515	−0.605265
$804$	23.5781	0.831535
$805$	−5.31585	−0.187359
$806$	−16.7089	−0.588546
$807$	11.2856	0.397274
$808$	19.8876	0.699642
$809$	38.5445	1.35515	0.677576	−	0.735453i	$-0.263031\pi$
$809$	38.5445	1.35515	0.677576	+	0.735453i	$0.263031\pi$
$810$	4.32810	0.152074
$811$	12.3404	0.433328	0.216664	−	0.976246i	$-0.430482\pi$
$811$	12.3404	0.433328	0.216664	+	0.976246i	$0.430482\pi$
$812$	−2.89658	−0.101650
$813$	3.34472	0.117304
$814$	−9.02856	−0.316451
$815$	29.3847	1.02930
$816$	2.37668	0.0832006
$817$	7.27559	0.254541
$818$	−5.77627	−0.201962
$819$	−3.06637	−0.107148
$820$	−12.6308	−0.441086
$821$	−17.1494	−0.598520	−0.299260	−	0.954172i	$-0.596740\pi$
$821$	−17.1494	−0.598520	−0.299260	+	0.954172i	$0.596740\pi$
$822$	2.11473	0.0737598
$823$	41.5041	1.44674	0.723370	−	0.690460i	$-0.242592\pi$
$823$	41.5041	1.44674	0.723370	+	0.690460i	$0.242592\pi$
$824$	2.98453	0.103971
$825$	1.98958	0.0692683
$826$	−13.8160	−0.480722
$827$	51.4961	1.79069	0.895347	−	0.445369i	$-0.146928\pi$
$827$	51.4961	1.79069	0.895347	+	0.445369i	$0.146928\pi$
$828$	−6.48411	−0.225339
$829$	−4.86936	−0.169120	−0.0845599	−	0.996418i	$-0.526948\pi$
$829$	−4.86936	−0.169120	−0.0845599	+	0.996418i	$0.526948\pi$
$830$	49.8461	1.73018
$831$	18.1585	0.629911
$832$	−34.3612	−1.19126
$833$	5.86250	0.203124
$834$	−1.96224	−0.0679468
$835$	38.0303	1.31609
$836$	−22.3682	−0.773620
$837$	2.70392	0.0934611
$838$	−14.7835	−0.510687
$839$	42.2692	1.45930	0.729648	−	0.683823i	$-0.239684\pi$
$839$	42.2692	1.45930	0.729648	+	0.683823i	$0.239684\pi$
$840$	−2.86043	−0.0986941
$841$	−27.9252	−0.962938
$842$	12.3604	0.425967
$843$	30.2152	1.04067
$844$	−61.3898	−2.11312
$845$	9.53272	0.327935
$846$	24.5533	0.844161
$847$	7.00495	0.240693
$848$	−11.4788	−0.394182
$849$	19.9956	0.686246
$850$	−2.03125	−0.0696714
$851$	4.93873	0.169297
$852$	−17.2294	−0.590270
$853$	36.5858	1.25268	0.626338	−	0.779552i	$-0.284553\pi$
$853$	36.5858	1.25268	0.626338	+	0.779552i	$0.284553\pi$
$854$	27.2596	0.932804
$855$	−8.16722	−0.279313
$856$	−23.1237	−0.790353
$857$	31.8095	1.08659	0.543296	−	0.839541i	$-0.317176\pi$
$857$	31.8095	1.08659	0.543296	+	0.839541i	$0.317176\pi$
$858$	13.0094	0.444133
$859$	−8.78783	−0.299837	−0.149918	−	0.988698i	$-0.547901\pi$
$859$	−8.78783	−0.299837	−0.149918	+	0.988698i	$0.547901\pi$
$860$	−9.46290	−0.322682
$861$	−2.55369	−0.0870295
$862$	9.24889	0.315019
$863$	23.4079	0.796813	0.398407	−	0.917209i	$-0.369563\pi$
$863$	23.4079	0.796813	0.398407	+	0.917209i	$0.369563\pi$
$864$	7.77205	0.264410
$865$	44.4514	1.51139
$866$	26.4300	0.898127
$867$	1.00000	0.0339618
$868$	−7.55467	−0.256422
$869$	−2.10525	−0.0714156
$870$	4.48706	0.152126
$871$	25.8769	0.876804
$872$	−25.5108	−0.863905
$873$	−17.4166	−0.589463
$874$	21.5771	0.729855
$875$	−12.7680	−0.431639
$876$	21.3425	0.721097
$877$	11.5381	0.389614	0.194807	−	0.980842i	$-0.437592\pi$
$877$	11.5381	0.389614	0.194807	+	0.980842i	$0.437592\pi$
