LMFDB - Embedded newform 1027.2.a.e.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1027,2,Mod(1,1027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1027, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1027 = 13 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1027.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:	$8.20063628759$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	1027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.313275 q^{2} +0.248152 q^{3} -1.90186 q^{4} -3.52042 q^{5} -0.0777396 q^{6} -3.93567 q^{7} +1.22235 q^{8} -2.93842 q^{9} +O(q^{10})$	\(q-0.313275 q^{2} +0.248152 q^{3} -1.90186 q^{4} -3.52042 q^{5} -0.0777396 q^{6} -3.93567 q^{7} +1.22235 q^{8} -2.93842 q^{9} +1.10286 q^{10} -2.24919 q^{11} -0.471949 q^{12} -1.00000 q^{13} +1.23295 q^{14} -0.873597 q^{15} +3.42079 q^{16} +5.61013 q^{17} +0.920533 q^{18} -4.47858 q^{19} +6.69533 q^{20} -0.976642 q^{21} +0.704616 q^{22} -3.96564 q^{23} +0.303329 q^{24} +7.39333 q^{25} +0.313275 q^{26} -1.47363 q^{27} +7.48509 q^{28} +0.549577 q^{29} +0.273676 q^{30} +6.23792 q^{31} -3.51635 q^{32} -0.558141 q^{33} -1.75751 q^{34} +13.8552 q^{35} +5.58846 q^{36} +5.16214 q^{37} +1.40303 q^{38} -0.248152 q^{39} -4.30319 q^{40} -4.91563 q^{41} +0.305957 q^{42} -7.56404 q^{43} +4.27765 q^{44} +10.3445 q^{45} +1.24234 q^{46} -4.39448 q^{47} +0.848873 q^{48} +8.48948 q^{49} -2.31614 q^{50} +1.39216 q^{51} +1.90186 q^{52} +5.11605 q^{53} +0.461651 q^{54} +7.91810 q^{55} -4.81078 q^{56} -1.11137 q^{57} -0.172169 q^{58} -12.6055 q^{59} +1.66146 q^{60} +8.07278 q^{61} -1.95418 q^{62} +11.5646 q^{63} -5.73999 q^{64} +3.52042 q^{65} +0.174852 q^{66} +1.00118 q^{67} -10.6697 q^{68} -0.984081 q^{69} -4.34048 q^{70} -1.73233 q^{71} -3.59179 q^{72} -15.8128 q^{73} -1.61717 q^{74} +1.83467 q^{75} +8.51764 q^{76} +8.85208 q^{77} +0.0777396 q^{78} +1.00000 q^{79} -12.0426 q^{80} +8.44958 q^{81} +1.53994 q^{82} +13.8048 q^{83} +1.85744 q^{84} -19.7500 q^{85} +2.36962 q^{86} +0.136378 q^{87} -2.74931 q^{88} +9.74322 q^{89} -3.24066 q^{90} +3.93567 q^{91} +7.54209 q^{92} +1.54795 q^{93} +1.37668 q^{94} +15.7665 q^{95} -0.872589 q^{96} -16.5846 q^{97} -2.65954 q^{98} +6.60908 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 8 q^{2} + 4 q^{3} + 26 q^{4} + 5 q^{5} + 2 q^{6} + 4 q^{7} + 24 q^{8} + 30 q^{9}+O(q^{10}) $ 22 * q + 8 * q^2 + 4 * q^3 + 26 * q^4 + 5 * q^5 + 2 * q^6 + 4 * q^7 + 24 * q^8 + 30 * q^9	\( 22 q + 8 q^{2} + 4 q^{3} + 26 q^{4} + 5 q^{5} + 2 q^{6} + 4 q^{7} + 24 q^{8} + 30 q^{9} + 4 q^{10} + 6 q^{11} + 11 q^{12} - 22 q^{13} + 6 q^{14} + 4 q^{15} + 42 q^{16} + 23 q^{17} + 27 q^{18} - 3 q^{19} + 11 q^{20} + 10 q^{21} + 14 q^{22} + 25 q^{23} + 18 q^{24} + 29 q^{25} - 8 q^{26} + 13 q^{27} + q^{28} + 44 q^{29} - 46 q^{30} - 9 q^{31} + 61 q^{32} + 8 q^{33} + 2 q^{34} + 14 q^{35} + 36 q^{36} + 22 q^{37} - 3 q^{38} - 4 q^{39} - 23 q^{41} - 27 q^{42} + 7 q^{43} - 9 q^{44} + 24 q^{45} + 28 q^{46} - 19 q^{47} + 25 q^{48} + 42 q^{49} + 28 q^{50} + 2 q^{51} - 26 q^{52} + 69 q^{53} - 16 q^{54} + 12 q^{55} - 11 q^{56} + 23 q^{57} + 14 q^{58} + q^{59} - 54 q^{60} + 22 q^{61} + 24 q^{62} + 47 q^{63} + 12 q^{64} - 5 q^{65} - 32 q^{66} + 53 q^{68} + 4 q^{69} - 77 q^{70} + 6 q^{71} + 80 q^{72} - 5 q^{73} + 74 q^{74} + 46 q^{75} - 46 q^{76} + 67 q^{77} - 2 q^{78} + 22 q^{79} - 16 q^{80} - 14 q^{81} - 66 q^{82} + 23 q^{83} - 37 q^{84} + 35 q^{85} - 53 q^{86} + 24 q^{87} + 26 q^{88} - 26 q^{89} - 34 q^{90} - 4 q^{91} + 60 q^{92} + 5 q^{93} - 40 q^{94} + 47 q^{95} - 16 q^{96} + 4 q^{97} + 31 q^{98} - 74 q^{99}+O(q^{100}) \) 22 * q + 8 * q^2 + 4 * q^3 + 26 * q^4 + 5 * q^5 + 2 * q^6 + 4 * q^7 + 24 * q^8 + 30 * q^9 + 4 * q^10 + 6 * q^11 + 11 * q^12 - 22 * q^13 + 6 * q^14 + 4 * q^15 + 42 * q^16 + 23 * q^17 + 27 * q^18 - 3 * q^19 + 11 * q^20 + 10 * q^21 + 14 * q^22 + 25 * q^23 + 18 * q^24 + 29 * q^25 - 8 * q^26 + 13 * q^27 + q^28 + 44 * q^29 - 46 * q^30 - 9 * q^31 + 61 * q^32 + 8 * q^33 + 2 * q^34 + 14 * q^35 + 36 * q^36 + 22 * q^37 - 3 * q^38 - 4 * q^39 - 23 * q^41 - 27 * q^42 + 7 * q^43 - 9 * q^44 + 24 * q^45 + 28 * q^46 - 19 * q^47 + 25 * q^48 + 42 * q^49 + 28 * q^50 + 2 * q^51 - 26 * q^52 + 69 * q^53 - 16 * q^54 + 12 * q^55 - 11 * q^56 + 23 * q^57 + 14 * q^58 + q^59 - 54 * q^60 + 22 * q^61 + 24 * q^62 + 47 * q^63 + 12 * q^64 - 5 * q^65 - 32 * q^66 + 53 * q^68 + 4 * q^69 - 77 * q^70 + 6 * q^71 + 80 * q^72 - 5 * q^73 + 74 * q^74 + 46 * q^75 - 46 * q^76 + 67 * q^77 - 2 * q^78 + 22 * q^79 - 16 * q^80 - 14 * q^81 - 66 * q^82 + 23 * q^83 - 37 * q^84 + 35 * q^85 - 53 * q^86 + 24 * q^87 + 26 * q^88 - 26 * q^89 - 34 * q^90 - 4 * q^91 + 60 * q^92 + 5 * q^93 - 40 * q^94 + 47 * q^95 - 16 * q^96 + 4 * q^97 + 31 * q^98 - 74 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.313275	−0.221519	−0.110759	−	0.993847i	$-0.535328\pi$
$2$	−0.313275	−0.221519	−0.110759	+	0.993847i	$0.535328\pi$
$3$	0.248152	0.143270	0.0716352	−	0.997431i	$-0.477178\pi$
$3$	0.248152	0.143270	0.0716352	+	0.997431i	$0.477178\pi$
$4$	−1.90186	−0.950929
$5$	−3.52042	−1.57438	−0.787189	−	0.616712i	$-0.788464\pi$
$5$	−3.52042	−1.57438	−0.787189	+	0.616712i	$0.788464\pi$
$6$	−0.0777396	−0.0317371
$7$	−3.93567	−1.48754	−0.743771	−	0.668434i	$-0.766965\pi$
$7$	−3.93567	−1.48754	−0.743771	+	0.668434i	$0.766965\pi$
$8$	1.22235	0.432167
$9$	−2.93842	−0.979474
$10$	1.10286	0.348754
$11$	−2.24919	−0.678158	−0.339079	−	0.940758i	$-0.610115\pi$
$11$	−2.24919	−0.678158	−0.339079	+	0.940758i	$0.610115\pi$
$12$	−0.471949	−0.136240
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	1.23295	0.329518
$15$	−0.873597	−0.225562
$16$	3.42079	0.855196
$17$	5.61013	1.36066	0.680328	−	0.732907i	$-0.261837\pi$
$17$	5.61013	1.36066	0.680328	+	0.732907i	$0.261837\pi$
$18$	0.920533	0.216972
$19$	−4.47858	−1.02746	−0.513729	−	0.857953i	$-0.671736\pi$
$19$	−4.47858	−1.02746	−0.513729	+	0.857953i	$0.671736\pi$
$20$	6.69533	1.49712
$21$	−0.976642	−0.213121
$22$	0.704616	0.150225
$23$	−3.96564	−0.826894	−0.413447	−	0.910528i	$-0.635675\pi$
$23$	−3.96564	−0.826894	−0.413447	+	0.910528i	$0.635675\pi$
$24$	0.303329	0.0619168
$25$	7.39333	1.47867
$26$	0.313275	0.0614382
$27$	−1.47363	−0.283600
$28$	7.48509	1.41455
$29$	0.549577	0.102054	0.0510270	−	0.998697i	$-0.483751\pi$
