LMFDB - Embedded newform 1441.2.a.f.1.8

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			1.8
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)

$f(q)$	$=$	$q-1.51851 q^{2} +2.67622 q^{3} +0.305884 q^{4} -2.61923 q^{5} -4.06387 q^{6} +2.29369 q^{7} +2.57254 q^{8} +4.16214 q^{9} +O(q^{10})$	\(q-1.51851 q^{2} +2.67622 q^{3} +0.305884 q^{4} -2.61923 q^{5} -4.06387 q^{6} +2.29369 q^{7} +2.57254 q^{8} +4.16214 q^{9} +3.97734 q^{10} -1.00000 q^{11} +0.818612 q^{12} -2.79485 q^{13} -3.48300 q^{14} -7.00963 q^{15} -4.51820 q^{16} +2.39944 q^{17} -6.32027 q^{18} +0.675710 q^{19} -0.801181 q^{20} +6.13842 q^{21} +1.51851 q^{22} +4.29812 q^{23} +6.88467 q^{24} +1.86037 q^{25} +4.24402 q^{26} +3.11015 q^{27} +0.701603 q^{28} +8.51738 q^{29} +10.6442 q^{30} +7.66822 q^{31} +1.71588 q^{32} -2.67622 q^{33} -3.64359 q^{34} -6.00771 q^{35} +1.27313 q^{36} -4.49966 q^{37} -1.02607 q^{38} -7.47963 q^{39} -6.73807 q^{40} +3.52656 q^{41} -9.32127 q^{42} -1.90865 q^{43} -0.305884 q^{44} -10.9016 q^{45} -6.52676 q^{46} +3.20141 q^{47} -12.0917 q^{48} -1.73898 q^{49} -2.82500 q^{50} +6.42144 q^{51} -0.854900 q^{52} +7.56915 q^{53} -4.72281 q^{54} +2.61923 q^{55} +5.90061 q^{56} +1.80835 q^{57} -12.9338 q^{58} +0.659379 q^{59} -2.14413 q^{60} -9.41508 q^{61} -11.6443 q^{62} +9.54667 q^{63} +6.43082 q^{64} +7.32036 q^{65} +4.06387 q^{66} +11.8226 q^{67} +0.733952 q^{68} +11.5027 q^{69} +9.12279 q^{70} +8.94172 q^{71} +10.7073 q^{72} -2.78947 q^{73} +6.83279 q^{74} +4.97876 q^{75} +0.206689 q^{76} -2.29369 q^{77} +11.3579 q^{78} +9.71178 q^{79} +11.8342 q^{80} -4.16299 q^{81} -5.35512 q^{82} -3.04050 q^{83} +1.87764 q^{84} -6.28470 q^{85} +2.89832 q^{86} +22.7944 q^{87} -2.57254 q^{88} +7.92921 q^{89} +16.5543 q^{90} -6.41052 q^{91} +1.31473 q^{92} +20.5218 q^{93} -4.86138 q^{94} -1.76984 q^{95} +4.59206 q^{96} +9.20963 q^{97} +2.64067 q^{98} -4.16214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.51851	−1.07375	−0.536876	−	0.843661i	$-0.680396\pi$
$2$	−1.51851	−1.07375	−0.536876	+	0.843661i	$0.680396\pi$
$3$	2.67622	1.54512	0.772558	−	0.634945i	$-0.218977\pi$
$3$	2.67622	1.54512	0.772558	+	0.634945i	$0.218977\pi$
$4$	0.305884	0.152942
$5$	−2.61923	−1.17136	−0.585678	−	0.810544i	$-0.699172\pi$
$5$	−2.61923	−1.17136	−0.585678	+	0.810544i	$0.699172\pi$
$6$	−4.06387	−1.65907
$7$	2.29369	0.866934	0.433467	−	0.901170i	$-0.357290\pi$
$7$	2.29369	0.866934	0.433467	+	0.901170i	$0.357290\pi$
$8$	2.57254	0.909530
$9$	4.16214	1.38738
$10$	3.97734	1.25774
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.818612	0.236313
$13$	−2.79485	−0.775152	−0.387576	−	0.921838i	$-0.626688\pi$
$13$	−2.79485	−0.775152	−0.387576	+	0.921838i	$0.626688\pi$
$14$	−3.48300	−0.930871
$15$	−7.00963	−1.80988
$16$	−4.51820	−1.12955
$17$	2.39944	0.581951	0.290975	−	0.956731i	$-0.406020\pi$
$17$	2.39944	0.581951	0.290975	+	0.956731i	$0.406020\pi$
$18$	−6.32027	−1.48970
$19$	0.675710	0.155018	0.0775092	−	0.996992i	$-0.475303\pi$
$19$	0.675710	0.155018	0.0775092	+	0.996992i	$0.475303\pi$
$20$	−0.801181	−0.179149
$21$	6.13842	1.33951
$22$	1.51851	0.323748
$23$	4.29812	0.896220	0.448110	−	0.893978i	$-0.352097\pi$
$23$	4.29812	0.896220	0.448110	+	0.893978i	$0.352097\pi$
$24$	6.88467	1.40533
$25$	1.86037	0.372074
$26$	4.24402	0.832320
$27$	3.11015	0.598549
$28$	0.701603	0.132591
$29$	8.51738	1.58164	0.790819	−	0.612050i	$-0.209655\pi$
$29$	8.51738	1.58164	0.790819	+	0.612050i	$0.209655\pi$
$30$	10.6442	1.94336
$31$	7.66822	1.37725	0.688626	−	0.725117i	$-0.258214\pi$
$31$	7.66822	1.37725	0.688626	+	0.725117i	$0.258214\pi$
$32$	1.71588	0.303327
$33$	−2.67622	−0.465870
$34$	−3.64359	−0.624870
$35$	−6.00771	−1.01549
$36$	1.27313	0.212189
$37$	−4.49966	−0.739739	−0.369869	−	0.929084i	$-0.620598\pi$
$37$	−4.49966	−0.739739	−0.369869	+	0.929084i	$0.620598\pi$
$38$	−1.02607	−0.166451
$39$	−7.47963	−1.19770
$40$	−6.73807	−1.06538
$41$	3.52656	0.550755	0.275378	−	0.961336i	$-0.411197\pi$
$41$	3.52656	0.550755	0.275378	+	0.961336i	$0.411197\pi$
$42$	−9.32127	−1.43830
$43$	−1.90865	−0.291067	−0.145534	−	0.989353i	$-0.546490\pi$
$43$	−1.90865	−0.291067	−0.145534	+	0.989353i	$0.546490\pi$
$44$	−0.305884	−0.0461137
$45$	−10.9016	−1.62512
$46$	−6.52676	−0.962318
$47$	3.20141	0.466973	0.233486	−	0.972360i	$-0.424987\pi$
$47$	3.20141	0.466973	0.233486	+	0.972360i	$0.424987\pi$
$48$	−12.0917	−1.74529
$49$	−1.73898	−0.248426
$50$	−2.82500	−0.399515
$51$	6.42144	0.899181
$52$	−0.854900	−0.118553
$53$	7.56915	1.03970	0.519851	−	0.854257i	$-0.325987\pi$
$53$	7.56915	1.03970	0.519851	+	0.854257i	$0.325987\pi$
$54$	−4.72281	−0.642693
$55$	2.61923	0.353177
$56$	5.90061	0.788502
$57$	1.80835	0.239521
$58$	−12.9338	−1.69829
$59$	0.659379	0.0858438	0.0429219	−	0.999078i	$-0.486333\pi$
$59$	0.659379	0.0858438	0.0429219	+	0.999078i	$0.486333\pi$
$60$	−2.14413	−0.276807
$61$	−9.41508	−1.20548	−0.602739	−	0.797939i	$-0.705924\pi$
$61$	−9.41508	−1.20548	−0.602739	+	0.797939i	$0.705924\pi$
$62$	−11.6443	−1.47883
$63$	9.54667	1.20277
$64$	6.43082	0.803853
$65$	7.32036	0.907979
$66$	4.06387	0.500228
$67$	11.8226	1.44436	0.722178	−	0.691707i	$-0.243141\pi$
$67$	11.8226	1.44436	0.722178	+	0.691707i	$0.243141\pi$
$68$	0.733952	0.0890047
$69$	11.5027	1.38476
$70$	9.12279	1.09038
$71$	8.94172	1.06119	0.530593	−	0.847626i	$-0.321969\pi$
$71$	8.94172	1.06119	0.530593	+	0.847626i	$0.321969\pi$
$72$	10.7073	1.26186
$73$	−2.78947	−0.326482	−0.163241	−	0.986586i	$-0.552195\pi$
$73$	−2.78947	−0.326482	−0.163241	+	0.986586i	$0.552195\pi$
$74$	6.83279	0.794295
