LMFDB - Embedded newform 6026.2.a.l.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.00646 q^{3} +1.00000 q^{4} +2.50601 q^{5} +3.00646 q^{6} -2.50762 q^{7} -1.00000 q^{8} +6.03882 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.00646 q^{3} +1.00000 q^{4} +2.50601 q^{5} +3.00646 q^{6} -2.50762 q^{7} -1.00000 q^{8} +6.03882 q^{9} -2.50601 q^{10} -1.29382 q^{11} -3.00646 q^{12} -6.66770 q^{13} +2.50762 q^{14} -7.53421 q^{15} +1.00000 q^{16} +1.24362 q^{17} -6.03882 q^{18} +8.26254 q^{19} +2.50601 q^{20} +7.53907 q^{21} +1.29382 q^{22} -1.00000 q^{23} +3.00646 q^{24} +1.28006 q^{25} +6.66770 q^{26} -9.13610 q^{27} -2.50762 q^{28} -9.40302 q^{29} +7.53421 q^{30} +0.137788 q^{31} -1.00000 q^{32} +3.88982 q^{33} -1.24362 q^{34} -6.28411 q^{35} +6.03882 q^{36} -8.52990 q^{37} -8.26254 q^{38} +20.0462 q^{39} -2.50601 q^{40} -4.48427 q^{41} -7.53907 q^{42} +2.37738 q^{43} -1.29382 q^{44} +15.1333 q^{45} +1.00000 q^{46} +9.29087 q^{47} -3.00646 q^{48} -0.711842 q^{49} -1.28006 q^{50} -3.73888 q^{51} -6.66770 q^{52} -12.9673 q^{53} +9.13610 q^{54} -3.24232 q^{55} +2.50762 q^{56} -24.8410 q^{57} +9.40302 q^{58} +10.9706 q^{59} -7.53421 q^{60} +13.0697 q^{61} -0.137788 q^{62} -15.1431 q^{63} +1.00000 q^{64} -16.7093 q^{65} -3.88982 q^{66} +3.80909 q^{67} +1.24362 q^{68} +3.00646 q^{69} +6.28411 q^{70} -6.69762 q^{71} -6.03882 q^{72} +4.66130 q^{73} +8.52990 q^{74} -3.84847 q^{75} +8.26254 q^{76} +3.24441 q^{77} -20.0462 q^{78} -8.73193 q^{79} +2.50601 q^{80} +9.35090 q^{81} +4.48427 q^{82} -0.628645 q^{83} +7.53907 q^{84} +3.11651 q^{85} -2.37738 q^{86} +28.2698 q^{87} +1.29382 q^{88} +9.00118 q^{89} -15.1333 q^{90} +16.7201 q^{91} -1.00000 q^{92} -0.414255 q^{93} -9.29087 q^{94} +20.7060 q^{95} +3.00646 q^{96} -12.5808 q^{97} +0.711842 q^{98} -7.81315 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) $ 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9} - q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 36 q^{16} - 4 q^{17} - 46 q^{18} + 29 q^{19} + q^{20} + 24 q^{21} - 14 q^{22} - 36 q^{23} - 4 q^{24} + 49 q^{25} - 4 q^{26} + 19 q^{27} + 13 q^{28} - 13 q^{29} - 10 q^{30} + 21 q^{31} - 36 q^{32} - 5 q^{33} + 4 q^{34} + 30 q^{35} + 46 q^{36} + 13 q^{37} - 29 q^{38} + 30 q^{39} - q^{40} - 8 q^{41} - 24 q^{42} + 42 q^{43} + 14 q^{44} + 30 q^{45} + 36 q^{46} - 14 q^{47} + 4 q^{48} + 61 q^{49} - 49 q^{50} + 46 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + 26 q^{55} - 13 q^{56} + 26 q^{57} + 13 q^{58} + 45 q^{59} + 10 q^{60} + 34 q^{61} - 21 q^{62} + 63 q^{63} + 36 q^{64} - 25 q^{65} + 5 q^{66} + 42 q^{67} - 4 q^{68} - 4 q^{69} - 30 q^{70} - 2 q^{71} - 46 q^{72} + 16 q^{73} - 13 q^{74} + 72 q^{75} + 29 q^{76} - 36 q^{77} - 30 q^{78} + 33 q^{79} + q^{80} + 96 q^{81} + 8 q^{82} + 8 q^{83} + 24 q^{84} + 18 q^{85} - 42 q^{86} + 11 q^{87} - 14 q^{88} + 21 q^{89} - 30 q^{90} + 60 q^{91} - 36 q^{92} - 27 q^{93} + 14 q^{94} - 44 q^{95} - 4 q^{96} + 20 q^{97} - 61 q^{98} + 76 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9 - q^10 + 14 * q^11 + 4 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 36 * q^16 - 4 * q^17 - 46 * q^18 + 29 * q^19 + q^20 + 24 * q^21 - 14 * q^22 - 36 * q^23 - 4 * q^24 + 49 * q^25 - 4 * q^26 + 19 * q^27 + 13 * q^28 - 13 * q^29 - 10 * q^30 + 21 * q^31 - 36 * q^32 - 5 * q^33 + 4 * q^34 + 30 * q^35 + 46 * q^36 + 13 * q^37 - 29 * q^38 + 30 * q^39 - q^40 - 8 * q^41 - 24 * q^42 + 42 * q^43 + 14 * q^44 + 30 * q^45 + 36 * q^46 - 14 * q^47 + 4 * q^48 + 61 * q^49 - 49 * q^50 + 46 * q^51 + 4 * q^52 - 3 * q^53 - 19 * q^54 + 26 * q^55 - 13 * q^56 + 26 * q^57 + 13 * q^58 + 45 * q^59 + 10 * q^60 + 34 * q^61 - 21 * q^62 + 63 * q^63 + 36 * q^64 - 25 * q^65 + 5 * q^66 + 42 * q^67 - 4 * q^68 - 4 * q^69 - 30 * q^70 - 2 * q^71 - 46 * q^72 + 16 * q^73 - 13 * q^74 + 72 * q^75 + 29 * q^76 - 36 * q^77 - 30 * q^78 + 33 * q^79 + q^80 + 96 * q^81 + 8 * q^82 + 8 * q^83 + 24 * q^84 + 18 * q^85 - 42 * q^86 + 11 * q^87 - 14 * q^88 + 21 * q^89 - 30 * q^90 + 60 * q^91 - 36 * q^92 - 27 * q^93 + 14 * q^94 - 44 * q^95 - 4 * q^96 + 20 * q^97 - 61 * q^98 + 76 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.00646	−1.73578	−0.867891	−	0.496754i	$-0.834525\pi$
$3$	−3.00646	−1.73578	−0.867891	+	0.496754i	$0.834525\pi$
$4$	1.00000	0.500000
$5$	2.50601	1.12072	0.560360	−	0.828249i	$-0.310663\pi$
$5$	2.50601	1.12072	0.560360	+	0.828249i	$0.310663\pi$
$6$	3.00646	1.22738
$7$	−2.50762	−0.947791	−0.473896	−	0.880581i	$-0.657153\pi$
$7$	−2.50762	−0.947791	−0.473896	+	0.880581i	$0.657153\pi$
$8$	−1.00000	−0.353553
$9$	6.03882	2.01294
$10$	−2.50601	−0.792469
$11$	−1.29382	−0.390101	−0.195051	−	0.980793i	$-0.562487\pi$
$11$	−1.29382	−0.390101	−0.195051	+	0.980793i	$0.562487\pi$
$12$	−3.00646	−0.867891
$13$	−6.66770	−1.84929	−0.924643	−	0.380834i	$-0.875637\pi$
$13$	−6.66770	−1.84929	−0.924643	+	0.380834i	$0.875637\pi$
$14$	2.50762	0.670190
$15$	−7.53421	−1.94533
$16$	1.00000	0.250000
$17$	1.24362	0.301621	0.150811	−	0.988563i	$-0.451812\pi$
$17$	1.24362	0.301621	0.150811	+	0.988563i	$0.451812\pi$
$18$	−6.03882	−1.42336
$19$	8.26254	1.89556	0.947778	−	0.318930i	$-0.103324\pi$
$19$	8.26254	1.89556	0.947778	+	0.318930i	$0.103324\pi$
$20$	2.50601	0.560360
$21$	7.53907	1.64516
$22$	1.29382	0.275843
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	3.00646	0.613692
$25$	1.28006	0.256013
$26$	6.66770	1.30764
$27$	−9.13610	−1.75824
$28$	−2.50762	−0.473896
$29$	−9.40302	−1.74610	−0.873048	−	0.487634i	$-0.837860\pi$
$29$	−9.40302	−1.74610	−0.873048	+	0.487634i	$0.837860\pi$
$30$	7.53421	1.37555
$31$	0.137788	0.0247475	0.0123738	−	0.999923i	$-0.496061\pi$
$31$	0.137788	0.0247475	0.0123738	+	0.999923i	$0.496061\pi$
$32$	−1.00000	−0.176777
$33$	3.88982	0.677131
$34$	−1.24362	−0.213278
$35$	−6.28411	−1.06221
$36$	6.03882	1.00647
$37$	−8.52990	−1.40231	−0.701154	−	0.713010i	$-0.747331\pi$
$37$	−8.52990	−1.40231	−0.701154	+	0.713010i	$0.747331\pi$
$38$	−8.26254	−1.34036
$39$	20.0462	3.20996
$40$	−2.50601	−0.396234
$41$	−4.48427	−0.700326	−0.350163	−	0.936689i	$-0.613874\pi$
