LMFDB - Embedded newform 1441.2.a.f.1.18

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			1.18
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)

$f(q)$	$=$	$q+0.800366 q^{2} -3.25822 q^{3} -1.35941 q^{4} +0.350077 q^{5} -2.60777 q^{6} -2.72656 q^{7} -2.68876 q^{8} +7.61603 q^{9} +O(q^{10})$	\(q+0.800366 q^{2} -3.25822 q^{3} -1.35941 q^{4} +0.350077 q^{5} -2.60777 q^{6} -2.72656 q^{7} -2.68876 q^{8} +7.61603 q^{9} +0.280189 q^{10} -1.00000 q^{11} +4.42928 q^{12} -6.49760 q^{13} -2.18224 q^{14} -1.14063 q^{15} +0.566834 q^{16} -7.27592 q^{17} +6.09561 q^{18} +2.26591 q^{19} -0.475899 q^{20} +8.88373 q^{21} -0.800366 q^{22} -0.681881 q^{23} +8.76059 q^{24} -4.87745 q^{25} -5.20046 q^{26} -15.0401 q^{27} +3.70652 q^{28} -8.89645 q^{29} -0.912920 q^{30} +1.04017 q^{31} +5.83120 q^{32} +3.25822 q^{33} -5.82340 q^{34} -0.954504 q^{35} -10.3533 q^{36} -4.67272 q^{37} +1.81356 q^{38} +21.1706 q^{39} -0.941272 q^{40} +7.70285 q^{41} +7.11024 q^{42} +7.15313 q^{43} +1.35941 q^{44} +2.66619 q^{45} -0.545755 q^{46} +10.9437 q^{47} -1.84687 q^{48} +0.434112 q^{49} -3.90374 q^{50} +23.7066 q^{51} +8.83292 q^{52} +10.3808 q^{53} -12.0376 q^{54} -0.350077 q^{55} +7.33106 q^{56} -7.38285 q^{57} -7.12042 q^{58} +1.67486 q^{59} +1.55059 q^{60} -4.14903 q^{61} +0.832517 q^{62} -20.7655 q^{63} +3.53343 q^{64} -2.27466 q^{65} +2.60777 q^{66} +7.24647 q^{67} +9.89098 q^{68} +2.22172 q^{69} -0.763952 q^{70} -1.59869 q^{71} -20.4777 q^{72} -11.8080 q^{73} -3.73988 q^{74} +15.8918 q^{75} -3.08031 q^{76} +2.72656 q^{77} +16.9443 q^{78} +2.14494 q^{79} +0.198435 q^{80} +26.1558 q^{81} +6.16510 q^{82} -13.4051 q^{83} -12.0767 q^{84} -2.54713 q^{85} +5.72512 q^{86} +28.9866 q^{87} +2.68876 q^{88} -2.83300 q^{89} +2.13393 q^{90} +17.7161 q^{91} +0.926959 q^{92} -3.38911 q^{93} +8.75896 q^{94} +0.793243 q^{95} -18.9994 q^{96} +16.4032 q^{97} +0.347449 q^{98} -7.61603 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.800366	0.565944	0.282972	−	0.959128i	$-0.408680\pi$
$2$	0.800366	0.565944	0.282972	+	0.959128i	$0.408680\pi$
$3$	−3.25822	−1.88114	−0.940568	−	0.339604i	$-0.889707\pi$
$3$	−3.25822	−1.88114	−0.940568	+	0.339604i	$0.889707\pi$
$4$	−1.35941	−0.679707
$5$	0.350077	0.156559	0.0782795	−	0.996931i	$-0.475057\pi$
$5$	0.350077	0.156559	0.0782795	+	0.996931i	$0.475057\pi$
$6$	−2.60777	−1.06462
$7$	−2.72656	−1.03054	−0.515271	−	0.857027i	$-0.672309\pi$
$7$	−2.72656	−1.03054	−0.515271	+	0.857027i	$0.672309\pi$
$8$	−2.68876	−0.950621
$9$	7.61603	2.53868
$10$	0.280189	0.0886037
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	4.42928	1.27862
$13$	−6.49760	−1.80211	−0.901054	−	0.433706i	$-0.857206\pi$
$13$	−6.49760	−1.80211	−0.901054	+	0.433706i	$0.857206\pi$
$14$	−2.18224	−0.583229
$15$	−1.14063	−0.294509
$16$	0.566834	0.141708
$17$	−7.27592	−1.76467	−0.882335	−	0.470622i	$-0.844029\pi$
$17$	−7.27592	−1.76467	−0.882335	+	0.470622i	$0.844029\pi$
$18$	6.09561	1.43675
$19$	2.26591	0.519836	0.259918	−	0.965631i	$-0.416304\pi$
$19$	2.26591	0.519836	0.259918	+	0.965631i	$0.416304\pi$
$20$	−0.475899	−0.106414
$21$	8.88373	1.93859
$22$	−0.800366	−0.170639
$23$	−0.681881	−0.142182	−0.0710910	−	0.997470i	$-0.522648\pi$
$23$	−0.681881	−0.142182	−0.0710910	+	0.997470i	$0.522648\pi$
$24$	8.76059	1.78825
$25$	−4.87745	−0.975489
$26$	−5.20046	−1.01989
$27$	−15.0401	−2.89446
$28$	3.70652	0.700466
$29$	−8.89645	−1.65203	−0.826015	−	0.563648i	$-0.809397\pi$
$29$	−8.89645	−1.65203	−0.826015	+	0.563648i	$0.809397\pi$
$30$	−0.912920	−0.166676
$31$	1.04017	0.186820	0.0934100	−	0.995628i	$-0.470223\pi$
$31$	1.04017	0.186820	0.0934100	+	0.995628i	$0.470223\pi$
$32$	5.83120	1.03082
$33$	3.25822	0.567184
$34$	−5.82340	−0.998705
$35$	−0.954504	−0.161341
$36$	−10.3533	−1.72556
$37$	−4.67272	−0.768190	−0.384095	−	0.923294i	$-0.625486\pi$
$37$	−4.67272	−0.768190	−0.384095	+	0.923294i	$0.625486\pi$
$38$	1.81356	0.294198
$39$	21.1706	3.39001
$40$	−0.941272	−0.148828
$41$	7.70285	1.20298	0.601492	−	0.798879i	$-0.294573\pi$
$41$	7.70285	1.20298	0.601492	+	0.798879i	$0.294573\pi$
$42$	7.11024	1.09713
$43$	7.15313	1.09084	0.545421	−	0.838162i	$-0.316370\pi$
$43$	7.15313	1.09084	0.545421	+	0.838162i	$0.316370\pi$
$44$	1.35941	0.204939
$45$	2.66619	0.397453
$46$	−0.545755	−0.0804671
$47$	10.9437	1.59630	0.798151	−	0.602458i	$-0.205812\pi$
$47$	10.9437	1.59630	0.798151	+	0.602458i	$0.205812\pi$
$48$	−1.84687	−0.266573
$49$	0.434112	0.0620160
$50$	−3.90374	−0.552073
$51$	23.7066	3.31958
$52$	8.83292	1.22491
$53$	10.3808	1.42591	0.712953	−	0.701211i	$-0.247357\pi$
$53$	10.3808	1.42591	0.712953	+	0.701211i	$0.247357\pi$
$54$	−12.0376	−1.63810
$55$	−0.350077	−0.0472043
$56$	7.33106	0.979654
$57$	−7.38285	−0.977883
$58$	−7.12042	−0.934957
$59$	1.67486	0.218048	0.109024	−	0.994039i	$-0.465227\pi$
$59$	1.67486	0.218048	0.109024	+	0.994039i	$0.465227\pi$
$60$	1.55059	0.200180
$61$	−4.14903	−0.531229	−0.265614	−	0.964079i	$-0.585575\pi$
$61$	−4.14903	−0.531229	−0.265614	+	0.964079i	$0.585575\pi$
$62$	0.832517	0.105730
$63$	−20.7655	−2.61621
$64$	3.53343	0.441678
$65$	−2.27466	−0.282136
$66$	2.60777	0.320995
$67$	7.24647	0.885297	0.442649	−	0.896695i	$-0.354039\pi$
$67$	7.24647	0.885297	0.442649	+	0.896695i	$0.354039\pi$
$68$	9.89098	1.19946
$69$	2.22172	0.267464
$70$	−0.763952	−0.0913098
$71$	−1.59869	−0.189729	−0.0948647	−	0.995490i	$-0.530242\pi$
$71$	−1.59869	−0.189729	−0.0948647	+	0.995490i	$0.530242\pi$
$72$	−20.4777	−2.41332
$73$	−11.8080	−1.38202	−0.691009	−	0.722846i	$-0.742834\pi$
$73$	−11.8080	−1.38202	−0.691009	+	0.722846i	$0.742834\pi$