$75$	4.97876	0.574898
$76$	0.206689	0.0237088
$77$	−2.29369	−0.261390
$78$	11.3579	1.28603
$79$	9.71178	1.09266	0.546330	−	0.837570i	$-0.316024\pi$
$79$	9.71178	1.09266	0.546330	+	0.837570i	$0.316024\pi$
$80$	11.8342	1.32311
$81$	−4.16299	−0.462554
$82$	−5.35512	−0.591374
$83$	−3.04050	−0.333738	−0.166869	−	0.985979i	$-0.553366\pi$
$83$	−3.04050	−0.333738	−0.166869	+	0.985979i	$0.553366\pi$
$84$	1.87764	0.204868
$85$	−6.28470	−0.681671
$86$	2.89832	0.312534
$87$	22.7944	2.44381
$88$	−2.57254	−0.274234
$89$	7.92921	0.840495	0.420247	−	0.907410i	$-0.361943\pi$
$89$	7.92921	0.840495	0.420247	+	0.907410i	$0.361943\pi$
$90$	16.5543	1.74497
$91$	−6.41052	−0.672005
$92$	1.31473	0.137070
$93$	20.5218	2.12801
$94$	−4.86138	−0.501413
$95$	−1.76984	−0.181582
$96$	4.59206	0.468675
$97$	9.20963	0.935096	0.467548	−	0.883968i	$-0.345138\pi$
$97$	9.20963	0.935096	0.467548	+	0.883968i	$0.345138\pi$
$98$	2.64067	0.266748
$99$	−4.16214	−0.418311
$100$	0.569058	0.0569058
$101$	−4.33073	−0.430923	−0.215462	−	0.976512i	$-0.569126\pi$
$101$	−4.33073	−0.430923	−0.215462	+	0.976512i	$0.569126\pi$
$102$	−9.75104	−0.965497
$103$	−11.7731	−1.16004	−0.580019	−	0.814603i	$-0.696955\pi$
$103$	−11.7731	−1.16004	−0.580019	+	0.814603i	$0.696955\pi$
$104$	−7.18986	−0.705024
$105$	−16.0779	−1.56905
$106$	−11.4939	−1.11638
$107$	6.91797	0.668786	0.334393	−	0.942434i	$-0.391469\pi$
$107$	6.91797	0.668786	0.334393	+	0.942434i	$0.391469\pi$
$108$	0.951345	0.0915432
$109$	−3.92878	−0.376309	−0.188154	−	0.982139i	$-0.560251\pi$
$109$	−3.92878	−0.376309	−0.188154	+	0.982139i	$0.560251\pi$
$110$	−3.97734	−0.379224
$111$	−12.0421	−1.14298
$112$	−10.3634	−0.979246
$113$	12.5489	1.18050	0.590248	−	0.807222i	$-0.299030\pi$
$113$	12.5489	1.18050	0.590248	+	0.807222i	$0.299030\pi$
$114$	−2.74600	−0.257186
$115$	−11.2578	−1.04979
$116$	2.60533	0.241899
$117$	−11.6326	−1.07543
$118$	−1.00128	−0.0921749
$119$	5.50358	0.504513
$120$	−18.0326	−1.64614
$121$	1.00000	0.0909091
$122$	14.2969	1.29438
$123$	9.43783	0.850981
$124$	2.34558	0.210640
$125$	8.22341	0.735524
$126$	−14.4968	−1.29147
$127$	−3.40528	−0.302170	−0.151085	−	0.988521i	$-0.548277\pi$
$127$	−3.40528	−0.302170	−0.151085	+	0.988521i	$0.548277\pi$
$128$	−13.1970	−1.16647
$129$	−5.10798	−0.449732
$130$	−11.1161	−0.974943
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−0.818612	−0.0712511
$133$	1.54987	0.134391
$134$	−17.9527	−1.55088
$135$	−8.14620	−0.701114
$136$	6.17266	0.529301
$137$	12.1882	1.04131	0.520653	−	0.853769i	$-0.325689\pi$
$137$	12.1882	1.04131	0.520653	+	0.853769i	$0.325689\pi$
$138$	−17.4670	−1.48689
$139$	−11.5210	−0.977197	−0.488598	−	0.872509i	$-0.662492\pi$
$139$	−11.5210	−0.977197	−0.488598	+	0.872509i	$0.662492\pi$
$140$	−1.83766	−0.155311
$141$	8.56766	0.721527
$142$	−13.5781	−1.13945
$143$	2.79485	0.233717
$144$	−18.8054	−1.56712
$145$	−22.3090	−1.85266
$146$	4.23584	0.350561
$147$	−4.65389	−0.383847
$148$	−1.37637	−0.113137
$149$	8.26961	0.677472	0.338736	−	0.940881i	$-0.390001\pi$
$149$	8.26961	0.677472	0.338736	+	0.940881i	$0.390001\pi$
$150$	−7.56032	−0.617297
$151$	21.0476	1.71283	0.856413	−	0.516291i	$-0.172688\pi$
$151$	21.0476	1.71283	0.856413	+	0.516291i	$0.172688\pi$
$152$	1.73829	0.140994
$153$	9.98683	0.807388
$154$	3.48300	0.280668
$155$	−20.0848	−1.61325
$156$	−2.28790	−0.183178
$157$	23.3090	1.86026	0.930128	−	0.367235i	$-0.119695\pi$
$157$	23.3090	1.86026	0.930128	+	0.367235i	$0.119695\pi$
$158$	−14.7475	−1.17325
$159$	20.2567	1.60646
$160$	−4.49428	−0.355304
$161$	9.85856	0.776964
$162$	6.32156	0.496669
$163$	4.67137	0.365890	0.182945	−	0.983123i	$-0.441437\pi$
$163$	4.67137	0.365890	0.182945	+	0.983123i	$0.441437\pi$
$164$	1.07872	0.0842336
$165$	7.00963	0.545699
$166$	4.61704	0.358352
$167$	−18.8101	−1.45557	−0.727785	−	0.685806i	$-0.759450\pi$
$167$	−18.8101	−1.45557	−0.727785	+	0.685806i	$0.759450\pi$
$168$	15.7913	1.21833
$169$	−5.18881	−0.399140
$170$	9.54340	0.731946
$171$	2.81240	0.215070
$172$	−0.583827	−0.0445164
$173$	−8.00665	−0.608734	−0.304367	−	0.952555i	$-0.598445\pi$
$173$	−8.00665	−0.608734	−0.304367	+	0.952555i	$0.598445\pi$
$174$	−34.6136	−2.62405
$175$	4.26712	0.322564
$176$	4.51820	0.340572
$177$	1.76464	0.132639
$178$	−12.0406	−0.902482
$179$	−21.8454	−1.63280	−0.816402	−	0.577484i	$-0.804035\pi$
$179$	−21.8454	−1.63280	−0.816402	+	0.577484i	$0.804035\pi$
$180$	−3.33463	−0.248549
$181$	0.0118387	0.000879962 0	0.000439981	−	1.00000i	$-0.499860\pi$
$181$	0.0118387	0.000879962 0	0.000439981		1.00000i	$0.499860\pi$
$182$	9.73447	0.721567
$183$	−25.1968	−1.86260
$184$	11.0571	0.815139
$185$	11.7856	0.866497
$186$	−31.1627	−2.28496
$187$	−2.39944	−0.175465
$188$	0.979259	0.0714198
$189$	7.13372	0.518902
$190$	2.68753	0.194974
$191$	9.93379	0.718784	0.359392	−	0.933187i	$-0.382984\pi$
$191$	9.93379	0.718784	0.359392	+	0.933187i	$0.382984\pi$
$192$	17.2103	1.24205
$193$	−12.4610	−0.896962	−0.448481	−	0.893792i	$-0.648035\pi$
$193$	−12.4610	−0.896962	−0.448481	+	0.893792i	$0.648035\pi$
$194$	−13.9849	−1.00406
$195$	19.5909	1.40293
$196$	−0.531927	−0.0379948
$197$	14.1528	1.00835	0.504173	−	0.863603i	$-0.331798\pi$
$197$	14.1528	1.00835	0.504173	+	0.863603i	$0.331798\pi$
$198$	6.32027	0.449162
$199$	−6.86858	−0.486901	−0.243450	−	0.969913i	$-0.578279\pi$
$199$	−6.86858	−0.486901	−0.243450	+	0.969913i	$0.578279\pi$
$200$	4.78588	0.338413
$201$	31.6398	2.23170
$202$	6.57627	0.462705
$203$	19.5362	1.37117
$204$	1.96421	0.137523
$205$	−9.23686	−0.645131
$206$	17.8776	1.24559
