LMFDB - Embedded newform 1441.2.a.f.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,2,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, 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("1441.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1441.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:	$11.5064429313$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.651423 q^{2} -0.506634 q^{3} -1.57565 q^{4} -2.90422 q^{5} -0.330033 q^{6} -3.71271 q^{7} -2.32926 q^{8} -2.74332 q^{9} +O(q^{10})$	\(q+0.651423 q^{2} -0.506634 q^{3} -1.57565 q^{4} -2.90422 q^{5} -0.330033 q^{6} -3.71271 q^{7} -2.32926 q^{8} -2.74332 q^{9} -1.89188 q^{10} -1.00000 q^{11} +0.798276 q^{12} +6.09113 q^{13} -2.41855 q^{14} +1.47138 q^{15} +1.63396 q^{16} -4.76895 q^{17} -1.78706 q^{18} -5.31656 q^{19} +4.57603 q^{20} +1.88098 q^{21} -0.651423 q^{22} +3.91581 q^{23} +1.18008 q^{24} +3.43449 q^{25} +3.96790 q^{26} +2.90976 q^{27} +5.84993 q^{28} -0.423928 q^{29} +0.958488 q^{30} -10.1238 q^{31} +5.72292 q^{32} +0.506634 q^{33} -3.10661 q^{34} +10.7825 q^{35} +4.32251 q^{36} +0.881930 q^{37} -3.46333 q^{38} -3.08597 q^{39} +6.76468 q^{40} -6.61348 q^{41} +1.22532 q^{42} +10.7055 q^{43} +1.57565 q^{44} +7.96721 q^{45} +2.55085 q^{46} +7.72037 q^{47} -0.827820 q^{48} +6.78423 q^{49} +2.23731 q^{50} +2.41611 q^{51} -9.59747 q^{52} +6.48972 q^{53} +1.89549 q^{54} +2.90422 q^{55} +8.64787 q^{56} +2.69355 q^{57} -0.276156 q^{58} +3.06788 q^{59} -2.31837 q^{60} -8.41482 q^{61} -6.59491 q^{62} +10.1852 q^{63} +0.460122 q^{64} -17.6900 q^{65} +0.330033 q^{66} +10.7940 q^{67} +7.51419 q^{68} -1.98388 q^{69} +7.02399 q^{70} -10.3216 q^{71} +6.38991 q^{72} -0.442041 q^{73} +0.574510 q^{74} -1.74003 q^{75} +8.37702 q^{76} +3.71271 q^{77} -2.01027 q^{78} -10.3477 q^{79} -4.74538 q^{80} +6.75578 q^{81} -4.30818 q^{82} +14.6146 q^{83} -2.96377 q^{84} +13.8501 q^{85} +6.97383 q^{86} +0.214776 q^{87} +2.32926 q^{88} +10.5047 q^{89} +5.19003 q^{90} -22.6146 q^{91} -6.16994 q^{92} +5.12908 q^{93} +5.02923 q^{94} +15.4405 q^{95} -2.89942 q^{96} -11.3473 q^{97} +4.41941 q^{98} +2.74332 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) $ 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9} - 8 q^{10} - 31 q^{11} + 10 q^{12} - 8 q^{13} + 29 q^{14} + 36 q^{15} + 52 q^{16} - q^{17} + 33 q^{18} - 2 q^{19} + 22 q^{20} - 13 q^{21} - 6 q^{22} + 45 q^{23} + 16 q^{24} + 41 q^{25} + 24 q^{26} + 22 q^{27} + 17 q^{28} + 5 q^{29} + 29 q^{30} + 28 q^{31} + 69 q^{32} - 4 q^{33} + 14 q^{34} + 36 q^{35} + 63 q^{36} - 3 q^{37} + 4 q^{38} + 40 q^{39} - 48 q^{40} + 21 q^{41} - 9 q^{42} - 20 q^{43} - 38 q^{44} + 28 q^{45} - 24 q^{46} + 57 q^{47} - 46 q^{48} + 37 q^{49} + 64 q^{50} + 17 q^{51} - 11 q^{52} + 32 q^{53} - 26 q^{54} - 8 q^{55} + 84 q^{56} + 10 q^{57} - 17 q^{58} + 70 q^{59} - 33 q^{60} - 51 q^{61} - 34 q^{62} + 32 q^{63} + 80 q^{64} - q^{65} - 7 q^{66} + 24 q^{67} - 13 q^{68} + 19 q^{69} - 9 q^{70} + 128 q^{71} + 118 q^{72} - 27 q^{73} - 23 q^{74} + 41 q^{75} - 34 q^{76} - 4 q^{77} + 9 q^{78} + 2 q^{79} - 45 q^{80} + 43 q^{81} - 18 q^{82} + 46 q^{83} - 103 q^{84} - 50 q^{85} + 78 q^{86} - 9 q^{87} - 24 q^{88} + 52 q^{89} - 46 q^{90} + 38 q^{91} + 54 q^{92} + 4 q^{93} + 3 q^{94} + 70 q^{95} - 21 q^{96} + 3 q^{97} - 120 q^{98} - 45 q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9 - 8 * q^10 - 31 * q^11 + 10 * q^12 - 8 * q^13 + 29 * q^14 + 36 * q^15 + 52 * q^16 - q^17 + 33 * q^18 - 2 * q^19 + 22 * q^20 - 13 * q^21 - 6 * q^22 + 45 * q^23 + 16 * q^24 + 41 * q^25 + 24 * q^26 + 22 * q^27 + 17 * q^28 + 5 * q^29 + 29 * q^30 + 28 * q^31 + 69 * q^32 - 4 * q^33 + 14 * q^34 + 36 * q^35 + 63 * q^36 - 3 * q^37 + 4 * q^38 + 40 * q^39 - 48 * q^40 + 21 * q^41 - 9 * q^42 - 20 * q^43 - 38 * q^44 + 28 * q^45 - 24 * q^46 + 57 * q^47 - 46 * q^48 + 37 * q^49 + 64 * q^50 + 17 * q^51 - 11 * q^52 + 32 * q^53 - 26 * q^54 - 8 * q^55 + 84 * q^56 + 10 * q^57 - 17 * q^58 + 70 * q^59 - 33 * q^60 - 51 * q^61 - 34 * q^62 + 32 * q^63 + 80 * q^64 - q^65 - 7 * q^66 + 24 * q^67 - 13 * q^68 + 19 * q^69 - 9 * q^70 + 128 * q^71 + 118 * q^72 - 27 * q^73 - 23 * q^74 + 41 * q^75 - 34 * q^76 - 4 * q^77 + 9 * q^78 + 2 * q^79 - 45 * q^80 + 43 * q^81 - 18 * q^82 + 46 * q^83 - 103 * q^84 - 50 * q^85 + 78 * q^86 - 9 * q^87 - 24 * q^88 + 52 * q^89 - 46 * q^90 + 38 * q^91 + 54 * q^92 + 4 * q^93 + 3 * q^94 + 70 * q^95 - 21 * q^96 + 3 * q^97 - 120 * q^98 - 45 * 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 $

$2$	0.651423	0.460626	0.230313	−	0.973117i	$-0.426025\pi$
$2$	0.651423	0.460626	0.230313	+	0.973117i	$0.426025\pi$
$3$	−0.506634	−0.292505	−0.146253	−	0.989247i	$-0.546721\pi$
$3$	−0.506634	−0.292505	−0.146253	+	0.989247i	$0.546721\pi$
$4$	−1.57565	−0.787824
$5$	−2.90422	−1.29881	−0.649403	−	0.760444i	$-0.724981\pi$
$5$	−2.90422	−1.29881	−0.649403	+	0.760444i	$0.724981\pi$
$6$	−0.330033	−0.134735
$7$	−3.71271	−1.40327	−0.701637	−	0.712535i	$-0.747547\pi$
$7$	−3.71271	−1.40327	−0.701637	+	0.712535i	$0.747547\pi$
$8$	−2.32926	−0.823518
$9$	−2.74332	−0.914441
$10$	−1.89188	−0.598264
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.798276	0.230442
$13$	6.09113	1.68937	0.844687	−	0.535260i	$-0.179786\pi$
$13$	6.09113	1.68937	0.844687	+	0.535260i	$0.179786\pi$
$14$	−2.41855	−0.646384
$15$	1.47138	0.379907
$16$	1.63396	0.408490
$17$	−4.76895	−1.15664	−0.578321	−	0.815810i	$-0.696292\pi$
$17$	−4.76895	−1.15664	−0.578321	+	0.815810i	$0.696292\pi$
$18$	−1.78706	−0.421215
$19$	−5.31656	−1.21970	−0.609851	−	0.792516i	$-0.708771\pi$
$19$	−5.31656	−1.21970	−0.609851	+	0.792516i	$0.708771\pi$
$20$	4.57603	1.02323
$21$	1.88098	0.410465
$22$	−0.651423	−0.138884
$23$	3.91581	0.816504	0.408252	−	0.912869i	$-0.366139\pi$
$23$	3.91581	0.816504	0.408252	+	0.912869i	$0.366139\pi$
$24$	1.18008	0.240883
$25$	3.43449	0.686898
$26$	3.96790	0.778170
$27$	2.90976	0.559984
$28$	5.84993	1.10553
$29$	−0.423928	−0.0787214	−0.0393607	−	0.999225i	$-0.512532\pi$
$29$	−0.423928	−0.0787214	−0.0393607	+	0.999225i	$0.512532\pi$
$30$	0.958488	0.174995
$31$	−10.1238	−1.81830	−0.909148	−	0.416472i	$-0.863266\pi$
$31$	−10.1238	−1.81830	−0.909148	+	0.416472i	$0.863266\pi$