$878$	9.46486	0.319423
$879$	−11.8017	−0.398062
$880$	−10.0755	−0.339645
$881$	−33.8501	−1.14044	−0.570220	−	0.821492i	$-0.693142\pi$
$881$	−33.8501	−1.14044	−0.570220	+	0.821492i	$0.693142\pi$
$882$	12.6005	0.424281
$883$	21.8777	0.736245	0.368122	−	0.929777i	$-0.380001\pi$
$883$	21.8777	0.736245	0.368122	+	0.929777i	$0.380001\pi$
$884$	−7.53173	−0.253319
$885$	12.1365	0.407965
$886$	58.3253	1.95948
$887$	9.98542	0.335278	0.167639	−	0.985848i	$-0.446386\pi$
$887$	9.98542	0.335278	0.167639	+	0.985848i	$0.446386\pi$
$888$	2.65750	0.0891798
$889$	6.12232	0.205336
$890$	−27.7818	−0.931247
$891$	−2.10525	−0.0705284
$892$	1.88856	0.0632337
$893$	−46.3327	−1.55046
$894$	0.528451	0.0176740
$895$	27.2763	0.911745
$896$	−10.8185	−0.361420
$897$	−7.11629	−0.237606
$898$	67.5958	2.25570
$899$	2.80322	0.0934928
$900$	−2.47574	−0.0825245
$901$	−4.82974	−0.160902
$902$	10.8343	0.360742
$903$	−1.91321	−0.0636676
$904$	17.1565	0.570616
$905$	−33.4376	−1.11150
$906$	33.1572	1.10157
$907$	9.30284	0.308896	0.154448	−	0.988001i	$-0.450640\pi$
$907$	9.30284	0.308896	0.154448	+	0.988001i	$0.450640\pi$
$908$	50.8897	1.68883
$909$	−14.9320	−0.495264
$910$	−13.2716	−0.439948
$911$	34.4975	1.14295	0.571476	−	0.820618i	$-0.306371\pi$
$911$	34.4975	1.14295	0.571476	+	0.820618i	$0.306371\pi$
$912$	−9.63948	−0.319195
$913$	−24.2458	−0.802419
$914$	−30.2685	−1.00119
$915$	−23.9459	−0.791625
$916$	−36.2900	−1.19906
$917$	−2.25254	−0.0743856
$918$	2.14934	0.0709388
$919$	34.0805	1.12421	0.562106	−	0.827065i	$-0.309991\pi$
$919$	34.0805	1.12421	0.562106	+	0.827065i	$0.309991\pi$
$920$	−6.63834	−0.218860
$921$	14.6021	0.481155
$922$	17.7790	0.585519
$923$	−18.9092	−0.622404
$924$	5.88200	0.193504
$925$	1.88568	0.0620009
$926$	−9.41590	−0.309426
$927$	−2.24085	−0.0735993
$928$	8.05749	0.264500
$929$	−58.3379	−1.91400	−0.957002	−	0.290082i	$-0.906317\pi$
$929$	−58.3379	−1.91400	−0.957002	+	0.290082i	$0.906317\pi$
$930$	11.7028	0.383751
$931$	−23.7774	−0.779274
$932$	−60.3119	−1.97558
$933$	−23.1875	−0.759123
$934$	65.4487	2.14155
$935$	−4.23931	−0.138640
$936$	−3.82923	−0.125162
$937$	35.5104	1.16007	0.580037	−	0.814590i	$-0.303038\pi$
$937$	35.5104	1.16007	0.580037	+	0.814590i	$0.303038\pi$
$938$	20.6321	0.673663
$939$	−16.6169	−0.542273
$940$	60.2620	1.96553
$941$	48.3898	1.57746	0.788730	−	0.614739i	$-0.210739\pi$
$941$	48.3898	1.57746	0.788730	+	0.614739i	$0.210739\pi$
$942$	−37.2757	−1.21451
$943$	−5.92648	−0.192993
$944$	14.3243	0.466217
$945$	2.14767	0.0698638
$946$	8.11698	0.263906
$947$	48.7826	1.58522	0.792611	−	0.609728i	$-0.208721\pi$
$947$	48.7826	1.58522	0.792611	+	0.609728i	$0.208721\pi$
$948$	2.61967	0.0850828
$949$	23.4233	0.760354
$950$	8.23846	0.267291
$951$	−2.40848	−0.0781003
$952$	−1.42049	−0.0460384
$953$	−10.3865	−0.336450	−0.168225	−	0.985749i	$-0.553804\pi$
$953$	−10.3865	−0.336450	−0.168225	+	0.985749i	$0.553804\pi$
$954$	−10.3808	−0.336089
$955$	10.7224	0.346969
$956$	52.0200	1.68245