$41$	−4.48427	−0.700326	−0.350163	+	0.936689i	$0.613874\pi$
$42$	−7.53907	−1.16330
$43$	2.37738	0.362547	0.181273	−	0.983433i	$-0.441978\pi$
$43$	2.37738	0.362547	0.181273	+	0.983433i	$0.441978\pi$
$44$	−1.29382	−0.195051
$45$	15.1333	2.25594
$46$	1.00000	0.147442
$47$	9.29087	1.35521	0.677606	−	0.735425i	$-0.263017\pi$
$47$	9.29087	1.35521	0.677606	+	0.735425i	$0.263017\pi$
$48$	−3.00646	−0.433946
$49$	−0.711842	−0.101692
$50$	−1.28006	−0.181028
$51$	−3.73888	−0.523549
$52$	−6.66770	−0.924643
$53$	−12.9673	−1.78119	−0.890596	−	0.454795i	$-0.849712\pi$
$53$	−12.9673	−1.78119	−0.890596	+	0.454795i	$0.849712\pi$
$54$	9.13610	1.24327
$55$	−3.24232	−0.437194
$56$	2.50762	0.335095
$57$	−24.8410	−3.29027
$58$	9.40302	1.23468
$59$	10.9706	1.42825	0.714125	−	0.700018i	$-0.246825\pi$
$59$	10.9706	1.42825	0.714125	+	0.700018i	$0.246825\pi$
$60$	−7.53421	−0.972663
$61$	13.0697	1.67341	0.836704	−	0.547656i	$-0.184480\pi$
$61$	13.0697	1.67341	0.836704	+	0.547656i	$0.184480\pi$
$62$	−0.137788	−0.0174991
$63$	−15.1431	−1.90785
$64$	1.00000	0.125000
$65$	−16.7093	−2.07253
$66$	−3.88982	−0.478804
$67$	3.80909	0.465354	0.232677	−	0.972554i	$-0.425251\pi$
$67$	3.80909	0.465354	0.232677	+	0.972554i	$0.425251\pi$
$68$	1.24362	0.150811
$69$	3.00646	0.361936
$70$	6.28411	0.751095
$71$	−6.69762	−0.794861	−0.397431	−	0.917632i	$-0.630098\pi$
$71$	−6.69762	−0.794861	−0.397431	+	0.917632i	$0.630098\pi$
$72$	−6.03882	−0.711682
$73$	4.66130	0.545564	0.272782	−	0.962076i	$-0.412056\pi$
$73$	4.66130	0.545564	0.272782	+	0.962076i	$0.412056\pi$
$74$	8.52990	0.991581
$75$	−3.84847	−0.444383
$76$	8.26254	0.947778
$77$	3.24441	0.369735
$78$	−20.0462	−2.26978
$79$	−8.73193	−0.982419	−0.491209	−	0.871042i	$-0.663445\pi$
$79$	−8.73193	−0.982419	−0.491209	+	0.871042i	$0.663445\pi$
$80$	2.50601	0.280180
$81$	9.35090	1.03899
$82$	4.48427	0.495205
$83$	−0.628645	−0.0690027	−0.0345014	−	0.999405i	$-0.510984\pi$
$83$	−0.628645	−0.0690027	−0.0345014	+	0.999405i	$0.510984\pi$
$84$	7.53907	0.822580
$85$	3.11651	0.338033
$86$	−2.37738	−0.256359
$87$	28.2698	3.03084
$88$	1.29382	0.137922
$89$	9.00118	0.954123	0.477062	−	0.878870i	$-0.341702\pi$
$89$	9.00118	0.954123	0.477062	+	0.878870i	$0.341702\pi$
$90$	−15.1333	−1.59519
$91$	16.7201	1.75274
$92$	−1.00000	−0.104257
$93$	−0.414255	−0.0429563
$94$	−9.29087	−0.958280
$95$	20.7060	2.12439
$96$	3.00646	0.306846
$97$	−12.5808	−1.27738	−0.638692	−	0.769463i	$-0.720524\pi$
$97$	−12.5808	−1.27738	−0.638692	+	0.769463i	$0.720524\pi$
$98$	0.711842	0.0719069
$99$	−7.81315	−0.785251
$100$	1.28006	0.128006
$101$	−2.20165	−0.219072	−0.109536	−	0.993983i	$-0.534937\pi$
$101$	−2.20165	−0.219072	−0.109536	+	0.993983i	$0.534937\pi$
$102$	3.73888	0.370205
$103$	−12.2384	−1.20589	−0.602944	−	0.797783i	$-0.706006\pi$
$103$	−12.2384	−1.20589	−0.602944	+	0.797783i	$0.706006\pi$
$104$	6.66770	0.653822
$105$	18.8929	1.84376
$106$	12.9673	1.25949
$107$	8.77167	0.847989	0.423995	−	0.905665i	$-0.360628\pi$
$107$	8.77167	0.847989	0.423995	+	0.905665i	$0.360628\pi$
$108$	−9.13610	−0.879122
$109$	12.0726	1.15635	0.578174	−	0.815913i	$-0.303765\pi$
$109$	12.0726	1.15635	0.578174	+	0.815913i	$0.303765\pi$
$110$	3.24232	0.309143
$111$	25.6448	2.43410
$112$	−2.50762	−0.236948
$113$	2.67688	0.251820	0.125910	−	0.992042i	$-0.459815\pi$
$113$	2.67688	0.251820	0.125910	+	0.992042i	$0.459815\pi$
$114$	24.8410	2.32657
$115$	−2.50601	−0.233686
$116$	−9.40302	−0.873048
$117$	−40.2650	−3.72250
$118$	−10.9706	−1.00993
$119$	−3.11852	−0.285874
$120$	7.53421	0.687776
$121$	−9.32603	−0.847821
$122$	−13.0697	−1.18328
$123$	13.4818	1.21561
$124$	0.137788	0.0123738
$125$	−9.32218	−0.833801
$126$	15.1431	1.34905
$127$	−2.44929	−0.217340	−0.108670	−	0.994078i	$-0.534659\pi$
$127$	−2.44929	−0.217340	−0.108670	+	0.994078i	$0.534659\pi$
$128$	−1.00000	−0.0883883
$129$	−7.14750	−0.629302
$130$	16.7093	1.46550
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	3.88982	0.338566
$133$	−20.7193	−1.79659
$134$	−3.80909	−0.329055
$135$	−22.8951	−1.97050
$136$	−1.24362	−0.106639
$137$	9.11192	0.778483	0.389242	−	0.921136i	$-0.372737\pi$
$137$	9.11192	0.778483	0.389242	+	0.921136i	$0.372737\pi$
$138$	−3.00646	−0.255927
$139$	−13.1183	−1.11268	−0.556338	−	0.830956i	$-0.687794\pi$
$139$	−13.1183	−1.11268	−0.556338	+	0.830956i	$0.687794\pi$
$140$	−6.28411	−0.531104
$141$	−27.9327	−2.35235
$142$	6.69762	0.562052
$143$	8.62680	0.721409
$144$	6.03882	0.503235
$145$	−23.5640	−1.95688
$146$	−4.66130	−0.385772
$147$	2.14013	0.176515
$148$	−8.52990	−0.701154
$149$	0.649281	0.0531912	0.0265956	−	0.999646i	$-0.491533\pi$
$149$	0.649281	0.0531912	0.0265956	+	0.999646i	$0.491533\pi$
$150$	3.84847	0.314226
$151$	−2.88254	−0.234578	−0.117289	−	0.993098i	$-0.537420\pi$
$151$	−2.88254	−0.234578	−0.117289	+	0.993098i	$0.537420\pi$
$152$	−8.26254	−0.670180
$153$	7.50997	0.607145
$154$	−3.24441	−0.261442
$155$	0.345298	0.0277350
$156$	20.0462	1.60498
$157$	12.8677	1.02695	0.513476	−	0.858104i	$-0.328358\pi$
$157$	12.8677	1.02695	0.513476	+	0.858104i	$0.328358\pi$
$158$	8.73193	0.694675
$159$	38.9856	3.09176
$160$	−2.50601	−0.198117
$161$	2.50762	0.197628
$162$	−9.35090	−0.734676
$163$	−22.3819	−1.75308	−0.876542	−	0.481326i	$-0.840155\pi$
$163$	−22.3819	−1.75308	−0.876542	+	0.481326i	$0.840155\pi$
$164$	−4.48427	−0.350163
$165$	9.74792	0.758874
$166$	0.628645	0.0487923
$167$	13.1566	1.01809	0.509043	−	0.860741i	$-0.329999\pi$
$167$	13.1566	1.01809	0.509043	+	0.860741i	$0.329999\pi$
$168$	−7.53907	−0.581652
$169$	31.4582	2.41986
$170$	−3.11651	−0.239025
$171$	49.8960	3.81564
$172$	2.37738	0.181273
$173$	7.94819	0.604290	0.302145	−	0.953262i	$-0.402297\pi$
$173$	7.94819	0.604290	0.302145	+	0.953262i	$0.402297\pi$
$174$	−28.2698	−2.14313
$175$	−3.20992	−0.242647
$176$	−1.29382	−0.0975253
$177$	−32.9827	−2.47913
$178$	−9.00118	−0.674667
$179$	−8.42458	−0.629683	−0.314841	−	0.949144i	$-0.601951\pi$
$179$	−8.42458	−0.629683	−0.314841	+	0.949144i	$0.601951\pi$
$180$	15.1333	1.12797
$181$	3.22355	0.239605	0.119802	−	0.992798i	$-0.461774\pi$