$32$	5.72292	1.01168
$33$	0.506634	0.0881936
$34$	−3.10661	−0.532779
$35$	10.7825	1.82258
$36$	4.32251	0.720418
$37$	0.881930	0.144988	0.0724942	−	0.997369i	$-0.476904\pi$
$37$	0.881930	0.144988	0.0724942	+	0.997369i	$0.476904\pi$
$38$	−3.46333	−0.561826
$39$	−3.08597	−0.494151
$40$	6.76468	1.06959
$41$	−6.61348	−1.03285	−0.516426	−	0.856332i	$-0.672738\pi$
$41$	−6.61348	−1.03285	−0.516426	+	0.856332i	$0.672738\pi$
$42$	1.22532	0.189071
$43$	10.7055	1.63258	0.816289	−	0.577644i	$-0.196028\pi$
$43$	10.7055	1.63258	0.816289	+	0.577644i	$0.196028\pi$
$44$	1.57565	0.237538
$45$	7.96721	1.18768
$46$	2.55085	0.376103
$47$	7.72037	1.12613	0.563065	−	0.826412i	$-0.309622\pi$
$47$	7.72037	1.12613	0.563065	+	0.826412i	$0.309622\pi$
$48$	−0.827820	−0.119485
$49$	6.78423	0.969176
$50$	2.23731	0.316403
$51$	2.41611	0.338323
$52$	−9.59747	−1.33093
$53$	6.48972	0.891432	0.445716	−	0.895174i	$-0.352949\pi$
$53$	6.48972	0.891432	0.445716	+	0.895174i	$0.352949\pi$
$54$	1.89549	0.257943
$55$	2.90422	0.391605
$56$	8.64787	1.15562
$57$	2.69355	0.356769
$58$	−0.276156	−0.0362611
$59$	3.06788	0.399404	0.199702	−	0.979857i	$-0.436003\pi$
$59$	3.06788	0.399404	0.199702	+	0.979857i	$0.436003\pi$
$60$	−2.31837	−0.299300
$61$	−8.41482	−1.07741	−0.538704	−	0.842495i	$-0.681086\pi$
$61$	−8.41482	−1.07741	−0.538704	+	0.842495i	$0.681086\pi$
$62$	−6.59491	−0.837554
$63$	10.1852	1.28321
$64$	0.460122	0.0575152
$65$	−17.6900	−2.19417
$66$	0.330033	0.0406243
$67$	10.7940	1.31870	0.659348	−	0.751838i	$-0.270832\pi$
$67$	10.7940	1.31870	0.659348	+	0.751838i	$0.270832\pi$
$68$	7.51419	0.911230
$69$	−1.98388	−0.238831
$70$	7.02399	0.839527
$71$	−10.3216	−1.22495	−0.612477	−	0.790489i	$-0.709827\pi$
$71$	−10.3216	−1.22495	−0.612477	+	0.790489i	$0.709827\pi$
$72$	6.38991	0.753058
$73$	−0.442041	−0.0517370	−0.0258685	−	0.999665i	$-0.508235\pi$
$73$	−0.442041	−0.0517370	−0.0258685	+	0.999665i	$0.508235\pi$
$74$	0.574510	0.0667854
$75$	−1.74003	−0.200921
$76$	8.37702	0.960911
$77$	3.71271	0.423103
$78$	−2.01027	−0.227619
$79$	−10.3477	−1.16420	−0.582102	−	0.813116i	$-0.697770\pi$
$79$	−10.3477	−1.16420	−0.582102	+	0.813116i	$0.697770\pi$
$80$	−4.74538	−0.530550
$81$	6.75578	0.750643
$82$	−4.30818	−0.475759
$83$	14.6146	1.60416	0.802081	−	0.597216i	$-0.203726\pi$
$83$	14.6146	1.60416	0.802081	+	0.597216i	$0.203726\pi$
$84$	−2.96377	−0.323374
$85$	13.8501	1.50225
$86$	6.97383	0.752008
$87$	0.214776	0.0230264
$88$	2.32926	0.248300
$89$	10.5047	1.11350	0.556750	−	0.830680i	$-0.312048\pi$
$89$	10.5047	1.11350	0.556750	+	0.830680i	$0.312048\pi$
$90$	5.19003	0.547077
$91$	−22.6146	−2.37065
$92$	−6.16994	−0.643261
$93$	5.12908	0.531861
$94$	5.02923	0.518725
$95$	15.4405	1.58416
$96$	−2.89942	−0.295921
$97$	−11.3473	−1.15214	−0.576069	−	0.817401i	$-0.695414\pi$
$97$	−11.3473	−1.15214	−0.576069	+	0.817401i	$0.695414\pi$
$98$	4.41941	0.446427
$99$	2.74332	0.275714
$100$	−5.41154	−0.541154
$101$	−11.5841	−1.15267	−0.576333	−	0.817215i	$-0.695517\pi$
$101$	−11.5841	−1.15267	−0.576333	+	0.817215i	$0.695517\pi$
$102$	1.57391	0.155841
$103$	−13.5025	−1.33044	−0.665220	−	0.746648i	$-0.731662\pi$
$103$	−13.5025	−1.33044	−0.665220	+	0.746648i	$0.731662\pi$
$104$	−14.1878	−1.39123
$105$	−5.46279	−0.533114
$106$	4.22756	0.410616
$107$	2.18842	0.211562	0.105781	−	0.994389i	$-0.466266\pi$
$107$	2.18842	0.211562	0.105781	+	0.994389i	$0.466266\pi$
$108$	−4.58476	−0.441168
$109$	−12.6877	−1.21526	−0.607630	−	0.794221i	$-0.707879\pi$
$109$	−12.6877	−1.21526	−0.607630	+	0.794221i	$0.707879\pi$
$110$	1.89188	0.180383
$111$	−0.446816	−0.0424099
$112$	−6.06643	−0.573223
$113$	−4.69816	−0.441966	−0.220983	−	0.975278i	$-0.570927\pi$
$113$	−4.69816	−0.441966	−0.220983	+	0.975278i	$0.570927\pi$
$114$	1.75464	0.164337
$115$	−11.3724	−1.06048
$116$	0.667961	0.0620186
$117$	−16.7099	−1.54483
$118$	1.99849	0.183976
$119$	17.7058	1.62308
$120$	−3.42722	−0.312861
$121$	1.00000	0.0909091
$122$	−5.48161	−0.496282
$123$	3.35061	0.302115
$124$	15.9516	1.43250
$125$	4.54659	0.406659
$126$	6.63485	0.591080
$127$	−11.5160	−1.02188	−0.510938	−	0.859618i	$-0.670702\pi$
$127$	−11.5160	−1.02188	−0.510938	+	0.859618i	$0.670702\pi$
$128$	−11.1461	−0.985186
$129$	−5.42378	−0.477537
$130$	−11.5237	−1.01069
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−0.798276	−0.0694810
$133$	19.7389	1.71158
$134$	7.03146	0.607425
$135$	−8.45058	−0.727310
$136$	11.1081	0.952515
$137$	−21.7530	−1.85848	−0.929240	−	0.369476i	$-0.879537\pi$
$137$	−21.7530	−1.85848	−0.929240	+	0.369476i	$0.879537\pi$
$138$	−1.29235	−0.110012
$139$	3.70254	0.314045	0.157023	−	0.987595i	$-0.449810\pi$
$139$	3.70254	0.314045	0.157023	+	0.987595i	$0.449810\pi$
$140$	−16.9895	−1.43587
$141$	−3.91140	−0.329399
$142$	−6.72376	−0.564245
$143$	−6.09113	−0.509366
$144$	−4.48248	−0.373540
$145$	1.23118	0.102244
$146$	−0.287956	−0.0238314
$147$	−3.43712	−0.283489
$148$	−1.38961	−0.114225
$149$	1.66849	0.136688	0.0683440	−	0.997662i	$-0.478228\pi$
$149$	1.66849	0.136688	0.0683440	+	0.997662i	$0.478228\pi$
$150$	−1.13349	−0.0925495
$151$	18.3733	1.49520	0.747601	−	0.664149i	$-0.231206\pi$
$151$	18.3733	1.49520	0.747601	+	0.664149i	$0.231206\pi$
$152$	12.3836	1.00445
$153$	13.0828	1.05768
$154$	2.41855	0.194892
$155$	29.4019	2.36162
$156$	4.86240	0.389304
$157$	0.108691	0.00867447	0.00433724	−	0.999991i	$-0.498619\pi$
$157$	0.108691	0.00867447	0.00433724	+	0.999991i	$0.498619\pi$
$158$	−6.74071	−0.536262
$159$	−3.28791	−0.260748
$160$	−16.6206	−1.31398
$161$	−14.5383	−1.14578
$162$	4.40088	0.345765
$163$	−3.35451	−0.262745	−0.131373	−	0.991333i	$-0.541938\pi$
$163$	−3.35451	−0.262745	−0.131373	+	0.991333i	$0.541938\pi$
$164$	10.4205	0.813706
$165$	−1.47138	−0.114546
$166$	9.52029	0.738918
$167$	18.5731	1.43723	0.718613	−	0.695410i	$-0.244777\pi$
$167$	18.5731	1.43723	0.718613	+	0.695410i	$0.244777\pi$
$168$	−4.38130	−0.338025
$169$	24.1018	1.85399
$170$	9.02227	0.691977
$171$	14.5850	1.11535
$172$	−16.8681	−1.28618
$173$	4.36190	0.331629	0.165814	−	0.986157i	$-0.446975\pi$
$173$	4.36190	0.331629	0.165814	+	0.986157i	$0.446975\pi$
$174$	0.139910	0.0106066
