LMFDB - Embedded newform 4011.2.a.k.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.105370 q^{2} +1.00000 q^{3} -1.98890 q^{4} -1.28706 q^{5} -0.105370 q^{6} +1.00000 q^{7} +0.420311 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.105370 q^{2} +1.00000 q^{3} -1.98890 q^{4} -1.28706 q^{5} -0.105370 q^{6} +1.00000 q^{7} +0.420311 q^{8} +1.00000 q^{9} +0.135618 q^{10} +2.67777 q^{11} -1.98890 q^{12} -2.17889 q^{13} -0.105370 q^{14} -1.28706 q^{15} +3.93351 q^{16} +0.182864 q^{17} -0.105370 q^{18} +6.98640 q^{19} +2.55984 q^{20} +1.00000 q^{21} -0.282158 q^{22} -6.16386 q^{23} +0.420311 q^{24} -3.34347 q^{25} +0.229591 q^{26} +1.00000 q^{27} -1.98890 q^{28} +4.36429 q^{29} +0.135618 q^{30} -5.43968 q^{31} -1.25510 q^{32} +2.67777 q^{33} -0.0192684 q^{34} -1.28706 q^{35} -1.98890 q^{36} +7.15698 q^{37} -0.736159 q^{38} -2.17889 q^{39} -0.540968 q^{40} +2.47459 q^{41} -0.105370 q^{42} -9.16115 q^{43} -5.32581 q^{44} -1.28706 q^{45} +0.649487 q^{46} +2.34053 q^{47} +3.93351 q^{48} +1.00000 q^{49} +0.352302 q^{50} +0.182864 q^{51} +4.33359 q^{52} +12.9384 q^{53} -0.105370 q^{54} -3.44647 q^{55} +0.420311 q^{56} +6.98640 q^{57} -0.459866 q^{58} -6.23777 q^{59} +2.55984 q^{60} -8.11932 q^{61} +0.573180 q^{62} +1.00000 q^{63} -7.73476 q^{64} +2.80438 q^{65} -0.282158 q^{66} -3.57311 q^{67} -0.363697 q^{68} -6.16386 q^{69} +0.135618 q^{70} -3.38085 q^{71} +0.420311 q^{72} +11.6011 q^{73} -0.754133 q^{74} -3.34347 q^{75} -13.8952 q^{76} +2.67777 q^{77} +0.229591 q^{78} +12.9776 q^{79} -5.06268 q^{80} +1.00000 q^{81} -0.260748 q^{82} +0.613844 q^{83} -1.98890 q^{84} -0.235358 q^{85} +0.965313 q^{86} +4.36429 q^{87} +1.12550 q^{88} +1.29328 q^{89} +0.135618 q^{90} -2.17889 q^{91} +12.2593 q^{92} -5.43968 q^{93} -0.246622 q^{94} -8.99195 q^{95} -1.25510 q^{96} -1.02897 q^{97} -0.105370 q^{98} +2.67777 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9}+O(q^{10}) $ 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9} + 10 q^{10} + 22 q^{11} + 31 q^{12} + 15 q^{13} + 9 q^{14} + 23 q^{15} + 39 q^{16} + 22 q^{17} + 9 q^{18} + 24 q^{19} + 46 q^{20} + 27 q^{21} - 19 q^{22} + 36 q^{23} + 18 q^{24} + 38 q^{25} + 19 q^{26} + 27 q^{27} + 31 q^{28} + 32 q^{29} + 10 q^{30} + 11 q^{31} + 15 q^{32} + 22 q^{33} - 4 q^{34} + 23 q^{35} + 31 q^{36} + 6 q^{37} + 8 q^{38} + 15 q^{39} + 16 q^{41} + 9 q^{42} - 11 q^{43} + 22 q^{44} + 23 q^{45} - 56 q^{46} + 39 q^{47} + 39 q^{48} + 27 q^{49} - 7 q^{50} + 22 q^{51} + 10 q^{52} + 24 q^{53} + 9 q^{54} + 16 q^{55} + 18 q^{56} + 24 q^{57} - 31 q^{58} + 31 q^{59} + 46 q^{60} + 28 q^{61} - 4 q^{62} + 27 q^{63} + 40 q^{64} + 33 q^{65} - 19 q^{66} - 7 q^{67} + 25 q^{68} + 36 q^{69} + 10 q^{70} + 49 q^{71} + 18 q^{72} - 13 q^{73} + 7 q^{74} + 38 q^{75} + 15 q^{76} + 22 q^{77} + 19 q^{78} - 18 q^{79} + 78 q^{80} + 27 q^{81} + 31 q^{82} + 59 q^{83} + 31 q^{84} - 20 q^{85} + 35 q^{86} + 32 q^{87} - 49 q^{88} + 49 q^{89} + 10 q^{90} + 15 q^{91} + 52 q^{92} + 11 q^{93} + 17 q^{94} + 38 q^{95} + 15 q^{96} - 7 q^{97} + 9 q^{98} + 22 q^{99}+O(q^{100}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9 + 10 * q^10 + 22 * q^11 + 31 * q^12 + 15 * q^13 + 9 * q^14 + 23 * q^15 + 39 * q^16 + 22 * q^17 + 9 * q^18 + 24 * q^19 + 46 * q^20 + 27 * q^21 - 19 * q^22 + 36 * q^23 + 18 * q^24 + 38 * q^25 + 19 * q^26 + 27 * q^27 + 31 * q^28 + 32 * q^29 + 10 * q^30 + 11 * q^31 + 15 * q^32 + 22 * q^33 - 4 * q^34 + 23 * q^35 + 31 * q^36 + 6 * q^37 + 8 * q^38 + 15 * q^39 + 16 * q^41 + 9 * q^42 - 11 * q^43 + 22 * q^44 + 23 * q^45 - 56 * q^46 + 39 * q^47 + 39 * q^48 + 27 * q^49 - 7 * q^50 + 22 * q^51 + 10 * q^52 + 24 * q^53 + 9 * q^54 + 16 * q^55 + 18 * q^56 + 24 * q^57 - 31 * q^58 + 31 * q^59 + 46 * q^60 + 28 * q^61 - 4 * q^62 + 27 * q^63 + 40 * q^64 + 33 * q^65 - 19 * q^66 - 7 * q^67 + 25 * q^68 + 36 * q^69 + 10 * q^70 + 49 * q^71 + 18 * q^72 - 13 * q^73 + 7 * q^74 + 38 * q^75 + 15 * q^76 + 22 * q^77 + 19 * q^78 - 18 * q^79 + 78 * q^80 + 27 * q^81 + 31 * q^82 + 59 * q^83 + 31 * q^84 - 20 * q^85 + 35 * q^86 + 32 * q^87 - 49 * q^88 + 49 * q^89 + 10 * q^90 + 15 * q^91 + 52 * q^92 + 11 * q^93 + 17 * q^94 + 38 * q^95 + 15 * q^96 - 7 * q^97 + 9 * q^98 + 22 * 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 $

$2$	−0.105370	−0.0745080	−0.0372540	−	0.999306i	$-0.511861\pi$
$2$	−0.105370	−0.0745080	−0.0372540	+	0.999306i	$0.511861\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.98890	−0.994449