$207$	17.8894	1.24340
$208$	12.6277	0.875573
$209$	−0.675710	−0.0467398
$210$	24.4146	1.68477
$211$	−11.0486	−0.760615	−0.380307	−	0.924860i	$-0.624182\pi$
$211$	−11.0486	−0.760615	−0.380307	+	0.924860i	$0.624182\pi$
$212$	2.31528	0.159014
$213$	23.9300	1.63966
$214$	−10.5050	−0.718109
$215$	4.99921	0.340943
$216$	8.00098	0.544398
$217$	17.5885	1.19399
$218$	5.96591	0.404062
$219$	−7.46522	−0.504453
$220$	0.801181	0.0540156
$221$	−6.70609	−0.451100
$222$	18.2860	1.22728
$223$	7.37011	0.493539	0.246769	−	0.969074i	$-0.420631\pi$
$223$	7.37011	0.493539	0.246769	+	0.969074i	$0.420631\pi$
$224$	3.93569	0.262964
$225$	7.74313	0.516209
$226$	−19.0556	−1.26756
$227$	6.62257	0.439555	0.219778	−	0.975550i	$-0.429467\pi$
$227$	6.62257	0.439555	0.219778	+	0.975550i	$0.429467\pi$
$228$	0.553144	0.0366329
$229$	−17.9480	−1.18604	−0.593020	−	0.805188i	$-0.702064\pi$
$229$	−17.9480	−1.18604	−0.593020	+	0.805188i	$0.702064\pi$
$230$	17.0951	1.12722
$231$	−6.13842	−0.403878
$232$	21.9113	1.43855
$233$	−0.536549	−0.0351505	−0.0175752	−	0.999846i	$-0.505595\pi$
$233$	−0.536549	−0.0351505	−0.0175752	+	0.999846i	$0.505595\pi$
$234$	17.6642	1.15475
$235$	−8.38522	−0.546991
$236$	0.201693	0.0131291
$237$	25.9908	1.68829
$238$	−8.35727	−0.541721
$239$	−26.7550	−1.73064	−0.865318	−	0.501223i	$-0.832884\pi$
$239$	−26.7550	−1.73064	−0.865318	+	0.501223i	$0.832884\pi$
$240$	31.6709	2.04435
$241$	−0.469160	−0.0302212	−0.0151106	−	0.999886i	$-0.504810\pi$
$241$	−0.469160	−0.0302212	−0.0151106	+	0.999886i	$0.504810\pi$
$242$	−1.51851	−0.0976138
$243$	−20.4715	−1.31325
$244$	−2.87992	−0.184368
$245$	4.55479	0.290995
$246$	−14.3315	−0.913742
$247$	−1.88851	−0.120163
$248$	19.7268	1.25265
$249$	−8.13704	−0.515664
$250$	−12.4874	−0.789770
$251$	−15.9354	−1.00583	−0.502916	−	0.864335i	$-0.667740\pi$
$251$	−15.9354	−1.00583	−0.502916	+	0.864335i	$0.667740\pi$
$252$	2.92017	0.183954
$253$	−4.29812	−0.270221
$254$	5.17096	0.324455
$255$	−16.8192	−1.05326
$256$	7.17825	0.448641
$257$	−14.5597	−0.908210	−0.454105	−	0.890948i	$-0.650041\pi$
$257$	−14.5597	−0.908210	−0.454105	+	0.890948i	$0.650041\pi$
$258$	7.75653	0.482901
$259$	−10.3208	−0.641304
$260$	2.23918	0.138868
$261$	35.4506	2.19433
$262$	−1.51851	−0.0938141
$263$	9.35315	0.576740	0.288370	−	0.957519i	$-0.406887\pi$
$263$	9.35315	0.576740	0.288370	+	0.957519i	$0.406887\pi$
$264$	−6.88467	−0.423722
$265$	−19.8254	−1.21786
$266$	−2.35350	−0.144302
$267$	21.2203	1.29866
$268$	3.61633	0.220903
$269$	12.3226	0.751325	0.375662	−	0.926757i	$-0.377415\pi$
$269$	12.3226	0.751325	0.375662	+	0.926757i	$0.377415\pi$
$270$	12.3701	0.752822
$271$	10.8429	0.658662	0.329331	−	0.944215i	$-0.393177\pi$
$271$	10.8429	0.658662	0.329331	+	0.944215i	$0.393177\pi$
$272$	−10.8412	−0.657343
$273$	−17.1560	−1.03833
$274$	−18.5079	−1.11810
$275$	−1.86037	−0.112185
$276$	3.51850	0.211789
$277$	22.4552	1.34920	0.674602	−	0.738182i	$-0.264315\pi$
$277$	22.4552	1.34920	0.674602	+	0.738182i	$0.264315\pi$
$278$	17.4948	1.04927
$279$	31.9162	1.91077
$280$	−15.4551	−0.923616
$281$	−19.1099	−1.14000	−0.570002	−	0.821644i	$-0.693057\pi$
$281$	−19.1099	−1.14000	−0.570002	+	0.821644i	$0.693057\pi$
$282$	−13.0101	−0.774741
$283$	−21.5832	−1.28299	−0.641493	−	0.767129i	$-0.721685\pi$
$283$	−21.5832	−1.28299	−0.641493	+	0.767129i	$0.721685\pi$
$284$	2.73513	0.162300
$285$	−4.73648	−0.280565
$286$	−4.24402	−0.250954
$287$	8.08883	0.477468
$288$	7.14172	0.420830
$289$	−11.2427	−0.661333
$290$	33.8765	1.98930
$291$	24.6470	1.44483
$292$	−0.853253	−0.0499329
$293$	−7.89498	−0.461230	−0.230615	−	0.973045i	$-0.574074\pi$
$293$	−7.89498	−0.461230	−0.230615	+	0.973045i	$0.574074\pi$
$294$	7.06700	0.412156
$295$	−1.72707	−0.100554
$296$	−11.5755	−0.672814
$297$	−3.11015	−0.180469
$298$	−12.5575	−0.727437
$299$	−12.0126	−0.694707
$300$	1.52292	0.0879260
$301$	−4.37786	−0.252336
$302$	−31.9610	−1.83915
$303$	−11.5900	−0.665826
$304$	−3.05299	−0.175101
$305$	24.6603	1.41204
$306$	−15.1651	−0.866933
$307$	−33.8546	−1.93218	−0.966092	−	0.258197i	$-0.916872\pi$
$307$	−33.8546	−1.93218	−0.966092	+	0.258197i	$0.916872\pi$
$308$	−0.701603	−0.0399776
$309$	−31.5074	−1.79239
$310$	30.4991	1.73223
$311$	9.18894	0.521057	0.260528	−	0.965466i	$-0.416103\pi$
$311$	9.18894	0.521057	0.260528	+	0.965466i	$0.416103\pi$
$312$	−19.2416	−1.08934
$313$	23.2090	1.31185	0.655924	−	0.754827i	$-0.272279\pi$
$313$	23.2090	1.31185	0.655924	+	0.754827i	$0.272279\pi$
$314$	−35.3950	−1.99745
$315$	−25.0049	−1.40887
$316$	2.97068	0.167114
$317$	−10.7007	−0.601012	−0.300506	−	0.953780i	$-0.597156\pi$
$317$	−10.7007	−0.601012	−0.300506	+	0.953780i	$0.597156\pi$
$318$	−30.7601	−1.72494
$319$	−8.51738	−0.476882
$320$	−16.8438	−0.941598
$321$	18.5140	1.03335
$322$	−14.9704	−0.834266
$323$	1.62133	0.0902131
$324$	−1.27339	−0.0707440
$325$	−5.19946	−0.288414
$326$	−7.09354	−0.392875
$327$	−10.5143	−0.581441
$328$	9.07220	0.500928
$329$	7.34303	0.404835
$330$	−10.6442	−0.585945
$331$	33.7091	1.85282	0.926410	−	0.376515i	$-0.122878\pi$
$331$	33.7091	1.85282	0.926410	+	0.376515i	$0.122878\pi$
$332$	−0.930040	−0.0510426
$333$	−18.7282	−1.02630
$334$	28.5634	1.56292
$335$	−30.9660	−1.69186
$336$	−27.7346	−1.51305
$337$	−3.65672	−0.199194	−0.0995971	−	0.995028i	$-0.531755\pi$
$337$	−3.65672	−0.199194	−0.0995971	+	0.995028i	$0.531755\pi$
$338$	7.87929	0.428577
$339$	33.5835	1.82400
$340$	−1.92239	−0.104256
$341$	−7.66822	−0.415257
$342$	−4.27067	−0.230931
$343$	−20.0445	−1.08230
$344$	−4.91009	−0.264734
$345$	−30.1283	−1.62205
$346$	12.1582	0.653629