$74$	−3.73988	−0.434753
$75$	15.8918	1.83503
$76$	−3.08031	−0.353336
$77$	2.72656	0.310720
$78$	16.9443	1.91856
$79$	2.14494	0.241324	0.120662	−	0.992694i	$-0.461498\pi$
$79$	2.14494	0.241324	0.120662	+	0.992694i	$0.461498\pi$
$80$	0.198435	0.0221857
$81$	26.1558	2.90620
$82$	6.16510	0.680821
$83$	−13.4051	−1.47140	−0.735700	−	0.677308i	$-0.763147\pi$
$83$	−13.4051	−1.47140	−0.735700	+	0.677308i	$0.763147\pi$
$84$	−12.0767	−1.31767
$85$	−2.54713	−0.276275
$86$	5.72512	0.617356
$87$	28.9866	3.10769
$88$	2.68876	0.286623
$89$	−2.83300	−0.300298	−0.150149	−	0.988663i	$-0.547975\pi$
$89$	−2.83300	−0.300298	−0.150149	+	0.988663i	$0.547975\pi$
$90$	2.13393	0.224936
$91$	17.7161	1.85715
$92$	0.926959	0.0966421
$93$	−3.38911	−0.351434
$94$	8.75896	0.903418
$95$	0.793243	0.0813850
$96$	−18.9994	−1.93911
$97$	16.4032	1.66549	0.832747	−	0.553653i	$-0.186767\pi$
$97$	16.4032	1.66549	0.832747	+	0.553653i	$0.186767\pi$
$98$	0.347449	0.0350976
$99$	−7.61603	−0.765440
$100$	6.63047	0.663047
$101$	−3.86740	−0.384820	−0.192410	−	0.981315i	$-0.561630\pi$
$101$	−3.86740	−0.384820	−0.192410	+	0.981315i	$0.561630\pi$
$102$	18.9739	1.87870
$103$	−6.79997	−0.670021	−0.335010	−	0.942214i	$-0.608740\pi$
$103$	−6.79997	−0.670021	−0.335010	+	0.942214i	$0.608740\pi$
$104$	17.4705	1.71312
$105$	3.10999	0.303504
$106$	8.30841	0.806984
$107$	−14.5525	−1.40685	−0.703423	−	0.710772i	$-0.748346\pi$
$107$	−14.5525	−1.40685	−0.703423	+	0.710772i	$0.748346\pi$
$108$	20.4457	1.96738
$109$	8.75280	0.838366	0.419183	−	0.907902i	$-0.362317\pi$
$109$	8.75280	0.838366	0.419183	+	0.907902i	$0.362317\pi$
$110$	−0.280189	−0.0267150
$111$	15.2248	1.44507
$112$	−1.54550	−0.146036
$113$	−15.0046	−1.41152	−0.705759	−	0.708452i	$-0.749394\pi$
$113$	−15.0046	−1.41152	−0.705759	+	0.708452i	$0.749394\pi$
$114$	−5.90899	−0.553427
$115$	−0.238711	−0.0222599
$116$	12.0940	1.12290
$117$	−49.4859	−4.57497
$118$	1.34050	0.123403
$119$	19.8382	1.81857
$120$	3.06688	0.279966
$121$	1.00000	0.0909091
$122$	−3.32074	−0.300646
$123$	−25.0976	−2.26298
$124$	−1.41402	−0.126983
$125$	−3.45786	−0.309281
$126$	−16.6200	−1.48063
$127$	14.4135	1.27899	0.639496	−	0.768794i	$-0.279143\pi$
$127$	14.4135	1.27899	0.639496	+	0.768794i	$0.279143\pi$
$128$	−8.83436	−0.780854
$129$	−23.3065	−2.05202
$130$	−1.82056	−0.159673
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−4.42928	−0.385519
$133$	−6.17814	−0.535713
$134$	5.79983	0.501029
$135$	−5.26517	−0.453154
$136$	19.5632	1.67753
$137$	7.64083	0.652800	0.326400	−	0.945232i	$-0.394164\pi$
$137$	7.64083	0.652800	0.326400	+	0.945232i	$0.394164\pi$
$138$	1.77819	0.151370
$139$	6.47209	0.548955	0.274478	−	0.961593i	$-0.411495\pi$
$139$	6.47209	0.548955	0.274478	+	0.961593i	$0.411495\pi$
$140$	1.29757	0.109664
$141$	−35.6570	−3.00286
$142$	−1.27954	−0.107376
$143$	6.49760	0.543356
$144$	4.31702	0.359752
$145$	−3.11444	−0.258640
$146$	−9.45070	−0.782146
$147$	−1.41444	−0.116661
$148$	6.35216	0.522144
$149$	2.92614	0.239719	0.119859	−	0.992791i	$-0.461756\pi$
$149$	2.92614	0.239719	0.119859	+	0.992791i	$0.461756\pi$
$150$	12.7193	1.03852
$151$	13.9771	1.13744	0.568718	−	0.822532i	$-0.307439\pi$
$151$	13.9771	1.13744	0.568718	+	0.822532i	$0.307439\pi$
$152$	−6.09250	−0.494167
$153$	−55.4136	−4.47992
$154$	2.18224	0.175850
$155$	0.364139	0.0292484
$156$	−28.7796	−2.30422
$157$	−5.09655	−0.406749	−0.203375	−	0.979101i	$-0.565191\pi$
$157$	−5.09655	−0.406749	−0.203375	+	0.979101i	$0.565191\pi$
$158$	1.71673	0.136576
$159$	−33.8228	−2.68233
$160$	2.04137	0.161384
$161$	1.85919	0.146525
$162$	20.9342	1.64475
$163$	−4.36880	−0.342191	−0.171096	−	0.985254i	$-0.554731\pi$
$163$	−4.36880	−0.342191	−0.171096	+	0.985254i	$0.554731\pi$
$164$	−10.4714	−0.817676
$165$	1.14063	0.0887978
$166$	−10.7290	−0.832730
$167$	−14.3702	−1.11200	−0.556001	−	0.831182i	$-0.687665\pi$
$167$	−14.3702	−1.11200	−0.556001	+	0.831182i	$0.687665\pi$
$168$	−23.8862	−1.84286
$169$	29.2187	2.24760
$170$	−2.03864	−0.156356
$171$	17.2573	1.31970
$172$	−9.72406	−0.741453
$173$	−18.8930	−1.43641	−0.718205	−	0.695831i	$-0.755036\pi$
$173$	−18.8930	−1.43641	−0.718205	+	0.695831i	$0.755036\pi$
$174$	23.1999	1.75878
$175$	13.2986	1.00528
$176$	−0.566834	−0.0427267
$177$	−5.45706	−0.410178
$178$	−2.26744	−0.169952
$179$	4.02594	0.300913	0.150456	−	0.988617i	$-0.451926\pi$
$179$	4.02594	0.300913	0.150456	+	0.988617i	$0.451926\pi$
$180$	−3.62446	−0.270151
$181$	−3.68584	−0.273966	−0.136983	−	0.990573i	$-0.543741\pi$
$181$	−3.68584	−0.273966	−0.136983	+	0.990573i	$0.543741\pi$
$182$	14.1793	1.05104
$183$	13.5185	0.999314
$184$	1.83342	0.135161
$185$	−1.63581	−0.120267
$186$	−2.71253	−0.198892
$187$	7.27592	0.532068
$188$	−14.8770	−1.08502
$189$	41.0076	2.98286
$190$	0.634885	0.0460594
$191$	7.10110	0.513818	0.256909	−	0.966436i	$-0.417296\pi$
$191$	7.10110	0.513818	0.256909	+	0.966436i	$0.417296\pi$
$192$	−11.5127	−0.830857
$193$	4.65433	0.335026	0.167513	−	0.985870i	$-0.446426\pi$
$193$	4.65433	0.335026	0.167513	+	0.985870i	$0.446426\pi$
$194$	13.1286	0.942577
$195$	7.41134	0.530737
$196$	−0.590138	−0.0421527
$197$	4.28332	0.305174	0.152587	−	0.988290i	$-0.451240\pi$
$197$	4.28332	0.305174	0.152587	+	0.988290i	$0.451240\pi$
$198$	−6.09561	−0.433196
$199$	−9.45653	−0.670355	−0.335178	−	0.942155i	$-0.608796\pi$
$199$	−9.45653	−0.670355	−0.335178	+	0.942155i	$0.608796\pi$
$200$	13.1143	0.927320
$201$	−23.6106	−1.66537
$202$	−3.09533	−0.217787
$203$	24.2567	1.70249
$204$	−32.2271	−2.25634
$205$	2.69659	0.188338