$5$	−1.28706	−0.575593	−0.287796	−	0.957692i	$-0.592923\pi$
$5$	−1.28706	−0.575593	−0.287796	+	0.957692i	$0.592923\pi$
$6$	−0.105370	−0.0430172
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.420311	0.148602
$9$	1.00000	0.333333
$10$	0.135618	0.0428863
$11$	2.67777	0.807379	0.403689	−	0.914896i	$-0.367728\pi$
$11$	2.67777	0.807379	0.403689	+	0.914896i	$0.367728\pi$
$12$	−1.98890	−0.574145
$13$	−2.17889	−0.604316	−0.302158	−	0.953258i	$-0.597707\pi$
$13$	−2.17889	−0.604316	−0.302158	+	0.953258i	$0.597707\pi$
$14$	−0.105370	−0.0281614
$15$	−1.28706	−0.332319
$16$	3.93351	0.983376
$17$	0.182864	0.0443510	0.0221755	−	0.999754i	$-0.492941\pi$
$17$	0.182864	0.0443510	0.0221755	+	0.999754i	$0.492941\pi$
$18$	−0.105370	−0.0248360
$19$	6.98640	1.60279	0.801395	−	0.598135i	$-0.204091\pi$
$19$	6.98640	1.60279	0.801395	+	0.598135i	$0.204091\pi$
$20$	2.55984	0.572397
$21$	1.00000	0.218218
$22$	−0.282158	−0.0601562
$23$	−6.16386	−1.28525	−0.642627	−	0.766180i	$-0.722155\pi$
$23$	−6.16386	−1.28525	−0.642627	+	0.766180i	$0.722155\pi$
$24$	0.420311	0.0857957
$25$	−3.34347	−0.668693
$26$	0.229591	0.0450264
$27$	1.00000	0.192450
$28$	−1.98890	−0.375866
$29$	4.36429	0.810428	0.405214	−	0.914222i	$-0.367197\pi$
$29$	4.36429	0.810428	0.405214	+	0.914222i	$0.367197\pi$
$30$	0.135618	0.0247604
$31$	−5.43968	−0.976995	−0.488497	−	0.872565i	$-0.662455\pi$
$31$	−5.43968	−0.976995	−0.488497	+	0.872565i	$0.662455\pi$
$32$	−1.25510	−0.221872
$33$	2.67777	0.466140
$34$	−0.0192684	−0.00330451
$35$	−1.28706	−0.217554
$36$	−1.98890	−0.331483
$37$	7.15698	1.17660	0.588300	−	0.808643i	$-0.299797\pi$
$37$	7.15698	1.17660	0.588300	+	0.808643i	$0.299797\pi$
$38$	−0.736159	−0.119421
$39$	−2.17889	−0.348902
$40$	−0.540968	−0.0855345
$41$	2.47459	0.386466	0.193233	−	0.981153i	$-0.438103\pi$
$41$	2.47459	0.386466	0.193233	+	0.981153i	$0.438103\pi$
$42$	−0.105370	−0.0162590
$43$	−9.16115	−1.39706	−0.698531	−	0.715580i	$-0.746163\pi$
$43$	−9.16115	−1.39706	−0.698531	+	0.715580i	$0.746163\pi$
$44$	−5.32581	−0.802897
$45$	−1.28706	−0.191864
$46$	0.649487	0.0957617
$47$	2.34053	0.341402	0.170701	−	0.985323i	$-0.445397\pi$
$47$	2.34053	0.341402	0.170701	+	0.985323i	$0.445397\pi$
$48$	3.93351	0.567753
$49$	1.00000	0.142857
$50$	0.352302	0.0498230
$51$	0.182864	0.0256061
$52$	4.33359	0.600961
$53$	12.9384	1.77723	0.888615	−	0.458655i	$-0.151669\pi$
$53$	12.9384	1.77723	0.888615	+	0.458655i	$0.151669\pi$
$54$	−0.105370	−0.0143391
$55$	−3.44647	−0.464721
$56$	0.420311	0.0561664
$57$	6.98640	0.925371
$58$	−0.459866	−0.0603834
$59$	−6.23777	−0.812088	−0.406044	−	0.913854i	$-0.633092\pi$
$59$	−6.23777	−0.812088	−0.406044	+	0.913854i	$0.633092\pi$
$60$	2.55984	0.330474
$61$	−8.11932	−1.03957	−0.519787	−	0.854296i	$-0.673989\pi$
$61$	−8.11932	−1.03957	−0.519787	+	0.854296i	$0.673989\pi$
$62$	0.573180	0.0727940
$63$	1.00000	0.125988
$64$	−7.73476	−0.966845
$65$	2.80438	0.347840
$66$	−0.282158	−0.0347312
$67$	−3.57311	−0.436525	−0.218263	−	0.975890i	$-0.570039\pi$
$67$	−3.57311	−0.436525	−0.218263	+	0.975890i	$0.570039\pi$
$68$	−0.363697	−0.0441048
$69$	−6.16386	−0.742041
$70$	0.135618	0.0162095
$71$	−3.38085	−0.401234	−0.200617	−	0.979670i	$-0.564295\pi$
$71$	−3.38085	−0.401234	−0.200617	+	0.979670i	$0.564295\pi$
$72$	0.420311	0.0495341
$73$	11.6011	1.35780	0.678902	−	0.734229i	$-0.262456\pi$
$73$	11.6011	1.35780	0.678902	+	0.734229i	$0.262456\pi$
$74$	−0.754133	−0.0876662
$75$	−3.34347	−0.386070
$76$	−13.8952	−1.59389
$77$	2.67777	0.305160
$78$	0.229591	0.0259960
$79$	12.9776	1.46010	0.730049	−	0.683395i	$-0.239497\pi$
$79$	12.9776	1.46010	0.730049	+	0.683395i	$0.239497\pi$
$80$	−5.06268	−0.566024
$81$	1.00000	0.111111
$82$	−0.260748	−0.0287948
$83$	0.613844	0.0673782	0.0336891	−	0.999432i	$-0.489274\pi$
$83$	0.613844	0.0673782	0.0336891	+	0.999432i	$0.489274\pi$
$84$	−1.98890	−0.217006
$85$	−0.235358	−0.0255281
$86$	0.965313	0.104092
$87$	4.36429	0.467901
$88$	1.12550	0.119978
$89$	1.29328	0.137087	0.0685435	−	0.997648i	$-0.478165\pi$
$89$	1.29328	0.137087	0.0685435	+	0.997648i	$0.478165\pi$
$90$	0.135618	0.0142954
$91$	−2.17889	−0.228410
$92$	12.2593	1.27812
$93$	−5.43968	−0.564068
$94$	−0.246622	−0.0254372
$95$	−8.99195	−0.922554
$96$	−1.25510	−0.128098
$97$	−1.02897	−0.104476	−0.0522380	−	0.998635i	$-0.516635\pi$
$97$	−1.02897	−0.104476	−0.0522380	+	0.998635i	$0.516635\pi$
$98$	−0.105370	−0.0106440