$181$	3.22355	0.239605	0.119802	+	0.992798i	$0.461774\pi$
$182$	−16.7201	−1.23937
$183$	−39.2937	−2.90467
$184$	1.00000	0.0737210
$185$	−21.3760	−1.57159
$186$	0.414255	0.0303747
$187$	−1.60901	−0.117663
$188$	9.29087	0.677606
$189$	22.9099	1.66645
$190$	−20.7060	−1.50217
$191$	21.3126	1.54212	0.771061	−	0.636761i	$-0.219726\pi$
$191$	21.3126	1.54212	0.771061	+	0.636761i	$0.219726\pi$
$192$	−3.00646	−0.216973
$193$	−15.8219	−1.13888	−0.569441	−	0.822032i	$-0.692840\pi$
$193$	−15.8219	−1.13888	−0.569441	+	0.822032i	$0.692840\pi$
$194$	12.5808	0.903247
$195$	50.2359	3.59746
$196$	−0.711842	−0.0508459
$197$	8.72935	0.621941	0.310970	−	0.950420i	$-0.399346\pi$
$197$	8.72935	0.621941	0.310970	+	0.950420i	$0.399346\pi$
$198$	7.81315	0.555256
$199$	−0.0574564	−0.00407297	−0.00203649	−	0.999998i	$-0.500648\pi$
$199$	−0.0574564	−0.00407297	−0.00203649	+	0.999998i	$0.500648\pi$
$200$	−1.28006	−0.0905142
$201$	−11.4519	−0.807754
$202$	2.20165	0.154907
$203$	23.5792	1.65493
$204$	−3.73888	−0.261774
$205$	−11.2376	−0.784869
$206$	12.2384	0.852692
$207$	−6.03882	−0.419727
$208$	−6.66770	−0.462322
$209$	−10.6902	−0.739459
$210$	−18.8929	−1.30374
$211$	−11.0923	−0.763625	−0.381812	−	0.924240i	$-0.624700\pi$
$211$	−11.0923	−0.763625	−0.381812	+	0.924240i	$0.624700\pi$
$212$	−12.9673	−0.890596
$213$	20.1362	1.37971
$214$	−8.77167	−0.599619
$215$	5.95772	0.406313
$216$	9.13610	0.621633
$217$	−0.345521	−0.0234555
$218$	−12.0726	−0.817662
$219$	−14.0140	−0.946980
$220$	−3.24232	−0.218597
$221$	−8.29205	−0.557784
$222$	−25.6448	−1.72117
$223$	0.488088	0.0326848	0.0163424	−	0.999866i	$-0.494798\pi$
$223$	0.488088	0.0326848	0.0163424	+	0.999866i	$0.494798\pi$
$224$	2.50762	0.167547
$225$	7.73008	0.515339
$226$	−2.67688	−0.178064
$227$	1.69420	0.112448	0.0562240	−	0.998418i	$-0.482094\pi$
$227$	1.69420	0.112448	0.0562240	+	0.998418i	$0.482094\pi$
$228$	−24.8410	−1.64514
$229$	−18.7418	−1.23850	−0.619248	−	0.785195i	$-0.712562\pi$
$229$	−18.7418	−1.23850	−0.619248	+	0.785195i	$0.712562\pi$
$230$	2.50601	0.165241
$231$	−9.75419	−0.641779
$232$	9.40302	0.617338
$233$	−28.2672	−1.85185	−0.925924	−	0.377709i	$-0.876712\pi$
$233$	−28.2672	−1.85185	−0.925924	+	0.377709i	$0.876712\pi$
$234$	40.2650	2.63221
$235$	23.2830	1.51881
$236$	10.9706	0.714125
$237$	26.2522	1.70526
$238$	3.11852	0.202143
$239$	−17.3711	−1.12365	−0.561823	−	0.827257i	$-0.689900\pi$
$239$	−17.3711	−1.12365	−0.561823	+	0.827257i	$0.689900\pi$
$240$	−7.53421	−0.486331
$241$	−16.4329	−1.05854	−0.529270	−	0.848454i	$-0.677534\pi$
$241$	−16.4329	−1.05854	−0.529270	+	0.848454i	$0.677534\pi$
$242$	9.32603	0.599500
$243$	−0.704814	−0.0452139
$244$	13.0697	0.836704
$245$	−1.78388	−0.113968
$246$	−13.4818	−0.859568
$247$	−55.0921	−3.50543
$248$	−0.137788	−0.00874956
$249$	1.89000	0.119774
$250$	9.32218	0.589586
$251$	−10.4372	−0.658790	−0.329395	−	0.944192i	$-0.606845\pi$
$251$	−10.4372	−0.658790	−0.329395	+	0.944192i	$0.606845\pi$
$252$	−15.1431	−0.953924
$253$	1.29382	0.0813418
$254$	2.44929	0.153682
$255$	−9.36967	−0.586751
$256$	1.00000	0.0625000
$257$	7.55134	0.471040	0.235520	−	0.971870i	$-0.424321\pi$
$257$	7.55134	0.471040	0.235520	+	0.971870i	$0.424321\pi$
$258$	7.14750	0.444984
$259$	21.3898	1.32909
$260$	−16.7093	−1.03627
$261$	−56.7831	−3.51479
$262$	−1.00000	−0.0617802
$263$	−12.9191	−0.796627	−0.398313	−	0.917249i	$-0.630404\pi$
$263$	−12.9191	−0.796627	−0.398313	+	0.917249i	$0.630404\pi$
$264$	−3.88982	−0.239402
$265$	−32.4961	−1.99622
$266$	20.7193	1.27038
$267$	−27.0617	−1.65615
$268$	3.80909	0.232677
$269$	1.51476	0.0923563	0.0461782	−	0.998933i	$-0.485296\pi$
$269$	1.51476	0.0923563	0.0461782	+	0.998933i	$0.485296\pi$
$270$	22.8951	1.39335
$271$	14.6479	0.889796	0.444898	−	0.895581i	$-0.353240\pi$
$271$	14.6479	0.889796	0.444898	+	0.895581i	$0.353240\pi$
$272$	1.24362	0.0754053
$273$	−50.2682	−3.04237
$274$	−9.11192	−0.550471
$275$	−1.65617	−0.0998710
$276$	3.00646	0.180968
$277$	30.2943	1.82021	0.910103	−	0.414381i	$-0.136002\pi$
$277$	30.2943	1.82021	0.910103	+	0.414381i	$0.136002\pi$
$278$	13.1183	0.786781
$279$	0.832079	0.0498152
$280$	6.28411	0.375547
$281$	7.23133	0.431385	0.215692	−	0.976461i	$-0.430799\pi$
$281$	7.23133	0.431385	0.215692	+	0.976461i	$0.430799\pi$
$282$	27.9327	1.66337
$283$	18.2907	1.08727	0.543635	−	0.839322i	$-0.317048\pi$
$283$	18.2907	1.08727	0.543635	+	0.839322i	$0.317048\pi$
$284$	−6.69762	−0.397431
$285$	−62.2517	−3.68747
$286$	−8.62680	−0.510113
$287$	11.2449	0.663763
$288$	−6.03882	−0.355841
$289$	−15.4534	−0.909025
$290$	23.5640	1.38373
$291$	37.8236	2.21726
$292$	4.66130	0.272782
$293$	1.00801	0.0588884	0.0294442	−	0.999566i	$-0.490626\pi$
$293$	1.00801	0.0588884	0.0294442	+	0.999566i	$0.490626\pi$
$294$	−2.14013	−0.124815
$295$	27.4924	1.60067
$296$	8.52990	0.495790
$297$	11.8205	0.685893
$298$	−0.649281	−0.0376118
$299$	6.66770	0.385603
$300$	−3.84847	−0.222191
$301$	−5.96156	−0.343619
$302$	2.88254	0.165872
$303$	6.61918	0.380262
$304$	8.26254	0.473889
$305$	32.7528	1.87542
$306$	−7.50997	−0.429317
$307$	4.30381	0.245631	0.122816	−	0.992429i	$-0.460808\pi$
$307$	4.30381	0.245631	0.122816	+	0.992429i	$0.460808\pi$
$308$	3.24441	0.184867
$309$	36.7944	2.09316
$310$	−0.345298	−0.0196116
$311$	15.5600	0.882326	0.441163	−	0.897427i	$-0.354566\pi$
$311$	15.5600	0.882326	0.441163	+	0.897427i	$0.354566\pi$
$312$	−20.0462	−1.13489
$313$	−25.5909	−1.44648	−0.723241	−	0.690596i	$-0.757348\pi$
$313$	−25.5909	−1.44648	−0.723241	+	0.690596i	$0.757348\pi$
$314$	−12.8677	−0.726165
$315$	−37.9486	−2.13816
$316$	−8.73193	−0.491209
$317$	−16.6767	−0.936658	−0.468329	−	0.883554i	$-0.655144\pi$
$317$	−16.6767	−0.936658	−0.468329	+	0.883554i	$0.655144\pi$
$318$	−38.9856	−2.18621
$319$	12.1658	0.681155
$320$	2.50601	0.140090
$321$	−26.3717	−1.47192
$322$	−2.50762	−0.139744
$323$	10.2754	0.571740
$324$	9.35090	0.519494
$325$	−8.53508	−0.473441
$326$	22.3819	1.23962
$327$	−36.2959	−2.00717
$328$	4.48427	0.247603
$329$	−23.2980	−1.28446
$330$	−9.74792	−0.536605
