LMFDB - Embedded newform 2011.2.a.a.1.66

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2011,2,Mod(1,2011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2011, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2011.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:	$16.0579158465$
Analytic rank:	$1$
Dimension:	$77$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.66
Character	$\chi$	$=$	2011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.90094 q^{2} -2.95651 q^{3} +1.61358 q^{4} -2.47933 q^{5} -5.62015 q^{6} +2.30280 q^{7} -0.734568 q^{8} +5.74096 q^{9} +O(q^{10})$	\(q+1.90094 q^{2} -2.95651 q^{3} +1.61358 q^{4} -2.47933 q^{5} -5.62015 q^{6} +2.30280 q^{7} -0.734568 q^{8} +5.74096 q^{9} -4.71306 q^{10} +3.67920 q^{11} -4.77056 q^{12} -2.90412 q^{13} +4.37749 q^{14} +7.33017 q^{15} -4.62352 q^{16} +7.26140 q^{17} +10.9132 q^{18} -6.29364 q^{19} -4.00059 q^{20} -6.80826 q^{21} +6.99394 q^{22} +0.305173 q^{23} +2.17176 q^{24} +1.14709 q^{25} -5.52057 q^{26} -8.10367 q^{27} +3.71575 q^{28} +6.92630 q^{29} +13.9342 q^{30} +0.422256 q^{31} -7.31991 q^{32} -10.8776 q^{33} +13.8035 q^{34} -5.70941 q^{35} +9.26348 q^{36} -10.3763 q^{37} -11.9638 q^{38} +8.58607 q^{39} +1.82124 q^{40} -2.35020 q^{41} -12.9421 q^{42} +4.31933 q^{43} +5.93667 q^{44} -14.2337 q^{45} +0.580115 q^{46} -8.17777 q^{47} +13.6695 q^{48} -1.69710 q^{49} +2.18054 q^{50} -21.4684 q^{51} -4.68602 q^{52} -8.80275 q^{53} -15.4046 q^{54} -9.12195 q^{55} -1.69157 q^{56} +18.6072 q^{57} +13.1665 q^{58} +2.45454 q^{59} +11.8278 q^{60} -14.5016 q^{61} +0.802685 q^{62} +13.2203 q^{63} -4.66767 q^{64} +7.20028 q^{65} -20.6777 q^{66} -5.33728 q^{67} +11.7168 q^{68} -0.902246 q^{69} -10.8533 q^{70} -3.01760 q^{71} -4.21712 q^{72} +8.15922 q^{73} -19.7247 q^{74} -3.39137 q^{75} -10.1553 q^{76} +8.47247 q^{77} +16.3216 q^{78} -4.28408 q^{79} +11.4632 q^{80} +6.73573 q^{81} -4.46759 q^{82} -4.92531 q^{83} -10.9857 q^{84} -18.0034 q^{85} +8.21078 q^{86} -20.4777 q^{87} -2.70262 q^{88} -12.7330 q^{89} -27.0575 q^{90} -6.68762 q^{91} +0.492419 q^{92} -1.24841 q^{93} -15.5455 q^{94} +15.6040 q^{95} +21.6414 q^{96} +5.14687 q^{97} -3.22608 q^{98} +21.1221 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 77 q - 13 q^{2} - 13 q^{3} + 67 q^{4} - 47 q^{5} - 20 q^{6} - 8 q^{7} - 33 q^{8} + 52 q^{9}+O(q^{10}) $ 77 * q - 13 * q^2 - 13 * q^3 + 67 * q^4 - 47 * q^5 - 20 * q^6 - 8 * q^7 - 33 * q^8 + 52 * q^9	\( 77 q - 13 q^{2} - 13 q^{3} + 67 q^{4} - 47 q^{5} - 20 q^{6} - 8 q^{7} - 33 q^{8} + 52 q^{9} - 21 q^{10} - 34 q^{11} - 36 q^{12} - 34 q^{13} - 49 q^{14} - 12 q^{15} + 47 q^{16} - 59 q^{17} - 24 q^{18} - 31 q^{19} - 82 q^{20} - 71 q^{21} - 3 q^{22} - 28 q^{23} - 50 q^{24} + 68 q^{25} - 54 q^{26} - 43 q^{27} - 2 q^{28} - 151 q^{29} + q^{30} - 37 q^{31} - 59 q^{32} - 35 q^{33} - q^{34} - 58 q^{35} + 19 q^{36} - 29 q^{37} - 22 q^{38} - 40 q^{39} - 41 q^{40} - 142 q^{41} + 16 q^{42} - 23 q^{43} - 89 q^{44} - 119 q^{45} - 6 q^{46} - 36 q^{47} - 46 q^{48} + 45 q^{49} - 29 q^{50} - 53 q^{51} - 11 q^{52} - 69 q^{53} - 50 q^{54} - 13 q^{55} - 122 q^{56} - 14 q^{57} + 31 q^{58} - 92 q^{59} + 20 q^{60} - 115 q^{61} - 66 q^{62} - 25 q^{63} + 37 q^{64} - 57 q^{65} - 17 q^{66} - 108 q^{68} - 160 q^{69} + 40 q^{70} - 67 q^{71} - 35 q^{72} - 36 q^{73} - 55 q^{74} - 51 q^{75} - 56 q^{76} - 116 q^{77} + 22 q^{78} - 42 q^{79} - 114 q^{80} + 37 q^{81} + 18 q^{82} - 42 q^{83} - 77 q^{84} - 18 q^{85} - 33 q^{86} - 7 q^{87} - 2 q^{88} - 93 q^{89} - 34 q^{90} - 37 q^{91} - 55 q^{92} - 8 q^{93} - 35 q^{94} - 64 q^{95} - 83 q^{96} - 16 q^{97} - 57 q^{98} - 65 q^{99}+O(q^{100}) \) 77 * q - 13 * q^2 - 13 * q^3 + 67 * q^4 - 47 * q^5 - 20 * q^6 - 8 * q^7 - 33 * q^8 + 52 * q^9 - 21 * q^10 - 34 * q^11 - 36 * q^12 - 34 * q^13 - 49 * q^14 - 12 * q^15 + 47 * q^16 - 59 * q^17 - 24 * q^18 - 31 * q^19 - 82 * q^20 - 71 * q^21 - 3 * q^22 - 28 * q^23 - 50 * q^24 + 68 * q^25 - 54 * q^26 - 43 * q^27 - 2 * q^28 - 151 * q^29 + q^30 - 37 * q^31 - 59 * q^32 - 35 * q^33 - q^34 - 58 * q^35 + 19 * q^36 - 29 * q^37 - 22 * q^38 - 40 * q^39 - 41 * q^40 - 142 * q^41 + 16 * q^42 - 23 * q^43 - 89 * q^44 - 119 * q^45 - 6 * q^46 - 36 * q^47 - 46 * q^48 + 45 * q^49 - 29 * q^50 - 53 * q^51 - 11 * q^52 - 69 * q^53 - 50 * q^54 - 13 * q^55 - 122 * q^56 - 14 * q^57 + 31 * q^58 - 92 * q^59 + 20 * q^60 - 115 * q^61 - 66 * q^62 - 25 * q^63 + 37 * q^64 - 57 * q^65 - 17 * q^66 - 108 * q^68 - 160 * q^69 + 40 * q^70 - 67 * q^71 - 35 * q^72 - 36 * q^73 - 55 * q^74 - 51 * q^75 - 56 * q^76 - 116 * q^77 + 22 * q^78 - 42 * q^79 - 114 * q^80 + 37 * q^81 + 18 * q^82 - 42 * q^83 - 77 * q^84 - 18 * q^85 - 33 * q^86 - 7 * q^87 - 2 * q^88 - 93 * q^89 - 34 * q^90 - 37 * q^91 - 55 * q^92 - 8 * q^93 - 35 * q^94 - 64 * q^95 - 83 * q^96 - 16 * q^97 - 57 * q^98 - 65 * 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 $

$2$	1.90094	1.34417	0.672084	−	0.740475i	$-0.265399\pi$
$2$	1.90094	1.34417	0.672084	+	0.740475i	$0.265399\pi$
$3$	−2.95651	−1.70694	−0.853471	−	0.521140i	$-0.825507\pi$
$3$	−2.95651	−1.70694	−0.853471	+	0.521140i	$0.825507\pi$
$4$	1.61358	0.806788
$5$	−2.47933	−1.10879	−0.554395	−	0.832253i	$-0.687050\pi$
$5$	−2.47933	−1.10879	−0.554395	+	0.832253i	$0.687050\pi$
$6$	−5.62015	−2.29442
$7$	2.30280	0.870378	0.435189	−	0.900339i	$-0.356682\pi$
$7$	2.30280	0.870378	0.435189	+	0.900339i	$0.356682\pi$
$8$	−0.734568	−0.259709
$9$	5.74096	1.91365
$10$	−4.71306	−1.49040
$11$	3.67920	1.10932	0.554660	−	0.832077i	$-0.312848\pi$
$11$	3.67920	1.10932	0.554660	+	0.832077i	$0.312848\pi$
$12$	−4.77056	−1.37714
$13$	−2.90412	−0.805459	−0.402729	−	0.915319i	$-0.631938\pi$
$13$	−2.90412	−0.805459	−0.402729	+	0.915319i	$0.631938\pi$
$14$	4.37749	1.16993
$15$	7.33017	1.89264
$16$	−4.62352	−1.15588
$17$	7.26140	1.76115	0.880574	−	0.473909i	$-0.157157\pi$
$17$	7.26140	1.76115	0.880574	+	0.473909i	$0.157157\pi$
$18$	10.9132	2.57227
$19$	−6.29364	−1.44386	−0.721930	−	0.691966i	$-0.756745\pi$
$19$	−6.29364	−1.44386	−0.721930	+	0.691966i	$0.756745\pi$
$20$	−4.00059	−0.894559
$21$	−6.80826	−1.48569
$22$	6.99394	1.49111
$23$	0.305173	0.0636329	0.0318164	−	0.999494i	$-0.489871\pi$
$23$	0.305173	0.0636329	0.0318164	+	0.999494i	$0.489871\pi$