$99$	2.67777	0.269126
$100$	6.64981	0.664981
$101$	9.67575	0.962773	0.481386	−	0.876508i	$-0.340133\pi$
$101$	9.67575	0.962773	0.481386	+	0.876508i	$0.340133\pi$
$102$	−0.0192684	−0.00190786
$103$	13.7740	1.35719	0.678597	−	0.734510i	$-0.262588\pi$
$103$	13.7740	1.35719	0.678597	+	0.734510i	$0.262588\pi$
$104$	−0.915813	−0.0898028
$105$	−1.28706	−0.125605
$106$	−1.36333	−0.132418
$107$	−12.0042	−1.16049	−0.580245	−	0.814442i	$-0.697043\pi$
$107$	−12.0042	−1.16049	−0.580245	+	0.814442i	$0.697043\pi$
$108$	−1.98890	−0.191382
$109$	17.8163	1.70649	0.853244	−	0.521512i	$-0.174632\pi$
$109$	17.8163	1.70649	0.853244	+	0.521512i	$0.174632\pi$
$110$	0.363155	0.0346255
$111$	7.15698	0.679311
$112$	3.93351	0.371681
$113$	7.91607	0.744681	0.372341	−	0.928096i	$-0.378555\pi$
$113$	7.91607	0.744681	0.372341	+	0.928096i	$0.378555\pi$
$114$	−0.736159	−0.0689476
$115$	7.93328	0.739782
$116$	−8.68012	−0.805929
$117$	−2.17889	−0.201439
$118$	0.657275	0.0605071
$119$	0.182864	0.0167631
$120$	−0.540968	−0.0493834
$121$	−3.82954	−0.348140
$122$	0.855536	0.0774565
$123$	2.47459	0.223126
$124$	10.8190	0.971571
$125$	10.7386	0.960488
$126$	−0.105370	−0.00938713
$127$	1.37269	0.121807	0.0609034	−	0.998144i	$-0.480602\pi$
$127$	1.37269	0.121807	0.0609034	+	0.998144i	$0.480602\pi$
$128$	3.32521	0.293910
$129$	−9.16115	−0.806594
$130$	−0.295498	−0.0259169
$131$	6.49809	0.567741	0.283870	−	0.958863i	$-0.408381\pi$
$131$	6.49809	0.567741	0.283870	+	0.958863i	$0.408381\pi$
$132$	−5.32581	−0.463553
$133$	6.98640	0.605798
$134$	0.376500	0.0325246
$135$	−1.28706	−0.110773
$136$	0.0768597	0.00659067
$137$	16.2780	1.39073	0.695364	−	0.718658i	$-0.255243\pi$
$137$	16.2780	1.39073	0.695364	+	0.718658i	$0.255243\pi$
$138$	0.649487	0.0552880
$139$	11.5195	0.977067	0.488534	−	0.872545i	$-0.337532\pi$
$139$	11.5195	0.977067	0.488534	+	0.872545i	$0.337532\pi$
$140$	2.55984	0.216346
$141$	2.34053	0.197108
$142$	0.356242	0.0298951
$143$	−5.83458	−0.487912
$144$	3.93351	0.327792
$145$	−5.61712	−0.466477
$146$	−1.22241	−0.101167
$147$	1.00000	0.0824786
$148$	−14.2345	−1.17007
$149$	−16.0629	−1.31592	−0.657960	−	0.753053i	$-0.728581\pi$
$149$	−16.0629	−1.31592	−0.657960	+	0.753053i	$0.728581\pi$
$150$	0.352302	0.0287653
$151$	6.61730	0.538508	0.269254	−	0.963069i	$-0.413223\pi$
$151$	6.61730	0.538508	0.269254	+	0.963069i	$0.413223\pi$
$152$	2.93646	0.238179
$153$	0.182864	0.0147837
$154$	−0.282158	−0.0227369
$155$	7.00121	0.562351
$156$	4.33359	0.346965
$157$	−16.2343	−1.29564	−0.647820	−	0.761793i	$-0.724319\pi$
$157$	−16.2343	−1.29564	−0.647820	+	0.761793i	$0.724319\pi$
$158$	−1.36746	−0.108789
$159$	12.9384	1.02608
$160$	1.61539	0.127708
$161$	−6.16386	−0.485780
$162$	−0.105370	−0.00827867
$163$	−13.2906	−1.04100	−0.520501	−	0.853861i	$-0.674255\pi$
$163$	−13.2906	−1.04100	−0.520501	+	0.853861i	$0.674255\pi$
$164$	−4.92171	−0.384321
$165$	−3.44647	−0.268307
$166$	−0.0646809	−0.00502021
$167$	17.9713	1.39066	0.695329	−	0.718691i	$-0.255259\pi$
$167$	17.9713	1.39066	0.695329	+	0.718691i	$0.255259\pi$
$168$	0.420311	0.0324277
$169$	−8.25243	−0.634802
$170$	0.0247997	0.00190205
$171$	6.98640	0.534263
$172$	18.2206	1.38931
$173$	14.4071	1.09535	0.547675	−	0.836691i	$-0.315513\pi$
$173$	14.4071	1.09535	0.547675	+	0.836691i	$0.315513\pi$
$174$	−0.459866	−0.0348624
$175$	−3.34347	−0.252742
$176$	10.5330	0.793957
$177$	−6.23777	−0.468859
$178$	−0.136273	−0.0102141
$179$	17.9465	1.34138	0.670690	−	0.741737i	$-0.265998\pi$
$179$	17.9465	1.34138	0.670690	+	0.741737i	$0.265998\pi$
$180$	2.55984	0.190799
$181$	0.487138	0.0362087	0.0181043	−	0.999836i	$-0.494237\pi$
$181$	0.487138	0.0362087	0.0181043	+	0.999836i	$0.494237\pi$
$182$	0.229591	0.0170184
$183$	−8.11932	−0.600198
$184$	−2.59074	−0.190992
$185$	−9.21150	−0.677243
$186$	0.573180	0.0420276
$187$	0.489668	0.0358081
$188$	−4.65508	−0.339506
$189$	1.00000	0.0727393
$190$	0.947484	0.0687377
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	−7.73476	−0.558208
$193$	1.14681	0.0825495	0.0412747	−	0.999148i	$-0.486858\pi$
$193$	1.14681	0.0825495	0.0412747	+	0.999148i	$0.486858\pi$
$194$	0.108423	0.00778430
$195$	2.80438	0.200825
$196$	−1.98890	−0.142064
$197$	−9.43348	−0.672108	−0.336054	−	0.941843i	$-0.609092\pi$
$197$	−9.43348	−0.672108	−0.336054	+	0.941843i	$0.609092\pi$
$198$	−0.282158	−0.0200521
$199$	16.3620	1.15987	0.579935	−	0.814663i	$-0.303078\pi$