$331$	21.9577	1.20690	0.603451	−	0.797400i	$-0.293792\pi$
$331$	21.9577	1.20690	0.603451	+	0.797400i	$0.293792\pi$
$332$	−0.628645	−0.0345014
$333$	−51.5106	−2.82276
$334$	−13.1566	−0.719896
$335$	9.54560	0.521532
$336$	7.53907	0.411290
$337$	1.85713	0.101164	0.0505821	−	0.998720i	$-0.483892\pi$
$337$	1.85713	0.101164	0.0505821	+	0.998720i	$0.483892\pi$
$338$	−31.4582	−1.71110
$339$	−8.04795	−0.437105
$340$	3.11651	0.169016
$341$	−0.178273	−0.00965403
$342$	−49.8960	−2.69807
$343$	19.3384	1.04417
$344$	−2.37738	−0.128180
$345$	7.53421	0.405628
$346$	−7.94819	−0.427297
$347$	−17.0612	−0.915894	−0.457947	−	0.888979i	$-0.651415\pi$
$347$	−17.0612	−0.915894	−0.457947	+	0.888979i	$0.651415\pi$
$348$	28.2698	1.51542
$349$	10.7333	0.574542	0.287271	−	0.957849i	$-0.407252\pi$
$349$	10.7333	0.574542	0.287271	+	0.957849i	$0.407252\pi$
$350$	3.20992	0.171577
$351$	60.9168	3.25150
$352$	1.29382	0.0689608
$353$	13.4006	0.713243	0.356622	−	0.934249i	$-0.383929\pi$
$353$	13.4006	0.713243	0.356622	+	0.934249i	$0.383929\pi$
$354$	32.9827	1.75301
$355$	−16.7843	−0.890817
$356$	9.00118	0.477062
$357$	9.37570	0.496215
$358$	8.42458	0.445253
$359$	18.7691	0.990595	0.495297	−	0.868723i	$-0.335059\pi$
$359$	18.7691	0.990595	0.495297	+	0.868723i	$0.335059\pi$
$360$	−15.1333	−0.797596
$361$	49.2696	2.59313
$362$	−3.22355	−0.169426
$363$	28.0384	1.47163
$364$	16.7201	0.876369
$365$	11.6812	0.611424
$366$	39.2937	2.05391
$367$	23.5902	1.23140	0.615698	−	0.787982i	$-0.288874\pi$
$367$	23.5902	1.23140	0.615698	+	0.787982i	$0.288874\pi$
$368$	−1.00000	−0.0521286
$369$	−27.0797	−1.40971
$370$	21.3760	1.11128
$371$	32.5170	1.68820
$372$	−0.414255	−0.0214781
$373$	29.0798	1.50570	0.752848	−	0.658194i	$-0.228679\pi$
$373$	29.0798	1.50570	0.752848	+	0.658194i	$0.228679\pi$
$374$	1.60901	0.0832002
$375$	28.0268	1.44730
$376$	−9.29087	−0.479140
$377$	62.6965	3.22903
$378$	−22.9099	−1.17836
$379$	31.1902	1.60213	0.801066	−	0.598576i	$-0.204267\pi$
$379$	31.1902	1.60213	0.801066	+	0.598576i	$0.204267\pi$
$380$	20.7060	1.06219
$381$	7.36371	0.377254
$382$	−21.3126	−1.09045
$383$	−11.2059	−0.572593	−0.286297	−	0.958141i	$-0.592424\pi$
$383$	−11.2059	−0.572593	−0.286297	+	0.958141i	$0.592424\pi$
$384$	3.00646	0.153423
$385$	8.13051	0.414369
$386$	15.8219	0.805311
$387$	14.3566	0.729785
$388$	−12.5808	−0.638692
$389$	1.01972	0.0517018	0.0258509	−	0.999666i	$-0.491770\pi$
$389$	1.01972	0.0517018	0.0258509	+	0.999666i	$0.491770\pi$
$390$	−50.2359	−2.54379
$391$	−1.24362	−0.0628923
$392$	0.711842	0.0359535
$393$	−3.00646	−0.151656
$394$	−8.72935	−0.439778
$395$	−21.8823	−1.10102
$396$	−7.81315	−0.392625
$397$	29.0224	1.45659	0.728296	−	0.685262i	$-0.240313\pi$
$397$	29.0224	1.45659	0.728296	+	0.685262i	$0.240313\pi$
$398$	0.0574564	0.00288003
$399$	62.2918	3.11849
$400$	1.28006	0.0640032
$401$	−18.1806	−0.907894	−0.453947	−	0.891029i	$-0.649984\pi$
$401$	−18.1806	−0.907894	−0.453947	+	0.891029i	$0.649984\pi$
$402$	11.4519	0.571168
$403$	−0.918730	−0.0457652
$404$	−2.20165	−0.109536
$405$	23.4334	1.16441
$406$	−23.5792	−1.17022
$407$	11.0362	0.547042
$408$	3.73888	0.185102
$409$	4.33010	0.214110	0.107055	−	0.994253i	$-0.465858\pi$
$409$	4.33010	0.214110	0.107055	+	0.994253i	$0.465858\pi$
$410$	11.2376	0.554986
$411$	−27.3946	−1.35128
$412$	−12.2384	−0.602944
$413$	−27.5101	−1.35368
$414$	6.03882	0.296792
$415$	−1.57539	−0.0773327
$416$	6.66770	0.326911
$417$	39.4396	1.93136
$418$	10.6902	0.522877
$419$	4.36757	0.213370	0.106685	−	0.994293i	$-0.465976\pi$
$419$	4.36757	0.213370	0.106685	+	0.994293i	$0.465976\pi$
$420$	18.8929	0.921881
$421$	11.5596	0.563378	0.281689	−	0.959506i	$-0.409105\pi$
$421$	11.5596	0.563378	0.281689	+	0.959506i	$0.409105\pi$
$422$	11.0923	0.539964
$423$	56.1059	2.72796
$424$	12.9673	0.629746
$425$	1.59191	0.0772189
$426$	−20.1362	−0.975600
$427$	−32.7739	−1.58604
$428$	8.77167	0.423995
$429$	−25.9362	−1.25221
$430$	−5.95772	−0.287307
$431$	−11.9835	−0.577226	−0.288613	−	0.957446i	$-0.593194\pi$
$431$	−11.9835	−0.577226	−0.288613	+	0.957446i	$0.593194\pi$
$432$	−9.13610	−0.439561
$433$	20.5266	0.986444	0.493222	−	0.869904i	$-0.335819\pi$
$433$	20.5266	0.986444	0.493222	+	0.869904i	$0.335819\pi$
$434$	0.345521	0.0165855
$435$	70.8443	3.39673
$436$	12.0726	0.578174
$437$	−8.26254	−0.395251
$438$	14.0140	0.669616
$439$	14.5210	0.693049	0.346524	−	0.938041i	$-0.387362\pi$
$439$	14.5210	0.693049	0.346524	+	0.938041i	$0.387362\pi$
$440$	3.24232	0.154572
$441$	−4.29869	−0.204699
$442$	8.29205	0.394413
$443$	37.2452	1.76957	0.884787	−	0.465996i	$-0.154304\pi$
$443$	37.2452	1.76957	0.884787	+	0.465996i	$0.154304\pi$
$444$	25.6448	1.21705
$445$	22.5570	1.06930
$446$	−0.488088	−0.0231116
$447$	−1.95204	−0.0923283
$448$	−2.50762	−0.118474
$449$	−9.48177	−0.447472	−0.223736	−	0.974650i	$-0.571825\pi$
$449$	−9.48177	−0.447472	−0.223736	+	0.974650i	$0.571825\pi$
$450$	−7.73008	−0.364400
$451$	5.80184	0.273198
$452$	2.67688	0.125910
$453$	8.66625	0.407176
$454$	−1.69420	−0.0795127
$455$	41.9005	1.96433
$456$	24.8410	1.16329
$457$	29.4795	1.37899	0.689497	−	0.724289i	$-0.257832\pi$
$457$	29.4795	1.37899	0.689497	+	0.724289i	$0.257832\pi$
$458$	18.7418	0.875749
$459$	−11.3618	−0.530323
$460$	−2.50601	−0.116843
$461$	9.25259	0.430936	0.215468	−	0.976511i	$-0.430872\pi$
$461$	9.25259	0.430936	0.215468	+	0.976511i	$0.430872\pi$
$462$	9.75419	0.453806
$463$	−33.2261	−1.54415	−0.772074	−	0.635532i	$-0.780781\pi$
$463$	−33.2261	−1.54415	−0.772074	+	0.635532i	$0.780781\pi$
$464$	−9.40302	−0.436524
$465$	−1.03813	−0.0481420
$466$	28.2672	1.30945
$467$	19.1458	0.885964	0.442982	−	0.896531i	$-0.353921\pi$
$467$	19.1458	0.885964	0.442982	+	0.896531i	$0.353921\pi$
$468$	−40.2650	−1.86125
$469$	−9.55175	−0.441059
$470$	−23.2830	−1.07396
$471$	−38.6862	−1.78257
$472$	−10.9706	−0.504963
$473$	−3.07590	−0.141430
$474$	−26.2522	−1.20580
$475$	10.5766	0.485287
$476$	−3.11852	−0.142937
$477$	−78.3070	−3.58543
$478$	17.3711	0.794538
$479$	−5.76393	−0.263361	−0.131680	−	0.991292i	$-0.542037\pi$
$479$	−5.76393	−0.263361	−0.131680	+	0.991292i	$0.542037\pi$