$24$	2.17176	0.443308
$25$	1.14709	0.229417
$26$	−5.52057	−1.08267
$27$	−8.10367	−1.55955
$28$	3.71575	0.702211
$29$	6.92630	1.28618	0.643091	−	0.765790i	$-0.277652\pi$
$29$	6.92630	1.28618	0.643091	+	0.765790i	$0.277652\pi$
$30$	13.9342	2.54403
$31$	0.422256	0.0758395	0.0379197	−	0.999281i	$-0.487927\pi$
$31$	0.422256	0.0758395	0.0379197	+	0.999281i	$0.487927\pi$
$32$	−7.31991	−1.29399
$33$	−10.8776	−1.89355
$34$	13.8035	2.36728
$35$	−5.70941	−0.965067
$36$	9.26348	1.54391
$37$	−10.3763	−1.70585	−0.852925	−	0.522033i	$-0.825174\pi$
$37$	−10.3763	−1.70585	−0.852925	+	0.522033i	$0.825174\pi$
$38$	−11.9638	−1.94079
$39$	8.58607	1.37487
$40$	1.82124	0.287963
$41$	−2.35020	−0.367039	−0.183520	−	0.983016i	$-0.558749\pi$
$41$	−2.35020	−0.367039	−0.183520	+	0.983016i	$0.558749\pi$
$42$	−12.9421	−1.99701
$43$	4.31933	0.658691	0.329346	−	0.944209i	$-0.393172\pi$
$43$	4.31933	0.658691	0.329346	+	0.944209i	$0.393172\pi$
$44$	5.93667	0.894987
$45$	−14.2337	−2.12184
$46$	0.580115	0.0855333
$47$	−8.17777	−1.19285	−0.596425	−	0.802669i	$-0.703413\pi$
$47$	−8.17777	−1.19285	−0.596425	+	0.802669i	$0.703413\pi$
$48$	13.6695	1.97302
$49$	−1.69710	−0.242442
$50$	2.18054	0.308375
$51$	−21.4684	−3.00618
$52$	−4.68602	−0.649835
$53$	−8.80275	−1.20915	−0.604575	−	0.796548i	$-0.706657\pi$
$53$	−8.80275	−1.20915	−0.604575	+	0.796548i	$0.706657\pi$
$54$	−15.4046	−2.09630
$55$	−9.12195	−1.23000
$56$	−1.69157	−0.226045
$57$	18.6072	2.46458
$58$	13.1665	1.72885
$59$	2.45454	0.319553	0.159777	−	0.987153i	$-0.448923\pi$
$59$	2.45454	0.319553	0.159777	+	0.987153i	$0.448923\pi$
$60$	11.8278	1.52696
$61$	−14.5016	−1.85674	−0.928372	−	0.371653i	$-0.878791\pi$
$61$	−14.5016	−1.85674	−0.928372	+	0.371653i	$0.878791\pi$
$62$	0.802685	0.101941
$63$	13.2203	1.66560
$64$	−4.66767	−0.583459
$65$	7.20028	0.893085
$66$	−20.6777	−2.54524
$67$	−5.33728	−0.652053	−0.326026	−	0.945361i	$-0.605710\pi$
$67$	−5.33728	−0.652053	−0.326026	+	0.945361i	$0.605710\pi$
$68$	11.7168	1.42087
$69$	−0.902246	−0.108618
$70$	−10.8533	−1.29721
$71$	−3.01760	−0.358123	−0.179061	−	0.983838i	$-0.557306\pi$
$71$	−3.01760	−0.358123	−0.179061	+	0.983838i	$0.557306\pi$
$72$	−4.21712	−0.496993
$73$	8.15922	0.954965	0.477482	−	0.878641i	$-0.341549\pi$
$73$	8.15922	0.954965	0.477482	+	0.878641i	$0.341549\pi$
$74$	−19.7247	−2.29295
$75$	−3.39137	−0.391602
$76$	−10.1553	−1.16489
$77$	8.47247	0.965528
$78$	16.3216	1.84806
$79$	−4.28408	−0.481996	−0.240998	−	0.970526i	$-0.577475\pi$
$79$	−4.28408	−0.481996	−0.240998	+	0.970526i	$0.577475\pi$
$80$	11.4632	1.28163
$81$	6.73573	0.748414
$82$	−4.46759	−0.493362
$83$	−4.92531	−0.540623	−0.270312	−	0.962773i	$-0.587127\pi$
$83$	−4.92531	−0.540623	−0.270312	+	0.962773i	$0.587127\pi$
$84$	−10.9857	−1.19863
$85$	−18.0034	−1.95274
$86$	8.21078	0.885392
$87$	−20.4777	−2.19544
$88$	−2.70262	−0.288100
$89$	−12.7330	−1.34970	−0.674849	−	0.737956i	$-0.735791\pi$
$89$	−12.7330	−1.34970	−0.674849	+	0.737956i	$0.735791\pi$
$90$	−27.0575	−2.85211
$91$	−6.68762	−0.701053
$92$	0.492419	0.0513383
$93$	−1.24841	−0.129454
$94$	−15.5455	−1.60339
$95$	15.6040	1.60094
$96$	21.6414	2.20877
$97$	5.14687	0.522585	0.261293	−	0.965260i	$-0.415851\pi$
$97$	5.14687	0.522585	0.261293	+	0.965260i	$0.415851\pi$
$98$	−3.22608	−0.325883
$99$	21.1221	2.12285
$100$	1.85091	0.185091
$101$	−8.42495	−0.838314	−0.419157	−	0.907914i	$-0.637674\pi$
$101$	−8.42495	−0.838314	−0.419157	+	0.907914i	$0.637674\pi$
$102$	−40.8102	−4.04081
$103$	−5.66913	−0.558595	−0.279298	−	0.960205i	$-0.590102\pi$
$103$	−5.66913	−0.558595	−0.279298	+	0.960205i	$0.590102\pi$
$104$	2.13328	0.209185
$105$	16.8799	1.64731
$106$	−16.7335	−1.62530
$107$	−1.95300	−0.188804	−0.0944020	−	0.995534i	$-0.530094\pi$
$107$	−1.95300	−0.188804	−0.0944020	+	0.995534i	$0.530094\pi$
$108$	−13.0759	−1.25823
$109$	12.8723	1.23294	0.616472	−	0.787377i	$-0.288561\pi$
$109$	12.8723	1.23294	0.616472	+	0.787377i	$0.288561\pi$
$110$	−17.3403	−1.65333
$111$	30.6776	2.91179
$112$	−10.6471	−1.00605
$113$	3.32846	0.313115	0.156558	−	0.987669i	$-0.449960\pi$
$113$	3.32846	0.313115	0.156558	+	0.987669i	$0.449960\pi$
$114$	35.3712	3.31282
$115$	−0.756624	−0.0705556
$116$	11.1761	1.03768
$117$	−16.6724	−1.54137
$118$	4.66593	0.429533
$119$	16.7216	1.53286
$120$	−5.38451	−0.491536
$121$	2.53650	0.230591
$122$	−27.5667	−2.49578
$123$	6.94838	0.626515
$124$	0.681343	0.0611864
$125$	9.55265	0.854415
$126$	25.1310	2.23885
$127$	−2.09875	−0.186234	−0.0931169	−	0.995655i	$-0.529683\pi$
$127$	−2.09875	−0.186234	−0.0931169	+	0.995655i	$0.529683\pi$
$128$	5.76686	0.509723
$129$	−12.7701	−1.12435
$130$	13.6873	1.20046
$131$	−10.4408	−0.912214	−0.456107	−	0.889925i	$-0.650757\pi$
$131$	−10.4408	−0.912214	−0.456107	+	0.889925i	$0.650757\pi$
$132$	−17.5518	−1.52769
$133$	−14.4930	−1.25670
$134$	−10.1459	−0.876469
$135$	20.0917	1.72922
$136$	−5.33399	−0.457386
$137$	22.2118	1.89768	0.948842	−	0.315751i	$-0.102257\pi$
$137$	22.2118	1.89768	0.948842	+	0.315751i	$0.102257\pi$
$138$	−1.71512	−0.146000
$139$	−13.0628	−1.10797	−0.553986	−	0.832526i	$-0.686894\pi$
$139$	−13.0628	−1.10797	−0.553986	+	0.832526i	$0.686894\pi$
$140$	−9.21258	−0.778605
$141$	24.1777	2.03613
$142$	−5.73627	−0.481377
$143$	−10.6848	−0.893512
$144$	−26.5435	−2.21195
$145$	−17.1726	−1.42611
$146$	15.5102	1.28363
$147$	5.01748	0.413835
$148$	−16.7429	−1.37626
$149$	−3.19182	−0.261484	−0.130742	−	0.991416i	$-0.541736\pi$
$149$	−3.19182	−0.261484	−0.130742	+	0.991416i	$0.541736\pi$
$150$	−6.44680	−0.526379
$151$	−19.3581	−1.57534	−0.787670	−	0.616098i	$-0.788713\pi$
$151$	−19.3581	−1.57534	−0.787670	+	0.616098i	$0.788713\pi$
$152$	4.62310	0.374983
$153$	41.6874	3.37023
$154$	16.1057	1.29783
$155$	−1.04691	−0.0840901
$156$	13.8543	1.10923
$157$	2.11008	0.168403	0.0842013	−	0.996449i	$-0.473166\pi$
$157$	2.11008	0.168403	0.0842013	+	0.996449i	$0.473166\pi$
$158$	−8.14378	−0.647884
$159$	26.0254	2.06395
$160$	18.1485	1.43476
$161$	0.702753	0.0553847
$162$	12.8042	1.00599
$163$	23.2552	1.82149	0.910745	−	0.412968i	$-0.135508\pi$
$163$	23.2552	1.82149	0.910745	+	0.412968i	$0.135508\pi$
$164$	−3.79222	−0.296123
$165$	26.9692	2.09955
$166$	−9.36273	−0.726688
$167$	−2.93470	−0.227094	−0.113547	−	0.993533i	$-0.536221\pi$