$199$	16.3620	1.15987	0.579935	+	0.814663i	$0.303078\pi$
$200$	−1.40530	−0.0993694
$201$	−3.57311	−0.252028
$202$	−1.01954	−0.0717343
$203$	4.36429	0.306313
$204$	−0.363697	−0.0254639
$205$	−3.18496	−0.222447
$206$	−1.45137	−0.101122
$207$	−6.16386	−0.428418
$208$	−8.57069	−0.594270
$209$	18.7080	1.29406
$210$	0.135618	0.00935855
$211$	7.82536	0.538720	0.269360	−	0.963040i	$-0.413188\pi$
$211$	7.82536	0.538720	0.269360	+	0.963040i	$0.413188\pi$
$212$	−25.7332	−1.76736
$213$	−3.38085	−0.231652
$214$	1.26489	0.0864658
$215$	11.7910	0.804139
$216$	0.420311	0.0285986
$217$	−5.43968	−0.369269
$218$	−1.87730	−0.127147
$219$	11.6011	0.783929
$220$	6.85466	0.462141
$221$	−0.398441	−0.0268020
$222$	−0.754133	−0.0506141
$223$	14.0393	0.940142	0.470071	−	0.882629i	$-0.344228\pi$
$223$	14.0393	0.940142	0.470071	+	0.882629i	$0.344228\pi$
$224$	−1.25510	−0.0838597
$225$	−3.34347	−0.222898
$226$	−0.834119	−0.0554847
$227$	7.27280	0.482712	0.241356	−	0.970437i	$-0.422408\pi$
$227$	7.27280	0.482712	0.241356	+	0.970437i	$0.422408\pi$
$228$	−13.8952	−0.920234
$229$	14.2377	0.940853	0.470426	−	0.882439i	$-0.344100\pi$
$229$	14.2377	0.940853	0.470426	+	0.882439i	$0.344100\pi$
$230$	−0.835932	−0.0551197
$231$	2.67777	0.176184
$232$	1.83436	0.120432
$233$	25.0706	1.64243	0.821213	−	0.570621i	$-0.193298\pi$
$233$	25.0706	1.64243	0.821213	+	0.570621i	$0.193298\pi$
$234$	0.229591	0.0150088
$235$	−3.01242	−0.196508
$236$	12.4063	0.807580
$237$	12.9776	0.842988
$238$	−0.0192684	−0.00124899
$239$	25.8283	1.67069	0.835347	−	0.549724i	$-0.185267\pi$
$239$	25.8283	1.67069	0.835347	+	0.549724i	$0.185267\pi$
$240$	−5.06268	−0.326794
$241$	−3.34346	−0.215371	−0.107686	−	0.994185i	$-0.534344\pi$
$241$	−3.34346	−0.215371	−0.107686	+	0.994185i	$0.534344\pi$
$242$	0.403519	0.0259392
$243$	1.00000	0.0641500
$244$	16.1485	1.03380
$245$	−1.28706	−0.0822275
$246$	−0.260748	−0.0166247
$247$	−15.2226	−0.968592
$248$	−2.28636	−0.145184
$249$	0.613844	0.0389008
$250$	−1.13153	−0.0715640
$251$	23.5381	1.48571	0.742856	−	0.669451i	$-0.233471\pi$
$251$	23.5381	1.48571	0.742856	+	0.669451i	$0.233471\pi$
$252$	−1.98890	−0.125289
$253$	−16.5054	−1.03769
$254$	−0.144641	−0.00907558
$255$	−0.235358	−0.0147387
$256$	15.1191	0.944947
$257$	−26.3492	−1.64362	−0.821808	−	0.569765i	$-0.807034\pi$
$257$	−26.3492	−1.64362	−0.821808	+	0.569765i	$0.807034\pi$
$258$	0.965313	0.0600977
$259$	7.15698	0.444713
$260$	−5.57761	−0.345909
$261$	4.36429	0.270143
$262$	−0.684705	−0.0423012
$263$	−19.7855	−1.22002	−0.610012	−	0.792392i	$-0.708835\pi$
$263$	−19.7855	−1.22002	−0.610012	+	0.792392i	$0.708835\pi$
$264$	1.12550	0.0692696
$265$	−16.6526	−1.02296
$266$	−0.736159	−0.0451368
$267$	1.29328	0.0791473
$268$	7.10655	0.434102
$269$	−5.26646	−0.321102	−0.160551	−	0.987028i	$-0.551327\pi$
$269$	−5.26646	−0.321102	−0.160551	+	0.987028i	$0.551327\pi$
$270$	0.135618	0.00825347
$271$	2.33908	0.142089	0.0710445	−	0.997473i	$-0.477367\pi$
$271$	2.33908	0.142089	0.0710445	+	0.997473i	$0.477367\pi$
$272$	0.719296	0.0436137
$273$	−2.17889	−0.131873
$274$	−1.71522	−0.103620
$275$	−8.95304	−0.539888
$276$	12.2593	0.737922
$277$	14.6041	0.877476	0.438738	−	0.898615i	$-0.355426\pi$
$277$	14.6041	0.877476	0.438738	+	0.898615i	$0.355426\pi$
$278$	−1.21381	−0.0727994
$279$	−5.43968	−0.325665
$280$	−0.540968	−0.0323290
$281$	11.8611	0.707576	0.353788	−	0.935326i	$-0.384893\pi$
$281$	11.8611	0.707576	0.353788	+	0.935326i	$0.384893\pi$
$282$	−0.246622	−0.0146862
$283$	−16.9826	−1.00951	−0.504755	−	0.863263i	$-0.668417\pi$
$283$	−16.9826	−1.00951	−0.504755	+	0.863263i	$0.668417\pi$
$284$	6.72417	0.399006
$285$	−8.99195	−0.532637
$286$	0.614791	0.0363534
$287$	2.47459	0.146071
$288$	−1.25510	−0.0739573
$289$	−16.9666	−0.998033
$290$	0.591878	0.0347563
$291$	−1.02897	−0.0603192
$292$	−23.0734	−1.35027
$293$	8.15198	0.476244	0.238122	−	0.971235i	$-0.423468\pi$
$293$	8.15198	0.476244	0.238122	+	0.971235i	$0.423468\pi$
$294$	−0.105370	−0.00614532
$295$	8.02841	0.467432
$296$	3.00816	0.174846
$297$	2.67777	0.155380
$298$	1.69255	0.0980467
$299$	13.4304	0.776699
$300$	6.64981	0.383927
$301$	−9.16115	−0.528040
$302$	−0.697267	−0.0401232
$303$	9.67575	0.555857
$304$	27.4810	1.57615
$305$	10.4501	0.598371
$306$	−0.0192684	−0.00110150
$307$	−6.01745	−0.343434	−0.171717	−	0.985146i	$-0.554931\pi$
$307$	−6.01745	−0.343434	−0.171717	+	0.985146i	$0.554931\pi$
$308$	−5.32581	−0.303466