$175$	−12.7513	−0.963905
$176$	−1.63396	−0.123164
$177$	−1.55429	−0.116828
$178$	6.84303	0.512907
$179$	−4.07113	−0.304291	−0.152145	−	0.988358i	$-0.548618\pi$
$179$	−4.07113	−0.304291	−0.152145	+	0.988358i	$0.548618\pi$
$180$	−12.5535	−0.935684
$181$	2.29816	0.170821	0.0854103	−	0.996346i	$-0.472780\pi$
$181$	2.29816	0.170821	0.0854103	+	0.996346i	$0.472780\pi$
$182$	−14.7317	−1.09198
$183$	4.26323	0.315147
$184$	−9.12095	−0.672405
$185$	−2.56132	−0.188312
$186$	3.34120	0.244989
$187$	4.76895	0.348740
$188$	−12.1646	−0.887193
$189$	−10.8031	−0.785810
$190$	10.0583	0.729704
$191$	12.1826	0.881506	0.440753	−	0.897629i	$-0.354712\pi$
$191$	12.1826	0.881506	0.440753	+	0.897629i	$0.354712\pi$
$192$	−0.233113	−0.0168235
$193$	−2.08357	−0.149979	−0.0749895	−	0.997184i	$-0.523892\pi$
$193$	−2.08357	−0.149979	−0.0749895	+	0.997184i	$0.523892\pi$
$194$	−7.39186	−0.530705
$195$	8.96233	0.641806
$196$	−10.6896	−0.763540
$197$	20.1218	1.43362	0.716809	−	0.697269i	$-0.245602\pi$
$197$	20.1218	1.43362	0.716809	+	0.697269i	$0.245602\pi$
$198$	1.78706	0.127001
$199$	−21.7433	−1.54134	−0.770672	−	0.637232i	$-0.780079\pi$
$199$	−21.7433	−1.54134	−0.770672	+	0.637232i	$0.780079\pi$
$200$	−7.99982	−0.565673
$201$	−5.46860	−0.385725
$202$	−7.54618	−0.530948
$203$	1.57392	0.110468
$204$	−3.80694	−0.266539
$205$	19.2070	1.34148
$206$	−8.79584	−0.612835
$207$	−10.7423	−0.746644
$208$	9.95266	0.690093
$209$	5.31656	0.367754
$210$	−3.55859	−0.245566
$211$	18.3535	1.26351	0.631755	−	0.775169i	$-0.282335\pi$
$211$	18.3535	1.26351	0.631755	+	0.775169i	$0.282335\pi$
$212$	−10.2255	−0.702291
$213$	5.22929	0.358305
$214$	1.42559	0.0974510
$215$	−31.0912	−2.12040
$216$	−6.77759	−0.461157
$217$	37.5869	2.55157
$218$	−8.26505	−0.559780
$219$	0.223953	0.0151333
$220$	−4.57603	−0.308516
$221$	−29.0483	−1.95400
$222$	−0.291066	−0.0195351
$223$	16.6871	1.11745	0.558725	−	0.829353i	$-0.311291\pi$
$223$	16.6871	1.11745	0.558725	+	0.829353i	$0.311291\pi$
$224$	−21.2476	−1.41966
$225$	−9.42191	−0.628127
$226$	−3.06049	−0.203581
$227$	−20.5179	−1.36182	−0.680911	−	0.732366i	$-0.738416\pi$
$227$	−20.5179	−1.36182	−0.680911	+	0.732366i	$0.738416\pi$
$228$	−4.24408	−0.281071
$229$	16.6458	1.09999	0.549993	−	0.835169i	$-0.314630\pi$
$229$	16.6458	1.09999	0.549993	+	0.835169i	$0.314630\pi$
$230$	−7.40824	−0.488485
$231$	−1.88098	−0.123760
$232$	0.987438	0.0648285
$233$	−6.86624	−0.449822	−0.224911	−	0.974379i	$-0.572209\pi$
$233$	−6.86624	−0.449822	−0.224911	+	0.974379i	$0.572209\pi$
$234$	−10.8852	−0.711590
$235$	−22.4216	−1.46263
$236$	−4.83390	−0.314660
$237$	5.24248	0.340535
$238$	11.5339	0.747634
$239$	8.52796	0.551628	0.275814	−	0.961211i	$-0.411053\pi$
$239$	8.52796	0.551628	0.275814	+	0.961211i	$0.411053\pi$
$240$	2.40417	0.155188
$241$	0.0475401	0.00306232	0.00153116	−	0.999999i	$-0.499513\pi$
$241$	0.0475401	0.00306232	0.00153116	+	0.999999i	$0.499513\pi$
$242$	0.651423	0.0418751
$243$	−12.1520	−0.779550
$244$	13.2588	0.848808
$245$	−19.7029	−1.25877
$246$	2.18267	0.139162
$247$	−32.3838	−2.06053
$248$	23.5811	1.49740
$249$	−7.40425	−0.469225
$250$	2.96175	0.187318
$251$	−22.2908	−1.40698	−0.703491	−	0.710704i	$-0.748376\pi$
$251$	−22.2908	−1.40698	−0.703491	+	0.710704i	$0.748376\pi$
$252$	−16.0482	−1.01094
$253$	−3.91581	−0.246185
$254$	−7.50176	−0.470702
$255$	−7.01692	−0.439417
$256$	−8.18108	−0.511317
$257$	11.0933	0.691979	0.345989	−	0.938238i	$-0.387543\pi$
$257$	11.0933	0.691979	0.345989	+	0.938238i	$0.387543\pi$
$258$	−3.53318	−0.219966
$259$	−3.27435	−0.203458
$260$	27.8732	1.72862
$261$	1.16297	0.0719860
$262$	0.651423	0.0402451
$263$	3.18561	0.196433	0.0982165	−	0.995165i	$-0.468686\pi$
$263$	3.18561	0.196433	0.0982165	+	0.995165i	$0.468686\pi$
$264$	−1.18008	−0.0726290
$265$	−18.8476	−1.15780
$266$	12.8583	0.788396
$267$	−5.32205	−0.325704
$268$	−17.0075	−1.03890
$269$	23.1882	1.41381	0.706904	−	0.707309i	$-0.250091\pi$
$269$	23.1882	1.41381	0.706904	+	0.707309i	$0.250091\pi$
$270$	−5.50491	−0.335018
$271$	18.1053	1.09982	0.549910	−	0.835224i	$-0.314662\pi$
$271$	18.1053	1.09982	0.549910	+	0.835224i	$0.314662\pi$
$272$	−7.79228	−0.472477
$273$	11.4573	0.693428
$274$	−14.1704	−0.856064
$275$	−3.43449	−0.207107
$276$	3.12590	0.188157
$277$	0.448996	0.0269776	0.0134888	−	0.999909i	$-0.495706\pi$
$277$	0.448996	0.0269776	0.0134888	+	0.999909i	$0.495706\pi$
$278$	2.41192	0.144657
$279$	27.7730	1.66272
$280$	−25.1153	−1.50093
$281$	0.106522	0.00635458	0.00317729	−	0.999995i	$-0.498989\pi$
$281$	0.106522	0.00635458	0.00317729	+	0.999995i	$0.498989\pi$
$282$	−2.54798	−0.151730
$283$	1.02391	0.0608654	0.0304327	−	0.999537i	$-0.490311\pi$
$283$	1.02391	0.0608654	0.0304327	+	0.999537i	$0.490311\pi$
$284$	16.2633	0.965047
$285$	−7.82265	−0.463374
$286$	−3.96790	−0.234627
$287$	24.5540	1.44937
$288$	−15.6998	−0.925121
$289$	5.74292	0.337819
$290$	0.802018	0.0470961
$291$	5.74890	0.337006
$292$	0.696501	0.0407596
$293$	0.542585	0.0316981	0.0158491	−	0.999874i	$-0.494955\pi$
$293$	0.542585	0.0316981	0.0158491	+	0.999874i	$0.494955\pi$
$294$	−2.23902	−0.130582
$295$	−8.90980	−0.518748
$296$	−2.05424	−0.119401
$297$	−2.90976	−0.168841
$298$	1.08689	0.0629620
$299$	23.8517	1.37938
$300$	2.74167	0.158290
$301$	−39.7466	−2.29095
$302$	11.9688	0.688728
$303$	5.86892	0.337161
$304$	−8.68705	−0.498236
$305$	24.4385	1.39934
$306$	8.52243	0.487195
$307$	24.6151	1.40486	0.702428	−	0.711754i	$-0.252099\pi$
$307$	24.6151	1.40486	0.702428	+	0.711754i	$0.252099\pi$
$308$	−5.84993	−0.333330
$309$	6.84082	0.389160
$310$	19.1531	1.08782
$311$	−0.557393	−0.0316069	−0.0158034	−	0.999875i	$-0.505031\pi$
$311$	−0.557393	−0.0316069	−0.0158034	+	0.999875i	$0.505031\pi$
$312$	7.18803	0.406942
$313$	−5.63236	−0.318360	−0.159180	−	0.987250i	$-0.550885\pi$
$313$	−5.63236	−0.318360	−0.159180	+	0.987250i	$0.550885\pi$
$314$	0.0708037	0.00399569
$315$	−29.5800	−1.66664
$316$	16.3043	0.917187
$317$	8.76845	0.492485	0.246243	−	0.969208i	$-0.420804\pi$
$317$	8.76845	0.492485	0.246243	+	0.969208i	$0.420804\pi$
$318$	−2.14182	−0.120107
$319$	0.423928	0.0237354
$320$	−1.33629	−0.0747012
$321$	−1.10873	−0.0618830