$167$	−2.93470	−0.227094	−0.113547	+	0.993533i	$0.536221\pi$
$168$	5.00113	0.385846
$169$	−4.56607	−0.351236
$170$	−34.2234	−2.62482
$171$	−36.1315	−2.76305
$172$	6.96956	0.531424
$173$	−19.4604	−1.47955	−0.739773	−	0.672856i	$-0.765067\pi$
$173$	−19.4604	−1.47955	−0.739773	+	0.672856i	$0.765067\pi$
$174$	−38.9269	−2.95104
$175$	2.64151	0.199680
$176$	−17.0109	−1.28224
$177$	−7.25686	−0.545459
$178$	−24.2047	−1.81422
$179$	1.74360	0.130323	0.0651614	−	0.997875i	$-0.479244\pi$
$179$	1.74360	0.130323	0.0651614	+	0.997875i	$0.479244\pi$
$180$	−22.9672	−1.71188
$181$	−12.3256	−0.916157	−0.458078	−	0.888912i	$-0.651462\pi$
$181$	−12.3256	−0.916157	−0.458078	+	0.888912i	$0.651462\pi$
$182$	−12.7128	−0.942334
$183$	42.8742	3.16935
$184$	−0.224170	−0.0165260
$185$	25.7262	1.89143
$186$	−2.37315	−0.174007
$187$	26.7161	1.95368
$188$	−13.1955	−0.962378
$189$	−18.6612	−1.35740
$190$	29.6623	2.15193
$191$	9.85949	0.713408	0.356704	−	0.934218i	$-0.383901\pi$
$191$	9.85949	0.713408	0.356704	+	0.934218i	$0.383901\pi$
$192$	13.8000	0.995930
$193$	20.4534	1.47227	0.736135	−	0.676834i	$-0.236649\pi$
$193$	20.4534	1.47227	0.736135	+	0.676834i	$0.236649\pi$
$194$	9.78389	0.702442
$195$	−21.2877	−1.52445
$196$	−2.73840	−0.195600
$197$	−6.54959	−0.466639	−0.233320	−	0.972400i	$-0.574959\pi$
$197$	−6.54959	−0.466639	−0.233320	+	0.972400i	$0.574959\pi$
$198$	40.1519	2.85347
$199$	18.6051	1.31888	0.659441	−	0.751756i	$-0.270793\pi$
$199$	18.6051	1.31888	0.659441	+	0.751756i	$0.270793\pi$
$200$	−0.842613	−0.0595817
$201$	15.7797	1.11302
$202$	−16.0153	−1.12683
$203$	15.9499	1.11946
$204$	−34.6409	−2.42535
$205$	5.82692	0.406970
$206$	−10.7767	−0.750846
$207$	1.75198	0.121771
$208$	13.4273	0.931014
$209$	−23.1555	−1.60170
$210$	32.0878	2.21427
$211$	16.5100	1.13660	0.568298	−	0.822822i	$-0.307602\pi$
$211$	16.5100	1.13660	0.568298	+	0.822822i	$0.307602\pi$
$212$	−14.2039	−0.975529
$213$	8.92156	0.611295
$214$	−3.71255	−0.253784
$215$	−10.7090	−0.730351
$216$	5.95270	0.405030
$217$	0.972373	0.0660090
$218$	24.4695	1.65728
$219$	−24.1228	−1.63007
$220$	−14.7190	−0.992353
$221$	−21.0880	−1.41853
$222$	58.3163	3.91393
$223$	1.17583	0.0787396	0.0393698	−	0.999225i	$-0.487465\pi$
$223$	1.17583	0.0787396	0.0393698	+	0.999225i	$0.487465\pi$
$224$	−16.8563	−1.12626
$225$	6.58537	0.439025
$226$	6.32721	0.420880
$227$	−10.3495	−0.686920	−0.343460	−	0.939167i	$-0.611599\pi$
$227$	−10.3495	−0.686920	−0.343460	+	0.939167i	$0.611599\pi$
$228$	30.0242	1.98840
$229$	4.67422	0.308881	0.154441	−	0.988002i	$-0.450642\pi$
$229$	4.67422	0.308881	0.154441	+	0.988002i	$0.450642\pi$
$230$	−1.43830	−0.0948386
$231$	−25.0490	−1.64810
$232$	−5.08784	−0.334033
$233$	−6.06242	−0.397162	−0.198581	−	0.980084i	$-0.563633\pi$
$233$	−6.06242	−0.397162	−0.198581	+	0.980084i	$0.563633\pi$
$234$	−31.6933	−2.07186
$235$	20.2754	1.32262
$236$	3.96058	0.257812
$237$	12.6659	0.822740
$238$	31.7867	2.06043
$239$	3.10780	0.201027	0.100514	−	0.994936i	$-0.467951\pi$
$239$	3.10780	0.201027	0.100514	+	0.994936i	$0.467951\pi$
$240$	−33.8912	−2.18767
$241$	−26.0392	−1.67733	−0.838665	−	0.544647i	$-0.816664\pi$
$241$	−26.0392	−1.67733	−0.838665	+	0.544647i	$0.816664\pi$
$242$	4.82174	0.309953
$243$	4.39677	0.282053
$244$	−23.3995	−1.49800
$245$	4.20767	0.268818
$246$	13.2085	0.842141
$247$	18.2775	1.16297
$248$	−0.310176	−0.0196962
$249$	14.5617	0.922813
$250$	18.1590	1.14848
$251$	27.1337	1.71267	0.856333	−	0.516425i	$-0.172737\pi$
$251$	27.1337	1.71267	0.856333	+	0.516425i	$0.172737\pi$
$252$	21.3320	1.34379
$253$	1.12279	0.0705892
$254$	−3.98960	−0.250330
$255$	53.2273	3.33322
$256$	20.2978	1.26861
$257$	−4.09744	−0.255591	−0.127796	−	0.991801i	$-0.540790\pi$
$257$	−4.09744	−0.255591	−0.127796	+	0.991801i	$0.540790\pi$
$258$	−24.2753	−1.51131
$259$	−23.8945	−1.48473
$260$	11.6182	0.720531
$261$	39.7636	2.46131
$262$	−19.8473	−1.22617
$263$	−20.3832	−1.25688	−0.628442	−	0.777856i	$-0.716307\pi$
$263$	−20.3832	−1.25688	−0.628442	+	0.777856i	$0.716307\pi$
$264$	7.99033	0.491771
$265$	21.8249	1.34070
$266$	−27.5504	−1.68922
$267$	37.6453	2.30386
$268$	−8.61211	−0.526068
$269$	−30.6902	−1.87122	−0.935608	−	0.353041i	$-0.885148\pi$
$269$	−30.6902	−1.87122	−0.935608	+	0.353041i	$0.885148\pi$
$270$	38.1931	2.32436
$271$	16.3721	0.994535	0.497267	−	0.867597i	$-0.334337\pi$
$271$	16.3721	0.994535	0.497267	+	0.867597i	$0.334337\pi$
$272$	−33.5733	−2.03568
$273$	19.7720	1.19666
$274$	42.2234	2.55081
$275$	4.22036	0.254497
$276$	−1.45584	−0.0876315
$277$	−1.22637	−0.0736853	−0.0368427	−	0.999321i	$-0.511730\pi$
$277$	−1.22637	−0.0736853	−0.0368427	+	0.999321i	$0.511730\pi$
$278$	−24.8316	−1.48930
$279$	2.42416	0.145130
$280$	4.19395	0.250637
$281$	−9.16737	−0.546880	−0.273440	−	0.961889i	$-0.588161\pi$
$281$	−9.16737	−0.546880	−0.273440	+	0.961889i	$0.588161\pi$
$282$	45.9603	2.73690
$283$	12.2945	0.730831	0.365415	−	0.930845i	$-0.380927\pi$
$283$	12.2945	0.730831	0.365415	+	0.930845i	$0.380927\pi$
$284$	−4.86912	−0.288929
$285$	−46.1334	−2.73271
$286$	−20.3113	−1.20103
$287$	−5.41204	−0.319463
$288$	−42.0233	−2.47625
$289$	35.7279	2.10164
$290$	−32.6441	−1.91693
$291$	−15.2168	−0.892023
$292$	13.1655	0.770454
$293$	11.2879	0.659447	0.329724	−	0.944077i	$-0.393044\pi$
$293$	11.2879	0.659447	0.329724	+	0.944077i	$0.393044\pi$
$294$	9.53794	0.556264
$295$	−6.08561	−0.354318
$296$	7.62209	0.443025
$297$	−29.8150	−1.73004
$298$	−6.06745	−0.351478
$299$	−0.886259	−0.0512537
$300$	−5.47224	−0.315940
$301$	9.94656	0.573310
$302$	−36.7986	−2.11752
$303$	24.9085	1.43095
$304$	29.0988	1.66893
$305$	35.9543	2.05874
$306$	79.2453	4.53015
$307$	21.0398	1.20080	0.600402	−	0.799699i	$-0.295007\pi$
$307$	21.0398	1.20080	0.600402	+	0.799699i	$0.295007\pi$
$308$	13.6710	0.778976
$309$	16.7608	0.953490
$310$	−1.99012	−0.113031
$311$	−8.98849	−0.509691	−0.254845	−	0.966982i	$-0.582025\pi$
$311$	−8.98849	−0.509691	−0.254845	+	0.966982i	$0.582025\pi$
$312$	−6.30705	−0.357067
$313$	−22.6904	−1.28254	−0.641270	−	0.767315i	$-0.721592\pi$
$313$	−22.6904	−1.28254	−0.641270	+	0.767315i	$0.721592\pi$
$314$	4.01114	0.226362
$315$	−32.7775	−1.84680
$316$	−6.91269	−0.388869
$317$	−17.8665	−1.00348	−0.501741	−	0.865018i	$-0.667307\pi$