$29$	0.549577	0.102054	0.0510270	+	0.998697i	$0.483751\pi$
$30$	0.273676	0.0499661
$31$	6.23792	1.12036	0.560182	−	0.828370i	$-0.310731\pi$
$31$	6.23792	1.12036	0.560182	+	0.828370i	$0.310731\pi$
$32$	−3.51635	−0.621609
$33$	−0.558141	−0.0971599
$34$	−1.75751	−0.301411
$35$	13.8552	2.34195
$36$	5.58846	0.931410
$37$	5.16214	0.848650	0.424325	−	0.905510i	$-0.360511\pi$
$37$	5.16214	0.848650	0.424325	+	0.905510i	$0.360511\pi$
$38$	1.40303	0.227601
$39$	−0.248152	−0.0397361
$40$	−4.30319	−0.680395
$41$	−4.91563	−0.767693	−0.383846	−	0.923397i	$-0.625401\pi$
$41$	−4.91563	−0.767693	−0.383846	+	0.923397i	$0.625401\pi$
$42$	0.305957	0.0472102
$43$	−7.56404	−1.15351	−0.576753	−	0.816919i	$-0.695680\pi$
$43$	−7.56404	−1.15351	−0.576753	+	0.816919i	$0.695680\pi$
$44$	4.27765	0.644880
$45$	10.3445	1.54206
$46$	1.24234	0.183172
$47$	−4.39448	−0.641001	−0.320501	−	0.947248i	$-0.603851\pi$
$47$	−4.39448	−0.641001	−0.320501	+	0.947248i	$0.603851\pi$
$48$	0.848873	0.122524
$49$	8.48948	1.21278
$50$	−2.31614	−0.327552
$51$	1.39216	0.194942
$52$	1.90186	0.263740
$53$	5.11605	0.702744	0.351372	−	0.936236i	$-0.385715\pi$
$53$	5.11605	0.702744	0.351372	+	0.936236i	$0.385715\pi$
$54$	0.461651	0.0628227
$55$	7.91810	1.06768
$56$	−4.81078	−0.642867
$57$	−1.11137	−0.147204
$58$	−0.172169	−0.0226068
$59$	−12.6055	−1.64109	−0.820547	−	0.571578i	$-0.806331\pi$
$59$	−12.6055	−1.64109	−0.820547	+	0.571578i	$0.806331\pi$
$60$	1.66146	0.214493
$61$	8.07278	1.03361	0.516807	−	0.856102i	$-0.327120\pi$
$61$	8.07278	1.03361	0.516807	+	0.856102i	$0.327120\pi$
$62$	−1.95418	−0.248182
$63$	11.5646	1.45701
$64$	−5.73999	−0.717498
$65$	3.52042	0.436654
$66$	0.174852	0.0215227
$67$	1.00118	0.122313	0.0611565	−	0.998128i	$-0.480521\pi$
$67$	1.00118	0.122313	0.0611565	+	0.998128i	$0.480521\pi$
$68$	−10.6697	−1.29389
$69$	−0.984081	−0.118469
$70$	−4.34048	−0.518787
$71$	−1.73233	−0.205589	−0.102795	−	0.994703i	$-0.532778\pi$
$71$	−1.73233	−0.205589	−0.102795	+	0.994703i	$0.532778\pi$
$72$	−3.59179	−0.423296
$73$	−15.8128	−1.85074	−0.925372	−	0.379060i	$-0.876247\pi$
$73$	−15.8128	−1.85074	−0.925372	+	0.379060i	$0.876247\pi$
$74$	−1.61717	−0.187992
$75$	1.83467	0.211849
$76$	8.51764	0.977040
$77$	8.85208	1.00879
$78$	0.0777396	0.00880228
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	−12.0426	−1.34640
$81$	8.44958	0.938842
$82$	1.53994	0.170058
$83$	13.8048	1.51527	0.757636	−	0.652678i	$-0.226354\pi$
$83$	13.8048	1.51527	0.757636	+	0.652678i	$0.226354\pi$
$84$	1.85744	0.202663
$85$	−19.7500	−2.14219
$86$	2.36962	0.255523
$87$	0.136378	0.0146213
$88$	−2.74931	−0.293078
$89$	9.74322	1.03278	0.516390	−	0.856354i	$-0.327276\pi$
$89$	9.74322	1.03278	0.516390	+	0.856354i	$0.327276\pi$
$90$	−3.24066	−0.341595
$91$	3.93567	0.412570
$92$	7.54209	0.786318
$93$	1.54795	0.160515
$94$	1.37668	0.141994
$95$	15.7665	1.61761
$96$	−0.872589	−0.0890582
$97$	−16.5846	−1.68391	−0.841955	−	0.539547i	$-0.818595\pi$
$97$	−16.5846	−1.68391	−0.841955	+	0.539547i	$0.818595\pi$
$98$	−2.65954	−0.268654
$99$	6.60908	0.664238
$100$	−14.0611	−1.40611
$101$	4.06470	0.404453	0.202227	−	0.979339i	$-0.435182\pi$
$101$	4.06470	0.404453	0.202227	+	0.979339i	$0.435182\pi$
$102$	−0.436130	−0.0431833
$103$	−7.59897	−0.748749	−0.374375	−	0.927278i	$-0.622143\pi$
$103$	−7.59897	−0.748749	−0.374375	+	0.927278i	$0.622143\pi$
$104$	−1.22235	−0.119862
$105$	3.43819	0.335533
$106$	−1.60273	−0.155671
$107$	6.52582	0.630875	0.315437	−	0.948946i	$-0.397849\pi$
$107$	6.52582	0.630875	0.315437	+	0.948946i	$0.397849\pi$
$108$	2.80263	0.269684
$109$	1.16204	0.111303	0.0556515	−	0.998450i	$-0.482276\pi$
$109$	1.16204	0.111303	0.0556515	+	0.998450i	$0.482276\pi$
$110$	−2.48054	−0.236510
$111$	1.28099	0.121586
$112$	−13.4631	−1.27214
$113$	−8.65893	−0.814564	−0.407282	−	0.913303i	$-0.633523\pi$
$113$	−8.65893	−0.814564	−0.407282	+	0.913303i	$0.633523\pi$
$114$	0.348164	0.0326085
$115$	13.9607	1.30184
$116$	−1.04522	−0.0970461
$117$	2.93842	0.271657
$118$	3.94898	0.363533
$119$	−22.0796	−2.02403
$120$	−1.06784	−0.0974804
$121$	−5.94112	−0.540102
$122$	−2.52900	−0.228965
$123$	−1.21982	−0.109988
$124$	−11.8637	−1.06539
$125$	−8.42551	−0.753601
$126$	−3.62291	−0.322755
$127$	−15.3947	−1.36605	−0.683027	−	0.730393i	$-0.739337\pi$
$127$	−15.3947	−1.36605	−0.683027	+	0.730393i	$0.739337\pi$
$128$	8.83090	0.780549
$129$	−1.87703	−0.165263
$130$	−1.10286	−0.0967270
$131$	−2.14130	−0.187087	−0.0935433	−	0.995615i	$-0.529819\pi$
$131$	−2.14130	−0.187087	−0.0935433	+	0.995615i	$0.529819\pi$
$132$	1.06151	0.0923923
$133$	17.6262	1.52839
$134$	−0.313643	−0.0270946
$135$	5.18779	0.446494
$136$	6.85757	0.588031
$137$	15.7743	1.34769	0.673843	−	0.738875i	$-0.264642\pi$
$137$	15.7743	1.34769	0.673843	+	0.738875i	$0.264642\pi$
$138$	0.308288	0.0262432
$139$	9.16778	0.777601	0.388800	−	0.921322i	$-0.372890\pi$
$139$	9.16778	0.777601	0.388800	+	0.921322i	$0.372890\pi$
$140$	−26.3506	−2.22703
$141$	−1.09050	−0.0918365
$142$	0.542694	0.0455419
$143$	2.24919	0.188087
$144$	−10.0517	−0.837642
$145$	−1.93474	−0.160671
$146$	4.95374	0.409974
$147$	2.10668	0.173756
$148$	−9.81766	−0.807006
$149$	−14.7086	−1.20498	−0.602488	−	0.798128i	$-0.705824\pi$
$149$	−14.7086	−1.20498	−0.602488	+	0.798128i	$0.705824\pi$
$150$	−0.574755	−0.0469285
$151$	17.3512	1.41202	0.706012	−	0.708200i	$-0.250493\pi$
$151$	17.3512	1.41202	0.706012	+	0.708200i	$0.250493\pi$
$152$	−5.47441	−0.444034
$153$	−16.4849	−1.33273
$154$	−2.77313	−0.223466
$155$	−21.9601	−1.76388
$156$	0.471949	0.0377862
$157$	19.2442	1.53585	0.767927	−	0.640537i	$-0.221288\pi$
$157$	19.2442	1.53585	0.767927	+	0.640537i	$0.221288\pi$
$158$	−0.313275	−0.0249228
$159$	1.26956	0.100682
$160$	12.3790	0.978648
$161$	15.6075	1.23004
$162$	−2.64704	−0.207971
$163$	−18.3030	−1.43360	−0.716802	−	0.697276i	$-0.754395\pi$
$163$	−18.3030	−1.43360	−0.716802	+	0.697276i	$0.754395\pi$
$164$	9.34884	0.730022
$165$	1.96489	0.152966
$166$	−4.32469	−0.335661
$167$	22.8656	1.76939	0.884695	−	0.466171i	$-0.154367\pi$
$167$	22.8656	1.76939	0.884695	+	0.466171i	$0.154367\pi$
$168$	−1.19380	−0.0921039
$169$	1.00000	0.0769231
$170$	6.18717	0.474535
$171$	13.1600	1.00637
$172$	14.3857	1.09690
$173$	18.0198	1.37002	0.685008	−	0.728535i	$-0.259799\pi$