$347$	−21.1845	−1.13724	−0.568621	−	0.822599i	$-0.692523\pi$
$347$	−21.1845	−1.13724	−0.568621	+	0.822599i	$0.692523\pi$
$348$	6.97243	0.373762
$349$	−16.5987	−0.888510	−0.444255	−	0.895900i	$-0.646532\pi$
$349$	−16.5987	−0.888510	−0.444255	+	0.895900i	$0.646532\pi$
$350$	−6.47968	−0.346353
$351$	−8.69240	−0.463966
$352$	−1.71588	−0.0914565
$353$	37.3007	1.98532	0.992658	−	0.120954i	$-0.0385954\pi$
$353$	37.3007	1.98532	0.992658	+	0.120954i	$0.0385954\pi$
$354$	−2.67963	−0.142421
$355$	−23.4204	−1.24303
$356$	2.42542	0.128547
$357$	14.7288	0.779530
$358$	33.1726	1.75323
$359$	−4.05181	−0.213847	−0.106923	−	0.994267i	$-0.534100\pi$
$359$	−4.05181	−0.213847	−0.106923	+	0.994267i	$0.534100\pi$
$360$	−28.0448	−1.47809
$361$	−18.5434	−0.975969
$362$	−0.0179772	−0.000944860 0
$363$	2.67622	0.140465
$364$	−1.96088	−0.102778
$365$	7.30626	0.382427
$366$	38.2617	1.99997
$367$	−1.14845	−0.0599487	−0.0299744	−	0.999551i	$-0.509543\pi$
$367$	−1.14845	−0.0599487	−0.0299744	+	0.999551i	$0.509543\pi$
$368$	−19.4198	−1.01233
$369$	14.6780	0.764108
$370$	−17.8967	−0.930403
$371$	17.3613	0.901354
$372$	6.27730	0.325463
$373$	−21.1507	−1.09514	−0.547571	−	0.836759i	$-0.684447\pi$
$373$	−21.1507	−1.09514	−0.547571	+	0.836759i	$0.684447\pi$
$374$	3.64359	0.188406
$375$	22.0076	1.13647
$376$	8.23574	0.424726
$377$	−23.8048	−1.22601
$378$	−10.8327	−0.557172
$379$	−7.37382	−0.378768	−0.189384	−	0.981903i	$-0.560649\pi$
$379$	−7.37382	−0.378768	−0.189384	+	0.981903i	$0.560649\pi$
$380$	−0.541366	−0.0277715
$381$	−9.11327	−0.466887
$382$	−15.0846	−0.771795
$383$	−14.5333	−0.742619	−0.371309	−	0.928509i	$-0.621091\pi$
$383$	−14.5333	−0.742619	−0.371309	+	0.928509i	$0.621091\pi$
$384$	−35.3182	−1.80232
$385$	6.00771	0.306181
$386$	18.9222	0.963114
$387$	−7.94409	−0.403821
$388$	2.81708	0.143015
$389$	14.1448	0.717170	0.358585	−	0.933497i	$-0.383259\pi$
$389$	14.1448	0.717170	0.358585	+	0.933497i	$0.383259\pi$
$390$	−29.7490	−1.50640
$391$	10.3131	0.521556
$392$	−4.47360	−0.225951
$393$	2.67622	0.134997
$394$	−21.4912	−1.08271
$395$	−25.4374	−1.27989
$396$	−1.27313	−0.0639774
$397$	13.5105	0.678074	0.339037	−	0.940773i	$-0.389899\pi$
$397$	13.5105	0.678074	0.339037	+	0.940773i	$0.389899\pi$
$398$	10.4300	0.522810
$399$	4.14779	0.207649
$400$	−8.40554	−0.420277
$401$	−24.2000	−1.20849	−0.604244	−	0.796799i	$-0.706525\pi$
$401$	−24.2000	−1.20849	−0.604244	+	0.796799i	$0.706525\pi$
$402$	−48.0454	−2.39629
$403$	−21.4315	−1.06758
$404$	−1.32470	−0.0659063
$405$	10.9038	0.541816
$406$	−29.6660	−1.47230
$407$	4.49966	0.223040
$408$	16.5194	0.817832
$409$	−3.36781	−0.166527	−0.0832637	−	0.996528i	$-0.526534\pi$
$409$	−3.36781	−0.166527	−0.0832637	+	0.996528i	$0.526534\pi$
$410$	14.0263	0.692710
$411$	32.6182	1.60894
$412$	−3.60120	−0.177419
$413$	1.51241	0.0744209
$414$	−27.1653	−1.33510
$415$	7.96377	0.390926
$416$	−4.79562	−0.235124
$417$	−30.8327	−1.50988
$418$	1.02607	0.0501869
$419$	−32.8184	−1.60328	−0.801641	−	0.597806i	$-0.796039\pi$
$419$	−32.8184	−1.60328	−0.801641	+	0.597806i	$0.796039\pi$
$420$	−4.91798	−0.239973
$421$	−10.1010	−0.492290	−0.246145	−	0.969233i	$-0.579164\pi$
$421$	−10.1010	−0.492290	−0.246145	+	0.969233i	$0.579164\pi$
$422$	16.7774	0.816711
$423$	13.3247	0.647870
$424$	19.4719	0.945641
$425$	4.46386	0.216529
$426$	−36.3380	−1.76058
$427$	−21.5953	−1.04507
$428$	2.11610	0.102285
$429$	7.47963	0.361120
$430$	−7.59136	−0.366088
$431$	−0.731603	−0.0352401	−0.0176200	−	0.999845i	$-0.505609\pi$
$431$	−0.731603	−0.0352401	−0.0176200	+	0.999845i	$0.505609\pi$
$432$	−14.0523	−0.676091
$433$	−3.73949	−0.179708	−0.0898542	−	0.995955i	$-0.528640\pi$
$433$	−3.73949	−0.179708	−0.0898542	+	0.995955i	$0.528640\pi$
$434$	−26.7084	−1.28204
$435$	−59.7037	−2.86257
$436$	−1.20175	−0.0575534
$437$	2.90428	0.138931
$438$	11.3360	0.541657
$439$	−13.7211	−0.654872	−0.327436	−	0.944873i	$-0.606185\pi$
$439$	−13.7211	−0.654872	−0.327436	+	0.944873i	$0.606185\pi$
$440$	6.73807	0.321225
$441$	−7.23789	−0.344661
$442$	10.1833	0.484369
$443$	−23.0035	−1.09293	−0.546466	−	0.837481i	$-0.684027\pi$
$443$	−23.0035	−1.09293	−0.546466	+	0.837481i	$0.684027\pi$
$444$	−3.68347	−0.174810
$445$	−20.7684	−0.984518
$446$	−11.1916	−0.529938
$447$	22.1313	1.04677
$448$	14.7503	0.696887
$449$	−14.0012	−0.660759	−0.330380	−	0.943848i	$-0.607177\pi$
$449$	−14.0012	−0.660759	−0.330380	+	0.943848i	$0.607177\pi$
$450$	−11.7581	−0.554280
$451$	−3.52656	−0.166059
$452$	3.83849	0.180547
$453$	56.3279	2.64651
$454$	−10.0565	−0.471973
$455$	16.7906	0.787157
$456$	4.65204	0.217852
$457$	0.917496	0.0429186	0.0214593	−	0.999770i	$-0.493169\pi$
$457$	0.917496	0.0429186	0.0214593	+	0.999770i	$0.493169\pi$
$458$	27.2543	1.27351
$459$	7.46263	0.348326
$460$	−3.44357	−0.160557
$461$	36.0541	1.67921	0.839604	−	0.543199i	$-0.182787\pi$
$461$	36.0541	1.67921	0.839604	+	0.543199i	$0.182787\pi$
$462$	9.32127	0.433665
$463$	−3.95546	−0.183826	−0.0919129	−	0.995767i	$-0.529298\pi$
$463$	−3.95546	−0.183826	−0.0919129	+	0.995767i	$0.529298\pi$
$464$	−38.4832	−1.78654
$465$	−53.7514	−2.49266
$466$	0.814757	0.0377429
$467$	−36.2597	−1.67790	−0.838949	−	0.544210i	$-0.816830\pi$
$467$	−36.2597	−1.67790	−0.838949	+	0.544210i	$0.816830\pi$
$468$	−3.55822	−0.164479
$469$	27.1173	1.25216
$470$	12.7331	0.587333
$471$	62.3798	2.87431
$472$	1.69628	0.0780775
$473$	1.90865	0.0877600
$474$	−39.4675	−1.81280
$475$	1.25707	0.0576784
$476$	1.68346	0.0771612
$477$	31.5039	1.44246
$478$	40.6278	1.85827
$479$	19.2398	0.879088	0.439544	−	0.898221i	$-0.355140\pi$