$309$	13.7740	0.783577
$310$	−0.737720	−0.0418997
$311$	19.7311	1.11885	0.559424	−	0.828882i	$-0.311022\pi$
$311$	19.7311	1.11885	0.559424	+	0.828882i	$0.311022\pi$
$312$	−0.915813	−0.0518477
$313$	−8.76906	−0.495657	−0.247828	−	0.968804i	$-0.579717\pi$
$313$	−8.76906	−0.495657	−0.247828	+	0.968804i	$0.579717\pi$
$314$	1.71062	0.0965357
$315$	−1.28706	−0.0725179
$316$	−25.8112	−1.45199
$317$	−9.36099	−0.525766	−0.262883	−	0.964828i	$-0.584673\pi$
$317$	−9.36099	−0.525766	−0.262883	+	0.964828i	$0.584673\pi$
$318$	−1.36333	−0.0764515
$319$	11.6866	0.654322
$320$	9.95514	0.556509
$321$	−12.0042	−0.670009
$322$	0.649487	0.0361945
$323$	1.27756	0.0710854
$324$	−1.98890	−0.110494
$325$	7.28505	0.404102
$326$	1.40044	0.0775630
$327$	17.8163	0.985241
$328$	1.04010	0.0574298
$329$	2.34053	0.129038
$330$	0.363155	0.0199910
$331$	−3.42752	−0.188393	−0.0941967	−	0.995554i	$-0.530028\pi$
$331$	−3.42752	−0.188393	−0.0941967	+	0.995554i	$0.530028\pi$
$332$	−1.22087	−0.0670041
$333$	7.15698	0.392200
$334$	−1.89364	−0.103615
$335$	4.59883	0.251261
$336$	3.93351	0.214590
$337$	−5.50712	−0.299992	−0.149996	−	0.988687i	$-0.547926\pi$
$337$	−5.50712	−0.299992	−0.149996	+	0.988687i	$0.547926\pi$
$338$	0.869561	0.0472979
$339$	7.91607	0.429942
$340$	0.468102	0.0253864
$341$	−14.5662	−0.788805
$342$	−0.736159	−0.0398069
$343$	1.00000	0.0539949
$344$	−3.85053	−0.207607
$345$	7.93328	0.427114
$346$	−1.51808	−0.0816123
$347$	3.99589	0.214510	0.107255	−	0.994232i	$-0.465794\pi$
$347$	3.99589	0.214510	0.107255	+	0.994232i	$0.465794\pi$
$348$	−8.68012	−0.465303
$349$	−29.6609	−1.58771	−0.793857	−	0.608105i	$-0.791930\pi$
$349$	−29.6609	−1.58771	−0.793857	+	0.608105i	$0.791930\pi$
$350$	0.352302	0.0188313
$351$	−2.17889	−0.116301
$352$	−3.36086	−0.179135
$353$	28.0581	1.49338	0.746690	−	0.665173i	$-0.231642\pi$
$353$	28.0581	1.49338	0.746690	+	0.665173i	$0.231642\pi$
$354$	0.657275	0.0349338
$355$	4.35138	0.230947
$356$	−2.57219	−0.136326
$357$	0.182864	0.00967818
$358$	−1.89102	−0.0999437
$359$	12.9795	0.685031	0.342516	−	0.939512i	$-0.388721\pi$
$359$	12.9795	0.685031	0.342516	+	0.939512i	$0.388721\pi$
$360$	−0.540968	−0.0285115
$361$	29.8098	1.56894
$362$	−0.0513299	−0.00269784
$363$	−3.82954	−0.200999
$364$	4.33359	0.227142
$365$	−14.9313	−0.781542
$366$	0.855536	0.0447196
$367$	−22.0814	−1.15264	−0.576320	−	0.817224i	$-0.695512\pi$
$367$	−22.0814	−1.15264	−0.576320	+	0.817224i	$0.695512\pi$
$368$	−24.2456	−1.26389
$369$	2.47459	0.128822
$370$	0.970618	0.0504600
$371$	12.9384	0.671729
$372$	10.8190	0.560937
$373$	4.78544	0.247781	0.123890	−	0.992296i	$-0.460463\pi$
$373$	4.78544	0.247781	0.123890	+	0.992296i	$0.460463\pi$
$374$	−0.0515964	−0.00266799
$375$	10.7386	0.554538
$376$	0.983752	0.0507331
$377$	−9.50932	−0.489755
$378$	−0.105370	−0.00541966
$379$	−4.88297	−0.250821	−0.125411	−	0.992105i	$-0.540025\pi$
$379$	−4.88297	−0.250821	−0.125411	+	0.992105i	$0.540025\pi$
$380$	17.8841	0.917433
$381$	1.37269	0.0703252
$382$	−0.105370	−0.00539121
$383$	−12.9495	−0.661688	−0.330844	−	0.943686i	$-0.607333\pi$
$383$	−12.9495	−0.661688	−0.330844	+	0.943686i	$0.607333\pi$
$384$	3.32521	0.169689
$385$	−3.44647	−0.175648
$386$	−0.120840	−0.00615060
$387$	−9.16115	−0.465687
$388$	2.04651	0.103896
$389$	33.4036	1.69363	0.846815	−	0.531887i	$-0.178517\pi$
$389$	33.4036	1.69363	0.846815	+	0.531887i	$0.178517\pi$
$390$	−0.295498	−0.0149631
$391$	−1.12715	−0.0570023
$392$	0.420311	0.0212289
$393$	6.49809	0.327785
$394$	0.994009	0.0500774
$395$	−16.7031	−0.840422
$396$	−5.32581	−0.267632
$397$	31.7776	1.59487	0.797435	−	0.603405i	$-0.206190\pi$
$397$	31.7776	1.59487	0.797435	+	0.603405i	$0.206190\pi$
$398$	−1.72407	−0.0864196
$399$	6.98640	0.349758
$400$	−13.1515	−0.657577
$401$	−14.9239	−0.745265	−0.372632	−	0.927979i	$-0.621545\pi$
$401$	−14.9239	−0.745265	−0.372632	+	0.927979i	$0.621545\pi$
$402$	0.376500	0.0187781
$403$	11.8525	0.590414
$404$	−19.2441	−0.957428
$405$	−1.28706	−0.0639547
$406$	−0.459866	−0.0228228
$407$	19.1648	0.949962
$408$	0.0768597	0.00380512
$409$	−39.7352	−1.96478	−0.982389	−	0.186845i	$-0.940174\pi$
$409$	−39.7352	−1.96478	−0.982389	+	0.186845i	$0.940174\pi$
$410$	0.335600	0.0165741
$411$	16.2780	0.802937
$412$	−27.3951	−1.34966
$413$	−6.23777	−0.306940
$414$	0.649487	0.0319206
$415$	−0.790057	−0.0387824
$416$	2.73472	0.134081
$417$	11.5195	0.564110
$418$	−1.97127	−0.0964178