$322$	−9.47058	−0.527775
$323$	25.3544	1.41076
$324$	−10.6447	−0.591374
$325$	20.9199	1.16043
$326$	−2.18521	−0.121027
$327$	6.42801	0.355470
$328$	15.4045	0.850572
$329$	−28.6635	−1.58027
$330$	−0.958488	−0.0527630
$331$	17.7219	0.974086	0.487043	−	0.873378i	$-0.338076\pi$
$331$	17.7219	0.974086	0.487043	+	0.873378i	$0.338076\pi$
$332$	−23.0275	−1.26380
$333$	−2.41942	−0.132583
$334$	12.0989	0.662024
$335$	−31.3481	−1.71273
$336$	3.07346	0.167671
$337$	2.55362	0.139105	0.0695523	−	0.997578i	$-0.477843\pi$
$337$	2.55362	0.139105	0.0695523	+	0.997578i	$0.477843\pi$
$338$	15.7005	0.853994
$339$	2.38025	0.129277
$340$	−21.8229	−1.18351
$341$	10.1238	0.548237
$342$	9.50103	0.513757
$343$	0.801090	0.0432548
$344$	−24.9360	−1.34446
$345$	5.76163	0.310196
$346$	2.84144	0.152757
$347$	−4.32832	−0.232357	−0.116178	−	0.993228i	$-0.537064\pi$
$347$	−4.32832	−0.232357	−0.116178	+	0.993228i	$0.537064\pi$
$348$	−0.338411	−0.0181408
$349$	−15.4272	−0.825800	−0.412900	−	0.910776i	$-0.635484\pi$
$349$	−15.4272	−0.825800	−0.412900	+	0.910776i	$0.635484\pi$
$350$	−8.30647	−0.444000
$351$	17.7237	0.946022
$352$	−5.72292	−0.305033
$353$	14.4116	0.767055	0.383527	−	0.923530i	$-0.374709\pi$
$353$	14.4116	0.767055	0.383527	+	0.923530i	$0.374709\pi$
$354$	−1.01250	−0.0538139
$355$	29.9763	1.59098
$356$	−16.5518	−0.877242
$357$	−8.97033	−0.474760
$358$	−2.65203	−0.140164
$359$	15.4932	0.817701	0.408851	−	0.912601i	$-0.365930\pi$
$359$	15.4932	0.817701	0.408851	+	0.912601i	$0.365930\pi$
$360$	−18.5577	−0.978077
$361$	9.26580	0.487674
$362$	1.49707	0.0786843
$363$	−0.506634	−0.0265914
$364$	35.6326	1.86766
$365$	1.28378	0.0671964
$366$	2.77717	0.145165
$367$	−9.22817	−0.481707	−0.240853	−	0.970562i	$-0.577427\pi$
$367$	−9.22817	−0.481707	−0.240853	+	0.970562i	$0.577427\pi$
$368$	6.39829	0.333534
$369$	18.1429	0.944482
$370$	−1.66850	−0.0867413
$371$	−24.0945	−1.25092
$372$	−8.08163	−0.419013
$373$	−20.3189	−1.05207	−0.526035	−	0.850463i	$-0.676322\pi$
$373$	−20.3189	−1.05207	−0.526035	+	0.850463i	$0.676322\pi$
$374$	3.10661	0.160639
$375$	−2.30345	−0.118950
$376$	−17.9827	−0.927389
$377$	−2.58220	−0.132990
$378$	−7.03739	−0.361964
$379$	30.6306	1.57339	0.786695	−	0.617342i	$-0.211790\pi$
$379$	30.6306	1.57339	0.786695	+	0.617342i	$0.211790\pi$
$380$	−24.3287	−1.24804
$381$	5.83437	0.298904
$382$	7.93606	0.406044
$383$	−1.98915	−0.101641	−0.0508205	−	0.998708i	$-0.516184\pi$
$383$	−1.98915	−0.101641	−0.0508205	+	0.998708i	$0.516184\pi$
$384$	5.64699	0.288172
$385$	−10.7825	−0.549529
$386$	−1.35729	−0.0690842
$387$	−29.3687	−1.49290
$388$	17.8793	0.907682
$389$	20.8857	1.05895	0.529474	−	0.848326i	$-0.322389\pi$
$389$	20.8857	1.05895	0.529474	+	0.848326i	$0.322389\pi$
$390$	5.83827	0.295632
$391$	−18.6743	−0.944402
$392$	−15.8022	−0.798134
$393$	−0.506634	−0.0255563
$394$	13.1078	0.660362
$395$	30.0519	1.51208
$396$	−4.32251	−0.217214
$397$	5.51386	0.276733	0.138366	−	0.990381i	$-0.455815\pi$
$397$	5.51386	0.276733	0.138366	+	0.990381i	$0.455815\pi$
$398$	−14.1641	−0.709983
$399$	−10.0004	−0.500645
$400$	5.61182	0.280591
$401$	−10.8217	−0.540411	−0.270205	−	0.962803i	$-0.587092\pi$
$401$	−10.8217	−0.540411	−0.270205	+	0.962803i	$0.587092\pi$
$402$	−3.56237	−0.177675
$403$	−61.6656	−3.07178
$404$	18.2525	0.908097
$405$	−19.6203	−0.974939
$406$	1.02529	0.0508842
$407$	−0.881930	−0.0437157
$408$	−5.62776	−0.278615
$409$	−25.6606	−1.26883	−0.634417	−	0.772991i	$-0.718760\pi$
$409$	−25.6606	−1.26883	−0.634417	+	0.772991i	$0.718760\pi$
$410$	12.5119	0.617918
$411$	11.0208	0.543615
$412$	21.2752	1.04815
$413$	−11.3902	−0.560473
$414$	−6.99781	−0.343924
$415$	−42.4440	−2.08349
$416$	34.8590	1.70910
$417$	−1.87583	−0.0918598
$418$	3.46333	0.169397
$419$	9.02665	0.440981	0.220490	−	0.975389i	$-0.429234\pi$
$419$	9.02665	0.440981	0.220490	+	0.975389i	$0.429234\pi$
$420$	8.60744	0.420000
$421$	19.2222	0.936834	0.468417	−	0.883507i	$-0.344824\pi$
$421$	19.2222	0.936834	0.468417	+	0.883507i	$0.344824\pi$
$422$	11.9559	0.582005
$423$	−21.1795	−1.02978
$424$	−15.1162	−0.734110
$425$	−16.3789	−0.794494
$426$	3.40648	0.165045
$427$	31.2418	1.51190
$428$	−3.44817	−0.166674
$429$	3.08597	0.148992
$430$	−20.2535	−0.976712
$431$	35.4320	1.70670	0.853349	−	0.521340i	$-0.174568\pi$
$431$	35.4320	1.70670	0.853349	+	0.521340i	$0.174568\pi$
$432$	4.75444	0.228748
$433$	−21.3493	−1.02598	−0.512990	−	0.858395i	$-0.671462\pi$
$433$	−21.3493	−1.02598	−0.512990	+	0.858395i	$0.671462\pi$
$434$	24.4850	1.17532
$435$	−0.623757	−0.0299068
$436$	19.9913	0.957410
$437$	−20.8187	−0.995891
$438$	0.145888	0.00697081
$439$	27.0024	1.28876	0.644378	−	0.764707i	$-0.277116\pi$
$439$	27.0024	1.28876	0.644378	+	0.764707i	$0.277116\pi$
$440$	−6.76468	−0.322494
$441$	−18.6113	−0.886254
$442$	−18.9227	−0.900063
$443$	−11.7592	−0.558694	−0.279347	−	0.960190i	$-0.590118\pi$
$443$	−11.7592	−0.558694	−0.279347	+	0.960190i	$0.590118\pi$
$444$	0.704024	0.0334115
$445$	−30.5081	−1.44622
$446$	10.8704	0.514726
$447$	−0.845313	−0.0399819
$448$	−1.70830	−0.0807096
$449$	35.9709	1.69757	0.848785	−	0.528737i	$-0.177334\pi$
$449$	35.9709	1.69757	0.848785	+	0.528737i	$0.177334\pi$
$450$	−6.13765	−0.289332
$451$	6.61348	0.311417
$452$	7.40265	0.348191
$453$	−9.30855	−0.437354
$454$	−13.3658	−0.627290
$455$	65.6778	3.07902
$456$	−6.27397	−0.293806
$457$	30.5645	1.42975	0.714874	−	0.699253i	$-0.246484\pi$
$457$	30.5645	1.42975	0.714874	+	0.699253i	$0.246484\pi$
$458$	10.8435	0.506682
$459$	−13.8765	−0.647700
$460$	17.9189	0.835472
$461$	−2.33700	−0.108845	−0.0544225	−	0.998518i	$-0.517332\pi$
$461$	−2.33700	−0.108845	−0.0544225	+	0.998518i	$0.517332\pi$
$462$	−1.22532	−0.0570069
$463$	−18.0693	−0.839753	−0.419876	−	0.907581i	$-0.637927\pi$
$463$	−18.0693	−0.839753	−0.419876	+	0.907581i	$0.637927\pi$
$464$	−0.692681	−0.0321569
$465$	−14.8960	−0.690784
$466$	−4.47283	−0.207200
$467$	6.64526	0.307506	0.153753	−	0.988109i	$-0.450864\pi$
$467$	6.64526	0.307506	0.153753	+	0.988109i	$0.450864\pi$
$468$	26.3290	1.21706
$469$	−40.0750	−1.85049
$470$	−14.6060	−0.673723
$471$	−0.0550664	−0.00253733
$472$	−7.14589	−0.328916
$473$	−10.7055	−0.492241