$206$	−5.44246	−0.379194
$207$	−5.19323	−0.360954
$208$	−3.68306	−0.255374
$209$	−2.26591	−0.156736
$210$	2.48913	0.171766
$211$	−6.38684	−0.439688	−0.219844	−	0.975535i	$-0.570555\pi$
$211$	−6.38684	−0.439688	−0.219844	+	0.975535i	$0.570555\pi$
$212$	−14.1117	−0.969199
$213$	5.20889	0.356907
$214$	−11.6473	−0.796196
$215$	2.50414	0.170781
$216$	40.4391	2.75153
$217$	−2.83608	−0.192526
$218$	7.00544	0.474468
$219$	38.4730	2.59977
$220$	0.475899	0.0320851
$221$	47.2760	3.18013
$222$	12.1854	0.817829
$223$	−0.487165	−0.0326230	−0.0163115	−	0.999867i	$-0.505192\pi$
$223$	−0.487165	−0.0326230	−0.0163115	+	0.999867i	$0.505192\pi$
$224$	−15.8991	−1.06230
$225$	−37.1468	−2.47645
$226$	−12.0092	−0.798841
$227$	0.0109216	0.000724895 0	0.000362447	−	1.00000i	$-0.499885\pi$
$227$	0.0109216	0.000724895 0	0.000362447		1.00000i	$0.499885\pi$
$228$	10.0364	0.664674
$229$	−11.5489	−0.763172	−0.381586	−	0.924333i	$-0.624622\pi$
$229$	−11.5489	−0.763172	−0.381586	+	0.924333i	$0.624622\pi$
$230$	−0.191056	−0.0125979
$231$	−8.88373	−0.584507
$232$	23.9204	1.57045
$233$	23.1266	1.51508	0.757538	−	0.652791i	$-0.226402\pi$
$233$	23.1266	1.51508	0.757538	+	0.652791i	$0.226402\pi$
$234$	−39.6068	−2.58918
$235$	3.83113	0.249915
$236$	−2.27682	−0.148209
$237$	−6.98868	−0.453964
$238$	15.8778	1.02921
$239$	10.5928	0.685188	0.342594	−	0.939484i	$-0.388694\pi$
$239$	10.5928	0.685188	0.342594	+	0.939484i	$0.388694\pi$
$240$	−0.646546	−0.0417344
$241$	−25.2948	−1.62938	−0.814690	−	0.579897i	$-0.803093\pi$
$241$	−25.2948	−1.62938	−0.814690	+	0.579897i	$0.803093\pi$
$242$	0.800366	0.0514495
$243$	−40.1013	−2.57250
$244$	5.64025	0.361080
$245$	0.151972	0.00970917
$246$	−20.0873	−1.28072
$247$	−14.7230	−0.936801
$248$	−2.79677	−0.177595
$249$	43.6768	2.76790
$250$	−2.76756	−0.175036
$251$	−15.8018	−0.997403	−0.498701	−	0.866774i	$-0.666190\pi$
$251$	−15.8018	−0.997403	−0.498701	+	0.866774i	$0.666190\pi$
$252$	28.2290	1.77826
$253$	0.681881	0.0428695
$254$	11.5361	0.723839
$255$	8.29912	0.519711
$256$	−14.1376	−0.883598
$257$	2.78734	0.173869	0.0869347	−	0.996214i	$-0.472293\pi$
$257$	2.78734	0.173869	0.0869347	+	0.996214i	$0.472293\pi$
$258$	−18.6537	−1.16133
$259$	12.7404	0.791652
$260$	3.09220	0.191770
$261$	−67.7557	−4.19397
$262$	0.800366	0.0494468
$263$	−24.3277	−1.50011	−0.750056	−	0.661374i	$-0.769974\pi$
$263$	−24.3277	−1.50011	−0.750056	+	0.661374i	$0.769974\pi$
$264$	−8.76059	−0.539177
$265$	3.63406	0.223239
$266$	−4.94478	−0.303184
$267$	9.23056	0.564901
$268$	−9.85095	−0.601743
$269$	7.66164	0.467138	0.233569	−	0.972340i	$-0.424959\pi$
$269$	7.66164	0.467138	0.233569	+	0.972340i	$0.424959\pi$
$270$	−4.21406	−0.256460
$271$	−18.2137	−1.10641	−0.553203	−	0.833046i	$-0.686595\pi$
$271$	−18.2137	−1.10641	−0.553203	+	0.833046i	$0.686595\pi$
$272$	−4.12424	−0.250069
$273$	−57.7229	−3.49355
$274$	6.11546	0.369448
$275$	4.87745	0.294121
$276$	−3.02024	−0.181797
$277$	−27.5589	−1.65585	−0.827927	−	0.560836i	$-0.810480\pi$
$277$	−27.5589	−1.65585	−0.827927	+	0.560836i	$0.810480\pi$
$278$	5.18004	0.310678
$279$	7.92197	0.474276
$280$	2.56643	0.153374
$281$	−13.7281	−0.818947	−0.409474	−	0.912322i	$-0.634288\pi$
$281$	−13.7281	−0.818947	−0.409474	+	0.912322i	$0.634288\pi$
$282$	−28.5387	−1.69945
$283$	8.23780	0.489687	0.244843	−	0.969563i	$-0.421263\pi$
$283$	8.23780	0.489687	0.244843	+	0.969563i	$0.421263\pi$
$284$	2.17328	0.128960
$285$	−2.58456	−0.153096
$286$	5.20046	0.307509
$287$	−21.0023	−1.23972
$288$	44.4106	2.61692
$289$	35.9390	2.11406
$290$	−2.49269	−0.146376
$291$	−53.4454	−3.13302
$292$	16.0519	0.939367
$293$	−5.46644	−0.319353	−0.159676	−	0.987169i	$-0.551045\pi$
$293$	−5.46644	−0.319353	−0.159676	+	0.987169i	$0.551045\pi$
$294$	−1.13207	−0.0660234
$295$	0.586328	0.0341373
$296$	12.5638	0.730257
$297$	15.0401	0.872713
$298$	2.34199	0.135668
$299$	4.43059	0.256227
$300$	−21.6036	−1.24728
$301$	−19.5034	−1.12416
$302$	11.1868	0.643726
$303$	12.6008	0.723900
$304$	1.28440	0.0736652
$305$	−1.45248	−0.0831686
$306$	−44.3512	−2.53539
$307$	−26.5129	−1.51317	−0.756585	−	0.653896i	$-0.773134\pi$
$307$	−26.5129	−1.51317	−0.756585	+	0.653896i	$0.773134\pi$
$308$	−3.70652	−0.211199
$309$	22.1558	1.26040
$310$	0.291445	0.0165529
$311$	26.0807	1.47890	0.739450	−	0.673211i	$-0.235086\pi$
$311$	26.0807	1.47890	0.739450	+	0.673211i	$0.235086\pi$
$312$	−56.9228	−3.22262
$313$	19.6151	1.10871	0.554355	−	0.832281i	$-0.312965\pi$
$313$	19.6151	1.10871	0.554355	+	0.832281i	$0.312965\pi$
$314$	−4.07911	−0.230197
$315$	−7.26953	−0.409591
$316$	−2.91586	−0.164030
$317$	14.8470	0.833888	0.416944	−	0.908932i	$-0.363101\pi$
$317$	14.8470	0.833888	0.416944	+	0.908932i	$0.363101\pi$
$318$	−27.0707	−1.51805
$319$	8.89645	0.498106
$320$	1.23697	0.0691487
$321$	47.4154	2.64647
$322$	1.48803	0.0829247
$323$	−16.4866	−0.917339
$324$	−35.5566	−1.97536
$325$	31.6917	1.75794
$326$	−3.49664	−0.193661
$327$	−28.5186	−1.57708
$328$	−20.7111	−1.14358
$329$	−29.8386	−1.64506
$330$	0.912920	0.0502546
$331$	11.4115	0.627235	0.313618	−	0.949549i	$-0.398459\pi$
$331$	11.4115	0.627235	0.313618	+	0.949549i	$0.398459\pi$
$332$	18.2231	1.00012
$333$	−35.5875	−1.95019
$334$	−11.5014	−0.629331
$335$	2.53682	0.138601
$336$	5.03560	0.274715
$337$	−9.76552	−0.531962	−0.265981	−	0.963978i	$-0.585696\pi$
$337$	−9.76552	−0.531962	−0.265981	+	0.963978i	$0.585696\pi$
$338$	23.3857	1.27201
$339$	48.8885	2.65526
$340$	3.46260	0.187786
$341$	−1.04017	−0.0563284
$342$	13.8121	0.746874
$343$	17.9023	0.966632
$344$	−19.2331	−1.03698
$345$	0.777773	0.0418739