$419$	−29.0666	−1.42000	−0.709999	−	0.704203i	$-0.751305\pi$
$419$	−29.0666	−1.42000	−0.709999	+	0.704203i	$0.751305\pi$
$420$	2.55984	0.124907
$421$	−27.2002	−1.32566	−0.662828	−	0.748772i	$-0.730644\pi$
$421$	−27.2002	−1.32566	−0.662828	+	0.748772i	$0.730644\pi$
$422$	−0.824560	−0.0401390
$423$	2.34053	0.113801
$424$	5.43816	0.264101
$425$	−0.611399	−0.0296572
$426$	0.356242	0.0172600
$427$	−8.11932	−0.392922
$428$	23.8751	1.15405
$429$	−5.83458	−0.281696
$430$	−1.24242	−0.0599148
$431$	38.5512	1.85695	0.928473	−	0.371399i	$-0.121122\pi$
$431$	38.5512	1.85695	0.928473	+	0.371399i	$0.121122\pi$
$432$	3.93351	0.189251
$433$	7.37841	0.354584	0.177292	−	0.984158i	$-0.443266\pi$
$433$	7.37841	0.354584	0.177292	+	0.984158i	$0.443266\pi$
$434$	0.573180	0.0275135
$435$	−5.61712	−0.269320
$436$	−35.4347	−1.69701
$437$	−43.0632	−2.05999
$438$	−1.22241	−0.0584090
$439$	−14.8645	−0.709446	−0.354723	−	0.934971i	$-0.615425\pi$
$439$	−14.8645	−0.709446	−0.354723	+	0.934971i	$0.615425\pi$
$440$	−1.44859	−0.0690587
$441$	1.00000	0.0476190
$442$	0.0419838	0.00199697
$443$	−31.4640	−1.49490	−0.747449	−	0.664319i	$-0.768722\pi$
$443$	−31.4640	−1.49490	−0.747449	+	0.664319i	$0.768722\pi$
$444$	−14.2345	−0.675539
$445$	−1.66453	−0.0789063
$446$	−1.47933	−0.0700481
$447$	−16.0629	−0.759747
$448$	−7.73476	−0.365433
$449$	−19.0621	−0.899596	−0.449798	−	0.893130i	$-0.648504\pi$
$449$	−19.0621	−0.899596	−0.449798	+	0.893130i	$0.648504\pi$
$450$	0.352302	0.0166077
$451$	6.62639	0.312025
$452$	−15.7443	−0.740547
$453$	6.61730	0.310908
$454$	−0.766337	−0.0359660
$455$	2.80438	0.131471
$456$	2.93646	0.137512
$457$	−39.9327	−1.86797	−0.933986	−	0.357309i	$-0.883694\pi$
$457$	−39.9327	−1.86797	−0.933986	+	0.357309i	$0.883694\pi$
$458$	−1.50023	−0.0701011
$459$	0.182864	0.00853535
$460$	−15.7785	−0.735676
$461$	−31.6992	−1.47638	−0.738190	−	0.674593i	$-0.764319\pi$
$461$	−31.6992	−1.47638	−0.738190	+	0.674593i	$0.764319\pi$
$462$	−0.282158	−0.0131272
$463$	−10.6580	−0.495318	−0.247659	−	0.968847i	$-0.579661\pi$
$463$	−10.6580	−0.495318	−0.247659	+	0.968847i	$0.579661\pi$
$464$	17.1670	0.796956
$465$	7.00121	0.324674
$466$	−2.64169	−0.122374
$467$	12.1233	0.561002	0.280501	−	0.959854i	$-0.409499\pi$
$467$	12.1233	0.561002	0.280501	+	0.959854i	$0.409499\pi$
$468$	4.33359	0.200320
$469$	−3.57311	−0.164991
$470$	0.317419	0.0146414
$471$	−16.2343	−0.748039
$472$	−2.62180	−0.120678
$473$	−24.5315	−1.12796
$474$	−1.36746	−0.0628094
$475$	−23.3588	−1.07177
$476$	−0.363697	−0.0166700
$477$	12.9384	0.592410
$478$	−2.72153	−0.124480
$479$	31.3870	1.43411	0.717055	−	0.697017i	$-0.245490\pi$
$479$	31.3870	1.43411	0.717055	+	0.697017i	$0.245490\pi$
$480$	1.61539	0.0737322
$481$	−15.5943	−0.711039
$482$	0.352302	0.0160469
$483$	−6.16386	−0.280465
$484$	7.61655	0.346207
$485$	1.32435	0.0601356
$486$	−0.105370	−0.00477969
$487$	−18.8563	−0.854462	−0.427231	−	0.904143i	$-0.640511\pi$
$487$	−18.8563	−0.854462	−0.427231	+	0.904143i	$0.640511\pi$
$488$	−3.41264	−0.154483
$489$	−13.2906	−0.601022
$490$	0.135618	0.00612661
$491$	−36.7677	−1.65930	−0.829652	−	0.558281i	$-0.811461\pi$
$491$	−36.7677	−1.65930	−0.829652	+	0.558281i	$0.811461\pi$
$492$	−4.92171	−0.221888
$493$	0.798071	0.0359433
$494$	1.60401	0.0721679
$495$	−3.44647	−0.154907
$496$	−21.3970	−0.960754
$497$	−3.38085	−0.151652
$498$	−0.0646809	−0.00289842
$499$	8.37001	0.374693	0.187346	−	0.982294i	$-0.440011\pi$
$499$	8.37001	0.374693	0.187346	+	0.982294i	$0.440011\pi$
$500$	−21.3579	−0.955155
$501$	17.9713	0.802897
$502$	−2.48022	−0.110698
$503$	11.5008	0.512796	0.256398	−	0.966571i	$-0.417464\pi$
$503$	11.5008	0.512796	0.256398	+	0.966571i	$0.417464\pi$
$504$	0.420311	0.0187221
$505$	−12.4533	−0.554165
$506$	1.73918	0.0773160
$507$	−8.25243	−0.366503
$508$	−2.73014	−0.121131
$509$	5.40995	0.239792	0.119896	−	0.992786i	$-0.461744\pi$
$509$	5.40995	0.239792	0.119896	+	0.992786i	$0.461744\pi$
$510$	0.0247997	0.00109815
$511$	11.6011	0.513202
$512$	−8.24352	−0.364316
$513$	6.98640	0.308457
$514$	2.77642	0.122463
$515$	−17.7281	−0.781192
$516$	18.2206	0.802116
$517$	6.26741	0.275640
$518$	−0.754133	−0.0331347
$519$	14.4071	0.632400
$520$	1.17871	0.0516899
$521$	29.9646	1.31277	0.656386	−	0.754425i	$-0.272084\pi$
$521$	29.9646	1.31277	0.656386	+	0.754425i	$0.272084\pi$
$522$	−0.459866	−0.0201278
$523$	4.61468	0.201786	0.100893	−	0.994897i	$-0.467830\pi$