$173$	18.0198	1.37002	0.685008	+	0.728535i	$0.259799\pi$
$174$	−0.0427239	−0.00323889
$175$	−29.0977	−2.19958
$176$	−7.69401	−0.579958
$177$	−3.12807	−0.235120
$178$	−3.05230	−0.228780
$179$	7.81890	0.584412	0.292206	−	0.956355i	$-0.405611\pi$
$179$	7.81890	0.584412	0.292206	+	0.956355i	$0.405611\pi$
$180$	−19.6737	−1.46639
$181$	−0.210236	−0.0156267	−0.00781334	−	0.999969i	$-0.502487\pi$
$181$	−0.210236	−0.0156267	−0.00781334	+	0.999969i	$0.502487\pi$
$182$	−1.23295	−0.0913920
$183$	2.00327	0.148086
$184$	−4.84742	−0.357356
$185$	−18.1729	−1.33610
$186$	−0.484934	−0.0355571
$187$	−12.6183	−0.922740
$188$	8.35769	0.609547
$189$	5.79971	0.421867
$190$	−4.93924	−0.358330
$191$	4.10600	0.297100	0.148550	−	0.988905i	$-0.452539\pi$
$191$	4.10600	0.297100	0.148550	+	0.988905i	$0.452539\pi$
$192$	−1.42439	−0.102796
$193$	7.28390	0.524306	0.262153	−	0.965026i	$-0.415567\pi$
$193$	7.28390	0.524306	0.262153	+	0.965026i	$0.415567\pi$
$194$	5.19553	0.373018
$195$	0.873597	0.0625596
$196$	−16.1458	−1.15327
$197$	12.0006	0.855008	0.427504	−	0.904013i	$-0.359393\pi$
$197$	12.0006	0.855008	0.427504	+	0.904013i	$0.359393\pi$
$198$	−2.07046	−0.147141
$199$	8.52286	0.604170	0.302085	−	0.953281i	$-0.402317\pi$
$199$	8.52286	0.604170	0.302085	+	0.953281i	$0.402317\pi$
$200$	9.03726	0.639031
$201$	0.248443	0.0175238
$202$	−1.27337	−0.0895939
$203$	−2.16295	−0.151810
$204$	−2.64770	−0.185376
$205$	17.3051	1.20864
$206$	2.38057	0.165862
$207$	11.6527	0.809921
$208$	−3.42079	−0.237189
$209$	10.0732	0.696778
$210$	−1.07710	−0.0743268
$211$	3.37860	0.232592	0.116296	−	0.993215i	$-0.462898\pi$
$211$	3.37860	0.232592	0.116296	+	0.993215i	$0.462898\pi$
$212$	−9.73001	−0.668260
$213$	−0.429880	−0.0294549
$214$	−2.04437	−0.139750
$215$	26.6286	1.81605
$216$	−1.80130	−0.122563
$217$	−24.5504	−1.66659
$218$	−0.364037	−0.0246557
$219$	−3.92396	−0.265157
$220$	−15.0591	−1.01529
$221$	−5.61013	−0.377378
$222$	−0.401303	−0.0269337
$223$	−4.82121	−0.322852	−0.161426	−	0.986885i	$-0.551609\pi$
$223$	−4.82121	−0.322852	−0.161426	+	0.986885i	$0.551609\pi$
$224$	13.8392	0.924670
$225$	−21.7247	−1.44831
$226$	2.71262	0.180441
$227$	9.40173	0.624015	0.312007	−	0.950080i	$-0.398999\pi$
$227$	9.40173	0.624015	0.312007	+	0.950080i	$0.398999\pi$
$228$	2.11367	0.139981
$229$	−28.4275	−1.87854	−0.939270	−	0.343180i	$-0.888496\pi$
$229$	−28.4275	−1.87854	−0.939270	+	0.343180i	$0.888496\pi$
$230$	−4.37354	−0.288383
$231$	2.19666	0.144530
$232$	0.671778	0.0441044
$233$	6.93034	0.454022	0.227011	−	0.973892i	$-0.427105\pi$
$233$	6.93034	0.454022	0.227011	+	0.973892i	$0.427105\pi$
$234$	−0.920533	−0.0601771
$235$	15.4704	1.00918
$236$	23.9739	1.56057
$237$	0.248152	0.0161192
$238$	6.91698	0.448362
$239$	−23.2431	−1.50347	−0.751735	−	0.659466i	$-0.770783\pi$
$239$	−23.2431	−1.50347	−0.751735	+	0.659466i	$0.770783\pi$
$240$	−2.98839	−0.192900
$241$	−18.4816	−1.19050	−0.595252	−	0.803539i	$-0.702948\pi$
$241$	−18.4816	−1.19050	−0.595252	+	0.803539i	$0.702948\pi$
$242$	1.86120	0.119643
$243$	6.51766	0.418108
$244$	−15.3533	−0.982894
$245$	−29.8865	−1.90938
$246$	0.382139	0.0243643
$247$	4.47858	0.284966
$248$	7.62495	0.484185
$249$	3.42568	0.217094
$250$	2.63950	0.166937
$251$	−12.5595	−0.792750	−0.396375	−	0.918089i	$-0.629732\pi$
$251$	−12.5595	−0.792750	−0.396375	+	0.918089i	$0.629732\pi$
$252$	−21.9943	−1.38551
$253$	8.91950	0.560764
$254$	4.82276	0.302607
$255$	−4.90099	−0.306912
$256$	8.71348	0.544592
$257$	−15.4693	−0.964946	−0.482473	−	0.875911i	$-0.660261\pi$
$257$	−15.4693	−0.964946	−0.482473	+	0.875911i	$0.660261\pi$
$258$	0.588026	0.0366089
$259$	−20.3165	−1.26240
$260$	−6.69533	−0.415227
$261$	−1.61489	−0.0999591
$262$	0.670816	0.0414432
$263$	−20.7447	−1.27918	−0.639588	−	0.768718i	$-0.720895\pi$
$263$	−20.7447	−1.27918	−0.639588	+	0.768718i	$0.720895\pi$
$264$	−0.682246	−0.0419893
$265$	−18.0106	−1.10638
$266$	−5.52185	−0.338566
$267$	2.41780	0.147967
$268$	−1.90410	−0.116311
$269$	18.6015	1.13415	0.567075	−	0.823666i	$-0.308075\pi$
$269$	18.6015	1.13415	0.567075	+	0.823666i	$0.308075\pi$
$270$	−1.62520	−0.0989067
$271$	25.5671	1.55309	0.776544	−	0.630063i	$-0.216971\pi$
$271$	25.5671	1.55309	0.776544	+	0.630063i	$0.216971\pi$
$272$	19.1911	1.16363
$273$	0.976642	0.0591091
$274$	−4.94168	−0.298538
$275$	−16.6290	−1.00277
$276$	1.87158	0.112656
$277$	−21.9368	−1.31806	−0.659028	−	0.752118i	$-0.729032\pi$
$277$	−21.9368	−1.31806	−0.659028	+	0.752118i	$0.729032\pi$
$278$	−2.87203	−0.172253
$279$	−18.3296	−1.09737
$280$	16.9359	1.01212
$281$	−6.42920	−0.383534	−0.191767	−	0.981441i	$-0.561422\pi$
$281$	−6.42920	−0.383534	−0.191767	+	0.981441i	$0.561422\pi$
$282$	0.341625	0.0203435
$283$	−21.1457	−1.25698	−0.628491	−	0.777817i	$-0.716327\pi$
$283$	−21.1457	−1.25698	−0.628491	+	0.777817i	$0.716327\pi$
$284$	3.29464	0.195501
$285$	3.91248	0.231755
$286$	−0.704616	−0.0416648
$287$	19.3463	1.14198
$288$	10.3325	0.608850
$289$	14.4736	0.851387
$290$	0.606105	0.0355917
$291$	−4.11549	−0.241255
$292$	30.0736	1.75993
$293$	7.27279	0.424881	0.212440	−	0.977174i	$-0.431859\pi$
$293$	7.27279	0.424881	0.212440	+	0.977174i	$0.431859\pi$
$294$	−0.659969	−0.0384902
$295$	44.3766	2.58370
$296$	6.30996	0.366759
$297$	3.31448	0.192326
$298$	4.60783	0.266925
$299$	3.96564	0.229339
$300$	−3.48928	−0.201453
$301$	29.7696	1.71589
$302$	−5.43570	−0.312790
$303$	1.00866	0.0579462
$304$	−15.3203	−0.878678
$305$	−28.4196	−1.62730
$306$	5.16431	0.295224
$307$	7.65609	0.436956	0.218478	−	0.975842i	$-0.429891\pi$
$307$	7.65609	0.436956	0.218478	+	0.975842i	$0.429891\pi$
$308$	−16.8354	−0.959287
$309$	−1.88570	−0.107274
$310$	6.87954	0.390732
$311$	−6.47679	−0.367265	−0.183632	−	0.982995i	$-0.558786\pi$
$311$	−6.47679	−0.367265	−0.183632	+	0.982995i	$0.558786\pi$
$312$	−0.303329	−0.0171726
$313$	−19.9867	−1.12972	−0.564859	−	0.825188i	$-0.691069\pi$
$313$	−19.9867	−1.12972	−0.564859	+	0.825188i	$0.691069\pi$
$314$	−6.02872	−0.340220
$315$	−40.7124	−2.29388
$316$	−1.90186	−0.106988
$317$	25.4162	1.42752	0.713759	−	0.700391i	$-0.246991\pi$
$317$	25.4162	1.42752	0.713759	+	0.700391i	$0.246991\pi$
$318$	−0.397720	−0.0223030
$319$	−1.23611	−0.0692087
$320$	20.2071	1.12961
$321$	1.61939	0.0903857