$346$	−15.1213	−0.812928
$347$	29.5221	1.58483	0.792416	−	0.609981i	$-0.208823\pi$
$347$	29.5221	1.58483	0.792416	+	0.609981i	$0.208823\pi$
$348$	−39.4049	−2.11232
$349$	0.0992308	0.00531171	0.00265585	−	0.999996i	$-0.499155\pi$
$349$	0.0992308	0.00531171	0.00265585	+	0.999996i	$0.499155\pi$
$350$	10.6438	0.568934
$351$	97.7242	5.21613
$352$	−5.83120	−0.310804
$353$	−12.2068	−0.649702	−0.324851	−	0.945765i	$-0.605314\pi$
$353$	−12.2068	−0.649702	−0.324851	+	0.945765i	$0.605314\pi$
$354$	−4.36765	−0.232138
$355$	−0.559663	−0.0297038
$356$	3.85122	0.204114
$357$	−64.6373	−3.42097
$358$	3.22223	0.170300
$359$	13.1998	0.696659	0.348329	−	0.937372i	$-0.386749\pi$
$359$	13.1998	0.696659	0.348329	+	0.937372i	$0.386749\pi$
$360$	−7.16876	−0.377827
$361$	−13.8656	−0.729770
$362$	−2.95002	−0.155050
$363$	−3.25822	−0.171012
$364$	−24.0835	−1.26232
$365$	−4.13369	−0.216367
$366$	10.8197	0.565556
$367$	25.3903	1.32536	0.662682	−	0.748901i	$-0.269418\pi$
$367$	25.3903	1.32536	0.662682	+	0.748901i	$0.269418\pi$
$368$	−0.386513	−0.0201484
$369$	58.6651	3.05398
$370$	−1.30925	−0.0680644
$371$	−28.3037	−1.46946
$372$	4.60720	0.238872
$373$	−13.0483	−0.675616	−0.337808	−	0.941215i	$-0.609686\pi$
$373$	−13.0483	−0.675616	−0.337808	+	0.941215i	$0.609686\pi$
$374$	5.82340	0.301121
$375$	11.2665	0.581799
$376$	−29.4250	−1.51748
$377$	57.8056	2.97714
$378$	32.8211	1.68813
$379$	−22.1593	−1.13825	−0.569125	−	0.822251i	$-0.692718\pi$
$379$	−22.1593	−1.13825	−0.569125	+	0.822251i	$0.692718\pi$
$380$	−1.07835	−0.0553180
$381$	−46.9625	−2.40596
$382$	5.68348	0.290792
$383$	11.0390	0.564069	0.282034	−	0.959404i	$-0.408991\pi$
$383$	11.0390	0.564069	0.282034	+	0.959404i	$0.408991\pi$
$384$	28.7843	1.46889
$385$	0.954504	0.0486460
$386$	3.72517	0.189606
$387$	54.4784	2.76929
$388$	−22.2988	−1.13205
$389$	24.0144	1.21758	0.608789	−	0.793332i	$-0.291656\pi$
$389$	24.0144	1.21758	0.608789	+	0.793332i	$0.291656\pi$
$390$	5.93179	0.300368
$391$	4.96131	0.250904
$392$	−1.16722	−0.0589537
$393$	−3.25822	−0.164356
$394$	3.42823	0.172712
$395$	0.750892	0.0377815
$396$	10.3533	0.520275
$397$	32.1617	1.61415	0.807074	−	0.590451i	$-0.201050\pi$
$397$	32.1617	1.61415	0.807074	+	0.590451i	$0.201050\pi$
$398$	−7.56869	−0.379384
$399$	20.1298	1.00775
$400$	−2.76470	−0.138235
$401$	−24.2967	−1.21332	−0.606660	−	0.794961i	$-0.707491\pi$
$401$	−24.2967	−1.21332	−0.606660	+	0.794961i	$0.707491\pi$
$402$	−18.8972	−0.942504
$403$	−6.75861	−0.336670
$404$	5.25739	0.261565
$405$	9.15653	0.454992
$406$	19.4142	0.963512
$407$	4.67272	0.231618
$408$	−63.7413	−3.15567
$409$	−4.27023	−0.211149	−0.105575	−	0.994411i	$-0.533668\pi$
$409$	−4.27023	−0.211149	−0.105575	+	0.994411i	$0.533668\pi$
$410$	2.15826	0.106589
$411$	−24.8955	−1.22801
$412$	9.24397	0.455418
$413$	−4.56659	−0.224707
$414$	−4.15648	−0.204280
$415$	−4.69281	−0.230361
$416$	−37.8888	−1.85765
$417$	−21.0875	−1.03266
$418$	−1.81356	−0.0887041
$419$	−27.1825	−1.32795	−0.663977	−	0.747753i	$-0.731133\pi$
$419$	−27.1825	−1.32795	−0.663977	+	0.747753i	$0.731133\pi$
$420$	−4.22776	−0.206294
$421$	−21.5081	−1.04824	−0.524119	−	0.851645i	$-0.675605\pi$
$421$	−21.5081	−1.04824	−0.524119	+	0.851645i	$0.675605\pi$
$422$	−5.11181	−0.248839
$423$	83.3475	4.05249
$424$	−27.9114	−1.35550
$425$	35.4879	1.72142
$426$	4.16902	0.201989
$427$	11.3126	0.547453
$428$	19.7829	0.956242
$429$	−21.1706	−1.02213
$430$	2.00423	0.0966526
$431$	26.1411	1.25917	0.629587	−	0.776930i	$-0.283224\pi$
$431$	26.1411	1.25917	0.629587	+	0.776930i	$0.283224\pi$
$432$	−8.52521	−0.410169
$433$	3.14902	0.151332	0.0756662	−	0.997133i	$-0.475892\pi$
$433$	3.14902	0.151332	0.0756662	+	0.997133i	$0.475892\pi$
$434$	−2.26991	−0.108959
$435$	10.1475	0.486538
$436$	−11.8987	−0.569843
$437$	−1.54508	−0.0739114
$438$	30.7925	1.47132
$439$	−3.40149	−0.162344	−0.0811721	−	0.996700i	$-0.525866\pi$
$439$	−3.40149	−0.162344	−0.0811721	+	0.996700i	$0.525866\pi$
$440$	0.941272	0.0448734
$441$	3.30621	0.157439
$442$	37.8381	1.79977
$443$	9.89242	0.470003	0.235002	−	0.971995i	$-0.424490\pi$
$443$	9.89242	0.470003	0.235002	+	0.971995i	$0.424490\pi$
$444$	−20.6968	−0.982224
$445$	−0.991767	−0.0470143
$446$	−0.389910	−0.0184628
$447$	−9.53403	−0.450944
$448$	−9.63409	−0.455168
$449$	13.3108	0.628177	0.314088	−	0.949394i	$-0.398301\pi$
$449$	13.3108	0.628177	0.314088	+	0.949394i	$0.398301\pi$
$450$	−29.7310	−1.40153
$451$	−7.70285	−0.362713
$452$	20.3975	0.959419
$453$	−45.5404	−2.13967
$454$	0.00874131	0.000410250 0
$455$	6.20198	0.290753
$456$	19.8507	0.929596
$457$	24.2031	1.13217	0.566086	−	0.824346i	$-0.308457\pi$
$457$	24.2031	1.13217	0.566086	+	0.824346i	$0.308457\pi$
$458$	−9.24333	−0.431913
$459$	109.430	5.10777
$460$	0.324506	0.0151302
$461$	37.4313	1.74335	0.871675	−	0.490084i	$-0.163034\pi$
$461$	37.4313	1.74335	0.871675	+	0.490084i	$0.163034\pi$
$462$	−7.11024	−0.330798
$463$	−24.3445	−1.13138	−0.565691	−	0.824617i	$-0.691391\pi$
$463$	−24.3445	−1.13138	−0.565691	+	0.824617i	$0.691391\pi$
$464$	−5.04281	−0.234107
$465$	−1.18645	−0.0550202
$466$	18.5098	0.857448
$467$	−19.0317	−0.880684	−0.440342	−	0.897830i	$-0.645143\pi$
$467$	−19.0317	−0.880684	−0.440342	+	0.897830i	$0.645143\pi$
$468$	67.2718	3.10964
$469$	−19.7579	−0.912336
$470$	3.06631	0.141438
$471$	16.6057	0.765151
$472$	−4.50329	−0.207281
$473$	−7.15313	−0.328901
$474$	−5.59351	−0.256918
$475$	−11.0519	−0.507095
$476$	−26.9683	−1.23609
$477$	79.0601	3.61992
$478$	8.47808	0.387778
$479$	−6.72455	−0.307252	−0.153626	−	0.988129i	$-0.549095\pi$