$474$	3.41507	0.156859
$475$	−18.2597	−0.837811
$476$	−27.8980	−1.27870
$477$	−17.8034	−0.815162
$478$	5.55531	0.254094
$479$	6.86237	0.313550	0.156775	−	0.987634i	$-0.449890\pi$
$479$	6.86237	0.313550	0.156775	+	0.987634i	$0.449890\pi$
$480$	8.42056	0.384344
$481$	5.37195	0.244940
$482$	0.0309687	0.00141059
$483$	7.36559	0.335146
$484$	−1.57565	−0.0716203
$485$	32.9549	1.49641
$486$	−7.91609	−0.359081
$487$	−30.5603	−1.38482	−0.692410	−	0.721505i	$-0.743451\pi$
$487$	−30.5603	−1.38482	−0.692410	+	0.721505i	$0.743451\pi$
$488$	19.6003	0.887265
$489$	1.69951	0.0768544
$490$	−12.8349	−0.579823
$491$	−9.41640	−0.424956	−0.212478	−	0.977166i	$-0.568153\pi$
$491$	−9.41640	−0.424956	−0.212478	+	0.977166i	$0.568153\pi$
$492$	−5.27939	−0.238013
$493$	2.02169	0.0910524
$494$	−21.0956	−0.949135
$495$	−7.96721	−0.358099
$496$	−16.5420	−0.742757
$497$	38.3213	1.71894
$498$	−4.82330	−0.216137
$499$	1.57738	0.0706133	0.0353067	−	0.999377i	$-0.488759\pi$
$499$	1.57738	0.0706133	0.0353067	+	0.999377i	$0.488759\pi$
$500$	−7.16382	−0.320376
$501$	−9.40974	−0.420396
$502$	−14.5207	−0.648092
$503$	7.32300	0.326517	0.163258	−	0.986583i	$-0.447800\pi$
$503$	7.32300	0.326517	0.163258	+	0.986583i	$0.447800\pi$
$504$	−23.7239	−1.05675
$505$	33.6429	1.49709
$506$	−2.55085	−0.113399
$507$	−12.2108	−0.542301
$508$	18.1451	0.805058
$509$	−42.1680	−1.86906	−0.934532	−	0.355880i	$-0.884181\pi$
$509$	−42.1680	−1.86906	−0.934532	+	0.355880i	$0.884181\pi$
$510$	−4.57099	−0.202407
$511$	1.64117	0.0726012
$512$	16.9629	0.749660
$513$	−15.4699	−0.683013
$514$	7.22641	0.318743
$515$	39.2142	1.72798
$516$	8.54597	0.376215
$517$	−7.72037	−0.339541
$518$	−2.13299	−0.0937182
$519$	−2.20988	−0.0970031
$520$	41.2045	1.80694
$521$	−16.4078	−0.718840	−0.359420	−	0.933176i	$-0.617025\pi$
$521$	−16.4078	−0.718840	−0.359420	+	0.933176i	$0.617025\pi$
$522$	0.757586	0.0331586
$523$	−37.1921	−1.62630	−0.813148	−	0.582056i	$-0.802248\pi$
$523$	−37.1921	−1.62630	−0.813148	+	0.582056i	$0.802248\pi$
$524$	−1.57565	−0.0688325
$525$	6.46022	0.281947
$526$	2.07518	0.0904821
$527$	48.2802	2.10312
$528$	0.827820	0.0360262
$529$	−7.66640	−0.333322
$530$	−12.2777	−0.533311
$531$	−8.41618	−0.365231
$532$	−31.1015	−1.34842
$533$	−40.2836	−1.74487
$534$	−3.46691	−0.150028
$535$	−6.35564	−0.274778
$536$	−25.1420	−1.08597
$537$	2.06257	0.0890066
$538$	15.1053	0.651237
$539$	−6.78423	−0.292217
$540$	13.3151	0.572992
$541$	−26.5443	−1.14123	−0.570613	−	0.821219i	$-0.693295\pi$
$541$	−26.5443	−1.14123	−0.570613	+	0.821219i	$0.693295\pi$
$542$	11.7942	0.506605
$543$	−1.16432	−0.0499659
$544$	−27.2923	−1.17015
$545$	36.8478	1.57839
$546$	7.46356	0.319411
$547$	−32.6580	−1.39636	−0.698178	−	0.715924i	$-0.746006\pi$
$547$	−32.6580	−1.39636	−0.698178	+	0.715924i	$0.746006\pi$
$548$	34.2750	1.46416
$549$	23.0846	0.985226
$550$	−2.23731	−0.0953991
$551$	2.25384	0.0960166
$552$	4.62098	0.196682
$553$	38.4179	1.63370
$554$	0.292486	0.0124266
$555$	1.29765	0.0550822
$556$	−5.83389	−0.247412
$557$	31.1396	1.31943	0.659715	−	0.751516i	$-0.270677\pi$
$557$	31.1396	1.31943	0.659715	+	0.751516i	$0.270677\pi$
$558$	18.0920	0.765894
$559$	65.2088	2.75804
$560$	17.6182	0.744506
$561$	−2.41611	−0.102008
$562$	0.0693910	0.00292708
$563$	45.7291	1.92725	0.963626	−	0.267255i	$-0.0861167\pi$
$563$	45.7291	1.92725	0.963626	+	0.267255i	$0.0861167\pi$
$564$	6.16298	0.259508
$565$	13.6445	0.574028
$566$	0.667002	0.0280362
$567$	−25.0823	−1.05336
$568$	24.0418	1.00877
$569$	0.927632	0.0388884	0.0194442	−	0.999811i	$-0.493810\pi$
$569$	0.927632	0.0388884	0.0194442	+	0.999811i	$0.493810\pi$
$570$	−5.09586	−0.213442
$571$	−43.8373	−1.83453	−0.917267	−	0.398272i	$-0.869610\pi$
$571$	−43.8373	−1.83453	−0.917267	+	0.398272i	$0.869610\pi$
$572$	9.59747	0.401290
$573$	−6.17214	−0.257845
$574$	15.9950	0.667619
$575$	13.4488	0.560855
$576$	−1.26226	−0.0525943
$577$	29.1043	1.21163	0.605813	−	0.795607i	$-0.292848\pi$
$577$	29.1043	1.21163	0.605813	+	0.795607i	$0.292848\pi$
$578$	3.74107	0.155608
$579$	1.05561	0.0438696
$580$	−1.93990	−0.0805501
$581$	−54.2598	−2.25108
$582$	3.74497	0.155234
$583$	−6.48972	−0.268777
$584$	1.02963	0.0426063
$585$	48.5293	2.00644
$586$	0.353452	0.0146010
$587$	24.9254	1.02878	0.514391	−	0.857556i	$-0.328018\pi$
$587$	24.9254	1.02878	0.514391	+	0.857556i	$0.328018\pi$
$588$	5.41569	0.223339
$589$	53.8240	2.21778
$590$	−5.80405	−0.238949
$591$	−10.1944	−0.419341
$592$	1.44104	0.0592264
$593$	−3.25283	−0.133578	−0.0667888	−	0.997767i	$-0.521275\pi$
$593$	−3.25283	−0.133578	−0.0667888	+	0.997767i	$0.521275\pi$
$594$	−1.89549	−0.0777727
$595$	−51.4214	−2.10807
$596$	−2.62895	−0.107686
$597$	11.0159	0.450851
$598$	15.5376	0.635378
$599$	18.7901	0.767742	0.383871	−	0.923387i	$-0.374591\pi$
$599$	18.7901	0.767742	0.383871	+	0.923387i	$0.374591\pi$
$600$	4.05298	0.165462
$601$	−36.8232	−1.50205	−0.751026	−	0.660273i	$-0.770441\pi$
$601$	−36.8232	−1.50205	−0.751026	+	0.660273i	$0.770441\pi$
$602$	−25.8918	−1.05527
$603$	−29.6114	−1.20587
$604$	−28.9499	−1.17796
$605$	−2.90422	−0.118073
$606$	3.82315	0.155305
$607$	−23.4379	−0.951316	−0.475658	−	0.879630i	$-0.657790\pi$
$607$	−23.4379	−0.951316	−0.475658	+	0.879630i	$0.657790\pi$
$608$	−30.4262	−1.23395
$609$	−0.797401	−0.0323123
$610$	15.9198	0.644574
$611$	47.0257	1.90246
$612$	−20.6138	−0.833265
$613$	−37.9012	−1.53082	−0.765408	−	0.643546i	$-0.777463\pi$
$613$	−37.9012	−1.53082	−0.765408	+	0.643546i	$0.777463\pi$
$614$	16.0348	0.647113
$615$	−9.73091	−0.392388
$616$	−8.64787	−0.348433
$617$	−17.5661	−0.707185	−0.353592	−	0.935400i	$-0.615040\pi$
$617$	−17.5661	−0.707185	−0.353592	+	0.935400i	$0.615040\pi$
$618$	4.45627	0.179257
$619$	6.96106	0.279788	0.139894	−	0.990166i	$-0.455324\pi$
$619$	6.96106	0.279788	0.139894	+	0.990166i	$0.455324\pi$
$620$	−46.3270	−1.86054
$621$	11.3941	0.457229
$622$	−0.363099	−0.0145589
$623$	−39.0011	−1.56254
$624$	−5.04235	−0.201856
$625$	−30.3767	−1.21507
$626$	−3.66905	−0.146645
$627$	−2.69355	−0.107570
$628$	−0.171258	−0.00683396
$629$	−4.20588	−0.167700
$630$	−19.2691	−0.767698
$631$	−4.85436	−0.193249	−0.0966246	−	0.995321i	$-0.530805\pi$