$523$	4.61468	0.201786	0.100893	+	0.994897i	$0.467830\pi$
$524$	−12.9240	−0.564589
$525$	−3.34347	−0.145921
$526$	2.08480	0.0909016
$527$	−0.994720	−0.0433307
$528$	10.5330	0.458391
$529$	14.9931	0.651876
$530$	1.75469	0.0762187
$531$	−6.23777	−0.270696
$532$	−13.8952	−0.602435
$533$	−5.39187	−0.233548
$534$	−0.136273	−0.00589711
$535$	15.4502	0.667969
$536$	−1.50182	−0.0648687
$537$	17.9465	0.774447
$538$	0.554928	0.0239247
$539$	2.67777	0.115340
$540$	2.55984	0.110158
$541$	35.4190	1.52278	0.761391	−	0.648293i	$-0.224517\pi$
$541$	35.4190	1.52278	0.761391	+	0.648293i	$0.224517\pi$
$542$	−0.246470	−0.0105868
$543$	0.487138	0.0209051
$544$	−0.229512	−0.00984024
$545$	−22.9307	−0.982242
$546$	0.229591	0.00982557
$547$	−14.1742	−0.606044	−0.303022	−	0.952984i	$-0.597996\pi$
$547$	−14.1742	−0.606044	−0.303022	+	0.952984i	$0.597996\pi$
$548$	−32.3754	−1.38301
$549$	−8.11932	−0.346524
$550$	0.943384	0.0402260
$551$	30.4907	1.29895
$552$	−2.59074	−0.110269
$553$	12.9776	0.551865
$554$	−1.53884	−0.0653790
$555$	−9.21150	−0.391006
$556$	−22.9110	−0.971643
$557$	28.9742	1.22768	0.613838	−	0.789432i	$-0.289625\pi$
$557$	28.9742	1.22768	0.613838	+	0.789432i	$0.289625\pi$
$558$	0.573180	0.0242647
$559$	19.9612	0.844267
$560$	−5.06268	−0.213937
$561$	0.489668	0.0206738
$562$	−1.24981	−0.0527201
$563$	13.7865	0.581030	0.290515	−	0.956870i	$-0.406173\pi$
$563$	13.7865	0.581030	0.290515	+	0.956870i	$0.406173\pi$
$564$	−4.65508	−0.196014
$565$	−10.1885	−0.428633
$566$	1.78946	0.0752166
$567$	1.00000	0.0419961
$568$	−1.42101	−0.0596243
$569$	−22.8063	−0.956090	−0.478045	−	0.878335i	$-0.658654\pi$
$569$	−22.8063	−0.956090	−0.478045	+	0.878335i	$0.658654\pi$
$570$	0.947484	0.0396857
$571$	33.9459	1.42059	0.710296	−	0.703904i	$-0.248561\pi$
$571$	33.9459	1.42059	0.710296	+	0.703904i	$0.248561\pi$
$572$	11.6044	0.485203
$573$	1.00000	0.0417756
$574$	−0.260748	−0.0108834
$575$	20.6086	0.859440
$576$	−7.73476	−0.322282
$577$	−31.8307	−1.32513	−0.662564	−	0.749005i	$-0.730532\pi$
$577$	−31.8307	−1.32513	−0.662564	+	0.749005i	$0.730532\pi$
$578$	1.78777	0.0743615
$579$	1.14681	0.0476600
$580$	11.1719	0.463887
$581$	0.613844	0.0254665
$582$	0.108423	0.00449427
$583$	34.6461	1.43490
$584$	4.87607	0.201773
$585$	2.80438	0.115947
$586$	−0.858976	−0.0354840
$587$	−41.8993	−1.72937	−0.864684	−	0.502315i	$-0.832482\pi$
$587$	−41.8993	−1.72937	−0.864684	+	0.502315i	$0.832482\pi$
$588$	−1.98890	−0.0820207
$589$	−38.0038	−1.56592
$590$	−0.845955	−0.0348274
$591$	−9.43348	−0.388042
$592$	28.1520	1.15704
$593$	30.0061	1.23220	0.616101	−	0.787667i	$-0.288711\pi$
$593$	30.0061	1.23220	0.616101	+	0.787667i	$0.288711\pi$
$594$	−0.282158	−0.0115771
$595$	−0.235358	−0.00964872
$596$	31.9474	1.30862
$597$	16.3620	0.669651
$598$	−1.41516	−0.0578703
$599$	−10.0175	−0.409305	−0.204653	−	0.978835i	$-0.565606\pi$
$599$	−10.0175	−0.409305	−0.204653	+	0.978835i	$0.565606\pi$
$600$	−1.40530	−0.0573710
$601$	25.6645	1.04688	0.523439	−	0.852063i	$-0.324649\pi$
$601$	25.6645	1.04688	0.523439	+	0.852063i	$0.324649\pi$
$602$	0.965313	0.0393432
$603$	−3.57311	−0.145508
$604$	−13.1611	−0.535519
$605$	4.92886	0.200387
$606$	−1.01954	−0.0414158
$607$	−26.8284	−1.08893	−0.544466	−	0.838783i	$-0.683268\pi$
$607$	−26.8284	−1.08893	−0.544466	+	0.838783i	$0.683268\pi$
$608$	−8.76861	−0.355614
$609$	4.36429	0.176850
$610$	−1.10113	−0.0445834
$611$	−5.09977	−0.206314
$612$	−0.363697	−0.0147016
$613$	2.12381	0.0857799	0.0428899	−	0.999080i	$-0.486344\pi$
$613$	2.12381	0.0857799	0.0428899	+	0.999080i	$0.486344\pi$
$614$	0.634060	0.0255886
$615$	−3.18496	−0.128430
$616$	1.12550	0.0453476
$617$	−30.3430	−1.22156	−0.610782	−	0.791799i	$-0.709145\pi$
$617$	−30.3430	−1.22156	−0.610782	+	0.791799i	$0.709145\pi$
$618$	−1.45137	−0.0583828
$619$	−10.4844	−0.421402	−0.210701	−	0.977551i	$-0.567575\pi$
$619$	−10.4844	−0.421402	−0.210701	+	0.977551i	$0.567575\pi$
$620$	−13.9247	−0.559229
$621$	−6.16386	−0.247347
$622$	−2.07907	−0.0833632
$623$	1.29328	0.0518140
$624$	−8.57069	−0.343102
$625$	2.89608	0.115843
$626$	0.923998	0.0369304
$627$	18.7080	0.747125
$628$	32.2884	1.28845
$629$	1.30875	0.0521834
$630$	0.135618	0.00540316
$631$	22.6523	0.901773	0.450886	−	0.892581i	$-0.351108\pi$
$631$	22.6523	0.901773	0.450886	+	0.892581i	$0.351108\pi$
$632$	5.45465	0.216974
$633$	7.82536	0.311030
$634$	0.986370	0.0391738
$635$	−1.76674	−0.0701111
$636$	−25.7332	−1.02039