$479$	−6.72455	−0.307252	−0.153626	+	0.988129i	$0.549095\pi$
$480$	−6.65123	−0.303586
$481$	30.3614	1.38436
$482$	−20.2451	−0.922139
$483$	−6.05765	−0.275633
$484$	−1.35941	−0.0617915
$485$	5.74238	0.260748
$486$	−32.0957	−1.45589
$487$	32.1194	1.45547	0.727733	−	0.685860i	$-0.240574\pi$
$487$	32.1194	1.45547	0.727733	+	0.685860i	$0.240574\pi$
$488$	11.1557	0.504997
$489$	14.2345	0.643708
$490$	0.121634	0.00549485
$491$	9.47797	0.427735	0.213867	−	0.976863i	$-0.431394\pi$
$491$	9.47797	0.427735	0.213867	+	0.976863i	$0.431394\pi$
$492$	34.1180	1.53816
$493$	64.7299	2.91529
$494$	−11.7838	−0.530177
$495$	−2.66619	−0.119836
$496$	0.589604	0.0264740
$497$	4.35891	0.195524
$498$	34.9574	1.56648
$499$	−35.9929	−1.61126	−0.805632	−	0.592416i	$-0.798174\pi$
$499$	−35.9929	−1.61126	−0.805632	+	0.592416i	$0.798174\pi$
$500$	4.70067	0.210220
$501$	46.8214	2.09183
$502$	−12.6473	−0.564474
$503$	40.3122	1.79743	0.898716	−	0.438531i	$-0.144501\pi$
$503$	40.3122	1.79743	0.898716	+	0.438531i	$0.144501\pi$
$504$	55.8336	2.48702
$505$	−1.35388	−0.0602471
$506$	0.545755	0.0242618
$507$	−95.2012	−4.22803
$508$	−19.5939	−0.869340
$509$	5.15385	0.228440	0.114220	−	0.993455i	$-0.463563\pi$
$509$	5.15385	0.228440	0.114220	+	0.993455i	$0.463563\pi$
$510$	6.64233	0.294127
$511$	32.1951	1.42423
$512$	6.35348	0.280787
$513$	−34.0795	−1.50464
$514$	2.23089	0.0984005
$515$	−2.38051	−0.104898
$516$	31.6832	1.39477
$517$	−10.9437	−0.481303
$518$	10.1970	0.448031
$519$	61.5577	2.70208
$520$	6.11601	0.268205
$521$	−18.5870	−0.814313	−0.407156	−	0.913359i	$-0.633480\pi$
$521$	−18.5870	−0.814313	−0.407156	+	0.913359i	$0.633480\pi$
$522$	−54.2293	−2.37355
$523$	34.1275	1.49229	0.746145	−	0.665783i	$-0.231903\pi$
$523$	34.1275	1.49229	0.746145	+	0.665783i	$0.231903\pi$
$524$	−1.35941	−0.0593863
$525$	−43.3299	−1.89107
$526$	−19.4711	−0.848980
$527$	−7.56819	−0.329676
$528$	1.84687	0.0803748
$529$	−22.5350	−0.979784
$530$	2.90858	0.126341
$531$	12.7558	0.553553
$532$	8.39865	0.364128
$533$	−50.0500	−2.16791
$534$	7.38783	0.319702
$535$	−5.09450	−0.220254
$536$	−19.4840	−0.841582
$537$	−13.1174	−0.566058
$538$	6.13212	0.264374
$539$	−0.434112	−0.0186985
$540$	7.15755	0.308012
$541$	−16.6283	−0.714905	−0.357452	−	0.933931i	$-0.616355\pi$
$541$	−16.6283	−0.714905	−0.357452	+	0.933931i	$0.616355\pi$
$542$	−14.5777	−0.626165
$543$	12.0093	0.515368
$544$	−42.4273	−1.81906
$545$	3.06415	0.131254
$546$	−46.1995	−1.97715
$547$	9.26921	0.396323	0.198161	−	0.980169i	$-0.436503\pi$
$547$	9.26921	0.396323	0.198161	+	0.980169i	$0.436503\pi$
$548$	−10.3870	−0.443713
$549$	−31.5991	−1.34862
$550$	3.90374	0.166456
$551$	−20.1586	−0.858785
$552$	−5.97368	−0.254257
$553$	−5.84829	−0.248695
$554$	−22.0572	−0.937121
$555$	5.32983	0.226239
$556$	−8.79825	−0.373129
$557$	−5.68432	−0.240852	−0.120426	−	0.992722i	$-0.538426\pi$
$557$	−5.68432	−0.240852	−0.120426	+	0.992722i	$0.538426\pi$
$558$	6.34047	0.268414
$559$	−46.4781	−1.96582
$560$	−0.541045	−0.0228633
$561$	−23.7066	−1.00089
$562$	−10.9875	−0.463479
$563$	3.09512	0.130444	0.0652218	−	0.997871i	$-0.479224\pi$
$563$	3.09512	0.130444	0.0652218	+	0.997871i	$0.479224\pi$
$564$	48.4726	2.04107
$565$	−5.25277	−0.220986
$566$	6.59326	0.277135
$567$	−71.3153	−2.99496
$568$	4.29849	0.180361
$569$	13.5310	0.567249	0.283624	−	0.958935i	$-0.408463\pi$
$569$	13.5310	0.567249	0.283624	+	0.958935i	$0.408463\pi$
$570$	−2.06860	−0.0866440
$571$	−38.8373	−1.62529	−0.812644	−	0.582760i	$-0.801973\pi$
$571$	−38.8373	−1.62529	−0.812644	+	0.582760i	$0.801973\pi$
$572$	−8.83292	−0.369323
$573$	−23.1370	−0.966561
$574$	−16.8095	−0.701615
$575$	3.32584	0.138697
$576$	26.9107	1.12128
$577$	26.9823	1.12329	0.561643	−	0.827379i	$-0.310169\pi$
$577$	26.9823	1.12329	0.561643	+	0.827379i	$0.310169\pi$
$578$	28.7644	1.19644
$579$	−15.1649	−0.630230
$580$	4.23381	0.175800
$581$	36.5497	1.51634
$582$	−42.7759	−1.77312
$583$	−10.3808	−0.429927
$584$	31.7488	1.31378
$585$	−17.3238	−0.716253
$586$	−4.37515	−0.180736
$587$	−10.5197	−0.434196	−0.217098	−	0.976150i	$-0.569659\pi$
$587$	−10.5197	−0.434196	−0.217098	+	0.976150i	$0.569659\pi$
$588$	1.92280	0.0792951
$589$	2.35694	0.0971158
$590$	0.469277	0.0193198
$591$	−13.9560	−0.574074
$592$	−2.64865	−0.108859
$593$	−37.7137	−1.54872	−0.774359	−	0.632747i	$-0.781927\pi$
$593$	−37.7137	−1.54872	−0.774359	+	0.632747i	$0.781927\pi$
$594$	12.0376	0.493907
$595$	6.94489	0.284713
$596$	−3.97784	−0.162939
$597$	30.8115	1.26103
$598$	3.54609	0.145011
$599$	39.3979	1.60975	0.804876	−	0.593443i	$-0.202232\pi$
$599$	39.3979	1.60975	0.804876	+	0.593443i	$0.202232\pi$
$600$	−42.7293	−1.74442
$601$	33.1585	1.35256	0.676281	−	0.736644i	$-0.263591\pi$
$601$	33.1585	1.35256	0.676281	+	0.736644i	$0.263591\pi$
$602$	−15.6099	−0.636211
$603$	55.1893	2.24748
$604$	−19.0006	−0.773124
$605$	0.350077	0.0142326
$606$	10.0853	0.409687
$607$	13.5667	0.550657	0.275329	−	0.961350i	$-0.411213\pi$
$607$	13.5667	0.550657	0.275329	+	0.961350i	$0.411213\pi$
$608$	13.2130	0.535857
$609$	−79.0337	−3.20261
$610$	−1.16251	−0.0470688
$611$	−71.1077	−2.87671
$612$	75.3300	3.04504
$613$	−1.55596	−0.0628445	−0.0314222	−	0.999506i	$-0.510004\pi$
$613$	−1.55596	−0.0628445	−0.0314222	+	0.999506i	$0.510004\pi$
$614$	−21.2200	−0.856370
$615$	−8.78609	−0.354289
$616$	−7.33106	−0.295377
$617$	27.7811	1.11843	0.559213	−	0.829024i	$-0.311103\pi$
$617$	27.7811	1.11843	0.559213	+	0.829024i	$0.311103\pi$
$618$	17.7328	0.713317
$619$	7.73865	0.311043	0.155521	−	0.987833i	$-0.450294\pi$
$619$	7.73865	0.311043	0.155521	+	0.987833i	$0.450294\pi$