$322$	−4.88942	−0.272477
$323$	−25.1254	−1.39802
$324$	−16.0699	−0.892773
$325$	−7.39333	−0.410108
$326$	5.73388	0.317570
$327$	0.288362	0.0159464
$328$	−6.00864	−0.331772
$329$	17.2952	0.953517
$330$	−0.615550	−0.0338849
$331$	10.2512	0.563457	0.281728	−	0.959494i	$-0.409092\pi$
$331$	10.2512	0.563457	0.281728	+	0.959494i	$0.409092\pi$
$332$	−26.2547	−1.44092
$333$	−15.1685	−0.831230
$334$	−7.16320	−0.391953
$335$	−3.52456	−0.192567
$336$	−3.34088	−0.182260
$337$	−31.6988	−1.72674	−0.863372	−	0.504567i	$-0.831652\pi$
$337$	−31.6988	−1.72674	−0.863372	+	0.504567i	$0.831652\pi$
$338$	−0.313275	−0.0170399
$339$	−2.14873	−0.116703
$340$	37.5617	2.03707
$341$	−14.0303	−0.759784
$342$	−4.12268	−0.222929
$343$	−5.86211	−0.316524
$344$	−9.24594	−0.498508
$345$	3.46437	0.186516
$346$	−5.64513	−0.303484
$347$	30.6932	1.64770	0.823850	−	0.566808i	$-0.191822\pi$
$347$	30.6932	1.64770	0.823850	+	0.566808i	$0.191822\pi$
$348$	−0.259373	−0.0139038
$349$	−28.2423	−1.51178	−0.755888	−	0.654701i	$-0.772795\pi$
$349$	−28.2423	−1.51178	−0.755888	+	0.654701i	$0.772795\pi$
$350$	9.11557	0.487248
$351$	1.47363	0.0786565
$352$	7.90896	0.421549
$353$	−3.11454	−0.165770	−0.0828851	−	0.996559i	$-0.526413\pi$
$353$	−3.11454	−0.165770	−0.0828851	+	0.996559i	$0.526413\pi$
$354$	0.979946	0.0520835
$355$	6.09851	0.323676
$356$	−18.5302	−0.982100
$357$	−5.47909	−0.289984
$358$	−2.44946	−0.129458
$359$	−4.25361	−0.224497	−0.112248	−	0.993680i	$-0.535805\pi$
$359$	−4.25361	−0.224497	−0.112248	+	0.993680i	$0.535805\pi$
$360$	12.6446	0.666429
$361$	1.05772	0.0556695
$362$	0.0658615	0.00346160
$363$	−1.47430	−0.0773806
$364$	−7.48509	−0.392325
$365$	55.6675	2.91377
$366$	−0.627575	−0.0328039
$367$	27.9341	1.45815	0.729074	−	0.684435i	$-0.239951\pi$
$367$	27.9341	1.45815	0.729074	+	0.684435i	$0.239951\pi$
$368$	−13.5656	−0.707156
$369$	14.4442	0.751935
$370$	5.69310	0.295970
$371$	−20.1351	−1.04536
$372$	−2.94398	−0.152638
$373$	25.6677	1.32902	0.664512	−	0.747278i	$-0.268640\pi$
$373$	25.6677	1.32902	0.664512	+	0.747278i	$0.268640\pi$
$374$	3.95299	0.204404
$375$	−2.09080	−0.107969
$376$	−5.37161	−0.277020
$377$	−0.549577	−0.0283047
$378$	−1.81690	−0.0934514
$379$	−34.7231	−1.78361	−0.891804	−	0.452423i	$-0.850560\pi$
$379$	−34.7231	−1.78361	−0.891804	+	0.452423i	$0.850560\pi$
$380$	−29.9856	−1.53823
$381$	−3.82021	−0.195715
$382$	−1.28631	−0.0658131
$383$	−3.30259	−0.168754	−0.0843772	−	0.996434i	$-0.526890\pi$
$383$	−3.30259	−0.168754	−0.0843772	+	0.996434i	$0.526890\pi$
$384$	2.19140	0.111830
$385$	−31.1630	−1.58821
$386$	−2.28186	−0.116144
$387$	22.2263	1.12983
$388$	31.5416	1.60128
$389$	13.7348	0.696384	0.348192	−	0.937423i	$-0.386796\pi$
$389$	13.7348	0.696384	0.348192	+	0.937423i	$0.386796\pi$
$390$	−0.273676	−0.0138581
$391$	−22.2478	−1.12512
$392$	10.3772	0.524125
$393$	−0.531368	−0.0268040
$394$	−3.75949	−0.189400
$395$	−3.52042	−0.177131
$396$	−12.5695	−0.631643
$397$	27.9219	1.40136	0.700679	−	0.713477i	$-0.252880\pi$
$397$	27.9219	1.40136	0.700679	+	0.713477i	$0.252880\pi$
$398$	−2.67000	−0.133835
$399$	4.37398	0.218973
$400$	25.2910	1.26455
$401$	33.0723	1.65155	0.825775	−	0.563999i	$-0.190738\pi$
$401$	33.0723	1.65155	0.825775	+	0.563999i	$0.190738\pi$
$402$	−0.0778310	−0.00388186
$403$	−6.23792	−0.310733
$404$	−7.73050	−0.384607
$405$	−29.7460	−1.47809
$406$	0.677599	0.0336287
$407$	−11.6107	−0.575519
$408$	1.70172	0.0842475
$409$	6.28921	0.310982	0.155491	−	0.987837i	$-0.450304\pi$
$409$	6.28921	0.310982	0.155491	+	0.987837i	$0.450304\pi$
$410$	−5.42124	−0.267736
$411$	3.91441	0.193084
$412$	14.4522	0.712008
$413$	49.6110	2.44120
$414$	−3.65050	−0.179413
$415$	−48.5986	−2.38561
$416$	3.51635	0.172403
$417$	2.27500	0.111407
$418$	−3.15568	−0.154349
$419$	16.8145	0.821444	0.410722	−	0.911761i	$-0.365277\pi$
$419$	16.8145	0.821444	0.410722	+	0.911761i	$0.365277\pi$
$420$	−6.53895	−0.319068
$421$	24.0806	1.17362	0.586809	−	0.809726i	$-0.300384\pi$
$421$	24.0806	1.17362	0.586809	+	0.809726i	$0.300384\pi$
$422$	−1.05843	−0.0515236
$423$	12.9128	0.627844
$424$	6.25362	0.303703
$425$	41.4775	2.01196
$426$	0.134671	0.00652481
$427$	−31.7718	−1.53754
$428$	−12.4112	−0.599917
$429$	0.558141	0.0269473
$430$	−8.34206	−0.402290
$431$	−4.34420	−0.209253	−0.104626	−	0.994512i	$-0.533365\pi$
$431$	−4.34420	−0.209253	−0.104626	+	0.994512i	$0.533365\pi$
$432$	−5.04097	−0.242534
$433$	21.2349	1.02048	0.510241	−	0.860032i	$-0.329556\pi$
$433$	21.2349	1.02048	0.510241	+	0.860032i	$0.329556\pi$
$434$	7.69102	0.369181
$435$	−0.480109	−0.0230195
$436$	−2.21003	−0.105841
$437$	17.7605	0.849598
$438$	1.22928	0.0587372
$439$	−6.25778	−0.298667	−0.149334	−	0.988787i	$-0.547713\pi$
$439$	−6.25778	−0.298667	−0.149334	+	0.988787i	$0.547713\pi$
$440$	9.67872	0.461415
$441$	−24.9457	−1.18789
$442$	1.75751	0.0835963
$443$	12.1732	0.578368	0.289184	−	0.957273i	$-0.406616\pi$
$443$	12.1732	0.578368	0.289184	+	0.957273i	$0.406616\pi$
$444$	−2.43627	−0.115620
$445$	−34.3002	−1.62598
$446$	1.51036	0.0715178
$447$	−3.64996	−0.172637
$448$	22.5907	1.06731
$449$	13.5325	0.638639	0.319320	−	0.947647i	$-0.396546\pi$
$449$	13.5325	0.638639	0.319320	+	0.947647i	$0.396546\pi$
$450$	6.80580	0.320829
$451$	11.0562	0.520617
$452$	16.4681	0.774592
$453$	4.30574	0.202301
$454$	−2.94532	−0.138231
$455$	−13.8552	−0.649541
$456$	−1.35848	−0.0636169
$457$	19.6816	0.920667	0.460333	−	0.887746i	$-0.347730\pi$
$457$	19.6816	0.920667	0.460333	+	0.887746i	$0.347730\pi$
$458$	8.90560	0.416132
$459$	−8.26725	−0.385882
$460$	−26.5513	−1.23796
$461$	1.75202	0.0815998	0.0407999	−	0.999167i	$-0.487009\pi$
$461$	1.75202	0.0815998	0.0407999	+	0.999167i	$0.487009\pi$
$462$	−0.688158	−0.0320160
$463$	8.73926	0.406148	0.203074	−	0.979163i	$-0.434907\pi$
$463$	8.73926	0.406148	0.203074	+	0.979163i	$0.434907\pi$
$464$	1.87999	0.0872761
$465$	−5.44943	−0.252711
$466$	−2.17110	−0.100574
$467$	−12.0233	−0.556370	−0.278185	−	0.960528i	$-0.589733\pi$
$467$	−12.0233	−0.556370	−0.278185	+	0.960528i	$0.589733\pi$
$468$	−5.58846	−0.258327
$469$	−3.94030	−0.181946
$470$	−4.84649	−0.223552
$471$	4.77548	0.220043
$472$	−15.4084	−0.709228
$473$	17.0130	0.782259
$474$	−0.0777396	−0.00357070
$475$	−33.1116	−1.51927
$476$	41.9923	1.92471
$477$	−15.0331	−0.688319