$631$	−4.85436	−0.193249	−0.0966246	+	0.995321i	$0.530805\pi$
$632$	24.1024	0.958743
$633$	−9.29852	−0.369583
$634$	5.71197	0.226852
$635$	33.4449	1.32722
$636$	5.18059	0.205424
$637$	41.3236	1.63730
$638$	0.276156	0.0109331
$639$	28.3156	1.12015
$640$	32.3707	1.27957
$641$	−16.5031	−0.651834	−0.325917	−	0.945398i	$-0.605673\pi$
$641$	−16.5031	−0.651834	−0.325917	+	0.945398i	$0.605673\pi$
$642$	−0.722250	−0.0285049
$643$	10.2971	0.406076	0.203038	−	0.979171i	$-0.434918\pi$
$643$	10.2971	0.406076	0.203038	+	0.979171i	$0.434918\pi$
$644$	22.9072	0.902671
$645$	15.7519	0.620229
$646$	16.5165	0.649832
$647$	−27.0520	−1.06352	−0.531761	−	0.846894i	$-0.678470\pi$
$647$	−27.0520	−1.06352	−0.531761	+	0.846894i	$0.678470\pi$
$648$	−15.7360	−0.618168
$649$	−3.06788	−0.120425
$650$	13.6277	0.534523
$651$	−19.0428	−0.746346
$652$	5.28553	0.206997
$653$	23.2976	0.911707	0.455853	−	0.890055i	$-0.349334\pi$
$653$	23.2976	0.911707	0.455853	+	0.890055i	$0.349334\pi$
$654$	4.18735	0.163738
$655$	−2.90422	−0.113477
$656$	−10.8062	−0.421910
$657$	1.21266	0.0473104
$658$	−18.6721	−0.727913
$659$	−26.0118	−1.01328	−0.506639	−	0.862159i	$-0.669112\pi$
$659$	−26.0118	−1.01328	−0.506639	+	0.862159i	$0.669112\pi$
$660$	2.31837	0.0902424
$661$	22.2668	0.866079	0.433039	−	0.901375i	$-0.357441\pi$
$661$	22.2668	0.866079	0.433039	+	0.901375i	$0.357441\pi$
$662$	11.5445	0.448689
$663$	14.7168	0.571555
$664$	−34.0412	−1.32106
$665$	−57.3260	−2.22301
$666$	−1.57607	−0.0610713
$667$	−1.66002	−0.0642763
$668$	−29.2646	−1.13228
$669$	−8.45424	−0.326860
$670$	−20.4209	−0.788928
$671$	8.41482	0.324851
$672$	10.7647	0.415258
$673$	−3.33279	−0.128470	−0.0642348	−	0.997935i	$-0.520461\pi$
$673$	−3.33279	−0.128470	−0.0642348	+	0.997935i	$0.520461\pi$
$674$	1.66349	0.0640752
$675$	9.99354	0.384652
$676$	−37.9760	−1.46061
$677$	−17.3072	−0.665171	−0.332586	−	0.943073i	$-0.607921\pi$
$677$	−17.3072	−0.665171	−0.332586	+	0.943073i	$0.607921\pi$
$678$	1.55055	0.0595485
$679$	42.1291	1.61677
$680$	−32.2605	−1.23713
$681$	10.3951	0.398340
$682$	6.59491	0.252532
$683$	44.6345	1.70789	0.853945	−	0.520363i	$-0.174203\pi$
$683$	44.6345	1.70789	0.853945	+	0.520363i	$0.174203\pi$
$684$	−22.9809	−0.878696
$685$	63.1754	2.41381
$686$	0.521848	0.0199243
$687$	−8.43332	−0.321751
$688$	17.4924	0.666892
$689$	39.5297	1.50596
$690$	3.75326	0.142884
$691$	13.7680	0.523760	0.261880	−	0.965100i	$-0.415658\pi$
$691$	13.7680	0.523760	0.261880	+	0.965100i	$0.415658\pi$
$692$	−6.87281	−0.261265
$693$	−10.1852	−0.386902
$694$	−2.81957	−0.107029
$695$	−10.7530	−0.407884
$696$	−0.500269	−0.0189627
$697$	31.5394	1.19464
$698$	−10.0496	−0.380385
$699$	3.47867	0.131575
$700$	20.0915	0.759388
$701$	−7.40794	−0.279794	−0.139897	−	0.990166i	$-0.544677\pi$
$701$	−7.40794	−0.279794	−0.139897	+	0.990166i	$0.544677\pi$
$702$	11.5456	0.435762
$703$	−4.68883	−0.176843
$704$	−0.460122	−0.0173415
$705$	11.3596	0.427826
$706$	9.38808	0.353325
$707$	43.0086	1.61750
$708$	2.44902	0.0920396
$709$	−5.12459	−0.192458	−0.0962290	−	0.995359i	$-0.530678\pi$
$709$	−5.12459	−0.192458	−0.0962290	+	0.995359i	$0.530678\pi$
$710$	19.5273	0.732845
$711$	28.3870	1.06460
$712$	−24.4683	−0.916987
$713$	−39.6431	−1.48465
$714$	−5.84348	−0.218687
$715$	17.6900	0.661567
$716$	6.41467	0.239727
$717$	−4.32055	−0.161354
$718$	10.0926	0.376654
$719$	28.2806	1.05469	0.527345	−	0.849652i	$-0.323188\pi$
$719$	28.2806	1.05469	0.527345	+	0.849652i	$0.323188\pi$
$720$	13.0181	0.485156
$721$	50.1309	1.86697
$722$	6.03596	0.224635
$723$	−0.0240854	−0.000895746 0
$724$	−3.62108	−0.134576
$725$	−1.45597	−0.0540735
$726$	−0.330033	−0.0122487
$727$	13.9760	0.518340	0.259170	−	0.965832i	$-0.416551\pi$
$727$	13.9760	0.518340	0.259170	+	0.965832i	$0.416551\pi$
$728$	52.6753	1.95228
$729$	−14.1107	−0.522620
$730$	0.836287	0.0309524
$731$	−51.0542	−1.88831
$732$	−6.71735	−0.248281
$733$	3.89690	0.143935	0.0719677	−	0.997407i	$-0.477072\pi$
$733$	3.89690	0.143935	0.0719677	+	0.997407i	$0.477072\pi$
$734$	−6.01145	−0.221887
$735$	9.98215	0.368197
$736$	22.4099	0.826040
$737$	−10.7940	−0.397602
$738$	11.8187	0.435053
$739$	32.5082	1.19584	0.597918	−	0.801558i	$-0.295995\pi$
$739$	32.5082	1.19584	0.597918	+	0.801558i	$0.295995\pi$
$740$	4.03574	0.148357
$741$	16.4067	0.602717
$742$	−15.6957	−0.576207
$743$	45.9861	1.68706	0.843532	−	0.537078i	$-0.180472\pi$
$743$	45.9861	1.68706	0.843532	+	0.537078i	$0.180472\pi$
$744$	−11.9470	−0.437997
$745$	−4.84566	−0.177531
$746$	−13.2362	−0.484611
$747$	−40.0926	−1.46691
$748$	−7.51419	−0.274746
$749$	−8.12496	−0.296880
$750$	−1.50052	−0.0547914
$751$	17.5173	0.639215	0.319607	−	0.947550i	$-0.396449\pi$
$751$	17.5173	0.639215	0.319607	+	0.947550i	$0.396449\pi$
$752$	12.6148	0.460014
$753$	11.2933	0.411549
$754$	−1.68210	−0.0612586
$755$	−53.3602	−1.94198
$756$	17.0219	0.619080
$757$	−8.64929	−0.314364	−0.157182	−	0.987570i	$-0.550241\pi$
$757$	−8.64929	−0.314364	−0.157182	+	0.987570i	$0.550241\pi$
$758$	19.9535	0.724744
$759$	1.98388	0.0720104
$760$	−35.9648	−1.30458
$761$	−50.3333	−1.82458	−0.912290	−	0.409545i	$-0.865687\pi$
$761$	−50.3333	−1.82458	−0.912290	+	0.409545i	$0.865687\pi$
$762$	3.80065	0.137683
$763$	47.1057	1.70534
$764$	−19.1956	−0.694471
$765$	−37.9953	−1.37372
$766$	−1.29578	−0.0468184
$767$	18.6868	0.674743
$768$	4.14481	0.149563
$769$	1.59980	0.0576902	0.0288451	−	0.999584i	$-0.490817\pi$
$769$	1.59980	0.0576902	0.0288451	+	0.999584i	$0.490817\pi$
$770$	−7.02399	−0.253127
$771$	−5.62022	−0.202407
$772$	3.28298	0.118157
$773$	43.9437	1.58054	0.790272	−	0.612757i	$-0.209939\pi$
$773$	43.9437	1.58054	0.790272	+	0.612757i	$0.209939\pi$
$774$	−19.1315	−0.687667
$775$	−34.7702	−1.24898
$776$	26.4307	0.948807
$777$	1.65890	0.0595126
$778$	13.6054	0.487779
$779$	35.1610	1.25977
$780$	−14.1215	−0.505630
$781$	10.3216	0.369337
$782$	−12.1649	−0.435016
$783$	−1.23353	−0.0440827
$784$	11.0852	0.395899
$785$	−0.315662	−0.0112665
$786$	−0.330033	−0.0117719
$787$	34.4826	1.22917	0.614586	−	0.788850i	$-0.289323\pi$
$787$	34.4826	1.22917	0.614586	+	0.788850i	$0.289323\pi$
$788$	−31.7049	−1.12944
$789$	−1.61394	−0.0574576
$790$	19.5765	0.696501