$620$	−0.495016	−0.0198803
$621$	10.2555	0.411540
$622$	20.8741	0.836975
$623$	7.72434	0.309469
$624$	12.0002	0.480394
$625$	23.1767	0.927069
$626$	15.6992	0.627468
$627$	7.38285	0.294843
$628$	6.92833	0.276470
$629$	33.9983	1.35560
$630$	−5.81828	−0.231806
$631$	5.03408	0.200404	0.100202	−	0.994967i	$-0.468051\pi$
$631$	5.03408	0.200404	0.100202	+	0.994967i	$0.468051\pi$
$632$	−5.76722	−0.229408
$633$	20.8098	0.827114
$634$	11.8830	0.471934
$635$	5.04583	0.200238
$636$	45.9792	1.82320
$637$	−2.82069	−0.111760
$638$	7.12042	0.281900
$639$	−12.1757	−0.481661
$640$	−3.09270	−0.122250
$641$	−29.5288	−1.16632	−0.583159	−	0.812358i	$-0.698184\pi$
$641$	−29.5288	−1.16632	−0.583159	+	0.812358i	$0.698184\pi$
$642$	37.9497	1.49775
$643$	−27.2755	−1.07564	−0.537820	−	0.843060i	$-0.680752\pi$
$643$	−27.2755	−1.07564	−0.537820	+	0.843060i	$0.680752\pi$
$644$	−2.52741	−0.0995937
$645$	−8.15906	−0.321263
$646$	−13.1953	−0.519163
$647$	−10.5757	−0.415775	−0.207888	−	0.978153i	$-0.566659\pi$
$647$	−10.5757	−0.415775	−0.207888	+	0.978153i	$0.566659\pi$
$648$	−70.3267	−2.76269
$649$	−1.67486	−0.0657439
$650$	25.3649	0.994895
$651$	9.24060	0.362168
$652$	5.93901	0.232590
$653$	−11.2738	−0.441180	−0.220590	−	0.975367i	$-0.570798\pi$
$653$	−11.2738	−0.441180	−0.220590	+	0.975367i	$0.570798\pi$
$654$	−22.8253	−0.892540
$655$	0.350077	0.0136786
$656$	4.36624	0.170473
$657$	−89.9298	−3.50850
$658$	−23.8818	−0.931010
$659$	19.4752	0.758648	0.379324	−	0.925264i	$-0.376157\pi$
$659$	19.4752	0.758648	0.379324	+	0.925264i	$0.376157\pi$
$660$	−1.55059	−0.0603565
$661$	23.4013	0.910205	0.455102	−	0.890439i	$-0.349603\pi$
$661$	23.4013	0.910205	0.455102	+	0.890439i	$0.349603\pi$
$662$	9.13341	0.354980
$663$	−154.036	−5.98225
$664$	36.0431	1.39874
$665$	−2.16282	−0.0838706
$666$	−28.4831	−1.10370
$667$	6.06632	0.234889
$668$	19.5351	0.755835
$669$	1.58729	0.0613683
$670$	2.03038	0.0784406
$671$	4.14903	0.160171
$672$	51.8028	1.99834
$673$	−7.31072	−0.281807	−0.140904	−	0.990023i	$-0.545001\pi$
$673$	−7.31072	−0.281807	−0.140904	+	0.990023i	$0.545001\pi$
$674$	−7.81599	−0.301061
$675$	73.3571	2.82352
$676$	−39.7204	−1.52771
$677$	−0.172624	−0.00663448	−0.00331724	−	0.999994i	$-0.501056\pi$
$677$	−0.172624	−0.00663448	−0.00331724	+	0.999994i	$0.501056\pi$
$678$	39.1287	1.50273
$679$	−44.7243	−1.71636
$680$	6.84862	0.262633
$681$	−0.0355852	−0.00136363
$682$	−0.832517	−0.0318787
$683$	14.0820	0.538833	0.269416	−	0.963024i	$-0.413169\pi$
$683$	14.0820	0.538833	0.269416	+	0.963024i	$0.413169\pi$
$684$	−23.4598	−0.897006
$685$	2.67487	0.102202
$686$	14.3284	0.547060
$687$	37.6289	1.43563
$688$	4.05463	0.154581
$689$	−67.4500	−2.56964
$690$	0.622503	0.0236983
$691$	−28.1186	−1.06968	−0.534841	−	0.844953i	$-0.679628\pi$
$691$	−28.1186	−1.06968	−0.534841	+	0.844953i	$0.679628\pi$
$692$	25.6834	0.976338
$693$	20.7655	0.788817
$694$	23.6285	0.896927
$695$	2.26573	0.0859439
$696$	−77.9382	−2.95424
$697$	−56.0453	−2.12287
$698$	0.0794210	0.00300613
$699$	−75.3517	−2.85006
$700$	−18.0783	−0.683297
$701$	43.5259	1.64395	0.821975	−	0.569523i	$-0.192872\pi$
$701$	43.5259	1.64395	0.821975	+	0.569523i	$0.192872\pi$
$702$	78.2152	2.95204
$703$	−10.5880	−0.399333
$704$	−3.53343	−0.133171
$705$	−12.4827	−0.470125
$706$	−9.76991	−0.367695
$707$	10.5447	0.396573
$708$	7.41840	0.278801
$709$	30.3143	1.13848	0.569238	−	0.822173i	$-0.307238\pi$
$709$	30.3143	1.13848	0.569238	+	0.822173i	$0.307238\pi$
$710$	−0.447936	−0.0168107
$711$	16.3359	0.612644
$712$	7.61727	0.285469
$713$	−0.709272	−0.0265625
$714$	−51.7335	−1.93608
$715$	2.27466	0.0850673
$716$	−5.47292	−0.204533
$717$	−34.5136	−1.28893
$718$	10.5647	0.394270
$719$	42.8197	1.59690	0.798452	−	0.602058i	$-0.205653\pi$
$719$	42.8197	1.59690	0.798452	+	0.602058i	$0.205653\pi$
$720$	1.51129	0.0563224
$721$	18.5405	0.690484
$722$	−11.0976	−0.413009
$723$	82.4161	3.06509
$724$	5.01058	0.186217
$725$	43.3920	1.61154
$726$	−2.60777	−0.0967835
$727$	−16.5031	−0.612066	−0.306033	−	0.952021i	$-0.599002\pi$
$727$	−16.5031	−0.612066	−0.306033	+	0.952021i	$0.599002\pi$
$728$	−47.6343	−1.76544
$729$	52.1917	1.93302
$730$	−3.30847	−0.122452
$731$	−52.0456	−1.92497
$732$	−18.3772	−0.679241
$733$	−41.2501	−1.52361	−0.761803	−	0.647809i	$-0.775685\pi$
$733$	−41.2501	−1.52361	−0.761803	+	0.647809i	$0.775685\pi$
$734$	20.3216	0.750083
$735$	−0.495161	−0.0182643
$736$	−3.97618	−0.146564
$737$	−7.24647	−0.266927
$738$	46.9536	1.72839
$739$	−31.8759	−1.17257	−0.586286	−	0.810104i	$-0.699411\pi$
$739$	−31.8759	−1.17257	−0.586286	+	0.810104i	$0.699411\pi$
$740$	2.22374	0.0817463
$741$	47.9708	1.76225
$742$	−22.6533	−0.831631
$743$	−22.7875	−0.835993	−0.417997	−	0.908449i	$-0.637268\pi$
$743$	−22.7875	−0.835993	−0.417997	+	0.908449i	$0.637268\pi$
$744$	9.11250	0.334081
$745$	1.02437	0.0375302
$746$	−10.4434	−0.382361
$747$	−102.094	−3.73541
$748$	−9.89098	−0.361650
$749$	39.6783	1.44981
$750$	9.01732	0.329266
$751$	6.30903	0.230220	0.115110	−	0.993353i	$-0.463278\pi$
$751$	6.30903	0.230220	0.115110	+	0.993353i	$0.463278\pi$
$752$	6.20326	0.226209
$753$	51.4859	1.87625
$754$	46.2656	1.68489
$755$	4.89304	0.178076
$756$	−55.7463	−2.02747
$757$	−6.82568	−0.248084	−0.124042	−	0.992277i	$-0.539586\pi$
$757$	−6.82568	−0.248084	−0.124042	+	0.992277i	$0.539586\pi$
$758$	−17.7356	−0.644186
$759$	−2.22172	−0.0806434
$760$	−2.13284	−0.0773663
$761$	−2.35739	−0.0854552	−0.0427276	−	0.999087i	$-0.513605\pi$
$761$	−2.35739	−0.0854552	−0.0427276	+	0.999087i	$0.513605\pi$
$762$	−37.5872	−1.36164