$478$	7.28147	0.333047
$479$	−28.8345	−1.31748	−0.658742	−	0.752369i	$-0.728911\pi$
$479$	−28.8345	−1.31748	−0.658742	+	0.752369i	$0.728911\pi$
$480$	3.07188	0.140211
$481$	−5.16214	−0.235373
$482$	5.78982	0.263719
$483$	3.87302	0.176228
$484$	11.2992	0.513599
$485$	58.3847	2.65111
$486$	−2.04182	−0.0926188
$487$	−1.00702	−0.0456325	−0.0228162	−	0.999740i	$-0.507263\pi$
$487$	−1.00702	−0.0456325	−0.0228162	+	0.999740i	$0.507263\pi$
$488$	9.86780	0.446694
$489$	−4.54193	−0.205393
$490$	9.36269	0.422963
$491$	−15.8570	−0.715615	−0.357807	−	0.933795i	$-0.616476\pi$
$491$	−15.8570	−0.715615	−0.357807	+	0.933795i	$0.616476\pi$
$492$	2.31993	0.104591
$493$	3.08320	0.138860
$494$	−1.40303	−0.0631252
$495$	−23.2667	−1.04576
$496$	21.3386	0.958131
$497$	6.81787	0.305823
$498$	−1.07318	−0.0480903
$499$	−16.8436	−0.754025	−0.377012	−	0.926208i	$-0.623049\pi$
$499$	−16.8436	−0.754025	−0.377012	+	0.926208i	$0.623049\pi$
$500$	16.0241	0.716621
$501$	5.67412	0.253501
$502$	3.93458	0.175609
$503$	26.4961	1.18140	0.590700	−	0.806891i	$-0.298852\pi$
$503$	26.4961	1.18140	0.590700	+	0.806891i	$0.298852\pi$
$504$	14.1361	0.629672
$505$	−14.3095	−0.636762
$506$	−2.79425	−0.124220
$507$	0.248152	0.0110208
$508$	29.2785	1.29902
$509$	31.1523	1.38080	0.690400	−	0.723428i	$-0.257434\pi$
$509$	31.1523	1.38080	0.690400	+	0.723428i	$0.257434\pi$
$510$	1.53536	0.0679868
$511$	62.2338	2.75306
$512$	−20.3915	−0.901186
$513$	6.59977	0.291387
$514$	4.84613	0.213754
$515$	26.7515	1.17881
$516$	3.56985	0.157154
$517$	9.88405	0.434700
$518$	6.36463	0.279646
$519$	4.47163	0.196283
$520$	4.30319	0.188708
$521$	32.5226	1.42484	0.712420	−	0.701753i	$-0.247599\pi$
$521$	32.5226	1.42484	0.712420	+	0.701753i	$0.247599\pi$
$522$	0.505904	0.0221428
$523$	7.99619	0.349649	0.174824	−	0.984600i	$-0.444064\pi$
$523$	7.99619	0.349649	0.174824	+	0.984600i	$0.444064\pi$
$524$	4.07246	0.177906
$525$	−7.22064	−0.315134
$526$	6.49880	0.283361
$527$	34.9956	1.52443
$528$	−1.90928	−0.0830908
$529$	−7.27368	−0.316247
$530$	5.64227	0.245085
$531$	37.0402	1.60741
$532$	−33.5226	−1.45339
$533$	4.91563	0.212920
$534$	−0.757434	−0.0327774
$535$	−22.9736	−0.993235
$536$	1.22379	0.0528597
$537$	1.94027	0.0837289
$538$	−5.82737	−0.251236
$539$	−19.0945	−0.822458
$540$	−9.86644	−0.424584
$541$	−19.4288	−0.835308	−0.417654	−	0.908606i	$-0.637148\pi$
$541$	−19.4288	−0.835308	−0.417654	+	0.908606i	$0.637148\pi$
$542$	−8.00951	−0.344038
$543$	−0.0521703	−0.00223884
$544$	−19.7272	−0.845797
$545$	−4.09086	−0.175233
$546$	−0.305957	−0.0130938
$547$	−12.8787	−0.550655	−0.275328	−	0.961350i	$-0.588786\pi$
$547$	−12.8787	−0.550655	−0.275328	+	0.961350i	$0.588786\pi$
$548$	−30.0004	−1.28155
$549$	−23.7212	−1.01240
$550$	5.20946	0.222132
$551$	−2.46133	−0.104856
$552$	−1.20289	−0.0511986
$553$	−3.93567	−0.167362
$554$	6.87226	0.291974
$555$	−4.50963	−0.191423
$556$	−17.4358	−0.739443
$557$	−1.75116	−0.0741989	−0.0370995	−	0.999312i	$-0.511812\pi$
$557$	−1.75116	−0.0741989	−0.0370995	+	0.999312i	$0.511812\pi$
$558$	5.74221	0.243087
$559$	7.56404	0.319925
$560$	47.3956	2.00283
$561$	−3.13125	−0.132201
$562$	2.01411	0.0849599
$563$	−6.81055	−0.287031	−0.143515	−	0.989648i	$-0.545841\pi$
$563$	−6.81055	−0.287031	−0.143515	+	0.989648i	$0.545841\pi$
$564$	2.07397	0.0873300
$565$	30.4830	1.28243
$566$	6.62442	0.278445
$567$	−33.2547	−1.39657
$568$	−2.11752	−0.0888491
$569$	29.2547	1.22642	0.613210	−	0.789920i	$-0.289878\pi$
$569$	29.2547	1.22642	0.613210	+	0.789920i	$0.289878\pi$
$570$	−1.22568	−0.0513381
$571$	21.3828	0.894844	0.447422	−	0.894323i	$-0.352342\pi$
$571$	21.3828	0.894844	0.447422	+	0.894323i	$0.352342\pi$
$572$	−4.27765	−0.178858
$573$	1.01891	0.0425656
$574$	−6.06070	−0.252969
$575$	−29.3193	−1.22270
$576$	16.8665	0.702771
$577$	6.34247	0.264040	0.132020	−	0.991247i	$-0.457854\pi$
$577$	6.34247	0.264040	0.132020	+	0.991247i	$0.457854\pi$
$578$	−4.53420	−0.188598
$579$	1.80751	0.0751176
$580$	3.67960	0.152787
$581$	−54.3310	−2.25403
$582$	1.28928	0.0534424
$583$	−11.5070	−0.476571
$584$	−19.3288	−0.799831
$585$	−10.3445	−0.427691
$586$	−2.27838	−0.0941191
$587$	−25.3054	−1.04447	−0.522233	−	0.852803i	$-0.674901\pi$
$587$	−25.3054	−1.04447	−0.522233	+	0.852803i	$0.674901\pi$
$588$	−4.00661	−0.165230
$589$	−27.9371	−1.15113
$590$	−13.9021	−0.572339
$591$	2.97797	0.122497
$592$	17.6586	0.725762
$593$	11.0679	0.454504	0.227252	−	0.973836i	$-0.427026\pi$
$593$	11.0679	0.454504	0.227252	+	0.973836i	$0.427026\pi$
$594$	−1.03834	−0.0426037
$595$	77.7294	3.18660
$596$	27.9737	1.14585
$597$	2.11496	0.0865596
$598$	−1.24234	−0.0508029
$599$	2.97279	0.121465	0.0607324	−	0.998154i	$-0.480656\pi$
$599$	2.97279	0.121465	0.0607324	+	0.998154i	$0.480656\pi$
$600$	2.24261	0.0915542
$601$	39.8218	1.62437	0.812183	−	0.583402i	$-0.198279\pi$
$601$	39.8218	1.62437	0.812183	+	0.583402i	$0.198279\pi$
$602$	−9.32605	−0.380102
$603$	−2.94188	−0.119802
$604$	−32.9996	−1.34273
$605$	20.9152	0.850325
$606$	−0.315989	−0.0128362
$607$	−39.8677	−1.61818	−0.809089	−	0.587686i	$-0.800039\pi$
$607$	−39.8677	−1.61818	−0.809089	+	0.587686i	$0.800039\pi$
$608$	15.7483	0.638677
$609$	−0.536740	−0.0217498
$610$	8.90313	0.360477
$611$	4.39448	0.177782
$612$	31.3520	1.26733
$613$	35.4036	1.42994	0.714969	−	0.699156i	$-0.246441\pi$
$613$	35.4036	1.42994	0.714969	+	0.699156i	$0.246441\pi$
$614$	−2.39846	−0.0967939
$615$	4.29428	0.173162
$616$	10.8204	0.435965
$617$	−24.1602	−0.972655	−0.486327	−	0.873777i	$-0.661664\pi$
$617$	−24.1602	−0.972655	−0.486327	+	0.873777i	$0.661664\pi$
$618$	0.590741	0.0237631
$619$	−29.1246	−1.17062	−0.585308	−	0.810811i	$-0.699026\pi$
$619$	−29.1246	−1.17062	−0.585308	+	0.810811i	$0.699026\pi$
$620$	41.7650	1.67732
$621$	5.84389	0.234507
$622$	2.02901	0.0813561
$623$	−38.3461	−1.53630
$624$	−0.848873	−0.0339821
$625$	−7.30534	−0.292214
$626$	6.26134	0.250253
$627$	2.49968	0.0998277
$628$	−36.5998	−1.46049
$629$	28.9603	1.15472
$630$	12.7542	0.508138
$631$	−38.2035	−1.52086	−0.760428	−	0.649422i	$-0.775011\pi$
$631$	−38.2035	−1.52086	−0.760428	+	0.649422i	$0.775011\pi$
$632$	1.22235	0.0486226
$633$	0.838405	0.0333236
$634$	−7.96226	−0.316222
$635$	54.1956	2.15069
$636$	−2.41452	−0.0957418
$637$	−8.48948	−0.336366