$480$	7.53421	0.343888
$481$	56.8748	2.59327
$482$	16.4329	0.748500
$483$	−7.53907	−0.343039
$484$	−9.32603	−0.423910
$485$	−31.5275	−1.43159
$486$	0.704814	0.0319710
$487$	31.9957	1.44986	0.724932	−	0.688821i	$-0.241871\pi$
$487$	31.9957	1.44986	0.724932	+	0.688821i	$0.241871\pi$
$488$	−13.0697	−0.591639
$489$	67.2903	3.04297
$490$	1.78388	0.0805875
$491$	15.9467	0.719665	0.359833	−	0.933017i	$-0.382834\pi$
$491$	15.9467	0.719665	0.359833	+	0.933017i	$0.382834\pi$
$492$	13.4818	0.607807
$493$	−11.6937	−0.526659
$494$	55.0921	2.47871
$495$	−19.5798	−0.880046
$496$	0.137788	0.00618688
$497$	16.7951	0.753363
$498$	−1.89000	−0.0846928
$499$	29.1343	1.30423	0.652116	−	0.758119i	$-0.273881\pi$
$499$	29.1343	1.30423	0.652116	+	0.758119i	$0.273881\pi$
$500$	−9.32218	−0.416901
$501$	−39.5548	−1.76718
$502$	10.4372	0.465835
$503$	7.91016	0.352697	0.176348	−	0.984328i	$-0.443571\pi$
$503$	7.91016	0.352697	0.176348	+	0.984328i	$0.443571\pi$
$504$	15.1431	0.674526
$505$	−5.51734	−0.245519
$506$	−1.29382	−0.0575173
$507$	−94.5779	−4.20035
$508$	−2.44929	−0.108670
$509$	15.7625	0.698663	0.349331	−	0.936999i	$-0.386409\pi$
$509$	15.7625	0.698663	0.349331	+	0.936999i	$0.386409\pi$
$510$	9.36967	0.414896
$511$	−11.6888	−0.517081
$512$	−1.00000	−0.0441942
$513$	−75.4874	−3.33285
$514$	−7.55134	−0.333075
$515$	−30.6696	−1.35146
$516$	−7.14750	−0.314651
$517$	−12.0207	−0.528670
$518$	−21.3898	−0.939812
$519$	−23.8959	−1.04892
$520$	16.7093	0.732751
$521$	8.00248	0.350595	0.175298	−	0.984515i	$-0.443911\pi$
$521$	8.00248	0.350595	0.175298	+	0.984515i	$0.443911\pi$
$522$	56.7831	2.48533
$523$	5.56669	0.243414	0.121707	−	0.992566i	$-0.461163\pi$
$523$	5.56669	0.243414	0.121707	+	0.992566i	$0.461163\pi$
$524$	1.00000	0.0436852
$525$	9.65049	0.421182
$526$	12.9191	0.563300
$527$	0.171356	0.00746437
$528$	3.88982	0.169283
$529$	1.00000	0.0434783
$530$	32.4961	1.41154
$531$	66.2495	2.87498
$532$	−20.7193	−0.898296
$533$	29.8998	1.29510
$534$	27.0617	1.17108
$535$	21.9818	0.950358
$536$	−3.80909	−0.164528
$537$	25.3282	1.09299
$538$	−1.51476	−0.0653058
$539$	0.920995	0.0396701
$540$	−22.8951	−0.985249
$541$	38.3104	1.64709	0.823545	−	0.567250i	$-0.191993\pi$
$541$	38.3104	1.64709	0.823545	+	0.567250i	$0.191993\pi$
$542$	−14.6479	−0.629181
$543$	−9.69150	−0.415902
$544$	−1.24362	−0.0533196
$545$	30.2541	1.29594
$546$	50.2682	2.15128
$547$	15.6170	0.667733	0.333867	−	0.942620i	$-0.391646\pi$
$547$	15.6170	0.667733	0.333867	+	0.942620i	$0.391646\pi$
$548$	9.11192	0.389242
$549$	78.9257	3.36847
$550$	1.65617	0.0706195
$551$	−77.6928	−3.30982
$552$	−3.00646	−0.127964
$553$	21.8964	0.931128
$554$	−30.2943	−1.28708
$555$	64.2661	2.72794
$556$	−13.1183	−0.556338
$557$	−18.3431	−0.777224	−0.388612	−	0.921401i	$-0.627045\pi$
$557$	−18.3431	−0.777224	−0.388612	+	0.921401i	$0.627045\pi$
$558$	−0.832079	−0.0352247
$559$	−15.8516	−0.670453
$560$	−6.28411	−0.265552
$561$	4.83744	0.204237
$562$	−7.23133	−0.305035
$563$	9.28543	0.391334	0.195667	−	0.980670i	$-0.437313\pi$
$563$	9.28543	0.391334	0.195667	+	0.980670i	$0.437313\pi$
$564$	−27.9327	−1.17618
$565$	6.70829	0.282220
$566$	−18.2907	−0.768816
$567$	−23.4485	−0.984744
$568$	6.69762	0.281026
$569$	27.2843	1.14382	0.571909	−	0.820317i	$-0.306203\pi$
$569$	27.2843	1.14382	0.571909	+	0.820317i	$0.306203\pi$
$570$	62.2517	2.60744
$571$	2.26041	0.0945952	0.0472976	−	0.998881i	$-0.484939\pi$
$571$	2.26041	0.0945952	0.0472976	+	0.998881i	$0.484939\pi$
$572$	8.62680	0.360705
$573$	−64.0754	−2.67679
$574$	−11.2449	−0.469351
$575$	−1.28006	−0.0533824
$576$	6.03882	0.251618
$577$	−2.71237	−0.112917	−0.0564587	−	0.998405i	$-0.517981\pi$
$577$	−2.71237	−0.112917	−0.0564587	+	0.998405i	$0.517981\pi$
$578$	15.4534	0.642778
$579$	47.5678	1.97685
$580$	−23.5640	−0.978442
$581$	1.57640	0.0654002
$582$	−37.8236	−1.56784
$583$	16.7773	0.694845
$584$	−4.66130	−0.192886
$585$	−100.904	−4.17188
$586$	−1.00801	−0.0416404
$587$	−27.3666	−1.12954	−0.564771	−	0.825248i	$-0.691035\pi$
$587$	−27.3666	−1.12954	−0.564771	+	0.825248i	$0.691035\pi$
$588$	2.14013	0.0882574
$589$	1.13848	0.0469103
$590$	−27.4924	−1.13184
$591$	−26.2445	−1.07955
$592$	−8.52990	−0.350577
$593$	36.2588	1.48897	0.744486	−	0.667638i	$-0.232695\pi$
$593$	36.2588	1.48897	0.744486	+	0.667638i	$0.232695\pi$
$594$	−11.8205	−0.485000
$595$	−7.81502	−0.320384
$596$	0.649281	0.0265956
$597$	0.172740	0.00706979
$598$	−6.66770	−0.272662
$599$	−40.0596	−1.63679	−0.818395	−	0.574657i	$-0.805136\pi$
$599$	−40.0596	−1.63679	−0.818395	+	0.574657i	$0.805136\pi$
$600$	3.84847	0.157113
$601$	12.5069	0.510168	0.255084	−	0.966919i	$-0.417897\pi$
$601$	12.5069	0.510168	0.255084	+	0.966919i	$0.417897\pi$
$602$	5.96156	0.242975
$603$	23.0024	0.936730
$604$	−2.88254	−0.117289
$605$	−23.3711	−0.950170
$606$	−6.61918	−0.268886
$607$	3.82039	0.155065	0.0775325	−	0.996990i	$-0.475296\pi$
$607$	3.82039	0.155065	0.0775325	+	0.996990i	$0.475296\pi$
$608$	−8.26254	−0.335090
$609$	−70.8900	−2.87261
$610$	−32.7528	−1.32612
$611$	−61.9487	−2.50618
$612$	7.50997	0.303573
$613$	−31.9859	−1.29190	−0.645949	−	0.763381i	$-0.723538\pi$
$613$	−31.9859	−1.29190	−0.645949	+	0.763381i	$0.723538\pi$
$614$	−4.30381	−0.173688
$615$	33.7855	1.36236
$616$	−3.24441	−0.130721
$617$	−4.76052	−0.191651	−0.0958256	−	0.995398i	$-0.530549\pi$
$617$	−4.76052	−0.191651	−0.0958256	+	0.995398i	$0.530549\pi$
$618$	−36.7944	−1.48009
$619$	4.60767	0.185198	0.0925989	−	0.995703i	$-0.470483\pi$
$619$	4.60767	0.185198	0.0925989	+	0.995703i	$0.470483\pi$
$620$	0.345298	0.0138675
$621$	9.13610	0.366619
$622$	−15.5600	−0.623899
$623$	−22.5715	−0.904310
$624$	20.0462	0.802490
$625$	−29.7618	−1.19047
$626$	25.5909	1.02282
$627$	32.1398	1.28354
$628$	12.8677	0.513476
$629$	−10.6079	−0.422965
$630$	37.9486	1.51191
$631$	−31.3497	−1.24801	−0.624007	−	0.781419i	$-0.714496\pi$
$631$	−31.3497	−1.24801	−0.624007	+	0.781419i	$0.714496\pi$
$632$	8.73193	0.347337
$633$	33.3486	1.32549
$634$	16.6767	0.662317
$635$	−6.13794	−0.243577
$636$	38.9856	1.54588