$317$	−17.8665	−1.00348	−0.501741	+	0.865018i	$0.667307\pi$
$318$	49.4728	2.77430
$319$	25.4832	1.42679
$320$	11.5727	0.646934
$321$	5.77408	0.322278
$322$	1.33589	0.0744463
$323$	−45.7006	−2.54285
$324$	10.8686	0.603812
$325$	−3.33128	−0.184786
$326$	44.2068	2.44839
$327$	−38.0571	−2.10456
$328$	1.72638	0.0953234
$329$	−18.8318	−1.03823
$330$	51.2668	2.82214
$331$	−31.6268	−1.73836	−0.869182	−	0.494492i	$-0.835354\pi$
$331$	−31.6268	−1.73836	−0.869182	+	0.494492i	$0.835354\pi$
$332$	−7.94737	−0.436168
$333$	−59.5698	−3.26440
$334$	−5.57870	−0.305253
$335$	13.2329	0.722990
$336$	31.4782	1.71727
$337$	−25.8834	−1.40996	−0.704979	−	0.709228i	$-0.749044\pi$
$337$	−25.8834	−1.40996	−0.704979	+	0.709228i	$0.749044\pi$
$338$	−8.67983	−0.472121
$339$	−9.84064	−0.534470
$340$	−29.0499	−1.57545
$341$	1.55357	0.0841303
$342$	−68.6839	−3.71400
$343$	−20.0277	−1.08139
$344$	−3.17284	−0.171068
$345$	2.23697	0.120434
$346$	−36.9931	−1.98876
$347$	−2.77631	−0.149040	−0.0745201	−	0.997220i	$-0.523742\pi$
$347$	−2.77631	−0.149040	−0.0745201	+	0.997220i	$0.523742\pi$
$348$	−33.0423	−1.77125
$349$	−1.13232	−0.0606120	−0.0303060	−	0.999541i	$-0.509648\pi$
$349$	−1.13232	−0.0606120	−0.0303060	+	0.999541i	$0.509648\pi$
$350$	5.02136	0.268403
$351$	23.5341	1.25616
$352$	−26.9314	−1.43545
$353$	−32.7600	−1.74364	−0.871819	−	0.489829i	$-0.837059\pi$
$353$	−32.7600	−1.74364	−0.871819	+	0.489829i	$0.837059\pi$
$354$	−13.7949	−0.733189
$355$	7.48162	0.397083
$356$	−20.5457	−1.08892
$357$	−49.4375	−2.61651
$358$	3.31448	0.175176
$359$	14.2432	0.751725	0.375863	−	0.926675i	$-0.377346\pi$
$359$	14.2432	0.751725	0.375863	+	0.926675i	$0.377346\pi$
$360$	10.4557	0.551061
$361$	20.6099	1.08473
$362$	−23.4303	−1.23147
$363$	−7.49920	−0.393606
$364$	−10.7910	−0.565602
$365$	−20.2294	−1.05886
$366$	81.5014	4.26014
$367$	23.0974	1.20567	0.602837	−	0.797864i	$-0.294037\pi$
$367$	23.0974	1.20567	0.602837	+	0.797864i	$0.294037\pi$
$368$	−1.41097	−0.0735520
$369$	−13.4924	−0.702385
$370$	48.9041	2.54240
$371$	−20.2710	−1.05242
$372$	−2.01440	−0.104442
$373$	2.46841	0.127810	0.0639048	−	0.997956i	$-0.479645\pi$
$373$	2.46841	0.127810	0.0639048	+	0.997956i	$0.479645\pi$
$374$	50.7858	2.62607
$375$	−28.2425	−1.45844
$376$	6.00713	0.309794
$377$	−20.1148	−1.03597
$378$	−35.4738	−1.82457
$379$	−14.3968	−0.739515	−0.369757	−	0.929128i	$-0.620559\pi$
$379$	−14.3968	−0.739515	−0.369757	+	0.929128i	$0.620559\pi$
$380$	25.1783	1.29162
$381$	6.20497	0.317890
$382$	18.7423	0.958940
$383$	−21.1501	−1.08072	−0.540359	−	0.841434i	$-0.681712\pi$
$383$	−21.1501	−1.08072	−0.540359	+	0.841434i	$0.681712\pi$
$384$	−17.0498	−0.870068
$385$	−21.0061	−1.07057
$386$	38.8808	1.97898
$387$	24.7971	1.26051
$388$	8.30486	0.421616
$389$	28.3652	1.43817	0.719086	−	0.694921i	$-0.244561\pi$
$389$	28.3652	1.43817	0.719086	+	0.694921i	$0.244561\pi$
$390$	−40.4667	−2.04911
$391$	2.21598	0.112067
$392$	1.24663	0.0629645
$393$	30.8682	1.55710
$394$	−12.4504	−0.627242
$395$	10.6217	0.534433
$396$	34.0822	1.71269
$397$	−19.7393	−0.990685	−0.495342	−	0.868698i	$-0.664957\pi$
$397$	−19.7393	−0.990685	−0.495342	+	0.868698i	$0.664957\pi$
$398$	35.3673	1.77280
$399$	42.8487	2.14512
$400$	−5.30358	−0.265179
$401$	−2.15304	−0.107518	−0.0537589	−	0.998554i	$-0.517120\pi$
$401$	−2.15304	−0.107518	−0.0537589	+	0.998554i	$0.517120\pi$
$402$	29.9963	1.49608
$403$	−1.22628	−0.0610856
$404$	−13.5943	−0.676342
$405$	−16.7001	−0.829835
$406$	30.3199	1.50475
$407$	−38.1764	−1.89233
$408$	15.7700	0.780732
$409$	−14.8855	−0.736040	−0.368020	−	0.929818i	$-0.619964\pi$
$409$	−14.8855	−0.736040	−0.368020	+	0.929818i	$0.619964\pi$
$410$	11.0766	0.547036
$411$	−65.6695	−3.23924
$412$	−9.14757	−0.450668
$413$	5.65231	0.278132
$414$	3.33042	0.163681
$415$	12.2115	0.599438
$416$	21.2579	1.04226
$417$	38.6203	1.89124
$418$	−44.0173	−2.15296
$419$	0.195962	0.00957339	0.00478670	−	0.999989i	$-0.498476\pi$
$419$	0.195962	0.00957339	0.00478670	+	0.999989i	$0.498476\pi$
$420$	27.2371	1.32903
$421$	0.0339982	0.00165697	0.000828485	−	1.00000i	$-0.499736\pi$
$421$	0.0339982	0.00165697	0.000828485		1.00000i	$0.499736\pi$
$422$	31.3846	1.52778
$423$	−46.9483	−2.28270
$424$	6.46622	0.314027
$425$	8.32945	0.404038
$426$	16.9594	0.821683
$427$	−33.3944	−1.61607
$428$	−3.15132	−0.152325
$429$	31.5899	1.52517
$430$	−20.3573	−0.981714
$431$	−23.7511	−1.14405	−0.572025	−	0.820236i	$-0.693842\pi$
$431$	−23.7511	−1.14405	−0.572025	+	0.820236i	$0.693842\pi$
$432$	37.4675	1.80266
$433$	20.5918	0.989579	0.494790	−	0.869013i	$-0.335245\pi$
$433$	20.5918	0.989579	0.494790	+	0.869013i	$0.335245\pi$
$434$	1.84842	0.0887272
$435$	50.7710	2.43428
$436$	20.7705	0.994725
$437$	−1.92065	−0.0918769
$438$	−45.8561	−2.19109
$439$	16.6862	0.796390	0.398195	−	0.917301i	$-0.369637\pi$
$439$	16.6862	0.796390	0.398195	+	0.917301i	$0.369637\pi$
$440$	6.70070	0.319443
$441$	−9.74296	−0.463950
$442$	−40.0870	−1.90675
$443$	23.6451	1.12341	0.561707	−	0.827336i	$-0.310145\pi$
$443$	23.6451	1.12341	0.561707	+	0.827336i	$0.310145\pi$
$444$	49.5006	2.34920
$445$	31.5694	1.49653
$446$	2.23519	0.105839
$447$	9.43664	0.446338
$448$	−10.7487	−0.507829
$449$	−13.8993	−0.655949	−0.327975	−	0.944687i	$-0.606366\pi$
$449$	−13.8993	−0.655949	−0.327975	+	0.944687i	$0.606366\pi$
$450$	12.5184	0.590123
$451$	−8.64684	−0.407164
$452$	5.37073	0.252618
$453$	57.2324	2.68901
$454$	−19.6738	−0.923336
$455$	16.5808	0.777322
$456$	−13.6683	−0.640075
$457$	−13.3687	−0.625363	−0.312682	−	0.949858i	$-0.601227\pi$
$457$	−13.3687	−0.625363	−0.312682	+	0.949858i	$0.601227\pi$
$458$	8.88542	0.415188
$459$	−58.8440	−2.74660
$460$	−1.22087	−0.0569234
$461$	−8.84817	−0.412100	−0.206050	−	0.978541i	$-0.566061\pi$
$461$	−8.84817	−0.412100	−0.206050	+	0.978541i	$0.566061\pi$
$462$	−47.6166	−2.21532
$463$	37.9039	1.76154	0.880771	−	0.473542i	$-0.157025\pi$
$463$	37.9039	1.76154	0.880771	+	0.473542i	$0.157025\pi$
$464$	−32.0239	−1.48667
$465$	3.09521	0.143537
$466$	−11.5243	−0.533853
$467$	−2.28619	−0.105792	−0.0528961	−	0.998600i	$-0.516845\pi$
$467$	−2.28619	−0.105792	−0.0528961	+	0.998600i	$0.516845\pi$
$468$	−26.9023	−1.24356
$469$	−12.2907	−0.567532
$470$	38.5424	1.77783