$957$	−2.18257	−0.0705523
$958$	−3.32997	−0.107586
$959$	1.04936	0.0338857
$960$	24.0664	0.776740
$961$	−23.6888	−0.764156
$962$	12.3300	0.397536
$963$	17.3618	0.559477
$964$	−8.96991	−0.288901
$965$	38.8769	1.25149
$966$	−5.67396	−0.182557
$967$	−27.7721	−0.893091	−0.446546	−	0.894761i	$-0.647346\pi$
$967$	−27.7721	−0.893091	−0.446546	+	0.894761i	$0.647346\pi$
$968$	8.74765	0.281160
$969$	−4.05585	−0.130293
$970$	−75.3809	−2.42034
$971$	−12.6377	−0.405563	−0.202782	−	0.979224i	$-0.564998\pi$
$971$	−12.6377	−0.405563	−0.202782	+	0.979224i	$0.564998\pi$
$972$	2.61967	0.0840258
$973$	−0.973694	−0.0312152
$974$	−38.9049	−1.24659
$975$	−2.71711	−0.0870172
$976$	−28.2624	−0.904658
$977$	−14.8647	−0.475563	−0.237781	−	0.971319i	$-0.576420\pi$
$977$	−14.8647	−0.475563	−0.237781	+	0.971319i	$0.576420\pi$
$978$	31.3642	1.00292
$979$	13.5134	0.431891
$980$	30.9258	0.987888
$981$	19.1541	0.611543
$982$	−75.7130	−2.41610
$983$	49.6867	1.58476	0.792381	−	0.610027i	$-0.208841\pi$
$983$	49.6867	1.58476	0.792381	+	0.610027i	$0.208841\pi$
$984$	−3.18900	−0.101662
$985$	−38.2008	−1.21718
$986$	2.22828	0.0709629
$987$	12.1838	0.387813
$988$	30.5476	0.971848
$989$	−4.44008	−0.141186
$990$	−9.11173	−0.289590
$991$	−32.1867	−1.02244	−0.511222	−	0.859449i	$-0.670807\pi$
$991$	−32.1867	−1.02244	−0.511222	+	0.859449i	$0.670807\pi$
$992$	21.0150	0.667226
$993$	−15.7714	−0.500491
$994$	−15.0767	−0.478203
$995$	5.06592	0.160600
$996$	30.1703	0.955982
$997$	31.8794	1.00963	0.504815	−	0.863228i	$-0.331561\pi$
$997$	31.8794	1.00963	0.504815	+	0.863228i	$0.331561\pi$
$998$	16.7840	0.531288
$999$	−1.99531	−0.0631288

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.h.1.5	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.h.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-2.14934 q^{2} +1.00000 q^{3} +2.61967 q^{4} -2.01369 q^{5} -2.14934 q^{6} -1.06654 q^{7} -1.33187 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.14934 q^{2} +1.00000 q^{3} +2.61967 q^{4} -2.01369 q^{5} -2.14934 q^{6} -1.06654 q^{7} -1.33187 q^{8} +1.00000 q^{9} +4.32810 q^{10} -2.10525 q^{11} +2.61967 q^{12} +2.87507 q^{13} +2.29235 q^{14} -2.01369 q^{15} -2.37668 q^{16} -1.00000 q^{17} -2.14934 q^{18} +4.05585 q^{19} -5.27519 q^{20} -1.06654 q^{21} +4.52489 q^{22} -2.47517 q^{23} -1.33187 q^{24} -0.945058 q^{25} -6.17951 q^{26} +1.00000 q^{27} -2.79397 q^{28} +1.03673 q^{29} +4.32810 q^{30} +2.70392 q^{31} +7.77205 q^{32} -2.10525 q^{33} +2.14934 q^{34} +2.14767 q^{35} +2.61967 q^{36} -1.99531 q^{37} -8.71741 q^{38} +2.87507 q^{39} +2.68198 q^{40} +2.39437 q^{41} +2.29235 q^{42} +1.79385 q^{43} -5.51504 q^{44} -2.01369 q^{45} +5.31998 q^{46} -11.4237 q^{47} -2.37668 q^{48} -5.86250 q^{49} +2.03125 q^{50} -1.00000 q^{51} +7.53173 q^{52} +4.82974 q^{53} -2.14934 q^{54} +4.23931 q^{55} +1.42049 q^{56} +4.05585 q^{57} -2.22828 q^{58} -6.02702 q^{59} -5.27519 q^{60} +11.8915 q^{61} -5.81164 q^{62} -1.06654 q^{63} -11.9514 