$479$	19.2398	0.879088	0.439544	+	0.898221i	$0.355140\pi$
$480$	−12.0277	−0.548985
$481$	12.5759	0.573410
$482$	0.712425	0.0324501
$483$	26.3837	1.20050
$484$	0.305884	0.0139038
$485$	−24.1221	−1.09533
$486$	31.0863	1.41010
$487$	−9.70357	−0.439711	−0.219855	−	0.975532i	$-0.570559\pi$
$487$	−9.70357	−0.439711	−0.219855	+	0.975532i	$0.570559\pi$
$488$	−24.2207	−1.09642
$489$	12.5016	0.565342
$490$	−6.91652	−0.312456
$491$	1.97421	0.0890949	0.0445475	−	0.999007i	$-0.485815\pi$
$491$	1.97421	0.0890949	0.0445475	+	0.999007i	$0.485815\pi$
$492$	2.88688	0.130151
$493$	20.4370	0.920435
$494$	2.86772	0.129025
$495$	10.9016	0.489991
$496$	−34.6466	−1.55568
$497$	20.5095	0.919979
$498$	12.3562	0.553695
$499$	32.7250	1.46497	0.732487	−	0.680782i	$-0.238360\pi$
$499$	32.7250	1.46497	0.732487	+	0.680782i	$0.238360\pi$
$500$	2.51541	0.112493
$501$	−50.3399	−2.24902
$502$	24.1981	1.08001
$503$	−32.3517	−1.44249	−0.721245	−	0.692680i	$-0.756430\pi$
$503$	−32.3517	−1.44249	−0.721245	+	0.692680i	$0.756430\pi$
$504$	24.5592	1.09395
$505$	11.3432	0.504765
$506$	6.52676	0.290150
$507$	−13.8864	−0.616717
$508$	−1.04162	−0.0462144
$509$	1.22908	0.0544781	0.0272391	−	0.999629i	$-0.491328\pi$
$509$	1.22908	0.0544781	0.0272391	+	0.999629i	$0.491328\pi$
$510$	25.5402	1.13094
$511$	−6.39817	−0.283038
$512$	15.4938	0.684737
$513$	2.10156	0.0927861
$514$	22.1091	0.975192
$515$	30.8365	1.35882
$516$	−1.56245	−0.0687829
$517$	−3.20141	−0.140798
$518$	15.6723	0.688602
$519$	−21.4275	−0.940565
$520$	18.8319	0.825834
$521$	28.6957	1.25718	0.628591	−	0.777736i	$-0.283632\pi$
$521$	28.6957	1.25718	0.628591	+	0.777736i	$0.283632\pi$
$522$	−53.8322	−2.35617
$523$	−3.48798	−0.152519	−0.0762593	−	0.997088i	$-0.524298\pi$
$523$	−3.48798	−0.152519	−0.0762593	+	0.997088i	$0.524298\pi$
$524$	0.305884	0.0133626
$525$	11.4197	0.498398
$526$	−14.2029	−0.619275
$527$	18.3995	0.801493
$528$	12.0917	0.526224
$529$	−4.52615	−0.196789
$530$	30.1051	1.30768
$531$	2.74443	0.119098
$532$	0.474080	0.0205540
$533$	−9.85619	−0.426919
$534$	−32.2233	−1.39444
$535$	−18.1198	−0.783386
$536$	30.4140	1.31368
$537$	−58.4631	−2.52287
$538$	−18.7121	−0.806736
$539$	1.73898	0.0749032
$540$	−2.49179	−0.107230
$541$	−8.81375	−0.378933	−0.189466	−	0.981887i	$-0.560676\pi$
$541$	−8.81375	−0.378933	−0.189466	+	0.981887i	$0.560676\pi$
$542$	−16.4652	−0.707239
$543$	0.0316829	0.00135964
$544$	4.11715	0.176521
$545$	10.2904	0.440792
$546$	26.0516	1.11490
$547$	−13.2365	−0.565953	−0.282977	−	0.959127i	$-0.591322\pi$
$547$	−13.2365	−0.565953	−0.282977	+	0.959127i	$0.591322\pi$
$548$	3.72816	0.159259
$549$	−39.1869	−1.67246
$550$	2.82500	0.120458
$551$	5.75528	0.245183
$552$	29.5912	1.25948
$553$	22.2758	0.947265
$554$	−34.0986	−1.44871
$555$	31.5409	1.33884
$556$	−3.52408	−0.149454
$557$	13.1804	0.558470	0.279235	−	0.960223i	$-0.409919\pi$
$557$	13.1804	0.558470	0.279235	+	0.960223i	$0.409919\pi$
$558$	−48.4652	−2.05170
$559$	5.33440	0.225621
$560$	27.1440	1.14705
$561$	−6.42144	−0.271113
$562$	29.0187	1.22408
$563$	−19.0631	−0.803413	−0.401707	−	0.915768i	$-0.631583\pi$
$563$	−19.0631	−0.803413	−0.401707	+	0.915768i	$0.631583\pi$
$564$	2.62071	0.110352
$565$	−32.8683	−1.38278
$566$	32.7743	1.37761
$567$	−9.54861	−0.401004
$568$	23.0029	0.965181
$569$	21.9102	0.918524	0.459262	−	0.888301i	$-0.348114\pi$
$569$	21.9102	0.918524	0.459262	+	0.888301i	$0.348114\pi$
$570$	7.19241	0.301257
$571$	−19.8527	−0.830811	−0.415406	−	0.909636i	$-0.636360\pi$
$571$	−19.8527	−0.830811	−0.415406	+	0.909636i	$0.636360\pi$
$572$	0.854900	0.0357452
$573$	26.5850	1.11060
$574$	−12.2830	−0.512682
$575$	7.99610	0.333461
$576$	26.7660	1.11525
$577$	−9.93466	−0.413585	−0.206793	−	0.978385i	$-0.566303\pi$
$577$	−9.93466	−0.413585	−0.206793	+	0.978385i	$0.566303\pi$
$578$	17.0721	0.710108
$579$	−33.3483	−1.38591
$580$	−6.82396	−0.283350
$581$	−6.97397	−0.289329
$582$	−37.4268	−1.55139
$583$	−7.56915	−0.313482
$584$	−7.17601	−0.296945
$585$	30.4684	1.25971
$586$	11.9886	0.495246
$587$	31.1163	1.28431	0.642153	−	0.766576i	$-0.278041\pi$
$587$	31.1163	1.28431	0.642153	+	0.766576i	$0.278041\pi$
$588$	−1.42355	−0.0587063
$589$	5.18149	0.213500
$590$	2.62257	0.107970
$591$	37.8760	1.55801
$592$	20.3304	0.835572
$593$	12.2393	0.502609	0.251304	−	0.967908i	$-0.419140\pi$
$593$	12.2393	0.502609	0.251304	+	0.967908i	$0.419140\pi$
$594$	4.72281	0.193779
$595$	−14.4152	−0.590964
$596$	2.52954	0.103614
$597$	−18.3818	−0.752318
$598$	18.2413	0.745942
$599$	1.84791	0.0755035	0.0377517	−	0.999287i	$-0.487980\pi$
$599$	1.84791	0.0755035	0.0377517	+	0.999287i	$0.487980\pi$
$600$	12.8081	0.522887
$601$	28.7387	1.17228	0.586139	−	0.810211i	$-0.300647\pi$
$601$	28.7387	1.17228	0.586139	+	0.810211i	$0.300647\pi$
$602$	6.64785	0.270946
$603$	49.2072	2.00387
$604$	6.43811	0.261963
$605$	−2.61923	−0.106487
$606$	17.5995	0.714932
$607$	−23.3112	−0.946173	−0.473087	−	0.881016i	$-0.656860\pi$
$607$	−23.3112	−0.946173	−0.473087	+	0.881016i	$0.656860\pi$
$608$	1.15943	0.0470213
$609$	52.2832	2.11862
$610$	−37.4470	−1.51618
$611$	−8.94745	−0.361975
$612$	3.05481	0.123483
$613$	12.5332	0.506212	0.253106	−	0.967439i	$-0.418548\pi$
$613$	12.5332	0.506212	0.253106	+	0.967439i	$0.418548\pi$
$614$	51.4087	2.07469
$615$	−24.7199	−0.996801
$616$	−5.90061	−0.237742
$617$	−38.4840	−1.54931	−0.774653	−	0.632386i	$-0.782076\pi$
$617$	−38.4840	−1.54931	−0.774653	+	0.632386i	$0.782076\pi$
$618$	47.8444	1.92458
$619$	−25.7583	−1.03531	−0.517656	−	0.855589i	$-0.673195\pi$