$471$	−6.23847	−0.287454
$472$	−1.80302	−0.0829909
$473$	15.8917	0.730699
$474$	24.0772	1.10590
$475$	−7.21934	−0.331246
$476$	26.9815	1.23670
$477$	−50.5362	−2.31390
$478$	5.90775	0.270214
$479$	−22.2551	−1.01686	−0.508430	−	0.861103i	$-0.669774\pi$
$479$	−22.2551	−1.01686	−0.508430	+	0.861103i	$0.669774\pi$
$480$	−53.6562	−2.44906
$481$	30.1340	1.37399
$482$	−49.4989	−2.25461
$483$	−2.07770	−0.0945384
$484$	4.09284	0.186038
$485$	−12.7608	−0.579438
$486$	8.35799	0.379126
$487$	10.8525	0.491772	0.245886	−	0.969299i	$-0.420921\pi$
$487$	10.8525	0.491772	0.245886	+	0.969299i	$0.420921\pi$
$488$	10.6524	0.482213
$489$	−68.7544	−3.10918
$490$	7.99852	0.361336
$491$	−36.1171	−1.62994	−0.814972	−	0.579501i	$-0.803248\pi$
$491$	−36.1171	−1.62994	−0.814972	+	0.579501i	$0.803248\pi$
$492$	11.2117	0.505465
$493$	50.2947	2.26516
$494$	34.7444	1.56323
$495$	−52.3688	−2.35380
$496$	−1.95231	−0.0876614
$497$	−6.94893	−0.311702
$498$	27.6810	1.24042
$499$	36.7933	1.64710	0.823548	−	0.567247i	$-0.191992\pi$
$499$	36.7933	1.64710	0.823548	+	0.567247i	$0.191992\pi$
$500$	15.4139	0.689332
$501$	8.67648	0.387637
$502$	51.5796	2.30211
$503$	20.5842	0.917804	0.458902	−	0.888487i	$-0.348243\pi$
$503$	20.5842	0.917804	0.458902	+	0.888487i	$0.348243\pi$
$504$	−9.71121	−0.432572
$505$	20.8882	0.929515
$506$	2.13436	0.0948838
$507$	13.4996	0.599540
$508$	−3.38649	−0.150251
$509$	8.29971	0.367878	0.183939	−	0.982938i	$-0.441115\pi$
$509$	8.29971	0.367878	0.183939	+	0.982938i	$0.441115\pi$
$510$	101.182	4.48041
$511$	18.7891	0.831180
$512$	27.0512	1.19550
$513$	51.0016	2.25177
$514$	−7.78899	−0.343558
$515$	14.0556	0.619366
$516$	−20.6056	−0.907111
$517$	−30.0877	−1.32325
$518$	−45.4221	−1.99573
$519$	57.5349	2.52550
$520$	−5.28910	−0.231942
$521$	45.0917	1.97550	0.987752	−	0.156033i	$-0.0498706\pi$
$521$	45.0917	1.97550	0.987752	+	0.156033i	$0.0498706\pi$
$522$	75.5883	3.30841
$523$	34.3414	1.50164	0.750821	−	0.660505i	$-0.229658\pi$
$523$	34.3414	1.50164	0.750821	+	0.660505i	$0.229658\pi$
$524$	−16.8470	−0.735963
$525$	−7.80966	−0.340842
$526$	−38.7473	−1.68946
$527$	3.06617	0.133565
$528$	50.2928	2.18871
$529$	−22.9069	−0.995951
$530$	41.4879	1.80212
$531$	14.0914	0.611514
$532$	−23.3856	−1.01389
$533$	6.82526	0.295635
$534$	71.5616	3.09677
$535$	4.84215	0.209344
$536$	3.92060	0.169344
$537$	−5.15497	−0.222454
$538$	−58.3403	−2.51523
$539$	−6.24396	−0.268946
$540$	32.4195	1.39511
$541$	27.4899	1.18189	0.590943	−	0.806714i	$-0.298756\pi$
$541$	27.4899	1.18189	0.590943	+	0.806714i	$0.298756\pi$
$542$	31.1224	1.33682
$543$	36.4409	1.56383
$544$	−53.1528	−2.27891
$545$	−31.9147	−1.36708
$546$	37.5855	1.60851
$547$	7.48390	0.319988	0.159994	−	0.987118i	$-0.448852\pi$
$547$	7.48390	0.319988	0.159994	+	0.987118i	$0.448852\pi$
$548$	35.8405	1.53103
$549$	−83.2532	−3.55316
$550$	8.02265	0.342087
$551$	−43.5916	−1.85707
$552$	0.662761	0.0282090
$553$	−9.86539	−0.419519
$554$	−2.33125	−0.0990455
$555$	−76.0599	−3.22856
$556$	−21.0778	−0.893899
$557$	−32.7591	−1.38805	−0.694024	−	0.719952i	$-0.744164\pi$
$557$	−32.7591	−1.38805	−0.694024	+	0.719952i	$0.744164\pi$
$558$	4.60818	0.195080
$559$	−12.5439	−0.530548
$560$	26.3976	1.11550
$561$	−78.9865	−3.33481
$562$	−17.4266	−0.735098
$563$	41.3172	1.74131	0.870657	−	0.491891i	$-0.163694\pi$
$563$	41.3172	1.74131	0.870657	+	0.491891i	$0.163694\pi$
$564$	39.0125	1.64272
$565$	−8.25236	−0.347179
$566$	23.3711	0.982360
$567$	15.5111	0.651403
$568$	2.21663	0.0930077
$569$	−10.4005	−0.436011	−0.218006	−	0.975948i	$-0.569955\pi$
$569$	−10.4005	−0.436011	−0.218006	+	0.975948i	$0.569955\pi$
$570$	−87.6970	−3.67322
$571$	−20.1418	−0.842908	−0.421454	−	0.906850i	$-0.638480\pi$
$571$	−20.1418	−0.842908	−0.421454	+	0.906850i	$0.638480\pi$
$572$	−17.2408	−0.720875
$573$	−29.1497	−1.21775
$574$	−10.2880	−0.429412
$575$	0.350059	0.0145985
$576$	−26.7969	−1.11654
$577$	−15.5295	−0.646502	−0.323251	−	0.946313i	$-0.604776\pi$
$577$	−15.5295	−0.646502	−0.323251	+	0.946313i	$0.604776\pi$
$578$	67.9167	2.82496
$579$	−60.4708	−2.51308
$580$	−27.7093	−1.15057
$581$	−11.3420	−0.470546
$582$	−28.9262	−1.19903
$583$	−32.3871	−1.34134
$584$	−5.99351	−0.248013
$585$	41.3365	1.70906
$586$	21.4577	0.886408
$587$	12.2104	0.503976	0.251988	−	0.967730i	$-0.418916\pi$
$587$	12.2104	0.503976	0.251988	+	0.967730i	$0.418916\pi$
$588$	8.09610	0.333877
$589$	−2.65753	−0.109502
$590$	−11.5684	−0.476263
$591$	19.3639	0.796526
$592$	47.9750	1.97176
$593$	38.6169	1.58581	0.792904	−	0.609347i	$-0.208568\pi$
$593$	38.6169	1.58581	0.792904	+	0.609347i	$0.208568\pi$
$594$	−56.6766	−2.32547
$595$	−41.4583	−1.69963
$596$	−5.15024	−0.210962
$597$	−55.0063	−2.25126
$598$	−1.68473	−0.0688935
$599$	21.0423	0.859765	0.429882	−	0.902885i	$-0.358555\pi$
$599$	21.0423	0.859765	0.429882	+	0.902885i	$0.358555\pi$
$600$	2.49119	0.101703
$601$	−14.3599	−0.585754	−0.292877	−	0.956150i	$-0.594613\pi$
$601$	−14.3599	−0.585754	−0.292877	+	0.956150i	$0.594613\pi$
$602$	18.9078	0.770625
$603$	−30.6411	−1.24780
$604$	−31.2358	−1.27097
$605$	−6.28883	−0.255677
$606$	47.3495	1.92344
$607$	−5.03005	−0.204164	−0.102082	−	0.994776i	$-0.532550\pi$
$607$	−5.03005	−0.204164	−0.102082	+	0.994776i	$0.532550\pi$
$608$	46.0689	1.86834
$609$	−47.1561	−1.91086
$610$	68.3471	2.76729
$611$	23.7493	0.960792
$612$	67.2658	2.71906
$613$	−34.5022	−1.39353	−0.696765	−	0.717299i	$-0.745378\pi$
$613$	−34.5022	−1.39353	−0.696765	+	0.717299i	$0.745378\pi$
$614$	39.9954	1.61408
$615$	−17.2273	−0.694674
$616$	−6.22361	−0.250756
$617$	−15.9817	−0.643399	−0.321700	−	0.946842i	$-0.604254\pi$
$617$	−15.9817	−0.643399	−0.321700	+	0.946842i	$0.604254\pi$
$618$	31.8614	1.28165
$619$	34.7537	1.39687	0.698434	−	0.715674i	$-0.253881\pi$
$619$	34.7537	1.39687	0.698434	+	0.715674i	$0.253881\pi$
$620$	−1.68928	−0.0678429
$621$	−2.47302	−0.0992389
$622$	−17.0866	−0.685110
$623$	−29.3217	−1.17475
$624$	−39.6979	−1.58919
$625$	−29.4196	−1.17678
$626$	−43.1332	−1.72395
$627$	68.4596	2.73401
$628$	3.40478	0.135865
$629$	−75.3463	−3.00425
$630$	−62.3081	−2.48241
$631$	−2.30998	−0.0919590	−0.0459795	−	0.998942i	$-0.514641\pi$
$631$	−2.30998	−0.0919590	−0.0459795	+	0.998942i	$0.514641\pi$
$632$	3.14695	0.125179