$638$	0.387241	0.0153310
$639$	5.09031	0.201369
$640$	−31.0884	−1.22888
$641$	3.94227	0.155710	0.0778551	−	0.996965i	$-0.475193\pi$
$641$	3.94227	0.155710	0.0778551	+	0.996965i	$0.475193\pi$
$642$	−0.507315	−0.0200221
$643$	29.9180	1.17985	0.589924	−	0.807458i	$-0.299158\pi$
$643$	29.9180	1.17985	0.589924	+	0.807458i	$0.299158\pi$
$644$	−29.6832	−1.16968
$645$	6.60793	0.260187
$646$	7.87117	0.309687
$647$	−0.541083	−0.0212722	−0.0106361	−	0.999943i	$-0.503386\pi$
$647$	−0.541083	−0.0212722	−0.0106361	+	0.999943i	$0.503386\pi$
$648$	10.3284	0.405737
$649$	28.3522	1.11292
$650$	2.31614	0.0908466
$651$	−6.09222	−0.238773
$652$	34.8098	1.36326
$653$	−1.55218	−0.0607414	−0.0303707	−	0.999539i	$-0.509669\pi$
$653$	−1.55218	−0.0607414	−0.0303707	+	0.999539i	$0.509669\pi$
$654$	−0.0903364	−0.00353243
$655$	7.53828	0.294545
$656$	−16.8153	−0.656528
$657$	46.4645	1.81275
$658$	−5.41816	−0.211222
$659$	19.9195	0.775954	0.387977	−	0.921669i	$-0.373174\pi$
$659$	19.9195	0.775954	0.387977	+	0.921669i	$0.373174\pi$
$660$	−3.73694	−0.145460
$661$	−11.5006	−0.447322	−0.223661	−	0.974667i	$-0.571801\pi$
$661$	−11.5006	−0.447322	−0.223661	+	0.974667i	$0.571801\pi$
$662$	−3.21144	−0.124816
$663$	−1.39216	−0.0540671
$664$	16.8743	0.654851
$665$	−62.0516	−2.40626
$666$	4.75192	0.184133
$667$	−2.17943	−0.0843877
$668$	−43.4871	−1.68256
$669$	−1.19639	−0.0462552
$670$	1.10415	0.0426572
$671$	−18.1573	−0.700953
$672$	3.43422	0.132478
$673$	18.5910	0.716630	0.358315	−	0.933601i	$-0.383351\pi$
$673$	18.5910	0.716630	0.358315	+	0.933601i	$0.383351\pi$
$674$	9.93044	0.382506
$675$	−10.8950	−0.419350
$676$	−1.90186	−0.0731484
$677$	−32.2707	−1.24026	−0.620132	−	0.784497i	$-0.712921\pi$
$677$	−32.2707	−1.24026	−0.620132	+	0.784497i	$0.712921\pi$
$678$	0.673142	0.0258519
$679$	65.2715	2.50489
$680$	−24.1415	−0.925784
$681$	2.33306	0.0894029
$682$	4.39534	0.168306
$683$	47.0324	1.79965	0.899823	−	0.436256i	$-0.143696\pi$
$683$	47.0324	1.79965	0.899823	+	0.436256i	$0.143696\pi$
$684$	−25.0284	−0.956985
$685$	−55.5320	−2.12177
$686$	1.83645	0.0701160
$687$	−7.05432	−0.269139
$688$	−25.8750	−0.986474
$689$	−5.11605	−0.194906
$690$	−1.08530	−0.0413167
$691$	−44.8872	−1.70759	−0.853794	−	0.520610i	$-0.825704\pi$
$691$	−44.8872	−1.70759	−0.853794	+	0.520610i	$0.825704\pi$
$692$	−34.2710	−1.30279
$693$	−26.0111	−0.988082
$694$	−9.61542	−0.364996
$695$	−32.2744	−1.22424
$696$	0.166703	0.00631885
$697$	−27.5773	−1.04457
$698$	8.84760	0.334887
$699$	1.71978	0.0650479
$700$	55.3397	2.09164
$701$	8.02349	0.303043	0.151521	−	0.988454i	$-0.451583\pi$
$701$	8.02349	0.303043	0.151521	+	0.988454i	$0.451583\pi$
$702$	−0.461651	−0.0174239
$703$	−23.1191	−0.871952
$704$	12.9103	0.486577
$705$	3.83901	0.144585
$706$	0.975707	0.0367212
$707$	−15.9973	−0.601641
$708$	5.94915	0.223583
$709$	13.6481	0.512565	0.256282	−	0.966602i	$-0.417502\pi$
$709$	13.6481	0.512565	0.256282	+	0.966602i	$0.417502\pi$
$710$	−1.91051	−0.0717002
$711$	−2.93842	−0.110199
$712$	11.9097	0.446333
$713$	−24.7374	−0.926422
$714$	1.71646	0.0642369
$715$	−7.91810	−0.296120
$716$	−14.8704	−0.555734
$717$	−5.76781	−0.215403
$718$	1.33255	0.0497302
$719$	−36.8521	−1.37435	−0.687177	−	0.726490i	$-0.741150\pi$
$719$	−36.8521	−1.37435	−0.687177	+	0.726490i	$0.741150\pi$
$720$	35.3862	1.31877
$721$	29.9070	1.11380
$722$	−0.331357	−0.0123318
$723$	−4.58624	−0.170564
$724$	0.399838	0.0148599
$725$	4.06320	0.150904
$726$	0.461861	0.0171413
$727$	18.8507	0.699133	0.349566	−	0.936912i	$-0.386329\pi$
$727$	18.8507	0.699133	0.349566	+	0.936912i	$0.386329\pi$
$728$	4.81078	0.178299
$729$	−23.7314	−0.878940
$730$	−17.4392	−0.645454
$731$	−42.4353	−1.56953
$732$	−3.80995	−0.140820
$733$	9.35644	0.345588	0.172794	−	0.984958i	$-0.444721\pi$
$733$	9.35644	0.345588	0.172794	+	0.984958i	$0.444721\pi$
$734$	−8.75104	−0.323007
$735$	−7.41639	−0.273558
$736$	13.9446	0.514005
$737$	−2.25184	−0.0829476
$738$	−4.52500	−0.166568
$739$	26.9397	0.990994	0.495497	−	0.868610i	$-0.334986\pi$
$739$	26.9397	0.990994	0.495497	+	0.868610i	$0.334986\pi$
$740$	34.5622	1.27053
$741$	1.11137	0.0408271
$742$	6.30781	0.231567
$743$	43.2638	1.58719	0.793597	−	0.608443i	$-0.208206\pi$
$743$	43.2638	1.58719	0.793597	+	0.608443i	$0.208206\pi$
$744$	1.89214	0.0693693
$745$	51.7804	1.89709
$746$	−8.04104	−0.294404
$747$	−40.5643	−1.48417
$748$	23.9982	0.877461
$749$	−25.6834	−0.938453
$750$	0.654996	0.0239171
$751$	35.6106	1.29945	0.649725	−	0.760169i	$-0.274884\pi$
$751$	35.6106	1.29945	0.649725	+	0.760169i	$0.274884\pi$
$752$	−15.0326	−0.548182
$753$	−3.11667	−0.113578
$754$	0.172169	0.00627001
$755$	−61.0836	−2.22306
$756$	−11.0302	−0.401166
$757$	16.0164	0.582125	0.291063	−	0.956704i	$-0.405991\pi$
$757$	16.0164	0.582125	0.291063	+	0.956704i	$0.405991\pi$
$758$	10.8779	0.395102
$759$	2.21339	0.0803409
$760$	19.2722	0.699077
$761$	−53.8271	−1.95123	−0.975616	−	0.219485i	$-0.929562\pi$
$761$	−53.8271	−1.95123	−0.975616	+	0.219485i	$0.929562\pi$
$762$	1.19677	0.0433546
$763$	−4.57339	−0.165568
$764$	−7.80903	−0.282521
$765$	58.0338	2.09822
$766$	1.03462	0.0373822
$767$	12.6055	0.455158
$768$	2.16226	0.0780240
$769$	−35.6171	−1.28439	−0.642193	−	0.766543i	$-0.721975\pi$
$769$	−35.6171	−1.28439	−0.642193	+	0.766543i	$0.721975\pi$
$770$	9.76259	0.351819
$771$	−3.83872	−0.138248
$772$	−13.8529	−0.498578
$773$	−11.4104	−0.410402	−0.205201	−	0.978720i	$-0.565785\pi$
$773$	−11.4104	−0.410402	−0.205201	+	0.978720i	$0.565785\pi$
$774$	−6.96295	−0.250278
$775$	46.1190	1.65664
$776$	−20.2722	−0.727731
$777$	−5.04156	−0.180865
$778$	−4.30278	−0.154262
$779$	22.0151	0.788772
$780$	−1.66146	−0.0594897
$781$	3.89634	0.139422
$782$	6.96967	0.249235
$783$	−0.809873	−0.0289425
$784$	29.0407	1.03717
$785$	−67.7476	−2.41802
$786$	0.166464	0.00593758
$787$	−30.7579	−1.09640	−0.548201	−	0.836347i	$-0.684687\pi$
$787$	−30.7579	−1.09640	−0.548201	+	0.836347i	$0.684687\pi$
$788$	−22.8235	−0.813053
$789$	−5.14784	−0.183268
$790$	1.10286	0.0392379
$791$	34.0787	1.21170
$792$	8.07863	0.287062
$793$	−8.07278	−0.286673
$794$	−8.74721	−0.310427
$795$	−4.46937	−0.158512
$796$	−16.2093	−0.574523
$797$	−32.4024	−1.14775	−0.573875	−	0.818943i	$-0.694561\pi$
$797$	−32.4024	−1.14775	−0.573875	+	0.818943i	$0.694561\pi$