$619$	−25.7583	−1.03531	−0.517656	+	0.855589i	$0.673195\pi$
$620$	−6.14363	−0.246734
$621$	13.3678	0.536432
$622$	−13.9535	−0.559485
$623$	18.1872	0.728653
$624$	33.7945	1.35286
$625$	−30.8409	−1.23364
$626$	−35.2431	−1.40860
$627$	−1.80835	−0.0722184
$628$	7.12983	0.284511
$629$	−10.7967	−0.430491
$630$	37.9703	1.51277
$631$	40.2376	1.60183	0.800916	−	0.598776i	$-0.204346\pi$
$631$	40.2376	1.60183	0.800916	+	0.598776i	$0.204346\pi$
$632$	24.9839	0.993808
$633$	−29.5684	−1.17524
$634$	16.2492	0.645338
$635$	8.91921	0.353948
$636$	6.19620	0.245695
$637$	4.86019	0.192568
$638$	12.9338	0.512052
$639$	37.2167	1.47227
$640$	34.5661	1.36635
$641$	−18.1000	−0.714907	−0.357453	−	0.933931i	$-0.616355\pi$
$641$	−18.1000	−0.714907	−0.357453	+	0.933931i	$0.616355\pi$
$642$	−28.1138	−1.10956
$643$	−35.9051	−1.41596	−0.707980	−	0.706233i	$-0.750393\pi$
$643$	−35.9051	−1.41596	−0.707980	+	0.706233i	$0.750393\pi$
$644$	3.01558	0.118830
$645$	13.3790	0.526796
$646$	−2.46201	−0.0968664
$647$	37.7289	1.48328	0.741639	−	0.670799i	$-0.234049\pi$
$647$	37.7289	1.48328	0.741639	+	0.670799i	$0.234049\pi$
$648$	−10.7095	−0.420707
$649$	−0.659379	−0.0258829
$650$	7.89545	0.309685
$651$	47.0707	1.84485
$652$	1.42890	0.0559599
$653$	15.1569	0.593136	0.296568	−	0.955012i	$-0.404158\pi$
$653$	15.1569	0.593136	0.296568	+	0.955012i	$0.404158\pi$
$654$	15.9661	0.624323
$655$	−2.61923	−0.102342
$656$	−15.9337	−0.622106
$657$	−11.6102	−0.452955
$658$	−11.1505	−0.434692
$659$	−39.7578	−1.54875	−0.774373	−	0.632729i	$-0.781935\pi$
$659$	−39.7578	−1.54875	−0.774373	+	0.632729i	$0.781935\pi$
$660$	2.14413	0.0834603
$661$	−21.0141	−0.817355	−0.408677	−	0.912679i	$-0.634010\pi$
$661$	−21.0141	−0.817355	−0.408677	+	0.912679i	$0.634010\pi$
$662$	−51.1878	−1.98947
$663$	−17.9470	−0.697002
$664$	−7.82180	−0.303545
$665$	−4.05947	−0.157419
$666$	28.4390	1.10199
$667$	36.6087	1.41750
$668$	−5.75371	−0.222618
$669$	19.7240	0.762575
$670$	47.0223	1.81663
$671$	9.41508	0.363465
$672$	10.5328	0.406310
$673$	−3.78549	−0.145920	−0.0729599	−	0.997335i	$-0.523245\pi$
$673$	−3.78549	−0.145920	−0.0729599	+	0.997335i	$0.523245\pi$
$674$	5.55278	0.213885
$675$	5.78604	0.222705
$676$	−1.58718	−0.0610452
$677$	−1.75684	−0.0675207	−0.0337604	−	0.999430i	$-0.510748\pi$
$677$	−1.75684	−0.0675207	−0.0337604	+	0.999430i	$0.510748\pi$
$678$	−50.9969	−1.95853
$679$	21.1240	0.810666
$680$	−16.1676	−0.620000
$681$	17.7234	0.679164
$682$	11.6443	0.445883
$683$	17.0146	0.651047	0.325524	−	0.945534i	$-0.394459\pi$
$683$	17.0146	0.651047	0.325524	+	0.945534i	$0.394459\pi$
$684$	0.860269	0.0328932
$685$	−31.9236	−1.21974
$686$	30.4379	1.16212
$687$	−48.0328	−1.83257
$688$	8.62369	0.328775
$689$	−21.1546	−0.805928
$690$	45.7502	1.74168
$691$	17.1164	0.651139	0.325570	−	0.945518i	$-0.394444\pi$
$691$	17.1164	0.651139	0.325570	+	0.945518i	$0.394444\pi$
$692$	−2.44911	−0.0931010
$693$	−9.54667	−0.362648
$694$	32.1689	1.22112
$695$	30.1761	1.14465
$696$	58.6394	2.22272
$697$	8.46177	0.320513
$698$	25.2054	0.954038
$699$	−1.43592	−0.0543116
$700$	1.30524	0.0493336
$701$	−4.10224	−0.154939	−0.0774697	−	0.996995i	$-0.524684\pi$
$701$	−4.10224	−0.154939	−0.0774697	+	0.996995i	$0.524684\pi$
$702$	13.1995	0.498184
$703$	−3.04046	−0.114673
$704$	−6.43082	−0.242371
$705$	−22.4407	−0.845165
$706$	−56.6416	−2.13174
$707$	−9.93335	−0.373582
$708$	0.539776	0.0202860
$709$	12.4468	0.467448	0.233724	−	0.972303i	$-0.424909\pi$
$709$	12.4468	0.467448	0.233724	+	0.972303i	$0.424909\pi$
$710$	35.5642	1.33470
$711$	40.4218	1.51594
$712$	20.3982	0.764455
$713$	32.9589	1.23432
$714$	−22.3659	−0.837022
$715$	−7.32036	−0.273766
$716$	−6.68217	−0.249724
$717$	−71.6022	−2.67403
$718$	6.15273	0.229618
$719$	−4.70447	−0.175447	−0.0877235	−	0.996145i	$-0.527959\pi$
$719$	−4.70447	−0.175447	−0.0877235	+	0.996145i	$0.527959\pi$
$720$	49.2557	1.83565
$721$	−27.0039	−1.00568
$722$	28.1584	1.04795
$723$	−1.25557	−0.0466953
$724$	0.00362126	0.000134583 0
$725$	15.8455	0.588487
$726$	−4.06387	−0.150825
$727$	22.0707	0.818557	0.409279	−	0.912409i	$-0.365780\pi$
$727$	22.0707	0.818557	0.409279	+	0.912409i	$0.365780\pi$
$728$	−16.4913	−0.611209
$729$	−42.2973	−1.56657
$730$	−11.0946	−0.410631
$731$	−4.57971	−0.169387
$732$	−7.70730	−0.284870
$733$	−2.56881	−0.0948811	−0.0474406	−	0.998874i	$-0.515106\pi$
$733$	−2.56881	−0.0948811	−0.0474406	+	0.998874i	$0.515106\pi$
$734$	1.74394	0.0643700
$735$	12.1896	0.449621
$736$	7.37505	0.271848
$737$	−11.8226	−0.435490
$738$	−22.2888	−0.820462
$739$	44.9156	1.65225	0.826123	−	0.563490i	$-0.190542\pi$
$739$	44.9156	1.65225	0.826123	+	0.563490i	$0.190542\pi$
$740$	3.60504	0.132524
$741$	−5.05406	−0.185665
$742$	−26.3634	−0.967830
$743$	33.5638	1.23134	0.615669	−	0.788005i	$-0.288886\pi$
$743$	33.5638	1.23134	0.615669	+	0.788005i	$0.288886\pi$
$744$	52.7932	1.93549
$745$	−21.6600	−0.793561
$746$	32.1176	1.17591
$747$	−12.6550	−0.463022
$748$	−0.733952	−0.0268359
$749$	15.8677	0.579793
$750$	−33.4189	−1.22029
$751$	−6.87699	−0.250945	−0.125472	−	0.992097i	$-0.540045\pi$
$751$	−6.87699	−0.250945	−0.125472	+	0.992097i	$0.540045\pi$
$752$	−14.4646	−0.527470
$753$	−42.6465	−1.55413
$754$	36.1479	1.31643
$755$	−55.1284	−2.00633
$756$	2.18209	0.0793619
$757$	10.9989	0.399763	0.199881	−	0.979820i	$-0.435944\pi$
$757$	10.9989	0.399763	0.199881	+	0.979820i	$0.435944\pi$
$758$	11.1972	0.406702
$759$	−11.5027	−0.417522
$760$	−4.55298	−0.165154
$761$	−15.0472	−0.545460	−0.272730	−	0.962091i	$-0.587927\pi$
$761$	−15.0472	−0.545460	−0.272730	+	0.962091i	$0.587927\pi$