$633$	−48.8121	−1.94011
$634$	−33.9631	−1.34885
$635$	5.20349	0.206494
$636$	41.9940	1.66517
$637$	4.92858	0.195277
$638$	48.4422	1.91784
$639$	−17.3239	−0.685323
$640$	−14.2980	−0.565176
$641$	34.5813	1.36588	0.682940	−	0.730474i	$-0.260701\pi$
$641$	34.5813	1.36588	0.682940	+	0.730474i	$0.260701\pi$
$642$	10.9762	0.433195
$643$	−2.94301	−0.116061	−0.0580304	−	0.998315i	$-0.518482\pi$
$643$	−2.94301	−0.116061	−0.0580304	+	0.998315i	$0.518482\pi$
$644$	1.13395	0.0446837
$645$	31.6614	1.24667
$646$	−86.8742	−3.41802
$647$	31.7930	1.24991	0.624955	−	0.780661i	$-0.285117\pi$
$647$	31.7930	1.24991	0.624955	+	0.780661i	$0.285117\pi$
$648$	−4.94785	−0.194370
$649$	9.03072	0.354487
$650$	−6.33256	−0.248384
$651$	−2.87483	−0.112674
$652$	37.5241	1.46956
$653$	−8.43350	−0.330028	−0.165014	−	0.986291i	$-0.552767\pi$
$653$	−8.43350	−0.330028	−0.165014	+	0.986291i	$0.552767\pi$
$654$	−72.3444	−2.82889
$655$	25.8861	1.01145
$656$	10.8662	0.424253
$657$	46.8418	1.82747
$658$	−35.7981	−1.39556
$659$	−27.7971	−1.08282	−0.541410	−	0.840758i	$-0.682109\pi$
$659$	−27.7971	−1.08282	−0.541410	+	0.840758i	$0.682109\pi$
$660$	43.5168	1.69389
$661$	−5.97968	−0.232583	−0.116291	−	0.993215i	$-0.537101\pi$
$661$	−5.97968	−0.232583	−0.116291	+	0.993215i	$0.537101\pi$
$662$	−60.1206	−2.33665
$663$	62.3469	2.42135
$664$	3.61798	0.140405
$665$	35.9330	1.39342
$666$	−113.239	−4.38791
$667$	2.11372	0.0818435
$668$	−4.73537	−0.183217
$669$	−3.47636	−0.134404
$670$	25.1549	0.971820
$671$	−53.3544	−2.05972
$672$	49.8359	1.92246
$673$	−20.8490	−0.803669	−0.401835	−	0.915712i	$-0.631627\pi$
$673$	−20.8490	−0.803669	−0.401835	+	0.915712i	$0.631627\pi$
$674$	−49.2028	−1.89522
$675$	−9.29561	−0.357788
$676$	−7.36771	−0.283373
$677$	−40.0690	−1.53998	−0.769989	−	0.638057i	$-0.779738\pi$
$677$	−40.0690	−1.53998	−0.769989	+	0.638057i	$0.779738\pi$
$678$	−18.7065	−0.718418
$679$	11.8522	0.454847
$680$	13.2247	0.507146
$681$	30.5984	1.17253
$682$	2.95324	0.113085
$683$	2.29001	0.0876246	0.0438123	−	0.999040i	$-0.486050\pi$
$683$	2.29001	0.0876246	0.0438123	+	0.999040i	$0.486050\pi$
$684$	−58.3010	−2.22919
$685$	−55.0705	−2.10413
$686$	−38.0715	−1.45358
$687$	−13.8194	−0.527243
$688$	−19.9705	−0.761368
$689$	25.5643	0.973921
$690$	4.25234	0.161884
$691$	−41.1639	−1.56595	−0.782974	−	0.622055i	$-0.786298\pi$
$691$	−41.1639	−1.56595	−0.782974	+	0.622055i	$0.786298\pi$
$692$	−31.4008	−1.19368
$693$	48.6401	1.84768
$694$	−5.27760	−0.200335
$695$	32.3870	1.22851
$696$	15.0423	0.570175
$697$	−17.0657	−0.646410
$698$	−2.15248	−0.0814727
$699$	17.9236	0.677933
$700$	4.26228	0.161099
$701$	−47.6011	−1.79787	−0.898934	−	0.438084i	$-0.855657\pi$
$701$	−47.6011	−1.79787	−0.898934	+	0.438084i	$0.855657\pi$
$702$	44.7369	1.68848
$703$	65.3045	2.46301
$704$	−17.1733	−0.647242
$705$	−59.9445	−2.25764
$706$	−62.2748	−2.34374
$707$	−19.4010	−0.729650
$708$	−11.7095	−0.440070
$709$	−11.4337	−0.429402	−0.214701	−	0.976680i	$-0.568878\pi$
$709$	−11.4337	−0.429402	−0.214701	+	0.976680i	$0.568878\pi$
$710$	14.2221	0.533747
$711$	−24.5947	−0.922374
$712$	9.35328	0.350529
$713$	0.128861	0.00482589
$714$	−93.9778	−3.51703
$715$	26.4913	0.990717
$716$	2.81343	0.105143
$717$	−9.18825	−0.343142
$718$	27.0754	1.01045
$719$	42.9643	1.60230	0.801149	−	0.598465i	$-0.204222\pi$
$719$	42.9643	1.60230	0.801149	+	0.598465i	$0.204222\pi$
$720$	65.8100	2.45260
$721$	−13.0549	−0.486189
$722$	39.1781	1.45806
$723$	76.9851	2.86311
$724$	−19.8883	−0.739145
$725$	7.94507	0.295072
$726$	−14.2555	−0.529073
$727$	1.37481	0.0509890	0.0254945	−	0.999675i	$-0.491884\pi$
$727$	1.37481	0.0509890	0.0254945	+	0.999675i	$0.491884\pi$
$728$	4.91251	0.182070
$729$	−33.2063	−1.22986
$730$	−38.4549	−1.42328
$731$	31.3644	1.16005
$732$	69.1808	2.55700
$733$	22.5001	0.831060	0.415530	−	0.909579i	$-0.363596\pi$
$733$	22.5001	0.831060	0.415530	+	0.909579i	$0.363596\pi$
$734$	43.9068	1.62063
$735$	−12.4400	−0.458857
$736$	−2.23384	−0.0823403
$737$	−19.6369	−0.723335
$738$	−25.6482	−0.944124
$739$	13.0207	0.478973	0.239487	−	0.970900i	$-0.423021\pi$
$739$	13.0207	0.478973	0.239487	+	0.970900i	$0.423021\pi$
$740$	41.5113	1.52598
$741$	−54.0376	−1.98512
$742$	−38.5340	−1.41463
$743$	−8.01877	−0.294180	−0.147090	−	0.989123i	$-0.546991\pi$
$743$	−8.01877	−0.294180	−0.147090	+	0.989123i	$0.546991\pi$
$744$	0.917039	0.0336203
$745$	7.91357	0.289931
$746$	4.69230	0.171797
$747$	−28.2760	−1.03456
$748$	43.1085	1.57620
$749$	−4.49738	−0.164331
$750$	−53.6874	−1.96039
$751$	−25.3446	−0.924839	−0.462419	−	0.886661i	$-0.653019\pi$
$751$	−25.3446	−0.924839	−0.462419	+	0.886661i	$0.653019\pi$
$752$	37.8101	1.37879
$753$	−80.2211	−2.92342
$754$	−38.2371	−1.39251
$755$	47.9951	1.74672
$756$	−30.1112	−1.09513
$757$	14.6168	0.531257	0.265628	−	0.964075i	$-0.414421\pi$
$757$	14.6168	0.531257	0.265628	+	0.964075i	$0.414421\pi$
$758$	−27.3675	−0.994032
$759$	−3.31954	−0.120492
$760$	−11.4622	−0.415778
$761$	41.0902	1.48952	0.744759	−	0.667334i	$-0.232564\pi$
$761$	41.0902	1.48952	0.744759	+	0.667334i	$0.232564\pi$
$762$	11.7953	0.427298
$763$	29.6424	1.07313
$764$	15.9090	0.575569
$765$	−103.357	−3.73688
$766$	−40.2051	−1.45267
$767$	−7.12827	−0.257387
$768$	−60.0106	−2.16545
$769$	23.2149	0.837150	0.418575	−	0.908182i	$-0.362530\pi$
$769$	23.2149	0.837150	0.418575	+	0.908182i	$0.362530\pi$
$770$	−39.9313	−1.43902
$771$	12.1141	0.436280
$772$	33.0032	1.18781
$773$	21.8774	0.786876	0.393438	−	0.919351i	$-0.371286\pi$
$773$	21.8774	0.786876	0.393438	+	0.919351i	$0.371286\pi$
$774$	47.1378	1.69433
$775$	0.484364	0.0173989
$776$	−3.78072	−0.135720
$777$	70.6445	2.53436
$778$	53.9206	1.93315
$779$	14.7913	0.529953
$780$	−34.3494	−1.22990
$781$	−11.1023	−0.397273
$782$	4.21245	0.150637
$783$	−56.1285	−2.00587
$784$	7.84657	0.280234
$785$	−5.23159	−0.186723
$786$	58.6787	2.09300
$787$	23.2752	0.829671	0.414836	−	0.909896i	$-0.363839\pi$
$787$	23.2752	0.829671	0.414836	+	0.909896i	$0.363839\pi$
$788$	−10.5683	−0.376479
$789$	60.2633	2.14543
$790$	20.1911	0.718368
$791$	7.66479	0.272529
$792$	−15.5156	−0.551324
$793$	42.1145	1.49553
$794$	−37.5232	−1.33165
$795$	−64.5257	−2.28849
$796$	30.0208	1.06406
$797$	22.3365	0.791199	0.395599	−	0.918423i	$-0.370537\pi$