$798$	−1.37026	−0.0485065
$799$	−24.6536	−0.872183
$800$	−25.9976	−0.919152
$801$	−28.6297	−1.01158
$802$	−10.3607	−0.365849
$803$	35.5660	1.25510
$804$	−0.472504	−0.0166639
$805$	−54.9447	−1.93655
$806$	1.95418	0.0688332
$807$	4.61598	0.162490
$808$	4.96851	0.174791
$809$	34.7605	1.22211	0.611057	−	0.791587i	$-0.290745\pi$
$809$	34.7605	1.22211	0.611057	+	0.791587i	$0.290745\pi$
$810$	9.31868	0.327425
$811$	−41.1470	−1.44487	−0.722433	−	0.691441i	$-0.756976\pi$
$811$	−41.1470	−1.44487	−0.722433	+	0.691441i	$0.756976\pi$
$812$	4.11363	0.144360
$813$	6.34451	0.222512
$814$	3.63732	0.127488
$815$	64.4343	2.25704
$816$	4.76229	0.166714
$817$	33.8762	1.18518
$818$	−1.97025	−0.0688882
$819$	−11.5646	−0.404102
$820$	−32.9118	−1.14933
$821$	43.6582	1.52368	0.761840	−	0.647765i	$-0.224296\pi$
$821$	43.6582	1.52368	0.761840	+	0.647765i	$0.224296\pi$
$822$	−1.22629	−0.0427716
$823$	39.0821	1.36232	0.681158	−	0.732136i	$-0.261477\pi$
$823$	39.0821	1.36232	0.681158	+	0.732136i	$0.261477\pi$
$824$	−9.28863	−0.323585
$825$	−4.12652	−0.143667
$826$	−15.5419	−0.540771
$827$	25.7947	0.896970	0.448485	−	0.893790i	$-0.351964\pi$
$827$	25.7947	0.896970	0.448485	+	0.893790i	$0.351964\pi$
$828$	−22.1618	−0.770177
$829$	−1.50169	−0.0521558	−0.0260779	−	0.999660i	$-0.508302\pi$
$829$	−1.50169	−0.0521558	−0.0260779	+	0.999660i	$0.508302\pi$
$830$	15.2247	0.528457
$831$	−5.44366	−0.188839
$832$	5.73999	0.198998
$833$	47.6271	1.65018
$834$	−0.712700	−0.0246788
$835$	−80.4962	−2.78569
$836$	−19.1578	−0.662587
$837$	−9.19238	−0.317735
$838$	−5.26757	−0.181965
$839$	17.9906	0.621104	0.310552	−	0.950556i	$-0.399486\pi$
$839$	17.9906	0.621104	0.310552	+	0.950556i	$0.399486\pi$
$840$	4.20268	0.145006
$841$	−28.6980	−0.989585
$842$	−7.54385	−0.259978
$843$	−1.59542	−0.0549490
$844$	−6.42562	−0.221179
$845$	−3.52042	−0.121106
$846$	−4.04527	−0.139079
$847$	23.3823	0.803425
$848$	17.5009	0.600984
$849$	−5.24734	−0.180088
$850$	−12.9939	−0.445686
$851$	−20.4712	−0.701743
$852$	0.817571	0.0280095
$853$	13.7975	0.472416	0.236208	−	0.971702i	$-0.424095\pi$
$853$	13.7975	0.472416	0.236208	+	0.971702i	$0.424095\pi$
$854$	9.95330	0.340595
$855$	−46.3286	−1.58440
$856$	7.97686	0.272643
$857$	5.47264	0.186942	0.0934708	−	0.995622i	$-0.470204\pi$
$857$	5.47264	0.186942	0.0934708	+	0.995622i	$0.470204\pi$
$858$	−0.174852	−0.00596933
$859$	−0.0427438	−0.00145840	−0.000729199	−	1.00000i	$-0.500232\pi$
$859$	−0.0427438	−0.00145840	−0.000729199		1.00000i	$0.500232\pi$
$860$	−50.6438	−1.72694
$861$	4.80081	0.163611
$862$	1.36093	0.0463534
$863$	40.8058	1.38905	0.694523	−	0.719471i	$-0.255615\pi$
$863$	40.8058	1.38905	0.694523	+	0.719471i	$0.255615\pi$
$864$	5.18180	0.176288
$865$	−63.4370	−2.15692
$866$	−6.65234	−0.226056
$867$	3.59164	0.121979
$868$	46.6914	1.58481
$869$	−2.24919	−0.0762987
$870$	0.150406	0.00509924
$871$	−1.00118	−0.0339235
$872$	1.42042	0.0481015
$873$	48.7325	1.64935
$874$	−5.56390	−0.188202
$875$	33.1600	1.12101
$876$	7.46282	0.252145
$877$	−14.3232	−0.483661	−0.241831	−	0.970318i	$-0.577748\pi$
$877$	−14.3232	−0.483661	−0.241831	+	0.970318i	$0.577748\pi$
$878$	1.96040	0.0661604
$879$	1.80476	0.0608729
$880$	27.0861	0.913073
$881$	22.3120	0.751710	0.375855	−	0.926678i	$-0.377349\pi$
$881$	22.3120	0.751710	0.375855	+	0.926678i	$0.377349\pi$
$882$	7.81485	0.263140
$883$	−6.05312	−0.203704	−0.101852	−	0.994800i	$-0.532477\pi$
$883$	−6.05312	−0.203704	−0.101852	+	0.994800i	$0.532477\pi$
$884$	10.6697	0.358860
$885$	11.0121	0.370168
$886$	−3.81357	−0.128119
$887$	−47.0926	−1.58121	−0.790607	−	0.612324i	$-0.790235\pi$
$887$	−47.0926	−1.58121	−0.790607	+	0.612324i	$0.790235\pi$
$888$	1.56583	0.0525457
$889$	60.5883	2.03207
$890$	10.7454	0.360186
$891$	−19.0047	−0.636683
$892$	9.16927	0.307010
$893$	19.6811	0.658602
$894$	1.14344	0.0382424
$895$	−27.5258	−0.920085
$896$	−34.7555	−1.16110
$897$	0.984081	0.0328575
$898$	−4.23940	−0.141471
$899$	3.42822	0.114338
$900$	41.3173	1.37724
$901$	28.7017	0.956193
$902$	−3.46363	−0.115326
$903$	7.38737	0.245836
$904$	−10.5843	−0.352028
$905$	0.740117	0.0246023
$906$	−1.34888	−0.0448135
$907$	−23.5344	−0.781448	−0.390724	−	0.920508i	$-0.627775\pi$
$907$	−23.5344	−0.781448	−0.390724	+	0.920508i	$0.627775\pi$
$908$	−17.8808	−0.593394
$909$	−11.9438	−0.396151
$910$	4.34048	0.143886
$911$	−38.4544	−1.27405	−0.637026	−	0.770842i	$-0.719836\pi$
$911$	−38.4544	−1.27405	−0.637026	+	0.770842i	$0.719836\pi$
$912$	−3.80175	−0.125889
$913$	−31.0496	−1.02759
$914$	−6.16575	−0.203945
$915$	−7.05236	−0.233144
$916$	54.0650	1.78636
$917$	8.42746	0.278299
$918$	2.58992	0.0854801
$919$	−35.3706	−1.16677	−0.583385	−	0.812196i	$-0.698272\pi$
$919$	−35.3706	−1.16677	−0.583385	+	0.812196i	$0.698272\pi$
$920$	17.0649	0.562614
$921$	1.89987	0.0626029
$922$	−0.548864	−0.0180759
$923$	1.73233	0.0570203
$924$	−4.17774	−0.137437
$925$	38.1654	1.25487
$926$	−2.73779	−0.0899693
$927$	22.3290	0.733380
$928$	−1.93251	−0.0634377
$929$	60.7791	1.99410	0.997049	−	0.0767715i	$-0.0244612\pi$
$929$	60.7791	1.99410	0.997049	+	0.0767715i	$0.0244612\pi$
$930$	1.70717	0.0559803
$931$	−38.0209	−1.24608
$932$	−13.1805	−0.431743
$933$	−1.60723	−0.0526182
$934$	3.76658	0.123246
$935$	44.4216	1.45274
$936$	3.59179	0.117401
$937$	−5.41406	−0.176870	−0.0884349	−	0.996082i	$-0.528187\pi$
$937$	−5.41406	−0.176870	−0.0884349	+	0.996082i	$0.528187\pi$
$938$	1.23440	0.0403044
$939$	−4.95974	−0.161855
$940$	−29.4225	−0.959657
$941$	−31.6810	−1.03277	−0.516385	−	0.856356i	$-0.672723\pi$
$941$	−31.6810	−1.03277	−0.516385	+	0.856356i	$0.672723\pi$
$942$	−1.49604	−0.0487435
$943$	19.4936	0.634800
$944$	−43.1207	−1.40346
$945$	−20.4174	−0.664178
$946$	−5.32975	−0.173285
$947$	23.9258	0.777484	0.388742	−	0.921347i	$-0.372910\pi$
$947$	23.9258	0.777484	0.388742	+	0.921347i	$0.372910\pi$
$948$	−0.471949	−0.0153282
$949$	15.8128	0.513304
$950$	10.3730	0.336546
$951$	6.30708	0.204521
$952$	−26.9891	−0.874722
$953$	18.3394	0.594070	0.297035	−	0.954867i	$-0.404002\pi$
$953$	18.3394	0.594070	0.297035	+	0.954867i	$0.404002\pi$
$954$	4.70949	0.152475
$955$	−14.4548	−0.467747
$956$	44.2050	1.42969
$957$	−0.306742	−0.00991555
$958$	9.03313	0.291847
$959$	−62.0823	−2.00474
$960$	5.01443	0.161840
$961$	7.91169	0.255216