$762$	13.8386	0.501320
$763$	−9.01141	−0.326235
$764$	3.03859	0.109932
$765$	−26.1578	−0.945738
$766$	22.0691	0.797388
$767$	−1.84286	−0.0665420
$768$	19.2106	0.693202
$769$	−24.5076	−0.883768	−0.441884	−	0.897072i	$-0.645690\pi$
$769$	−24.5076	−0.883768	−0.441884	+	0.897072i	$0.645690\pi$
$770$	−9.12279	−0.328762
$771$	−38.9650	−1.40329
$772$	−3.81162	−0.137183
$773$	−20.4803	−0.736626	−0.368313	−	0.929702i	$-0.620065\pi$
$773$	−20.4803	−0.736626	−0.368313	+	0.929702i	$0.620065\pi$
$774$	12.0632	0.433603
$775$	14.2657	0.512440
$776$	23.6921	0.850498
$777$	−27.6208	−0.990889
$778$	−21.4791	−0.770063
$779$	2.38293	0.0853773
$780$	5.99254	0.214567
$781$	−8.94172	−0.319960
$782$	−15.6606	−0.560022
$783$	26.4903	0.946687
$784$	7.85707	0.280610
$785$	−61.0515	−2.17902
$786$	−4.06387	−0.144954
$787$	12.8697	0.458755	0.229378	−	0.973338i	$-0.426331\pi$
$787$	12.8697	0.458755	0.229378	+	0.973338i	$0.426331\pi$
$788$	4.32911	0.154218
$789$	25.0311	0.891130
$790$	38.6270	1.37429
$791$	28.7832	1.02341
$792$	−10.7073	−0.380466
$793$	26.3137	0.934428
$794$	−20.5159	−0.728082
$795$	−53.0570	−1.88174
$796$	−2.10099	−0.0744676
$797$	4.87208	0.172578	0.0862890	−	0.996270i	$-0.472499\pi$
$797$	4.87208	0.172578	0.0862890	+	0.996270i	$0.472499\pi$
$798$	−6.29847	−0.222964
$799$	7.68159	0.271755
$800$	3.19217	0.112860
$801$	33.0025	1.16609
$802$	36.7480	1.29762
$803$	2.78947	0.0984381
$804$	9.67810	0.341320
$805$	−25.8219	−0.910101
$806$	32.5440	1.14632
$807$	32.9781	1.16088
$808$	−11.1410	−0.391938
$809$	47.5220	1.67079	0.835393	−	0.549654i	$-0.185240\pi$
$809$	47.5220	1.67079	0.835393	+	0.549654i	$0.185240\pi$
$810$	−16.5576	−0.581776
$811$	−37.2759	−1.30893	−0.654466	−	0.756091i	$-0.727107\pi$
$811$	−37.2759	−1.30893	−0.654466	+	0.756091i	$0.727107\pi$
$812$	5.97582	0.209710
$813$	29.0181	1.01771
$814$	−6.83279	−0.239489
$815$	−12.2354	−0.428587
$816$	−29.0134	−1.01567
$817$	−1.28970	−0.0451208
$818$	5.11406	0.178809
$819$	−26.6815	−0.932328
$820$	−2.82541	−0.0986676
$821$	32.1330	1.12145	0.560725	−	0.828002i	$-0.310522\pi$
$821$	32.1330	1.12145	0.560725	+	0.828002i	$0.310522\pi$
$822$	−49.5312	−1.72760
$823$	54.6627	1.90542	0.952711	−	0.303877i	$-0.0982813\pi$
$823$	54.6627	1.90542	0.952711	+	0.303877i	$0.0982813\pi$
$824$	−30.2868	−1.05509
$825$	−4.97876	−0.173338
$826$	−2.29662	−0.0799095
$827$	3.08073	0.107128	0.0535638	−	0.998564i	$-0.482942\pi$
$827$	3.08073	0.107128	0.0535638	+	0.998564i	$0.482942\pi$
$828$	5.47208	0.190168
$829$	−20.4983	−0.711935	−0.355968	−	0.934498i	$-0.615849\pi$
$829$	−20.4983	−0.711935	−0.355968	+	0.934498i	$0.615849\pi$
$830$	−12.0931	−0.419757
$831$	60.0951	2.08467
$832$	−17.9732	−0.623108
$833$	−4.17259	−0.144572
$834$	46.8198	1.62124
$835$	49.2680	1.70499
$836$	−0.206689	−0.00714848
$837$	23.8493	0.824353
$838$	49.8351	1.72153
$839$	−0.331370	−0.0114402	−0.00572009	−	0.999984i	$-0.501821\pi$
$839$	−0.331370	−0.0114402	−0.00572009	+	0.999984i	$0.501821\pi$
$840$	−41.3611	−1.42709
$841$	43.5457	1.50158
$842$	15.3384	0.528597
$843$	−51.1424	−1.76144
$844$	−3.37958	−0.116330
$845$	13.5907	0.467534
$846$	−20.2338	−0.695651
$847$	2.29369	0.0788122
$848$	−34.1990	−1.17440
$849$	−57.7612	−1.98236
$850$	−6.77843	−0.232498
$851$	−19.3401	−0.662969
$852$	7.31980	0.250772
$853$	4.05398	0.138806	0.0694029	−	0.997589i	$-0.477891\pi$
$853$	4.05398	0.138806	0.0694029	+	0.997589i	$0.477891\pi$
$854$	32.7927	1.12214
$855$	−7.36633	−0.251923
$856$	17.7967	0.608280
$857$	11.2365	0.383830	0.191915	−	0.981412i	$-0.438530\pi$
$857$	11.2365	0.383830	0.191915	+	0.981412i	$0.438530\pi$
$858$	−11.3579	−0.387753
$859$	−24.7993	−0.846142	−0.423071	−	0.906096i	$-0.639048\pi$
$859$	−24.7993	−0.846142	−0.423071	+	0.906096i	$0.639048\pi$
$860$	1.52918	0.0521445
$861$	21.6475	0.737744
$862$	1.11095	0.0378391
$863$	42.0796	1.43241	0.716203	−	0.697892i	$-0.245878\pi$
$863$	42.0796	1.43241	0.716203	+	0.697892i	$0.245878\pi$
$864$	5.33663	0.181556
$865$	20.9713	0.713044
$866$	5.67847	0.192962
$867$	−30.0878	−1.02184
$868$	5.38005	0.182611
$869$	−9.71178	−0.329450
$870$	90.6609	3.07369
$871$	−33.0423	−1.11960
$872$	−10.1069	−0.342264
$873$	38.3318	1.29733
$874$	−4.41019	−0.149177
$875$	18.8620	0.637651
$876$	−2.28349	−0.0771520
$877$	−49.5081	−1.67177	−0.835886	−	0.548904i	$-0.815045\pi$
$877$	−49.5081	−1.67177	−0.835886	+	0.548904i	$0.815045\pi$
$878$	20.8357	0.703169
$879$	−21.1287	−0.712653
$880$	−11.8342	−0.398931
$881$	27.4046	0.923285	0.461643	−	0.887066i	$-0.347260\pi$
$881$	27.4046	0.923285	0.461643	+	0.887066i	$0.347260\pi$
$882$	10.9908	0.370081
$883$	−17.2994	−0.582171	−0.291085	−	0.956697i	$-0.594016\pi$
$883$	−17.2994	−0.582171	−0.291085	+	0.956697i	$0.594016\pi$
$884$	−2.05128	−0.0689922
$885$	−4.62200	−0.155367
$886$	34.9312	1.17354
$887$	26.4580	0.888371	0.444186	−	0.895935i	$-0.353493\pi$
$887$	26.4580	0.888371	0.444186	+	0.895935i	$0.353493\pi$
$888$	−30.9787	−1.03958
$889$	−7.81066	−0.261961
$890$	31.5372	1.05713
$891$	4.16299	0.139465
$892$	2.25440	0.0754828
$893$	2.16322	0.0723894
$894$	−33.6066	−1.12397
$895$	57.2182	1.91259
$896$	−30.2699	−1.01125
$897$	−32.1484	−1.07340
$898$	21.2611	0.709491
$899$	65.3131	2.17831
$900$	2.36850	0.0789500
$901$	18.1618	0.605056
$902$	5.35512	0.178306
$903$	−11.7161	−0.389888
$904$	32.2824	1.07370
$905$	−0.0310082	−0.00103075
$906$	−85.5346	−2.84170
$907$	−14.4080	−0.478409	−0.239205	−	0.970969i	$-0.576887\pi$
$907$	−14.4080	−0.478409	−0.239205	+	0.970969i	$0.576887\pi$
$908$	2.02574	0.0672265
$909$	−18.0251	−0.597855