$637$	4.74635	0.188057
$638$	−12.1658	−0.481649
$639$	−40.4457	−1.60001
$640$	−2.50601	−0.0990586
$641$	39.4387	1.55774	0.778868	−	0.627188i	$-0.215794\pi$
$641$	39.4387	1.55774	0.778868	+	0.627188i	$0.215794\pi$
$642$	26.3717	1.04081
$643$	0.148218	0.00584517	0.00292258	−	0.999996i	$-0.499070\pi$
$643$	0.148218	0.00584517	0.00292258	+	0.999996i	$0.499070\pi$
$644$	2.50762	0.0988141
$645$	−17.9117	−0.705271
$646$	−10.2754	−0.404281
$647$	15.8739	0.624067	0.312034	−	0.950071i	$-0.398990\pi$
$647$	15.8739	0.624067	0.312034	+	0.950071i	$0.398990\pi$
$648$	−9.35090	−0.367338
$649$	−14.1940	−0.557162
$650$	8.53508	0.334774
$651$	1.03879	0.0407136
$652$	−22.3819	−0.876542
$653$	−4.34118	−0.169883	−0.0849417	−	0.996386i	$-0.527070\pi$
$653$	−4.34118	−0.169883	−0.0849417	+	0.996386i	$0.527070\pi$
$654$	36.2959	1.41928
$655$	2.50601	0.0979177
$656$	−4.48427	−0.175081
$657$	28.1488	1.09819
$658$	23.2980	0.908249
$659$	48.1801	1.87683	0.938416	−	0.345509i	$-0.112294\pi$
$659$	48.1801	1.87683	0.938416	+	0.345509i	$0.112294\pi$
$660$	9.74792	0.379437
$661$	−12.7146	−0.494541	−0.247271	−	0.968946i	$-0.579534\pi$
$661$	−12.7146	−0.494541	−0.247271	+	0.968946i	$0.579534\pi$
$662$	−21.9577	−0.853409
$663$	24.9298	0.968191
$664$	0.628645	0.0243962
$665$	−51.9227	−2.01348
$666$	51.5106	1.99599
$667$	9.40302	0.364086
$668$	13.1566	0.509043
$669$	−1.46742	−0.0567336
$670$	−9.54560	−0.368779
$671$	−16.9099	−0.652798
$672$	−7.53907	−0.290826
$673$	−50.7422	−1.95597	−0.977984	−	0.208682i	$-0.933083\pi$
$673$	−50.7422	−1.95597	−0.977984	+	0.208682i	$0.933083\pi$
$674$	−1.85713	−0.0715339
$675$	−11.6948	−0.450133
$676$	31.4582	1.20993
$677$	−36.0949	−1.38724	−0.693620	−	0.720341i	$-0.743985\pi$
$677$	−36.0949	−1.38724	−0.693620	+	0.720341i	$0.743985\pi$
$678$	8.04795	0.309080
$679$	31.5478	1.21069
$680$	−3.11651	−0.119513
$681$	−5.09355	−0.195185
$682$	0.178273	0.00682643
$683$	−13.4796	−0.515782	−0.257891	−	0.966174i	$-0.583028\pi$
$683$	−13.4796	−0.515782	−0.257891	+	0.966174i	$0.583028\pi$
$684$	49.8960	1.90782
$685$	22.8345	0.872462
$686$	−19.3384	−0.738342
$687$	56.3467	2.14976
$688$	2.37738	0.0906367
$689$	86.4618	3.29393
$690$	−7.53421	−0.286823
$691$	−7.90424	−0.300691	−0.150346	−	0.988633i	$-0.548039\pi$
$691$	−7.90424	−0.300691	−0.150346	+	0.988633i	$0.548039\pi$
$692$	7.94819	0.302145
$693$	19.5924	0.744254
$694$	17.0612	0.647635
$695$	−32.8744	−1.24700
$696$	−28.2698	−1.07156
$697$	−5.57671	−0.211233
$698$	−10.7333	−0.406263
$699$	84.9844	3.21441
$700$	−3.20992	−0.121323
$701$	−29.9288	−1.13040	−0.565198	−	0.824955i	$-0.691200\pi$
$701$	−29.9288	−1.13040	−0.565198	+	0.824955i	$0.691200\pi$
$702$	−60.9168	−2.29916
$703$	−70.4786	−2.65815
$704$	−1.29382	−0.0487627
$705$	−69.9994	−2.63633
$706$	−13.4006	−0.504339
$707$	5.52090	0.207635
$708$	−32.9827	−1.23957
$709$	14.6163	0.548928	0.274464	−	0.961597i	$-0.411500\pi$
$709$	14.6163	0.548928	0.274464	+	0.961597i	$0.411500\pi$
$710$	16.7843	0.629903
$711$	−52.7305	−1.97755
$712$	−9.00118	−0.337334
$713$	−0.137788	−0.00516021
$714$	−9.37570	−0.350877
$715$	21.6188	0.808498
$716$	−8.42458	−0.314841
$717$	52.2257	1.95040
$718$	−18.7691	−0.700456
$719$	10.8679	0.405303	0.202652	−	0.979251i	$-0.435044\pi$
$719$	10.8679	0.405303	0.202652	+	0.979251i	$0.435044\pi$
$720$	15.1333	0.563986
$721$	30.6893	1.14293
$722$	−49.2696	−1.83362
$723$	49.4050	1.83739
$724$	3.22355	0.119802
$725$	−12.0365	−0.447023
$726$	−28.0384	−1.04060
$727$	13.3073	0.493539	0.246769	−	0.969074i	$-0.420631\pi$
$727$	13.3073	0.493539	0.246769	+	0.969074i	$0.420631\pi$
$728$	−16.7201	−0.619686
$729$	−25.9337	−0.960507
$730$	−11.6812	−0.432342
$731$	2.95654	0.109352
$732$	−39.2937	−1.45234
$733$	32.0026	1.18204	0.591021	−	0.806656i	$-0.298725\pi$
$733$	32.0026	1.18204	0.591021	+	0.806656i	$0.298725\pi$
$734$	−23.5902	−0.870728
$735$	5.36317	0.197824
$736$	1.00000	0.0368605
$737$	−4.92827	−0.181535
$738$	27.0797	0.996818
$739$	24.9320	0.917139	0.458569	−	0.888659i	$-0.348362\pi$
$739$	24.9320	0.917139	0.458569	+	0.888659i	$0.348362\pi$
$740$	−21.3760	−0.785797
$741$	165.632	6.08466
$742$	−32.5170	−1.19374
$743$	48.1523	1.76654	0.883269	−	0.468867i	$-0.155338\pi$
$743$	48.1523	1.76654	0.883269	+	0.468867i	$0.155338\pi$
$744$	0.414255	0.0151873
$745$	1.62710	0.0596124
$746$	−29.0798	−1.06469
$747$	−3.79627	−0.138898
$748$	−1.60901	−0.0588314
$749$	−21.9960	−0.803717
$750$	−28.0268	−1.02339
$751$	−16.9359	−0.618001	−0.309000	−	0.951062i	$-0.599994\pi$
$751$	−16.9359	−0.618001	−0.309000	+	0.951062i	$0.599994\pi$
$752$	9.29087	0.338803
$753$	31.3790	1.14352
$754$	−62.6965	−2.28327
$755$	−7.22366	−0.262896
$756$	22.9099	0.833224
$757$	5.73444	0.208422	0.104211	−	0.994555i	$-0.466768\pi$
$757$	5.73444	0.208422	0.104211	+	0.994555i	$0.466768\pi$
$758$	−31.1902	−1.13288
$759$	−3.88982	−0.141192
$760$	−20.7060	−0.751084
$761$	0.883686	0.0320336	0.0160168	−	0.999872i	$-0.494901\pi$
$761$	0.883686	0.0320336	0.0160168	+	0.999872i	$0.494901\pi$
$762$	−7.36371	−0.266759
$763$	−30.2736	−1.09598
$764$	21.3126	0.771061
$765$	18.8200	0.680440
$766$	11.2059	0.404885
$767$	−73.1486	−2.64124
$768$	−3.00646	−0.108486
$769$	−23.4257	−0.844751	−0.422375	−	0.906421i	$-0.638804\pi$
$769$	−23.4257	−0.844751	−0.422375	+	0.906421i	$0.638804\pi$
$770$	−8.13051	−0.293003
$771$	−22.7028	−0.817623
$772$	−15.8219	−0.569441
$773$	−37.3644	−1.34390	−0.671952	−	0.740595i	$-0.734544\pi$
$773$	−37.3644	−1.34390	−0.671952	+	0.740595i	$0.734544\pi$
$774$	−14.3566	−0.516036
$775$	0.176378	0.00633568
$776$	12.5808	0.451623
$777$	−64.3075	−2.30702
$778$	−1.01972	−0.0365587
$779$	−37.0515	−1.32751
$780$	50.2359	1.79873
$781$	8.66551	0.310076
$782$	1.24362	0.0444716
$783$	85.9069	3.07006
$784$	−0.711842	−0.0254229
$785$	32.2465	1.15093
$786$	3.00646	0.107237
$787$	27.9523	0.996393	0.498196	−	0.867064i	$-0.333996\pi$
$787$	27.9523	0.996393	0.498196	+	0.867064i	$0.333996\pi$
$788$	8.72935	0.310970
$789$	38.8409	1.38277
$790$	21.8823	0.778536
$791$	−6.71261	−0.238673
$792$	7.81315	0.277628
$793$	−87.1450	−3.09461