$962$	1.61717	0.0521396
$963$	−19.1756	−0.617925
$964$	35.1494	1.13209
$965$	−25.6423	−0.825456
$966$	−1.21332	−0.0390379
$967$	18.4417	0.593045	0.296522	−	0.955026i	$-0.404173\pi$
$967$	18.4417	0.593045	0.296522	+	0.955026i	$0.404173\pi$
$968$	−7.26215	−0.233414
$969$	−6.23492	−0.200295
$970$	−18.2904	−0.587271
$971$	−11.2369	−0.360609	−0.180305	−	0.983611i	$-0.557708\pi$
$971$	−11.2369	−0.360609	−0.180305	+	0.983611i	$0.557708\pi$
$972$	−12.3957	−0.397592
$973$	−36.0813	−1.15671
$974$	0.315474	0.0101084
$975$	−1.83467	−0.0587563
$976$	27.6153	0.883943
$977$	−43.2118	−1.38247	−0.691234	−	0.722631i	$-0.742932\pi$
$977$	−43.2118	−1.38247	−0.691234	+	0.722631i	$0.742932\pi$
$978$	1.42287	0.0454984
$979$	−21.9144	−0.700387
$980$	56.8399	1.81568
$981$	−3.41456	−0.109018
$982$	4.96759	0.158522
$983$	−46.7660	−1.49160	−0.745801	−	0.666169i	$-0.767933\pi$
$983$	−46.7660	−1.49160	−0.745801	+	0.666169i	$0.767933\pi$
$984$	−1.49105	−0.0475331
$985$	−42.2472	−1.34611
$986$	−0.965889	−0.0307602
$987$	4.29184	0.136611
$988$	−8.51764	−0.270982
$989$	29.9963	0.953827
$990$	7.28887	0.231656
$991$	−17.6865	−0.561829	−0.280915	−	0.959733i	$-0.590638\pi$
$991$	−17.6865	−0.561829	−0.280915	+	0.959733i	$0.590638\pi$
$992$	−21.9347	−0.696429
$993$	2.54385	0.0807267
$994$	−2.13587	−0.0677455
$995$	−30.0040	−0.951191
$996$	−6.51516	−0.206441
$997$	52.9328	1.67640	0.838199	−	0.545365i	$-0.183609\pi$
$997$	52.9328	1.67640	0.838199	+	0.545365i	$0.183609\pi$
$998$	5.27669	0.167031
$999$	−7.60707	−0.240677

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1027.2.a.e.1.8	✓	22
3.2	odd	2		9243.2.a.q.1.15		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1027.2.a.e.1.8	✓	22	1.1	even	1	trivial
9243.2.a.q.1.15		22	3.2	odd	2

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:	\( N \)	\(=\)	\( 1027 = 13 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1027.a (trivial)

\(f(q)\)	\(=\)	\(q-0.313275 q^{2} +0.248152 q^{3} -1.90186 q^{4} -3.52042 q^{5} -0.0777396 q^{6} -3.93567 q^{7} +1.22235 q^{8} -2.93842 q^{9} +O(q^{10})\)	\(q-0.313275 q^{2} +0.248152 q^{3} -1.90186 q^{4} -3.52042 q^{5} -0.0777396 q^{6} -3.93567 q^{7} +1.22235 q^{8} -2.93842 q^{9} +1.10286 q^{10} -2.24919 q^{11} -0.471949 q^{12} -1.00000 q^{13} +1.23295 q^{14} -0.873597 q^{15} +3.42079 q^{16} +5.61013 q^{17} +0.920533 q^{18} -4.47858 q^{19} +6.69533 q^{20} -0.976642 q^{21} +0.704616 q^{22} -3.96564 q^{23} +0.303329 q^{24} +7.39333 q^{25} +0.313275 q^{26} -1.47363 q^{27} +7.48509 q^{28} +0.549577 q^{29} +0.273676 q^{30} +6.23792 q^{31} -3.51635 q^{32} -0.558141 q^{33} -1.75751 q^{34} +13.8552 q^{35} +5.58846 q^{36} +5.16214 q^{37} +1.40303 q^{38} -0.248152 q^{39} -4.30319 q^{40} -4.91563 q^{41} +0.305957 q^{42} -7.56404 q^{43} +4.27765 q^{44} +10.3445 q^{45} +1.24234 q^{46} -4.39448 q^{47} +0.848873 q^{48} +8.48948 q^{49} -2.31614 q^{50} +1.39216 q^{51} +1.90186 q^{52} +5.11605 q^{53} +0.461651 q^{54} +7.91810 q^{55} -4.81078 q^{56} -1.11137 q^{57} -0.172169 q^{58} -12.6055 q^{59} +1.66146 q^{60} +8.07278 q^{61} -1.95418 q^{62} +11.5646 q^{63} -5.73999 q^{64} +3.52042 q^{65} +0.174852 q^{66} +1.00118 q^{67} -10.6697 q^{68} -0.984081 q^{69} -4.34048 q^{70} -1.73233 q^{71} -3.59179 q^{72} -15.8128 q^{73} -1.61717 q^{74} +1.83467 q^{75} +8.51764 q^{76} +8.85208 q^{77} +0.0777396 q^{78} +1.00000 q^{79} -12.0426 q^{80} +8.44958 q^{81} +1.53994 q^{82} +13.8048 q^{83} +1.85744 q^{84} -19.7500 q^{85} +2.36962 q^{86} +0.136378 q^{87} -2.74931 q^{88} +9.74322 q^{89} -3.24066 q^{90} +3.93567 q^{91} +7.54209 q^{92} +1.54795 q^{93} +1.37668 q^{94} +15.7665 q^{95} -0.872589 q^{96} -16.5846 q^{97} -2.65954 q^{98} +6.60908 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 8 q^{2} + 4 q^{3} + 26 q^{4} + 5 q^{5} + 2 q^{6} + 4 q^{7} + 24 q^{8} + 30 q^{9}+O(q^{10}) \) 22 * q + 8 * q^2 + 4 * q^3 + 26 * q^4 + 5 * q^5 + 2 * q^6 + 4 * q^7 + 24 * q^8 + 30 * q^9	\( 22 q + 8 q^{2} + 4 q^{3} + 26 q^{4} + 5 q^{5} + 2 q^{6} + 4 q^{7} + 24 q^{8} + 30 q^{9} + 4 q^{10} + 6 q^{11} + 11 q^{12} - 22 q^{13} + 6 q^{14} + 4 q^{15} + 42 q^{16} + 23 q^{17} + 27 q^{18} - 3 q^{19} + 11 q^{20} + 10 q^{21} + 14 q^{22} + 25 q^{23} + 18 q^{24} + 29 q^{25} - 8 q^{26} + 13 q^{27} + q^{28} + 44 q^{29} - 46 q^{30} - 9 q^{31} + 61 q^{32} + 8 q^{33} + 2 q^{34} + 14 q^{35} + 36 q^{36} + 22 q^{37} - 3 q^{38} - 4 q^{39} - 23 q^{41} - 27 q^{42} + 7 q^{43} - 9 q^{44} + 24 q^{45} + 28 q^{46} - 19 q^{47} + 25 q^{48} + 42 q^{49} + 28 q^{50} + 2 q^{51} - 26 q^{52} + 69 q^{53} - 16 q^{54} + 12 q^{55} - 11 q^{56} + 23 q^{57} + 14 q^{58} + q^{59} - 54 q^{60} + 22 q^{61} + 24 q^{62} + 47 q^{63} + 12 q^{64} - 5 q^{65} - 32 q^{66} + 53 q^{68} + 4 q^{69} - 77 q^{70} + 6 q^{71} + 80 q^{72} - 5 q^{73} + 74 q^{74} + 46 q^{75} - 46 q^{76} + 67 q^{77} - 2 q^{78} + 22 q^{79} - 16 q^{80} - 14 q^{81} - 66 q^{82} + 23 q^{83} - 37 q^{84} + 35 q^{85} - 53 q^{86} + 24 q^{87} + 26 q^{88} - 26 q^{89} - 34 q^{90} - 4 q^{91} + 60 q^{92} + 5 q^{93} - 40 q^{94} + 47 q^{95} - 16 q^{96} + 4 q^{97} + 31 q^{98} - 74 q^{99}+O(q^{100}) \) 22 * q + 8 * q^2 + 4 * q^3 + 26 * q^4 + 5 * q^5 + 2 * q^6 + 4 * q^7 + 24 * q^8 + 30 * q^9 + 4 * q^10 + 6 * q^11 + 11 * q^12 - 22 * q^13 + 6 * q^14 + 4 * q^15 + 42 * q^16 + 23 * q^17 + 27 * q^18 - 3 * q^19 + 11 * q^20 + 10 * q^21 + 14 * q^22 + 25 * q^23 + 18 * q^24 + 29 * q^25 - 8 * q^26 + 13 * q^27 + q^28 + 44 * q^29 - 46 * q^30 - 9 * q^31 + 61 * q^32 + 8 * q^33 + 2 * q^34 + 14 * q^35 + 36 * q^36 + 22 * q^37 - 3 * q^38 - 4 * q^39 - 23 * q^41 - 27 * q^42 + 7 * q^43 - 9 * q^44 + 24 * q^45 + 28 * q^46 - 19 * q^47 + 25 * q^48 + 42 * q^49 + 28 * q^50 + 2 * q^51 - 26 * q^52 + 69 * q^53 - 16 * q^54 + 12 * q^55 - 11 * q^56 + 23 * q^57 + 14 * q^58 + q^59 - 54 * q^60 + 22 * q^61 + 24 * q^62 + 47 * q^63 + 12 * q^64 - 5 * q^65 - 32 * q^66 + 53 * q^68 + 4 * q^69 - 77 * q^70 + 6 * q^71 + 80 * q^72 - 5 * q^73 + 74 * q^74 + 46 * q^75 - 46 * q^76 + 67 * q^77 - 2 * q^78 + 22 * q^79 - 16 * q^80 - 14 * q^81 - 66 * q^82 + 23 * q^83 - 37 * q^84 + 35 * q^85 - 53 * q^86 + 24 * q^87 + 26 * q^88 - 26 * q^89 - 34 * q^90 - 4 * q^91 + 60 * q^92 + 5 * q^93 - 40 * q^94 + 47 * q^95 - 16 * q^96 + 4 * q^97 + 31 * q^98 - 74 * q^99

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