$763$	−23.8650	−0.863971
$764$	−9.65333	−0.349245
$765$	−19.3990	−0.701372
$766$	8.83528	0.319232
$767$	−10.8825	−0.392946
$768$	46.0634	1.66217
$769$	−33.8229	−1.21969	−0.609843	−	0.792522i	$-0.708767\pi$
$769$	−33.8229	−1.21969	−0.609843	+	0.792522i	$0.708767\pi$
$770$	0.763952	0.0275309
$771$	−9.08178	−0.327072
$772$	−6.32717	−0.227720
$773$	5.41501	0.194764	0.0973822	−	0.995247i	$-0.468953\pi$
$773$	5.41501	0.194764	0.0973822	+	0.995247i	$0.468953\pi$
$774$	43.6027	1.56727
$775$	−5.07337	−0.182241
$776$	−44.1044	−1.58325
$777$	−41.5112	−1.48921
$778$	19.2203	0.689081
$779$	17.4540	0.625354
$780$	−10.0751	−0.360746
$781$	1.59869	0.0572056
$782$	3.97087	0.141998
$783$	133.803	4.78174
$784$	0.246069	0.00878820
$785$	−1.78418	−0.0636802
$786$	−2.60777	−0.0930162
$787$	−12.7879	−0.455839	−0.227919	−	0.973680i	$-0.573192\pi$
$787$	−12.7879	−0.455839	−0.227919	+	0.973680i	$0.573192\pi$
$788$	−5.82281	−0.207429
$789$	79.2652	2.82192
$790$	0.600988	0.0213822
$791$	40.9110	1.45463
$792$	20.4777	0.727643
$793$	26.9587	0.957332
$794$	25.7411	0.913518
$795$	−11.8406	−0.419942
$796$	12.8553	0.455645
$797$	10.8911	0.385783	0.192892	−	0.981220i	$-0.438213\pi$
$797$	10.8911	0.385783	0.192892	+	0.981220i	$0.438213\pi$
$798$	16.1112	0.570330
$799$	−79.6254	−2.81695
$800$	−28.4414	−1.00555
$801$	−21.5762	−0.762358
$802$	−19.4463	−0.686672
$803$	11.8080	0.416694
$804$	32.0966	1.13196
$805$	0.650858	0.0229397
$806$	−5.40936	−0.190537
$807$	−24.9633	−0.878751
$808$	10.3985	0.365818
$809$	14.9428	0.525361	0.262681	−	0.964883i	$-0.415393\pi$
$809$	14.9428	0.525361	0.262681	+	0.964883i	$0.415393\pi$
$810$	7.32858	0.257500
$811$	8.85916	0.311087	0.155544	−	0.987829i	$-0.450287\pi$
$811$	8.85916	0.311087	0.155544	+	0.987829i	$0.450287\pi$
$812$	−32.9749	−1.15719
$813$	59.3445	2.08130
$814$	3.73988	0.131083
$815$	−1.52942	−0.0535731
$816$	13.4377	0.470413
$817$	16.2084	0.567059
$818$	−3.41774	−0.119499
$819$	134.926	4.71470
$820$	−3.66578	−0.128014
$821$	44.4262	1.55049	0.775243	−	0.631663i	$-0.217627\pi$
$821$	44.4262	1.55049	0.775243	+	0.631663i	$0.217627\pi$
$822$	−19.9255	−0.694983
$823$	12.9715	0.452157	0.226079	−	0.974109i	$-0.427409\pi$
$823$	12.9715	0.452157	0.226079	+	0.974109i	$0.427409\pi$
$824$	18.2835	0.636935
$825$	−15.8918	−0.553282
$826$	−3.65495	−0.127172
$827$	26.9564	0.937365	0.468683	−	0.883367i	$-0.344729\pi$
$827$	26.9564	0.937365	0.468683	+	0.883367i	$0.344729\pi$
$828$	7.05974	0.245343
$829$	37.0459	1.28666	0.643328	−	0.765591i	$-0.277553\pi$
$829$	37.0459	1.28666	0.643328	+	0.765591i	$0.277553\pi$
$830$	−3.75596	−0.130371
$831$	89.7931	3.11489
$832$	−22.9588	−0.795952
$833$	−3.15857	−0.109438
$834$	−16.8777	−0.584428
$835$	−5.03068	−0.174094
$836$	3.08031	0.106535
$837$	−15.6442	−0.540743
$838$	−21.7560	−0.751548
$839$	−32.2245	−1.11251	−0.556257	−	0.831011i	$-0.687763\pi$
$839$	−32.2245	−1.11251	−0.556257	+	0.831011i	$0.687763\pi$
$840$	−8.36201	−0.288517
$841$	50.1469	1.72920
$842$	−17.2143	−0.593245
$843$	44.7291	1.54055
$844$	8.68236	0.298859
$845$	10.2288	0.351881
$846$	66.7085	2.29349
$847$	−2.72656	−0.0936856
$848$	5.88416	0.202063
$849$	−26.8406	−0.921168
$850$	28.4033	0.974226
$851$	3.18624	0.109223
$852$	−7.08103	−0.242592
$853$	−39.4441	−1.35054	−0.675270	−	0.737570i	$-0.735973\pi$
$853$	−39.4441	−1.35054	−0.675270	+	0.737570i	$0.735973\pi$
$854$	9.05419	0.309828
$855$	6.04136	0.206610
$856$	39.1283	1.33738
$857$	36.7483	1.25530	0.627648	−	0.778497i	$-0.284018\pi$
$857$	36.7483	1.25530	0.627648	+	0.778497i	$0.284018\pi$
$858$	−16.9443	−0.578467
$859$	−55.9578	−1.90926	−0.954628	−	0.297800i	$-0.903747\pi$
$859$	−55.9578	−1.90926	−0.954628	+	0.297800i	$0.903747\pi$
$860$	−3.40416	−0.116081
$861$	68.4301	2.33209
$862$	20.9225	0.712622
$863$	−32.6078	−1.10998	−0.554991	−	0.831856i	$-0.687278\pi$
$863$	−32.6078	−1.10998	−0.554991	+	0.831856i	$0.687278\pi$
$864$	−87.7015	−2.98367
$865$	−6.61401	−0.224883
$866$	2.52037	0.0856458
$867$	−117.097	−3.97683
$868$	3.85541	0.130861
$869$	−2.14494	−0.0727620
$870$	8.12175	0.275353
$871$	−47.0846	−1.59540
$872$	−23.5342	−0.796968
$873$	124.927	4.22815
$874$	−1.23663	−0.0418297
$875$	9.42806	0.318727
$876$	−52.3008	−1.76708
$877$	−20.9521	−0.707503	−0.353751	−	0.935339i	$-0.615094\pi$
$877$	−20.9521	−0.707503	−0.353751	+	0.935339i	$0.615094\pi$
$878$	−2.72244	−0.0918778
$879$	17.8109	0.600746
$880$	−0.198435	−0.00668925
$881$	−7.21316	−0.243018	−0.121509	−	0.992590i	$-0.538773\pi$
$881$	−7.21316	−0.243018	−0.121509	+	0.992590i	$0.538773\pi$
$882$	2.64618	0.0891015
$883$	−22.6933	−0.763690	−0.381845	−	0.924226i	$-0.624711\pi$
$883$	−22.6933	−0.763690	−0.381845	+	0.924226i	$0.624711\pi$
$884$	−64.2676	−2.16155
$885$	−1.91039	−0.0642170
$886$	7.91756	0.265996
$887$	−27.5669	−0.925606	−0.462803	−	0.886461i	$-0.653156\pi$
$887$	−27.5669	−0.925606	−0.462803	+	0.886461i	$0.653156\pi$
$888$	−40.9358	−1.37371
$889$	−39.2993	−1.31805
$890$	−0.793777	−0.0266075
$891$	−26.1558	−0.876252
$892$	0.662259	0.0221741
$893$	24.7975	0.829815
$894$	−7.63072	−0.255209
$895$	1.40939	0.0471106
$896$	24.0874	0.804703
$897$	−14.4358	−0.481999
$898$	10.6535	0.355513
$899$	−9.25383	−0.308632
$900$	50.4978	1.68326
$901$	−75.5296	−2.51625
$902$	−6.16510	−0.205275
$903$	63.5465	2.11469
$904$	40.3439	1.34182
$905$	−1.29033	−0.0428919
$906$	−36.4490	−1.21094
$907$	−40.8098	−1.35507	−0.677534	−	0.735492i	$-0.736951\pi$
$907$	−40.8098	−1.35507	−0.677534	+	0.735492i	$0.736951\pi$
$908$	−0.0148470	−0.000492716 0
$909$	−29.4542	−0.976934