$794$	−29.0224	−1.02997
$795$	97.6982	3.46500
$796$	−0.0574564	−0.00203649
$797$	17.7259	0.627884	0.313942	−	0.949442i	$-0.398350\pi$
$797$	17.7259	0.627884	0.313942	+	0.949442i	$0.398350\pi$
$798$	−62.2918	−2.20511
$799$	11.5543	0.408761
$800$	−1.28006	−0.0452571
$801$	54.3565	1.92059
$802$	18.1806	0.641978
$803$	−6.03088	−0.212825
$804$	−11.4519	−0.403877
$805$	6.28411	0.221486
$806$	0.918730	0.0323609
$807$	−4.55406	−0.160310
$808$	2.20165	0.0774537
$809$	40.2717	1.41588	0.707939	−	0.706273i	$-0.249625\pi$
$809$	40.2717	1.41588	0.707939	+	0.706273i	$0.249625\pi$
$810$	−23.4334	−0.823366
$811$	−37.2097	−1.30661	−0.653305	−	0.757095i	$-0.726618\pi$
$811$	−37.2097	−1.30661	−0.653305	+	0.757095i	$0.726618\pi$
$812$	23.5792	0.827467
$813$	−44.0383	−1.54449
$814$	−11.0362	−0.386817
$815$	−56.0891	−1.96472
$816$	−3.73888	−0.130887
$817$	19.6432	0.687228
$818$	−4.33010	−0.151398
$819$	100.969	3.52816
$820$	−11.2376	−0.392435
$821$	−25.3003	−0.882986	−0.441493	−	0.897265i	$-0.645551\pi$
$821$	−25.3003	−0.882986	−0.441493	+	0.897265i	$0.645551\pi$
$822$	27.3946	0.955498
$823$	26.7790	0.933457	0.466728	−	0.884401i	$-0.345433\pi$
$823$	26.7790	0.933457	0.466728	+	0.884401i	$0.345433\pi$
$824$	12.2384	0.426346
$825$	4.97922	0.173354
$826$	27.5101	0.957198
$827$	29.2494	1.01710	0.508550	−	0.861033i	$-0.330182\pi$
$827$	29.2494	1.01710	0.508550	+	0.861033i	$0.330182\pi$
$828$	−6.03882	−0.209864
$829$	47.7439	1.65821	0.829107	−	0.559090i	$-0.188849\pi$
$829$	47.7439	1.65821	0.829107	+	0.559090i	$0.188849\pi$
$830$	1.57539	0.0546825
$831$	−91.0786	−3.15948
$832$	−6.66770	−0.231161
$833$	−0.885258	−0.0306724
$834$	−39.4396	−1.36568
$835$	32.9705	1.14099
$836$	−10.6902	−0.369730
$837$	−1.25885	−0.0435121
$838$	−4.36757	−0.150875
$839$	−12.0941	−0.417536	−0.208768	−	0.977965i	$-0.566945\pi$
$839$	−12.0941	−0.417536	−0.208768	+	0.977965i	$0.566945\pi$
$840$	−18.8929	−0.651869
$841$	59.4167	2.04885
$842$	−11.5596	−0.398368
$843$	−21.7407	−0.748790
$844$	−11.0923	−0.381812
$845$	78.8344	2.71199
$846$	−56.1059	−1.92896
$847$	23.3861	0.803557
$848$	−12.9673	−0.445298
$849$	−54.9903	−1.88726
$850$	−1.59191	−0.0546020
$851$	8.52990	0.292401
$852$	20.1362	0.689853
$853$	−47.6477	−1.63143	−0.815713	−	0.578457i	$-0.803655\pi$
$853$	−47.6477	−1.63143	−0.815713	+	0.578457i	$0.803655\pi$
$854$	32.7739	1.12150
$855$	125.040	4.27627
$856$	−8.77167	−0.299809
$857$	43.3971	1.48242	0.741209	−	0.671275i	$-0.234253\pi$
$857$	43.3971	1.48242	0.741209	+	0.671275i	$0.234253\pi$
$858$	25.9362	0.885446
$859$	9.01637	0.307634	0.153817	−	0.988099i	$-0.450843\pi$
$859$	9.01637	0.307634	0.153817	+	0.988099i	$0.450843\pi$
$860$	5.95772	0.203157
$861$	−33.8072	−1.15215
$862$	11.9835	0.408161
$863$	32.2714	1.09853	0.549266	−	0.835648i	$-0.314907\pi$
$863$	32.2714	1.09853	0.549266	+	0.835648i	$0.314907\pi$
$864$	9.13610	0.310817
$865$	19.9182	0.677239
$866$	−20.5266	−0.697521
$867$	46.4601	1.57787
$868$	−0.345521	−0.0117277
$869$	11.2975	0.383243
$870$	−70.8443	−2.40185
$871$	−25.3978	−0.860573
$872$	−12.0726	−0.408831
$873$	−75.9730	−2.57130
$874$	8.26254	0.279485
$875$	23.3765	0.790269
$876$	−14.0140	−0.473490
$877$	−14.2562	−0.481398	−0.240699	−	0.970600i	$-0.577377\pi$
$877$	−14.2562	−0.481398	−0.240699	+	0.970600i	$0.577377\pi$
$878$	−14.5210	−0.490059
$879$	−3.03054	−0.102217
$880$	−3.24232	−0.109299
$881$	−40.9721	−1.38039	−0.690193	−	0.723626i	$-0.742474\pi$
$881$	−40.9721	−1.38039	−0.690193	+	0.723626i	$0.742474\pi$
$882$	4.29869	0.144744
$883$	28.9293	0.973549	0.486774	−	0.873528i	$-0.338173\pi$
$883$	28.9293	0.973549	0.486774	+	0.873528i	$0.338173\pi$
$884$	−8.29205	−0.278892
$885$	−82.6548	−2.77841
$886$	−37.2452	−1.25128
$887$	17.7682	0.596597	0.298299	−	0.954473i	$-0.403581\pi$
$887$	17.7682	0.596597	0.298299	+	0.954473i	$0.403581\pi$
$888$	−25.6448	−0.860584
$889$	6.14189	0.205993
$890$	−22.5570	−0.756113
$891$	−12.0984	−0.405311
$892$	0.488088	0.0163424
$893$	76.7662	2.56888
$894$	1.95204	0.0652860
$895$	−21.1121	−0.705698
$896$	2.50762	0.0837737
$897$	−20.0462	−0.669323
$898$	9.48177	0.316411
$899$	−1.29563	−0.0432115
$900$	7.73008	0.257669
$901$	−16.1263	−0.537245
$902$	−5.80184	−0.193180
$903$	17.9232	0.596447
$904$	−2.67688	−0.0890318
$905$	8.07825	0.268530
$906$	−8.66625	−0.287917
$907$	35.8386	1.19000	0.595000	−	0.803726i	$-0.297152\pi$
$907$	35.8386	1.19000	0.595000	+	0.803726i	$0.297152\pi$
$908$	1.69420	0.0562240
$909$	−13.2954	−0.440979
$910$	−41.9005	−1.38899
$911$	−22.5982	−0.748712	−0.374356	−	0.927285i	$-0.622136\pi$
$911$	−22.5982	−0.748712	−0.374356	+	0.927285i	$0.622136\pi$
$912$	−24.8410	−0.822568
$913$	0.813353	0.0269181
$914$	−29.4795	−0.975095
$915$	−98.4701	−3.25532
$916$	−18.7418	−0.619248
$917$	−2.50762	−0.0828089
$918$	11.3618	0.374995
$919$	−18.8232	−0.620919	−0.310459	−	0.950587i	$-0.600483\pi$
$919$	−18.8232	−0.620919	−0.310459	+	0.950587i	$0.600483\pi$
$920$	2.50601	0.0826206
$921$	−12.9392	−0.426363
$922$	−9.25259	−0.304718
$923$	44.6577	1.46993
$924$	−9.75419	−0.320889
$925$	−10.9188	−0.359009
$926$	33.2261	1.09188
$927$	−73.9057	−2.42738
$928$	9.40302	0.308669
$929$	−15.0327	−0.493208	−0.246604	−	0.969116i	$-0.579315\pi$
$929$	−15.0327	−0.493208	−0.246604	+	0.969116i	$0.579315\pi$
$930$	1.03813	0.0340415
$931$	−5.88162	−0.192762
$932$	−28.2672	−0.925924
$933$	−46.7805	−1.53153
$934$	−19.1458	−0.626471
$935$	−4.03220	−0.131867
$936$	40.2650	1.31610
$937$	27.5421	0.899761	0.449880	−	0.893089i	$-0.351467\pi$
$937$	27.5421	0.899761	0.449880	+	0.893089i	$0.351467\pi$
$938$	9.55175	0.311876
$939$	76.9380	2.51078
$940$	23.2830	0.759407
$941$	0.624238	0.0203496	0.0101748	−	0.999948i	$-0.496761\pi$
$941$	0.624238	0.0203496	0.0101748	+	0.999948i	$0.496761\pi$
$942$	38.6862	1.26046
$943$	4.48427	0.146028
$944$	10.9706	0.357062
$945$	57.4123	1.86762
$946$	3.07590	0.100006
$947$	7.32667	0.238085	0.119042	−	0.992889i	$-0.462018\pi$
$947$	7.32667	0.238085	0.119042	+	0.992889i	$0.462018\pi$
$948$	26.2522	0.852632
$949$	−31.0801	−1.00890
$950$	−10.5766	−0.343150