q^{64} -5.78950 q^{65} +4.52489 q^{66} +9.00042 q^{67} -2.61967 q^{68} -2.47517 q^{69} -4.61608 q^{70} -6.57695 q^{71} -1.33187 q^{72} +8.14705 q^{73} +4.28860 q^{74} -0.945058 q^{75} +10.6250 q^{76} +2.24532 q^{77} -6.17951 q^{78} +1.00000 q^{79} +4.78590 q^{80} +1.00000 q^{81} -5.14633 q^{82} +11.5168 q^{83} -2.79397 q^{84} +2.01369 q^{85} -3.85560 q^{86} +1.03673 q^{87} +2.80392 q^{88} -6.41893 q^{89} +4.32810 q^{90} -3.06637 q^{91} -6.48411 q^{92} +2.70392 q^{93} +24.5533 q^{94} -8.16722 q^{95} +7.77205 q^{96} -17.4166 q^{97} +12.6005 q^{98} -2.10525 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9	\( 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9} - 9 q^{10} - 19 q^{11} + 21 q^{12} - 12 q^{13} - 15 q^{14} - 12 q^{15} + q^{16} - 25 q^{17} - 7 q^{18} - 35 q^{19} - 11 q^{20} - 4 q^{21} - 2 q^{22} - 16 q^{23} - 21 q^{24} + 19 q^{25} - 5 q^{26} + 25 q^{27} + 3 q^{28} - 37 q^{29} - 9 q^{30} - 28 q^{31} - 19 q^{32} - 19 q^{33} + 7 q^{34} - 42 q^{35} + 21 q^{36} + 8 q^{37} - 35 q^{38} - 12 q^{39} - 9 q^{40} - 34 q^{41} - 15 q^{42} - 19 q^{43} - 56 q^{44} - 12 q^{45} + q^{46} - 25 q^{47} + q^{48} + 25 q^{49} - 7 q^{50} - 25 q^{51} - 37 q^{52} - 44 q^{53} - 7 q^{54} - 11 q^{55} - 18 q^{56} - 35 q^{57} - 3 q^{58} - 47 q^{59} - 11 q^{60} - 28 q^{61} + 11 q^{62} - 4 q^{63} - 9 q^{64} - 63 q^{65} - 2 q^{66} - 28 q^{67} - 21 q^{68} - 16 q^{69} + 5 q^{70} - 27 q^{71} - 21 q^{72} - 21 q^{73} - 18 q^{74} + 19 q^{75} - 50 q^{76} - 58 q^{77} - 5 q^{78} + 25 q^{79} - 56 q^{80} + 25 q^{81} - 5 q^{82} - 61 q^{83} + 3 q^{84} + 12 q^{85} - 28 q^{86} - 37 q^{87} + 15 q^{88} - 34 q^{89} - 9 q^{90} - 30 q^{91} - 31 q^{92} - 28 q^{93} + q^{94} - 32 q^{95} - 19 q^{96} - 11 q^{97} - 66 q^{98} - 19 q^{99}+O(q^{100}) \) 25 * q - 7 * q^2 + 25 * q^3 + 21 * q^4 - 12 * q^5 - 7 * q^6 - 4 * q^7 - 21 * q^8 + 25 * q^9 - 9 * q^10 - 19 * q^11 + 21 * q^12 - 12 * q^13 - 15 * q^14 - 12 * q^15 + q^16 - 25 * q^17 - 7 * q^18 - 35 * q^19 - 11 * q^20 - 4 * q^21 - 2 * q^22 - 16 * q^23 - 21 * q^24 + 19 * q^25 - 5 * q^26 + 25 * q^27 + 3 * q^28 - 37 * q^29 - 9 * q^30 - 28 * q^31 - 19 * q^32 - 19 * q^33 + 7 * q^34 - 42 * q^35 + 21 * q^36 + 8 * q^37 - 35 * q^38 - 12 * q^39 - 9 * q^40 - 34 * q^41 - 15 * q^42 - 19 * q^43 - 56 * q^44 - 12 * q^45 + q^46 - 25 * q^47 + q^48 + 25 * q^49 - 7 * q^50 - 25 * q^51 - 37 * q^52 - 44 * q^53 - 7 * q^54 - 11 * q^55 - 18 * q^56 - 35 * q^57 - 3 * q^58 - 47 * q^59 - 11 * q^60 - 28 * q^61 + 11 * q^62 - 4 * q^63 - 9 * q^64 - 63 * q^65 - 2 * q^66 - 28 * q^67 - 21 * q^68 - 16 * q^69 + 5 * q^70 - 27 * q^71 - 21 * q^72 - 21 * q^73 - 18 * q^74 + 19 * q^75 - 50 * q^76 - 58 * q^77 - 5 * q^78 + 25 * q^79 - 56 * q^80 + 25 * q^81 - 5 * q^82 - 61 * q^83 + 3 * q^84 + 12 * q^85 - 28 * q^86 - 37 * q^87 + 15 * q^88 - 34 * q^89 - 9 * q^90 - 30 * q^91 - 31 * q^92 - 28 * q^93 + q^94 - 32 * q^95 - 19 * q^96 - 11 * q^97 - 66 * q^98 - 19 * q^99

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