$797$	22.3365	0.791199	0.395599	+	0.918423i	$0.370537\pi$
$798$	81.4529	2.88340
$799$	−59.3821	−2.10079
$800$	−8.39657	−0.296863
$801$	−73.0998	−2.58285
$802$	−4.09280	−0.144522
$803$	30.0194	1.05936
$804$	25.4618	0.897969
$805$	−1.74236	−0.0614100
$806$	−2.33109	−0.0821093
$807$	90.7360	3.19406
$808$	6.18870	0.217718
$809$	−7.52574	−0.264591	−0.132295	−	0.991210i	$-0.542235\pi$
$809$	−7.52574	−0.264591	−0.132295	+	0.991210i	$0.542235\pi$
$810$	−31.7459	−1.11544
$811$	−2.58921	−0.0909196	−0.0454598	−	0.998966i	$-0.514475\pi$
$811$	−2.58921	−0.0909196	−0.0454598	+	0.998966i	$0.514475\pi$
$812$	25.7364	0.903171
$813$	−48.4043	−1.69761
$814$	−72.5711	−2.54362
$815$	−57.6574	−2.01965
$816$	99.2597	3.47478
$817$	−27.1843	−0.951057
$818$	−28.2964	−0.989362
$819$	−38.3934	−1.34157
$820$	9.40218	0.328338
$821$	14.7461	0.514641	0.257321	−	0.966326i	$-0.417160\pi$
$821$	14.7461	0.514641	0.257321	+	0.966326i	$0.417160\pi$
$822$	−124.834	−4.35408
$823$	−11.4362	−0.398642	−0.199321	−	0.979934i	$-0.563874\pi$
$823$	−11.4362	−0.398642	−0.199321	+	0.979934i	$0.563874\pi$
$824$	4.16436	0.145072
$825$	−12.4775	−0.434412
$826$	10.7447	0.373856
$827$	32.2667	1.12202	0.561012	−	0.827807i	$-0.310412\pi$
$827$	32.2667	1.12202	0.561012	+	0.827807i	$0.310412\pi$
$828$	2.82696	0.0982436
$829$	−42.9062	−1.49020	−0.745098	−	0.666955i	$-0.767597\pi$
$829$	−42.9062	−1.49020	−0.745098	+	0.666955i	$0.767597\pi$
$830$	23.2133	0.805745
$831$	3.62577	0.125777
$832$	13.5555	0.469952
$833$	−12.3233	−0.426977
$834$	73.4149	2.54215
$835$	7.27610	0.251800
$836$	−37.3632	−1.29223
$837$	−3.42183	−0.118276
$838$	0.372513	0.0128683
$839$	4.64560	0.160384	0.0801920	−	0.996779i	$-0.474447\pi$
$839$	4.64560	0.160384	0.0801920	+	0.996779i	$0.474447\pi$
$840$	−12.3995	−0.427822
$841$	18.9737	0.654265
$842$	0.0646285	0.00222725
$843$	27.1034	0.933492
$844$	26.6402	0.916993
$845$	11.3208	0.389448
$846$	−89.2459	−3.06834
$847$	5.84107	0.200701
$848$	40.6997	1.39763
$849$	−36.3488	−1.24749
$850$	15.8338	0.543095
$851$	−3.16656	−0.108548
$852$	14.3956	0.493186
$853$	45.5312	1.55896	0.779480	−	0.626427i	$-0.215484\pi$
$853$	45.5312	1.55896	0.779480	+	0.626427i	$0.215484\pi$
$854$	−63.4808	−2.17227
$855$	89.5820	3.06364
$856$	1.43461	0.0490341
$857$	28.2883	0.966311	0.483155	−	0.875535i	$-0.339491\pi$
$857$	28.2883	0.966311	0.483155	+	0.875535i	$0.339491\pi$
$858$	60.0505	2.05009
$859$	20.9879	0.716099	0.358049	−	0.933703i	$-0.383442\pi$
$859$	20.9879	0.716099	0.358049	+	0.933703i	$0.383442\pi$
$860$	−17.2799	−0.589238
$861$	16.0008	0.545304
$862$	−45.1494	−1.53779
$863$	−30.3191	−1.03208	−0.516038	−	0.856566i	$-0.672594\pi$
$863$	−30.3191	−1.03208	−0.516038	+	0.856566i	$0.672594\pi$
$864$	59.3182	2.01804
$865$	48.2488	1.64051
$866$	39.1438	1.33016
$867$	−105.630	−3.58738
$868$	1.56900	0.0532553
$869$	−15.7620	−0.534688
$870$	96.5127	3.27209
$871$	15.5001	0.525201
$872$	−9.45559	−0.320207
$873$	29.5479	1.00005
$874$	−3.65103	−0.123498
$875$	21.9979	0.743664
$876$	−38.9240	−1.31512
$877$	29.3467	0.990967	0.495484	−	0.868617i	$-0.334991\pi$
$877$	29.3467	0.990967	0.495484	+	0.868617i	$0.334991\pi$
$878$	31.7195	1.07048
$879$	−33.3729	−1.12564
$880$	42.1756	1.42174
$881$	0.465305	0.0156765	0.00783825	−	0.999969i	$-0.497505\pi$
$881$	0.465305	0.0156765	0.00783825	+	0.999969i	$0.497505\pi$
$882$	−18.5208	−0.623628
$883$	45.7258	1.53880	0.769398	−	0.638770i	$-0.220556\pi$
$883$	45.7258	1.53880	0.769398	+	0.638770i	$0.220556\pi$
$884$	−34.0271	−1.14445
$885$	17.9922	0.604800
$886$	44.9480	1.51006
$887$	−28.6974	−0.963565	−0.481783	−	0.876291i	$-0.660010\pi$
$887$	−28.6974	−0.963565	−0.481783	+	0.876291i	$0.660010\pi$
$888$	−22.5348	−0.756218
$889$	−4.83301	−0.162094
$890$	60.0116	2.01159
$891$	24.7821	0.830231
$892$	1.89730	0.0635262
$893$	51.4679	1.72231
$894$	17.9385	0.599953
$895$	−4.32296	−0.144501
$896$	13.2799	0.443652
$897$	2.62023	0.0874871
$898$	−26.4218	−0.881706
$899$	2.92468	0.0975434
$900$	10.6260	0.354200
$901$	−63.9203	−2.12949
$902$	−16.4371	−0.547297
$903$	−29.4071	−0.978607
$904$	−2.44498	−0.0813189
$905$	30.5593	1.01583
$906$	108.795	3.61449
$907$	43.5698	1.44671	0.723355	−	0.690476i	$-0.242599\pi$
$907$	43.5698	1.44671	0.723355	+	0.690476i	$0.242599\pi$
$908$	−16.6997	−0.554199
$909$	−48.3673	−1.60424
$910$	31.5192	1.04485
$911$	29.0425	0.962220	0.481110	−	0.876660i	$-0.340234\pi$
$911$	29.0425	0.962220	0.481110	+	0.876660i	$0.340234\pi$
$912$	−86.0309	−2.84877
$913$	−18.1212	−0.599724
$914$	−25.4132	−0.840594
$915$	−106.299	−3.51415
$916$	7.54222	0.249202
$917$	−24.0430	−0.793971
$918$	−111.859	−3.69190
$919$	−38.5615	−1.27203	−0.636013	−	0.771678i	$-0.719418\pi$
$919$	−38.5615	−1.27203	−0.636013	+	0.771678i	$0.719418\pi$
$920$	0.555792	0.0183239
$921$	−62.2043	−2.04970
$922$	−16.8199	−0.553932
$923$	8.76347	0.288453
$924$	−40.4184	−1.32967
$925$	−11.9025	−0.391351
$926$	72.0530	2.36781
$927$	−32.5462	−1.06896
$928$	−50.6999	−1.66431
$929$	−38.0021	−1.24681	−0.623404	−	0.781900i	$-0.714251\pi$
$929$	−38.0021	−1.24681	−0.623404	+	0.781900i	$0.714251\pi$
$930$	5.88382	0.192938
$931$	10.6809	0.350053
$932$	−9.78218	−0.320426
$933$	26.5746	0.870013
$934$	−4.34591	−0.142203
$935$	−66.2382	−2.16622
$936$	12.2470	0.400307
$937$	58.4802	1.91046	0.955232	−	0.295857i	$-0.0956050\pi$
$937$	58.4802	1.91046	0.955232	+	0.295857i	$0.0956050\pi$
$938$	−23.3639	−0.762859
$939$	67.0846	2.18922
$940$	32.7159	1.06708
$941$	28.5274	0.929968	0.464984	−	0.885319i	$-0.346060\pi$
$941$	28.5274	0.929968	0.464984	+	0.885319i	$0.346060\pi$
$942$	−11.8590	−0.386386
$943$	−0.717216	−0.0233558
$944$	−11.3486	−0.369366
$945$	46.2672	1.50507
$946$	30.2091	0.982183
$947$	−23.8063	−0.773600	−0.386800	−	0.922164i	$-0.626420\pi$
$947$	−23.8063	−0.773600	−0.386800	+	0.922164i	$0.626420\pi$
$948$	20.4374	0.663777
$949$	−23.6954	−0.769185
$950$	−13.7235	−0.445251
$951$	52.8225	1.71289
$952$	−12.2831	−0.398099
$953$	−12.3624	−0.400458	−0.200229	−	0.979749i	$-0.564169\pi$
$953$	−12.3624	−0.400458	−0.200229	+	0.979749i	$0.564169\pi$
$954$	−96.0664	−3.11026
$955$	−24.4449	−0.791020
$956$	5.01468	0.162186
$957$	−75.3415	−2.43545
$958$	−42.3056	−1.36683
$959$	51.1495	1.65170
$960$	−34.2148	−1.10428