$910$	−25.4968	−0.845211
$911$	48.9798	1.62277	0.811386	−	0.584511i	$-0.198713\pi$
$911$	48.9798	1.62277	0.811386	+	0.584511i	$0.198713\pi$
$912$	−8.17048	−0.270552
$913$	3.04050	0.100626
$914$	−1.39323	−0.0460839
$915$	65.9963	2.18177
$916$	−5.49001	−0.181395
$917$	2.29369	0.0757444
$918$	−11.3321	−0.374015
$919$	−36.5929	−1.20709	−0.603544	−	0.797330i	$-0.706245\pi$
$919$	−36.5929	−1.20709	−0.603544	+	0.797330i	$0.706245\pi$
$920$	−28.9611	−0.954818
$921$	−90.6023	−2.98545
$922$	−54.7487	−1.80305
$923$	−24.9908	−0.822581
$924$	−1.87764	−0.0617699
$925$	−8.37103	−0.275238
$926$	6.00642	0.197383
$927$	−49.0013	−1.60942
$928$	14.6148	0.479753
$929$	−0.558547	−0.0183253	−0.00916267	−	0.999958i	$-0.502917\pi$
$929$	−0.558547	−0.0183253	−0.00916267	+	0.999958i	$0.502917\pi$
$930$	81.6222	2.67650
$931$	−1.17505	−0.0385106
$932$	−0.164122	−0.00537599
$933$	24.5916	0.805093
$934$	55.0608	1.80165
$935$	6.28470	0.205532
$936$	−29.9252	−0.978137
$937$	19.6312	0.641322	0.320661	−	0.947194i	$-0.396095\pi$
$937$	19.6312	0.641322	0.320661	+	0.947194i	$0.396095\pi$
$938$	−41.1780	−1.34451
$939$	62.1123	2.02696
$940$	−2.56490	−0.0836580
$941$	7.76990	0.253292	0.126646	−	0.991948i	$-0.459579\pi$
$941$	7.76990	0.253292	0.126646	+	0.991948i	$0.459579\pi$
$942$	−94.7246	−3.08630
$943$	15.1576	0.493598
$944$	−2.97921	−0.0969649
$945$	−18.6849	−0.607819
$946$	−2.89832	−0.0942324
$947$	−33.9357	−1.10276	−0.551380	−	0.834254i	$-0.685899\pi$
$947$	−33.9357	−1.10276	−0.551380	+	0.834254i	$0.685899\pi$
$948$	7.95018	0.258210
$949$	7.79614	0.253073
$950$	−1.90888	−0.0619323
$951$	−28.6374	−0.928633
$952$	14.1582	0.458869
$953$	−57.1030	−1.84975	−0.924873	−	0.380276i	$-0.875829\pi$
$953$	−57.1030	−1.84975	−0.924873	+	0.380276i	$0.875829\pi$
$954$	−47.8391	−1.54885
$955$	−26.0189	−0.841951
$956$	−8.18392	−0.264687
$957$	−22.7944	−0.736837
$958$	−29.2159	−0.943922
$959$	27.9559	0.902743
$960$	−45.0777	−1.45488
$961$	27.8015	0.896824
$962$	−19.0966	−0.615700
$963$	28.7936	0.927861
$964$	−0.143508	−0.00462210
$965$	32.6382	1.05066
$966$	−40.0640	−1.28904
$967$	11.2490	0.361743	0.180872	−	0.983507i	$-0.442108\pi$
$967$	11.2490	0.361743	0.180872	+	0.983507i	$0.442108\pi$
$968$	2.57254	0.0826845
$969$	4.33903	0.139390
$970$	36.6298	1.17611
$971$	44.6017	1.43134	0.715668	−	0.698440i	$-0.246122\pi$
$971$	44.6017	1.43134	0.715668	+	0.698440i	$0.246122\pi$
$972$	−6.26191	−0.200851
$973$	−26.4256	−0.847165
$974$	14.7350	0.472140
$975$	−13.9149	−0.445633
$976$	42.5392	1.36165
$977$	−33.8175	−1.08192	−0.540959	−	0.841049i	$-0.681939\pi$
$977$	−33.8175	−1.08192	−0.540959	+	0.841049i	$0.681939\pi$
$978$	−18.9839	−0.607037
$979$	−7.92921	−0.253419
$980$	1.39324	0.0445054
$981$	−16.3522	−0.522084
$982$	−2.99787	−0.0956658
$983$	18.0752	0.576509	0.288254	−	0.957554i	$-0.406925\pi$
$983$	18.0752	0.576509	0.288254	+	0.957554i	$0.406925\pi$
$984$	24.2792	0.773992
$985$	−37.0694	−1.18113
$986$	−31.0338	−0.988318
$987$	19.6516	0.625516
$988$	−0.577664	−0.0183779
$989$	−8.20363	−0.260860
$990$	−16.5543	−0.526129
$991$	−16.7265	−0.531336	−0.265668	−	0.964065i	$-0.585592\pi$
$991$	−16.7265	−0.531336	−0.265668	+	0.964065i	$0.585592\pi$
$992$	13.1577	0.417758
$993$	90.2130	2.86282
$994$	−31.1440	−0.987828
$995$	17.9904	0.570334
$996$	−2.48899	−0.0788667
$997$	24.5670	0.778045	0.389023	−	0.921228i	$-0.372813\pi$
$997$	24.5670	0.778045	0.389023	+	0.921228i	$0.372813\pi$
$998$	−49.6934	−1.57302
$999$	−13.9946	−0.442770

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.f.1.8	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.f.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-1.51851 q^{2} +2.67622 q^{3} +0.305884 q^{4} -2.61923 q^{5} -4.06387 q^{6} +2.29369 q^{7} +2.57254 q^{8} +4.16214 q^{9} +O(q^{10})\)	\(q-1.51851 q^{2} +2.67622 q^{3} +0.305884 q^{4} -2.61923 q^{5} -4.06387 q^{6} +2.29369 q^{7} +2.57254 q^{8} +4.16214 q^{9} +3.97734 q^{10} -1.00000 q^{11} +0.818612 q^{12} -2.79485 q^{13} -3.48300 q^{14} -7.00963 q^{15} -4.51820 q^{16} +2.39944 q^{17} -6.32027 q^{18} +0.675710 q^{19} -0.801181 q^{20} +6.13842 q^{21} +1.51851 q^{22} +4.29812 q^{23} +6.88467 q^{24} +1.86037 q^{25} +4.24402 q^{26} +3.11015 q^{27} +0.701603 q^{28} +8.51738 q^{29} +10.6442 q^{30} +7.66822 q^{31} +1.71588 q^{32} -2.67622 q^{33} -3.64359 q^{34} -6.00771 q^{35} +1.27313 q^{36} -4.49966 q^{37} -1.02607 q^{38} -7.47963 q^{39} -6.73807 q^{40} +3.52656 q^{41} -9.32127 q^{42} -1.90865 q^{43} -0.305884 q^{44} -10.9016 q^{45} -6.52676 q^{46} +3.20141 q^{47} -12.0917 q^{48} -1.73898 q^{49} -2.82500 q^{50} +6.42144 q^{51} -0.854900 q^{52} +7.56915 q^{53} -4.72281 q^{54} +2.61923 q^{55} +5.90061 q^{56} +1.80835 q^{57} -12.9338 q^{58} +0.659379 q^{59} -2.14413 q^{60} -9.41508 q^{61} -11.6443 q^{62} +9.54667 q^{63} +6.43082 q^{64} +7.32036 q^{65} +4.06387 q^{66} +11.8226 q^{67} +0.733952 q^{68} +11.5027 q^{69} +9.12279 q^{70} +8.94172 q^{71} +10.7073 q^{72} -2.78947 q^{73} +6.83279 q^{74} +4.97876 q^{75} +0.206689 q^{76} -2.29369 q^{77} +11.3579 q^{78} +9.71178 q^{79} +11.8342 q^{80} -4.16299 q^{81} -5.35512 q^{82} -3.04050 q^{83} +1.87764 q^{84} -6.28470 q^{85} +2.89832 q^{86} +22.7944 q^{87} -2.57254 q^{88} +7.92921 q^{89} +16.5543 q^{90} -6.41052 q^{91} +1.31473 q^{92} +20.5218 q^{93} -4.86138 q^{94} -1.76984 q^{95} +4.59206 q^{96} +9.20963 q^{97} +2.64067 q^{98} -4.16214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) \) 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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