$910$	4.96385	0.164550
$911$	0.123093	0.00407825	0.00203913	−	0.999998i	$-0.499351\pi$
$911$	0.123093	0.00407825	0.00203913	+	0.999998i	$0.499351\pi$
$912$	−4.18485	−0.138574
$913$	13.4051	0.443644
$914$	19.3713	0.640746
$915$	4.73250	0.156452
$916$	15.6997	0.518733
$917$	−2.72656	−0.0900388
$918$	87.5843	2.89071
$919$	43.8307	1.44584	0.722920	−	0.690931i	$-0.242799\pi$
$919$	43.8307	1.44584	0.722920	+	0.690931i	$0.242799\pi$
$920$	0.641836	0.0211607
$921$	86.3849	2.84648
$922$	29.9588	0.986639
$923$	10.3876	0.341913
$924$	12.0767	0.397293
$925$	22.7909	0.749361
$926$	−19.4845	−0.640300
$927$	−51.7887	−1.70097
$928$	−51.8770	−1.70295
$929$	−10.1869	−0.334222	−0.167111	−	0.985938i	$-0.553444\pi$
$929$	−10.1869	−0.334222	−0.167111	+	0.985938i	$0.553444\pi$
$930$	−0.949592	−0.0311384
$931$	0.983661	0.0322382
$932$	−31.4387	−1.02981
$933$	−84.9768	−2.78201
$934$	−15.2324	−0.498418
$935$	2.54713	0.0833000
$936$	133.056	4.34906
$937$	18.7090	0.611195	0.305598	−	0.952161i	$-0.401144\pi$
$937$	18.7090	0.611195	0.305598	+	0.952161i	$0.401144\pi$
$938$	−15.8136	−0.516331
$939$	−63.9103	−2.08563
$940$	−5.20809	−0.169869
$941$	−35.8736	−1.16945	−0.584723	−	0.811233i	$-0.698797\pi$
$941$	−35.8736	−1.16945	−0.584723	+	0.811233i	$0.698797\pi$
$942$	13.2907	0.433033
$943$	−5.25243	−0.171043
$944$	0.949366	0.0308992
$945$	14.3558	0.466994
$946$	−5.72512	−0.186140
$947$	49.2832	1.60149	0.800745	−	0.599006i	$-0.204437\pi$
$947$	49.2832	1.60149	0.800745	+	0.599006i	$0.204437\pi$
$948$	9.50051	0.308562
$949$	76.7234	2.49055
$950$	−8.84554	−0.286987
$951$	−48.3747	−1.56866
$952$	−53.3402	−1.72877
$953$	42.6967	1.38308	0.691541	−	0.722337i	$-0.256932\pi$
$953$	42.6967	1.38308	0.691541	+	0.722337i	$0.256932\pi$
$954$	63.2771	2.04867
$955$	2.48593	0.0804428
$956$	−14.3999	−0.465727
$957$	−28.9866	−0.937005
$958$	−5.38210	−0.173888
$959$	−20.8331	−0.672737
$960$	−4.03032	−0.130078
$961$	−29.9180	−0.965098
$962$	24.3003	0.783472
$963$	−110.832	−3.57152
$964$	34.3861	1.10750
$965$	1.62937	0.0524514
$966$	−4.84834	−0.155993
$967$	−12.5373	−0.403171	−0.201586	−	0.979471i	$-0.564609\pi$
$967$	−12.5373	−0.403171	−0.201586	+	0.979471i	$0.564609\pi$
$968$	−2.68876	−0.0864201
$969$	53.7170	1.72564
$970$	4.59601	0.147569
$971$	51.3460	1.64777	0.823886	−	0.566755i	$-0.191801\pi$
$971$	51.3460	1.64777	0.823886	+	0.566755i	$0.191801\pi$
$972$	54.5143	1.74855
$973$	−17.6465	−0.565721
$974$	25.7072	0.823713
$975$	−103.259	−3.30692
$976$	−2.35181	−0.0752796
$977$	−33.8316	−1.08237	−0.541184	−	0.840904i	$-0.682024\pi$
$977$	−33.8316	−1.08237	−0.541184	+	0.840904i	$0.682024\pi$
$978$	11.3928	0.364303
$979$	2.83300	0.0905431
$980$	−0.206594	−0.00659939
$981$	66.6615	2.12834
$982$	7.58584	0.242074
$983$	−17.6032	−0.561456	−0.280728	−	0.959787i	$-0.590576\pi$
$983$	−17.6032	−0.561456	−0.280728	+	0.959787i	$0.590576\pi$
$984$	67.4815	2.15123
$985$	1.49949	0.0477778
$986$	51.8076	1.64989
$987$	97.2209	3.09457
$988$	20.0146	0.636750
$989$	−4.87758	−0.155098
$990$	−2.13393	−0.0678208
$991$	−21.9343	−0.696765	−0.348382	−	0.937353i	$-0.613269\pi$
$991$	−21.9343	−0.696765	−0.348382	+	0.937353i	$0.613269\pi$
$992$	6.06544	0.192578
$993$	−37.1814	−1.17992
$994$	3.48873	0.110656
$995$	−3.31051	−0.104950
$996$	−59.3748	−1.88136
$997$	−3.82914	−0.121270	−0.0606351	−	0.998160i	$-0.519313\pi$
$997$	−3.82914	−0.121270	−0.0606351	+	0.998160i	$0.519313\pi$
$998$	−28.8075	−0.911886
$999$	70.2779	2.22350

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.f.1.18	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.f.1.18	✓	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)

\(f(q)\)	\(=\)	\(q+0.800366 q^{2} -3.25822 q^{3} -1.35941 q^{4} +0.350077 q^{5} -2.60777 q^{6} -2.72656 q^{7} -2.68876 q^{8} +7.61603 q^{9} +O(q^{10})\)	\(q+0.800366 q^{2} -3.25822 q^{3} -1.35941 q^{4} +0.350077 q^{5} -2.60777 q^{6} -2.72656 q^{7} -2.68876 q^{8} +7.61603 q^{9} +0.280189 q^{10} -1.00000 q^{11} +4.42928 q^{12} -6.49760 q^{13} -2.18224 q^{14} -1.14063 q^{15} +0.566834 q^{16} -7.27592 q^{17} +6.09561 q^{18} +2.26591 q^{19} -0.475899 q^{20} +8.88373 q^{21} -0.800366 q^{22} -0.681881 q^{23} +8.76059 q^{24} -4.87745 q^{25} -5.20046 q^{26} -15.0401 q^{27} +3.70652 q^{28} -8.89645 q^{29} -0.912920 q^{30} +1.04017 q^{31} +5.83120 q^{32} +3.25822 q^{33} -5.82340 q^{34} -0.954504 q^{35} -10.3533 q^{36} -4.67272 q^{37} +1.81356 q^{38} +21.1706 q^{39} -0.941272 q^{40} +7.70285 q^{41} +7.11024 q^{42} +7.15313 q^{43} +1.35941 q^{44} +2.66619 q^{45} -0.545755 q^{46} +10.9437 q^{47} -1.84687 q^{48} +0.434112 q^{49} -3.90374 q^{50} +23.7066 q^{51} +8.83292 q^{52} +10.3808 q^{53} -12.0376 q^{54} -0.350077 q^{55} +7.33106 q^{56} -7.38285 q^{57} -7.12042 q^{58} +1.67486 q^{59} +1.55059 q^{60} -4.14903 q^{61} +0.832517 q^{62} -20.7655 q^{63} +3.53343 q^{64} -2.27466 q^{65} +2.60777 q^{66} +7.24647 q^{67} +9.89098 q^{68} +2.22172 q^{69} -0.763952 q^{70} -1.59869 q^{71} -20.4777 q^{72} -11.8080 q^{73} -3.73988 q^{74} +15.8918 q^{75} -3.08031 q^{76} +2.72656 q^{77} +16.9443 q^{78} +2.14494 q^{79} +0.198435 q^{80} +26.1558 q^{81} +6.16510 q^{82} -13.4051 q^{83} -12.0767 q^{84} -2.54713 q^{85} +5.72512 q^{86} +28.9866 q^{87} +2.68876 q^{88} -2.83300 q^{89} +2.13393 q^{90} +17.7161 q^{91} +0.926959 q^{92} -3.38911 q^{93} +8.75896 q^{94} +0.793243 q^{95} -18.9994 q^{96} +16.4032 q^{97} +0.347449 q^{98} -7.61603 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) \) 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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