$951$	50.1379	1.62583
$952$	3.11852	0.101072
$953$	−45.6407	−1.47845	−0.739224	−	0.673460i	$-0.764808\pi$
$953$	−45.6407	−1.47845	−0.739224	+	0.673460i	$0.764808\pi$
$954$	78.3070	2.53528
$955$	53.4094	1.72829
$956$	−17.3711	−0.561823
$957$	−36.5761	−1.18234
$958$	5.76393	0.186224
$959$	−22.8492	−0.737840
$960$	−7.53421	−0.243166
$961$	−30.9810	−0.999388
$962$	−56.8748	−1.83372
$963$	52.9705	1.70695
$964$	−16.4329	−0.529270
$965$	−39.6496	−1.27637
$966$	7.53907	0.242566
$967$	27.2242	0.875472	0.437736	−	0.899104i	$-0.355780\pi$
$967$	27.2242	0.875472	0.437736	+	0.899104i	$0.355780\pi$
$968$	9.32603	0.299750
$969$	−30.8927	−0.992416
$970$	31.5275	1.01229
$971$	23.7469	0.762074	0.381037	−	0.924560i	$-0.375567\pi$
$971$	23.7469	0.762074	0.381037	+	0.924560i	$0.375567\pi$
$972$	−0.704814	−0.0226069
$973$	32.8956	1.05458
$974$	−31.9957	−1.02521
$975$	25.6604	0.821791
$976$	13.0697	0.418352
$977$	46.0924	1.47463	0.737313	−	0.675552i	$-0.236094\pi$
$977$	46.0924	1.47463	0.737313	+	0.675552i	$0.236094\pi$
$978$	−67.2903	−2.15171
$979$	−11.6459	−0.372205
$980$	−1.78388	−0.0569840
$981$	72.9044	2.32766
$982$	−15.9467	−0.508880
$983$	−54.6896	−1.74433	−0.872164	−	0.489213i	$-0.837284\pi$
$983$	−54.6896	−1.74433	−0.872164	+	0.489213i	$0.837284\pi$
$984$	−13.4818	−0.429784
$985$	21.8758	0.697021
$986$	11.6937	0.372404
$987$	70.0445	2.22954
$988$	−55.0921	−1.75271
$989$	−2.37738	−0.0755962
$990$	19.5798	0.622287
$991$	54.1577	1.72038	0.860189	−	0.509976i	$-0.170346\pi$
$991$	54.1577	1.72038	0.860189	+	0.509976i	$0.170346\pi$
$992$	−0.137788	−0.00437478
$993$	−66.0149	−2.09492
$994$	−16.7951	−0.532708
$995$	−0.143986	−0.00456466
$996$	1.89000	0.0598869
$997$	10.2079	0.323289	0.161644	−	0.986849i	$-0.448320\pi$
$997$	10.2079	0.323289	0.161644	+	0.986849i	$0.448320\pi$
$998$	−29.1343	−0.922231
$999$	77.9301	2.46560

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.l.1.2	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.l.1.2	✓	36	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.00646 q^{3} +1.00000 q^{4} +2.50601 q^{5} +3.00646 q^{6} -2.50762 q^{7} -1.00000 q^{8} +6.03882 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.00646 q^{3} +1.00000 q^{4} +2.50601 q^{5} +3.00646 q^{6} -2.50762 q^{7} -1.00000 q^{8} +6.03882 q^{9} -2.50601 q^{10} -1.29382 q^{11} -3.00646 q^{12} -6.66770 q^{13} +2.50762 q^{14} -7.53421 q^{15} +1.00000 q^{16} +1.24362 q^{17} -6.03882 q^{18} +8.26254 q^{19} +2.50601 q^{20} +7.53907 q^{21} +1.29382 q^{22} -1.00000 q^{23} +3.00646 q^{24} +1.28006 q^{25} +6.66770 q^{26} -9.13610 q^{27} -2.50762 q^{28} -9.40302 q^{29} +7.53421 q^{30} +0.137788 q^{31} -1.00000 q^{32} +3.88982 q^{33} -1.24362 q^{34} -6.28411 q^{35} +6.03882 q^{36} -8.52990 q^{37} -8.26254 q^{38} +20.0462 q^{39} -2.50601 q^{40} -4.48427 q^{41} -7.53907 q^{42} +2.37738 q^{43} -1.29382 q^{44} +15.1333 q^{45} +1.00000 q^{46} +9.29087 q^{47} -3.00646 q^{48} -0.711842 q^{49} -1.28006 q^{50} -3.73888 q^{51} -6.66770 q^{52} -12.9673 q^{53} +9.13610 q^{54} -3.24232 q^{55} +2.50762 q^{56} -24.8410 q^{57} +9.40302 q^{58} +10.9706 q^{59} -7.53421 q^{60} +13.0697 q^{61} -0.137788 q^{62} -15.1431 q^{63} +1.00000 q^{64} -16.7093 q^{65} -3.88982 q^{66} +3.80909 q^{67} +1.24362 q^{68} +3.00646 q^{69} +6.28411 q^{70} -6.69762 q^{71} -6.03882 q^{72} +4.66130 q^{73} +8.52990 q^{74} -3.84847 q^{75} +8.26254 q^{76} +3.24441 q^{77} -20.0462 q^{78} -8.73193 q^{79} +2.50601 q^{80} +9.35090 q^{81} +4.48427 q^{82} -0.628645 q^{83} +7.53907 q^{84} +3.11651 q^{85} -2.37738 q^{86} +28.2698 q^{87} +1.29382 q^{88} +9.00118 q^{89} -15.1333 q^{90} +16.7201 q^{91} -1.00000 q^{92} -0.414255 q^{93} -9.29087 q^{94} +20.7060 q^{95} +3.00646 q^{96} -12.5808 q^{97} +0.711842 q^{98} -7.81315 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9} - q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 36 q^{16} - 4 q^{17} - 46 q^{18} + 29 q^{19} + q^{20} + 24 q^{21} - 14 q^{22} - 36 q^{23} - 4 q^{24} + 49 q^{25} - 4 q^{26} + 19 q^{27} + 13 q^{28} - 13 q^{29} - 10 q^{30} + 21 q^{31} - 36 q^{32} - 5 q^{33} + 4 q^{34} + 30 q^{35} + 46 q^{36} + 13 q^{37} - 29 q^{38} + 30 q^{39} - q^{40} - 8 q^{41} - 24 q^{42} + 42 q^{43} + 14 q^{44} + 30 q^{45} + 36 q^{46} - 14 q^{47} + 4 q^{48} + 61 q^{49} - 49 q^{50} + 46 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + 26 q^{55} - 13 q^{56} + 26 q^{57} + 13 q^{58} + 45 q^{59} + 10 q^{60} + 34 q^{61} - 21 q^{62} + 63 q^{63} + 36 q^{64} - 25 q^{65} + 5 q^{66} + 42 q^{67} - 4 q^{68} - 4 q^{69} - 30 q^{70} - 2 q^{71} - 46 q^{72} + 16 q^{73} - 13 q^{74} + 72 q^{75} + 29 q^{76} - 36 q^{77} - 30 q^{78} + 33 q^{79} + q^{80} + 96 q^{81} + 8 q^{82} + 8 q^{83} + 24 q^{84} + 18 q^{85} - 42 q^{86} + 11 q^{87} - 14 q^{88} + 21 q^{89} - 30 q^{90} + 60 q^{91} - 36 q^{92} - 27 q^{93} + 14 q^{94} - 44 q^{95} - 4 q^{96} + 20 q^{97} - 61 q^{98} + 76 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9 - q^10 + 14 * q^11 + 4 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 36 * q^16 - 4 * q^17 - 46 * q^18 + 29 * q^19 + q^20 + 24 * q^21 - 14 * q^22 - 36 * q^23 - 4 * q^24 + 49 * q^25 - 4 * q^26 + 19 * q^27 + 13 * q^28 - 13 * q^29 - 10 * q^30 + 21 * q^31 - 36 * q^32 - 5 * q^33 + 4 * q^34 + 30 * q^35 + 46 * q^36 + 13 * q^37 - 29 * q^38 + 30 * q^39 - q^40 - 8 * q^41 - 24 * q^42 + 42 * q^43 + 14 * q^44 + 30 * q^45 + 36 * q^46 - 14 * q^47 + 4 * q^48 + 61 * q^49 - 49 * q^50 + 46 * q^51 + 4 * q^52 - 3 * q^53 - 19 * q^54 + 26 * q^55 - 13 * q^56 + 26 * q^57 + 13 * q^58 + 45 * q^59 + 10 * q^60 + 34 * q^61 - 21 * q^62 + 63 * q^63 + 36 * q^64 - 25 * q^65 + 5 * q^66 + 42 * q^67 - 4 * q^68 - 4 * q^69 - 30 * q^70 - 2 * q^71 - 46 * q^72 + 16 * q^73 - 13 * q^74 + 72 * q^75 + 29 * q^76 - 36 * q^77 - 30 * q^78 + 33 * q^79 + q^80 + 96 * q^81 + 8 * q^82 + 8 * q^83 + 24 * q^84 + 18 * q^85 - 42 * q^86 + 11 * q^87 - 14 * q^88 + 21 * q^89 - 30 * q^90 + 60 * q^91 - 36 * q^92 - 27 * q^93 + 14 * q^94 - 44 * q^95 - 4 * q^96 + 20 * q^97 - 61 * q^98 + 76 * q^99

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