$961$	−30.8217	−0.994248
$962$	57.2829	1.84688
$963$	−11.2121	−0.361305
$964$	−42.0162	−1.35325
$965$	−50.7109	−1.63244
$966$	−3.94958	−0.127076
$967$	40.0690	1.28853	0.644266	−	0.764802i	$-0.277163\pi$
$967$	40.0690	1.28853	0.644266	+	0.764802i	$0.277163\pi$
$968$	−1.86323	−0.0598866
$969$	135.114	4.34050
$970$	−24.2575	−0.778862
$971$	−23.2052	−0.744689	−0.372345	−	0.928095i	$-0.621446\pi$
$971$	−23.2052	−0.744689	−0.372345	+	0.928095i	$0.621446\pi$
$972$	7.09452	0.227557
$973$	−30.0810	−0.964354
$974$	20.6299	0.661025
$975$	9.84896	0.315419
$976$	67.0486	2.14617
$977$	35.6890	1.14179	0.570897	−	0.821022i	$-0.306596\pi$
$977$	35.6890	1.14179	0.570897	+	0.821022i	$0.306596\pi$
$978$	−130.698	−4.17926
$979$	−46.8473	−1.49725
$980$	6.78939	0.216879
$981$	73.8994	2.35943
$982$	−68.6565	−2.19092
$983$	21.2688	0.678368	0.339184	−	0.940720i	$-0.389849\pi$
$983$	21.2688	0.678368	0.339184	+	0.940720i	$0.389849\pi$
$984$	−5.10406	−0.162712
$985$	16.2386	0.517405
$986$	95.6072	3.04475
$987$	55.6764	1.77220
$988$	29.4921	0.938270
$989$	1.31814	0.0419144
$990$	−99.5499	−3.16390
$991$	−32.3094	−1.02634	−0.513170	−	0.858287i	$-0.671529\pi$
$991$	−32.3094	−1.02634	−0.513170	+	0.858287i	$0.671529\pi$
$992$	−3.09088	−0.0981355
$993$	93.5049	2.96729
$994$	−13.2095	−0.418980
$995$	−46.1283	−1.46237
$996$	23.4965	0.744514
$997$	−18.4297	−0.583676	−0.291838	−	0.956468i	$-0.594267\pi$
$997$	−18.4297	−0.583676	−0.291838	+	0.956468i	$0.594267\pi$
$998$	69.9419	2.21397
$999$	84.0860	2.66036

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2011.2.a.a.1.66	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2011.2.a.a.1.66	✓	77	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:	\( N \)	\(=\)	\( 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2011.a (trivial)

\(f(q)\)	\(=\)	\(q+1.90094 q^{2} -2.95651 q^{3} +1.61358 q^{4} -2.47933 q^{5} -5.62015 q^{6} +2.30280 q^{7} -0.734568 q^{8} +5.74096 q^{9} +O(q^{10})\)	\(q+1.90094 q^{2} -2.95651 q^{3} +1.61358 q^{4} -2.47933 q^{5} -5.62015 q^{6} +2.30280 q^{7} -0.734568 q^{8} +5.74096 q^{9} -4.71306 q^{10} +3.67920 q^{11} -4.77056 q^{12} -2.90412 q^{13} +4.37749 q^{14} +7.33017 q^{15} -4.62352 q^{16} +7.26140 q^{17} +10.9132 q^{18} -6.29364 q^{19} -4.00059 q^{20} -6.80826 q^{21} +6.99394 q^{22} +0.305173 q^{23} +2.17176 q^{24} +1.14709 q^{25} -5.52057 q^{26} -8.10367 q^{27} +3.71575 q^{28} +6.92630 q^{29} +13.9342 q^{30} +0.422256 q^{31} -7.31991 q^{32} -10.8776 q^{33} +13.8035 q^{34} -5.70941 q^{35} +9.26348 q^{36} -10.3763 q^{37} -11.9638 q^{38} +8.58607 q^{39} +1.82124 q^{40} -2.35020 q^{41} -12.9421 q^{42} +4.31933 q^{43} +5.93667 q^{44} -14.2337 q^{45} +0.580115 q^{46} -8.17777 q^{47} +13.6695 q^{48} -1.69710 q^{49} +2.18054 q^{50} -21.4684 q^{51} -4.68602 q^{52} -8.80275 q^{53} -15.4046 q^{54} -9.12195 q^{55} -1.69157 q^{56} +18.6072 q^{57} +13.1665 q^{58} +2.45454 q^{59} +11.8278 q^{60} -14.5016 q^{61} +0.802685 q^{62} +13.2203 q^{63} -4.66767 q^{64} +7.20028 q^{65} -20.6777 q^{66} -5.33728 q^{67} +11.7168 q^{68} -0.902246 q^{69} -10.8533 q^{70} -3.01760 q^{71} -4.21712 q^{72} +8.15922 q^{73} -19.7247 q^{74} -3.39137 q^{75} -10.1553 q^{76} +8.47247 q^{77} +16.3216 q^{78} -4.28408 q^{79} +11.4632 q^{80} +6.73573 q^{81} -4.46759 q^{82} -4.92531 q^{83} -10.9857 q^{84} -18.0034 q^{85} +8.21078 q^{86} -20.4777 q^{87} -2.70262 q^{88} -12.7330 q^{89} -27.0575 q^{90} -6.68762 q^{91} +0.492419 q^{92} -1.24841 q^{93} -15.5455 q^{94} +15.6040 q^{95} +21.6414 q^{96} +5.14687 q^{97} -3.22608 q^{98} +21.1221 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 13 q^{2} - 13 q^{3} + 67 q^{4} - 47 q^{5} - 20 q^{6} - 8 q^{7} - 33 q^{8} + 52 q^{9}+O(q^{10}) \) 77 * q - 13 * q^2 - 13 * q^3 + 67 * q^4 - 47 * q^5 - 20 * q^6 - 8 * q^7 - 33 * q^8 + 52 * q^9	\( 77 q - 13 q^{2} - 13 q^{3} + 67 q^{4} - 47 q^{5} - 20 q^{6} - 8 q^{7} - 33 q^{8} + 52 q^{9} - 21 q^{10} - 34 q^{11} - 36 q^{12} - 34 q^{13} - 49 q^{14} - 12 q^{15} + 47 q^{16} - 59 q^{17} - 24 q^{18} - 31 q^{19} - 82 q^{20} - 71 q^{21} - 3 q^{22} - 28 q^{23} - 50 q^{24} + 68 q^{25} - 54 q^{26} - 43 q^{27} - 2 q^{28} - 151 q^{29} + q^{30} - 37 q^{31} - 59 q^{32} - 35 q^{33} - q^{34} - 58 q^{35} + 19 q^{36} - 29 q^{37} - 22 q^{38} - 40 q^{39} - 41 q^{40} - 142 q^{41} + 16 q^{42} - 23 q^{43} - 89 q^{44} - 119 q^{45} - 6 q^{46} - 36 q^{47} - 46 q^{48} + 45 q^{49} - 29 q^{50} - 53 q^{51} - 11 q^{52} - 69 q^{53} - 50 q^{54} - 13 q^{55} - 122 q^{56} - 14 q^{57} + 31 q^{58} - 92 q^{59} + 20 q^{60} - 115 q^{61} - 66 q^{62} - 25 q^{63} + 37 q^{64} - 57 q^{65} - 17 q^{66} - 108 q^{68} - 160 q^{69} + 40 q^{70} - 67 q^{71} - 35 q^{72} - 36 q^{73} - 55 q^{74} - 51 q^{75} - 56 q^{76} - 116 q^{77} + 22 q^{78} - 42 q^{79} - 114 q^{80} + 37 q^{81} + 18 q^{82} - 42 q^{83} - 77 q^{84} - 18 q^{85} - 33 q^{86} - 7 q^{87} - 2 q^{88} - 93 q^{89} - 34 q^{90} - 37 q^{91} - 55 q^{92} - 8 q^{93} - 35 q^{94} - 64 q^{95} - 83 q^{96} - 16 q^{97} - 57 q^{98} - 65 q^{99}+O(q^{100}) \) 77 * q - 13 * q^2 - 13 * q^3 + 67 * q^4 - 47 * q^5 - 20 * q^6 - 8 * q^7 - 33 * q^8 + 52 * q^9 - 21 * q^10 - 34 * q^11 - 36 * q^12 - 34 * q^13 - 49 * q^14 - 12 * q^15 + 47 * q^16 - 59 * q^17 - 24 * q^18 - 31 * q^19 - 82 * q^20 - 71 * q^21 - 3 * q^22 - 28 * q^23 - 50 * q^24 + 68 * q^25 - 54 * q^26 - 43 * q^27 - 2 * q^28 - 151 * q^29 + q^30 - 37 * q^31 - 59 * q^32 - 35 * q^33 - q^34 - 58 * q^35 + 19 * q^36 - 29 * q^37 - 22 * q^38 - 40 * q^39 - 41 * q^40 - 142 * q^41 + 16 * q^42 - 23 * q^43 - 89 * q^44 - 119 * q^45 - 6 * q^46 - 36 * q^47 - 46 * q^48 + 45 * q^49 - 29 * q^50 - 53 * q^51 - 11 * q^52 - 69 * q^53 - 50 * q^54 - 13 * q^55 - 122 * q^56 - 14 * q^57 + 31 * q^58 - 92 * q^59 + 20 * q^60 - 115 * q^61 - 66 * q^62 - 25 * q^63 + 37 * q^64 - 57 * q^65 - 17 * q^66 - 108 * q^68 - 160 * q^69 + 40 * q^70 - 67 * q^71 - 35 * q^72 - 36 * q^73 - 55 * q^74 - 51 * q^75 - 56 * q^76 - 116 * q^77 + 22 * q^78 - 42 * q^79 - 114 * q^80 + 37 * q^81 + 18 * q^82 - 42 * q^83 - 77 * q^84 - 18 * q^85 - 33 * q^86 - 7 * q^87 - 2 * q^88 - 93 * q^89 - 34 * q^90 - 37 * q^91 - 55 * q^92 - 8 * q^93 - 35 * q^94 - 64 * q^95 - 83 * q^96 - 16 * q^97 - 57 * q^98 - 65 * q^99

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