$791$	17.4429	0.620199
$792$	−6.38991	−0.227056
$793$	−51.2558	−1.82015
$794$	3.59186	0.127470
$795$	9.54881	0.338662
$796$	34.2598	1.21431
$797$	15.5211	0.549786	0.274893	−	0.961475i	$-0.411358\pi$
$797$	15.5211	0.549786	0.274893	+	0.961475i	$0.411358\pi$
$798$	−6.51447	−0.230610
$799$	−36.8181	−1.30253
$800$	19.6553	0.694920
$801$	−28.8179	−1.01823
$802$	−7.04952	−0.248927
$803$	0.442041	0.0155993
$804$	8.61659	0.303884
$805$	42.2224	1.48814
$806$	−40.1704	−1.41494
$807$	−11.7479	−0.413546
$808$	26.9825	0.949241
$809$	14.9540	0.525755	0.262877	−	0.964829i	$-0.415329\pi$
$809$	14.9540	0.525755	0.262877	+	0.964829i	$0.415329\pi$
$810$	−12.7811	−0.449082
$811$	21.2895	0.747576	0.373788	−	0.927514i	$-0.378059\pi$
$811$	21.2895	0.747576	0.373788	+	0.927514i	$0.378059\pi$
$812$	−2.47995	−0.0870290
$813$	−9.17276	−0.321703
$814$	−0.574510	−0.0201366
$815$	9.74223	0.341255
$816$	3.94783	0.138202
$817$	−56.9166	−1.99126
$818$	−16.7159	−0.584457
$819$	62.0391	2.16782
$820$	−30.2635	−1.05685
$821$	36.9885	1.29091	0.645454	−	0.763799i	$-0.276668\pi$
$821$	36.9885	1.29091	0.645454	+	0.763799i	$0.276668\pi$
$822$	7.17919	0.250403
$823$	53.6666	1.87070	0.935349	−	0.353725i	$-0.115085\pi$
$823$	53.6666	1.87070	0.935349	+	0.353725i	$0.115085\pi$
$824$	31.4508	1.09564
$825$	1.74003	0.0605800
$826$	−7.41981	−0.258168
$827$	−10.5862	−0.368120	−0.184060	−	0.982915i	$-0.558924\pi$
$827$	−10.5862	−0.368120	−0.184060	+	0.982915i	$0.558924\pi$
$828$	16.9261	0.588224
$829$	−34.3625	−1.19346	−0.596730	−	0.802442i	$-0.703534\pi$
$829$	−34.3625	−1.19346	−0.596730	+	0.802442i	$0.703534\pi$
$830$	−27.6490	−0.959711
$831$	−0.227477	−0.00789107
$832$	2.80266	0.0971648
$833$	−32.3537	−1.12099
$834$	−1.22196	−0.0423130
$835$	−53.9402	−1.86668
$836$	−8.37702	−0.289725
$837$	−29.4580	−1.01822
$838$	5.88017	0.203127
$839$	18.5698	0.641101	0.320551	−	0.947231i	$-0.396132\pi$
$839$	18.5698	0.641101	0.320551	+	0.947231i	$0.396132\pi$
$840$	12.7243	0.439029
$841$	−28.8203	−0.993803
$842$	12.5218	0.431530
$843$	−0.0539677	−0.00185875
$844$	−28.9187	−0.995423
$845$	−69.9970	−2.40797
$846$	−13.7968	−0.474343
$847$	−3.71271	−0.127570
$848$	10.6040	0.364141
$849$	−0.518750	−0.0178034
$850$	−10.6696	−0.365965
$851$	3.45347	0.118384
$852$	−8.23952	−0.282281
$853$	41.5030	1.42104	0.710519	−	0.703678i	$-0.248460\pi$
$853$	41.5030	1.42104	0.710519	+	0.703678i	$0.248460\pi$
$854$	20.3516	0.696419
$855$	−42.3581	−1.44862
$856$	−5.09739	−0.174225
$857$	−33.2591	−1.13611	−0.568055	−	0.822991i	$-0.692304\pi$
$857$	−33.2591	−1.13611	−0.568055	+	0.822991i	$0.692304\pi$
$858$	2.01027	0.0686296
$859$	−35.4296	−1.20884	−0.604421	−	0.796665i	$-0.706595\pi$
$859$	−35.4296	−1.20884	−0.604421	+	0.796665i	$0.706595\pi$
$860$	48.9888	1.67050
$861$	−12.4399	−0.423949
$862$	23.0812	0.786149
$863$	5.06175	0.172304	0.0861520	−	0.996282i	$-0.472543\pi$
$863$	5.06175	0.172304	0.0861520	+	0.996282i	$0.472543\pi$
$864$	16.6523	0.566524
$865$	−12.6679	−0.430722
$866$	−13.9074	−0.472593
$867$	−2.90956	−0.0988138
$868$	−59.2238	−2.01019
$869$	10.3477	0.351021
$870$	−0.406330	−0.0137759
$871$	65.7476	2.22777
$872$	29.5529	1.00079
$873$	31.1292	1.05356
$874$	−13.5618	−0.458733
$875$	−16.8802	−0.570654
$876$	−0.352871	−0.0119224
$877$	28.7035	0.969248	0.484624	−	0.874723i	$-0.338956\pi$
$877$	28.7035	0.969248	0.484624	+	0.874723i	$0.338956\pi$
$878$	17.5900	0.593634
$879$	−0.274892	−0.00927187
$880$	4.74538	0.159967
$881$	24.7610	0.834220	0.417110	−	0.908856i	$-0.363043\pi$
$881$	24.7610	0.834220	0.417110	+	0.908856i	$0.363043\pi$
$882$	−12.1239	−0.408231
$883$	33.4074	1.12425	0.562124	−	0.827053i	$-0.309984\pi$
$883$	33.4074	1.12425	0.562124	+	0.827053i	$0.309984\pi$
$884$	45.7699	1.53941
$885$	4.51400	0.151737
$886$	−7.66019	−0.257349
$887$	21.4977	0.721822	0.360911	−	0.932600i	$-0.382466\pi$
$887$	21.4977	0.721822	0.360911	+	0.932600i	$0.382466\pi$
$888$	1.04075	0.0349253
$889$	42.7554	1.43397
$890$	−19.8737	−0.666167
$891$	−6.75578	−0.226327
$892$	−26.2930	−0.880353
$893$	−41.0458	−1.37354
$894$	−0.550656	−0.0184167
$895$	11.8235	0.395215
$896$	41.3823	1.38249
$897$	−12.0841	−0.403476
$898$	23.4323	0.781945
$899$	4.29178	0.143139
$900$	14.8456	0.494854
$901$	−30.9492	−1.03107
$902$	4.30818	0.143447
$903$	20.1369	0.670116
$904$	10.9432	0.363967
$905$	−6.67435	−0.221863
$906$	−6.06381	−0.201457
$907$	5.49050	0.182309	0.0911544	−	0.995837i	$-0.470944\pi$
$907$	5.49050	0.182309	0.0911544	+	0.995837i	$0.470944\pi$
$908$	32.3290	1.07288
$909$	31.7790	1.05404
$910$	42.7840	1.41828
$911$	36.9142	1.22302	0.611512	−	0.791235i	$-0.290562\pi$
$911$	36.9142	1.22302	0.611512	+	0.791235i	$0.290562\pi$
$912$	4.40115	0.145737
$913$	−14.6146	−0.483673
$914$	19.9104	0.658579
$915$	−12.3814	−0.409315
$916$	−26.2279	−0.866595
$917$	−3.71271	−0.122605
$918$	−9.03948	−0.298347
$919$	−44.8205	−1.47849	−0.739246	−	0.673435i	$-0.764818\pi$
$919$	−44.8205	−1.47849	−0.739246	+	0.673435i	$0.764818\pi$
$920$	26.4892	0.873324
$921$	−12.4708	−0.410928
$922$	−1.52238	−0.0501368
$923$	−62.8704	−2.06940
$924$	2.96377	0.0975009
$925$	3.02898	0.0995922
$926$	−11.7708	−0.386812
$927$	37.0417	1.21661
$928$	−2.42610	−0.0796408
$929$	−27.6172	−0.906091	−0.453046	−	0.891487i	$-0.649663\pi$
$929$	−27.6172	−0.906091	−0.453046	+	0.891487i	$0.649663\pi$
$930$	−9.70359	−0.318193
$931$	−36.0688	−1.18211
$932$	10.8188	0.354381
$933$	0.282394	0.00924517
$934$	4.32888	0.141645
$935$	−13.8501	−0.452946
$936$	38.9218	1.27220
$937$	−35.5423	−1.16112	−0.580558	−	0.814219i	$-0.697166\pi$
$937$	−35.5423	−1.16112	−0.580558	+	0.814219i	$0.697166\pi$
$938$	−26.1058	−0.852384
$939$	2.85354	0.0931218
$940$	35.3286	1.15229
$941$	−57.3672	−1.87012	−0.935059	−	0.354493i	$-0.884654\pi$
$941$	−57.3672	−1.87012	−0.935059	+	0.354493i	$0.884654\pi$
$942$	−0.0358716	−0.00116876
$943$	−25.8972	−0.843328
$944$	5.01280	0.163153
$945$	31.3746	1.02062
$946$	−6.97383	−0.226739
$947$	−12.3197	−0.400336	−0.200168	−	0.979762i	$-0.564149\pi$
$947$	−12.3197	−0.400336	−0.200168	+	0.979762i	$0.564149\pi$
$948$	−8.26030	−0.268282
$949$	−2.69253	−0.0874032
$950$	−11.8948	−0.385917
$951$	−4.44239	−0.144054
$952$	−41.2413	−1.33664
$953$	15.0111	0.486256	0.243128	−	0.969994i	$-0.421827\pi$
$953$	15.0111	0.486256	0.243128	+	0.969994i	$0.421827\pi$
$954$	−11.5975	−0.375484
$955$	−35.3811	−1.14491
$956$	−13.4371	−0.434586
$957$	−0.214776	−0.00694272
$958$	4.47031	0.144429
$959$	80.7625	2.60796
$960$	0.677012	0.0218505
$961$	71.4923	2.30620
$962$	3.49941	0.112826
$963$	−6.00353	−0.193461
$964$	−0.0749064	−0.00241257
$965$	6.05116	0.194794
$966$	4.79812	0.154377
$967$	−50.3287	−1.61846	−0.809230	−	0.587492i	$-0.800116\pi$
$967$	−50.3287	−1.61846	−0.809230	+	0.587492i	$0.800116\pi$
$968$	−2.32926	−0.0748653
$969$	−12.8454	−0.412654
$970$	21.4676	0.689283
$971$	−7.18367	−0.230535	−0.115268	−	0.993334i	$-0.536773\pi$
$971$	−7.18367	−0.230535	−0.115268	+	0.993334i	$0.536773\pi$
$972$	19.1473	0.614148
$973$	−13.7465	−0.440691
$974$	−19.9077	−0.637884
$975$	−10.5987	−0.339431
$976$	−13.7495	−0.440111
$977$	34.2063	1.09436	0.547178	−	0.837016i	$-0.315702\pi$
$977$	34.2063	1.09436	0.547178	+	0.837016i	$0.315702\pi$
$978$	1.10710	0.0354011
$979$	−10.5047	−0.335733
$980$	31.0448	0.991690
$981$	34.8064	1.11128
$982$	−6.13406	−0.195746
$983$	−6.57074	−0.209574	−0.104787	−	0.994495i	$-0.533416\pi$
$983$	−6.57074	−0.209574	−0.104787	+	0.994495i	$0.533416\pi$
$984$	−7.80445	−0.248797
$985$	−58.4381	−1.86199
$986$	1.31698	0.0419411
$987$	14.5219	0.462237
$988$	51.0255	1.62334
$989$	41.9209	1.33301
$990$	−5.19003	−0.164950
$991$	41.5807	1.32086	0.660428	−	0.750890i	$-0.270375\pi$
$991$	41.5807	1.32086	0.660428	+	0.750890i	$0.270375\pi$
$992$	−57.9380	−1.83953
$993$	−8.97853	−0.284925
$994$	24.9634	0.791790
$995$	63.1474	2.00191
$996$	11.6665	0.369667
$997$	−26.6445	−0.843841	−0.421921	−	0.906633i	$-0.638644\pi$
$997$	−26.6445	−0.843841	−0.421921	+	0.906633i	$0.638644\pi$
$998$	1.02754	0.0325263
$999$	2.56621	0.0811912

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.f.1.17	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.f.1.17	✓	31	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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q+0.651423 q^{2} -0.506634 q^{3} -1.57565 q^{4} -2.90422 q^{5} -0.330033 q^{6} -3.71271 q^{7} -2.32926 q^{8} -2.74332 q^{9} +O(q^{10})\)	\(q+0.651423 q^{2} -0.506634 q^{3} -1.57565 q^{4} -2.90422 q^{5} -0.330033 q^{6} -3.71271 q^{7} -2.32926 q^{8} -2.74332 q^{9} -1.89188 q^{10} -1.00000 q^{11} +0.798276 q^{12} +6.09113 q^{13} -2.41855 q^{14} +1.47138 q^{15} +1.63396 q^{16} -4.76895 q^{17} -1.78706 q^{18} -5.31656 q^{19} +4.57603 q^{20} +1.88098 q^{21} -0.651423 q^{22} +3.91581 q^{23} +1.18008 q^{24} +3.43449 q^{25} +3.96790 q^{26} +2.90976 q^{27} +5.84993 q^{28} -0.423928 q^{29} +0.958488 q^{30} -10.1238 q^{31} +5.72292 q^{32} +0.506634 q^{33} -3.10661 q^{34} +10.7825 q^{35} +4.32251 q^{36} +0.881930 q^{37} -3.46333 q^{38} -3.08597 q^{39} +6.76468 q^{40} -6.61348 q^{41} +1.22532 q^{42} +10.7055 q^{43} +1.57565 q^{44} +7.96721 q^{45} +2.55085 q^{46} +7.72037 q^{47} -0.827820 q^{48} +6.78423 q^{49} +2.23731 q^{50} +2.41611 q^{51} -9.59747 q^{52} +6.48972 q^{53} +1.89549 q^{54} +2.90422 q^{55} +8.64787 q^{56} +2.69355 q^{57} -0.276156 q^{58} +3.06788 q^{59} -2.31837 q^{60} -8.41482 q^{61} -6.59491 q^{62} +10.1852 q^{63} +0.460122 q^{64} -17.6900 q^{65} +0.330033 q^{66} +10.7940 q^{67} +7.51419 q^{68} -1.98388 q^{69} +7.02399 q^{70} -10.3216 q^{71} +6.38991 q^{72} -0.442041 q^{73} +0.574510 q^{74} -1.74003 q^{75} +8.37702 q^{76} +3.71271 q^{77} -2.01027 q^{78} -10.3477 q^{79} -4.74538 q^{80} +6.75578 q^{81} -4.30818 q^{82} +14.6146 q^{83} -2.96377 q^{84} +13.8501 q^{85} +6.97383 q^{86} +0.214776 q^{87} +2.32926 q^{88} +10.5047 q^{89} +5.19003 q^{90} -22.6146 q^{91} -6.16994 q^{92} +5.12908 q^{93} +5.02923 q^{94} +15.4405 q^{95} -2.89942 q^{96} -11.3473 q^{97} +4.41941 q^{98} +2.74332 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9} - 8 q^{10} - 31 q^{11} + 10 q^{12} - 8 q^{13} + 29 q^{14} + 36 q^{15} + 52 q^{16} - q^{17} + 33 q^{18} - 2 q^{19} + 22 q^{20} - 13 q^{21} - 6 q^{22} + 45 q^{23} + 16 q^{24} + 41 q^{25} + 24 q^{26} + 22 q^{27} + 17 q^{28} + 5 q^{29} + 29 q^{30} + 28 q^{31} + 69 q^{32} - 4 q^{33} + 14 q^{34} + 36 q^{35} + 63 q^{36} - 3 q^{37} + 4 q^{38} + 40 q^{39} - 48 q^{40} + 21 q^{41} - 9 q^{42} - 20 q^{43} - 38 q^{44} + 28 q^{45} - 24 q^{46} + 57 q^{47} - 46 q^{48} + 37 q^{49} + 64 q^{50} + 17 q^{51} - 11 q^{52} + 32 q^{53} - 26 q^{54} - 8 q^{55} + 84 q^{56} + 10 q^{57} - 17 q^{58} + 70 q^{59} - 33 q^{60} - 51 q^{61} - 34 q^{62} + 32 q^{63} + 80 q^{64} - q^{65} - 7 q^{66} + 24 q^{67} - 13 q^{68} + 19 q^{69} - 9 q^{70} + 128 q^{71} + 118 q^{72} - 27 q^{73} - 23 q^{74} + 41 q^{75} - 34 q^{76} - 4 q^{77} + 9 q^{78} + 2 q^{79} - 45 q^{80} + 43 q^{81} - 18 q^{82} + 46 q^{83} - 103 q^{84} - 50 q^{85} + 78 q^{86} - 9 q^{87} - 24 q^{88} + 52 q^{89} - 46 q^{90} + 38 q^{91} + 54 q^{92} + 4 q^{93} + 3 q^{94} + 70 q^{95} - 21 q^{96} + 3 q^{97} - 120 q^{98} - 45 q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9 - 8 * q^10 - 31 * q^11 + 10 * q^12 - 8 * q^13 + 29 * q^14 + 36 * q^15 + 52 * q^16 - q^17 + 33 * q^18 - 2 * q^19 + 22 * q^20 - 13 * q^21 - 6 * q^22 + 45 * q^23 + 16 * q^24 + 41 * q^25 + 24 * q^26 + 22 * q^27 + 17 * q^28 + 5 * q^29 + 29 * q^30 + 28 * q^31 + 69 * q^32 - 4 * q^33 + 14 * q^34 + 36 * q^35 + 63 * q^36 - 3 * q^37 + 4 * q^38 + 40 * q^39 - 48 * q^40 + 21 * q^41 - 9 * q^42 - 20 * q^43 - 38 * q^44 + 28 * q^45 - 24 * q^46 + 57 * q^47 - 46 * q^48 + 37 * q^49 + 64 * q^50 + 17 * q^51 - 11 * q^52 + 32 * q^53 - 26 * q^54 - 8 * q^55 + 84 * q^56 + 10 * q^57 - 17 * q^58 + 70 * q^59 - 33 * q^60 - 51 * q^61 - 34 * q^62 + 32 * q^63 + 80 * q^64 - q^65 - 7 * q^66 + 24 * q^67 - 13 * q^68 + 19 * q^69 - 9 * q^70 + 128 * q^71 + 118 * q^72 - 27 * q^73 - 23 * q^74 + 41 * q^75 - 34 * q^76 - 4 * q^77 + 9 * q^78 + 2 * q^79 - 45 * q^80 + 43 * q^81 - 18 * q^82 + 46 * q^83 - 103 * q^84 - 50 * q^85 + 78 * q^86 - 9 * q^87 - 24 * q^88 + 52 * q^89 - 46 * q^90 + 38 * q^91 + 54 * q^92 + 4 * q^93 + 3 * q^94 + 70 * q^95 - 21 * q^96 + 3 * q^97 - 120 * q^98 - 45 * q^99

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