$637$	−2.17889	−0.0863309
$638$	−1.23142	−0.0487523
$639$	−3.38085	−0.133745
$640$	−4.27976	−0.169172
$641$	28.1578	1.11216	0.556082	−	0.831127i	$-0.312304\pi$
$641$	28.1578	1.11216	0.556082	+	0.831127i	$0.312304\pi$
$642$	1.26489	0.0499211
$643$	16.2313	0.640100	0.320050	−	0.947401i	$-0.396300\pi$
$643$	16.2313	0.640100	0.320050	+	0.947401i	$0.396300\pi$
$644$	12.2593	0.483083
$645$	11.7910	0.464270
$646$	−0.134617	−0.00529643
$647$	40.8302	1.60520	0.802601	−	0.596516i	$-0.203449\pi$
$647$	40.8302	1.60520	0.802601	+	0.596516i	$0.203449\pi$
$648$	0.420311	0.0165114
$649$	−16.7033	−0.655663
$650$	−0.767628	−0.0301088
$651$	−5.43968	−0.213198
$652$	26.4337	1.03522
$653$	9.91706	0.388084	0.194042	−	0.980993i	$-0.437840\pi$
$653$	9.91706	0.388084	0.194042	+	0.980993i	$0.437840\pi$
$654$	−1.87730	−0.0734084
$655$	−8.36346	−0.326787
$656$	9.73382	0.380042
$657$	11.6011	0.452601
$658$	−0.246622	−0.00961434
$659$	11.7798	0.458876	0.229438	−	0.973323i	$-0.426311\pi$
$659$	11.7798	0.458876	0.229438	+	0.973323i	$0.426311\pi$
$660$	6.85466	0.266817
$661$	20.6934	0.804878	0.402439	−	0.915447i	$-0.368163\pi$
$661$	20.6934	0.804878	0.402439	+	0.915447i	$0.368163\pi$
$662$	0.361159	0.0140368
$663$	−0.398441	−0.0154742
$664$	0.258006	0.0100126
$665$	−8.99195	−0.348693
$666$	−0.754133	−0.0292221
$667$	−26.9009	−1.04161
$668$	−35.7430	−1.38294
$669$	14.0393	0.542791
$670$	−0.484580	−0.0187209
$671$	−21.7417	−0.839329
$672$	−1.25510	−0.0484164
$673$	29.7379	1.14631	0.573155	−	0.819447i	$-0.305719\pi$
$673$	29.7379	1.14631	0.573155	+	0.819447i	$0.305719\pi$
$674$	0.580287	0.0223518
$675$	−3.34347	−0.128690
$676$	16.4132	0.631278
$677$	12.8820	0.495097	0.247549	−	0.968875i	$-0.420375\pi$
$677$	12.8820	0.495097	0.247549	+	0.968875i	$0.420375\pi$
$678$	−0.834119	−0.0320341
$679$	−1.02897	−0.0394882
$680$	−0.0989234	−0.00379354
$681$	7.27280	0.278694
$682$	1.53485	0.0587723
$683$	−28.5447	−1.09223	−0.546116	−	0.837710i	$-0.683894\pi$
$683$	−28.5447	−1.09223	−0.546116	+	0.837710i	$0.683894\pi$
$684$	−13.8952	−0.531297
$685$	−20.9509	−0.800492
$686$	−0.105370	−0.00402306
$687$	14.2377	0.543202
$688$	−36.0354	−1.37384
$689$	−28.1914	−1.07401
$690$	−0.835932	−0.0318234
$691$	−27.2854	−1.03799	−0.518993	−	0.854779i	$-0.673693\pi$
$691$	−27.2854	−1.03799	−0.518993	+	0.854779i	$0.673693\pi$
$692$	−28.6542	−1.08927
$693$	2.67777	0.101720
$694$	−0.421048	−0.0159828
$695$	−14.8263	−0.562393
$696$	1.83436	0.0695312
$697$	0.452513	0.0171402
$698$	3.12538	0.118297
$699$	25.0706	0.948255
$700$	6.64981	0.251339
$701$	−0.616926	−0.0233010	−0.0116505	−	0.999932i	$-0.503709\pi$
$701$	−0.616926	−0.0233010	−0.0116505	+	0.999932i	$0.503709\pi$
$702$	0.229591	0.00866534
$703$	50.0015	1.88584
$704$	−20.7119	−0.780610
$705$	−3.01242	−0.113454
$706$	−2.95648	−0.111269
$707$	9.67575	0.363894
$708$	12.4063	0.466256
$709$	28.1480	1.05712	0.528561	−	0.848895i	$-0.322732\pi$
$709$	28.1480	1.05712	0.528561	+	0.848895i	$0.322732\pi$
$710$	−0.458506	−0.0172074
$711$	12.9776	0.486699
$712$	0.543579	0.0203715
$713$	33.5294	1.25569
$714$	−0.0192684	−0.000721102 0
$715$	7.50948	0.280839
$716$	−35.6936	−1.33393
$717$	25.8283	0.964575
$718$	−1.36765	−0.0510403
$719$	−2.30071	−0.0858018	−0.0429009	−	0.999079i	$-0.513660\pi$
$719$	−2.30071	−0.0858018	−0.0429009	+	0.999079i	$0.513660\pi$
$720$	−5.06268	−0.188675
$721$	13.7740	0.512971
$722$	−3.14107	−0.116898
$723$	−3.34346	−0.124345
$724$	−0.968868	−0.0360077
$725$	−14.5918	−0.541928
$726$	0.403519	0.0149760
$727$	−36.9329	−1.36977	−0.684883	−	0.728653i	$-0.740147\pi$
$727$	−36.9329	−1.36977	−0.684883	+	0.728653i	$0.740147\pi$
$728$	−0.915813	−0.0339423
$729$	1.00000	0.0370370
$730$	1.57332	0.0582312
$731$	−1.67524	−0.0619611
$732$	16.1485	0.596866
$733$	−39.7068	−1.46660	−0.733301	−	0.679904i	$-0.762021\pi$
$733$	−39.7068	−1.46660	−0.733301	+	0.679904i	$0.762021\pi$
$734$	2.32672	0.0858810
$735$	−1.28706	−0.0474741
$736$	7.73624	0.285162
$737$	−9.56798	−0.352441
$738$	−0.260748	−0.00959828
$739$	−50.9193	−1.87310	−0.936548	−	0.350540i	$-0.885998\pi$
$739$	−50.9193	−1.87310	−0.936548	+	0.350540i	$0.885998\pi$
$740$	18.3207	0.673483
$741$	−15.2226	−0.559217
$742$	−1.36333	−0.0500492
$743$	27.2139	0.998381	0.499190	−	0.866492i	$-0.333631\pi$
$743$	27.2139	0.998381	0.499190	+	0.866492i	$0.333631\pi$
$744$	−2.28636	−0.0838219
$745$	20.6739	0.757434
$746$	−0.504243	−0.0184617
$747$	0.613844	0.0224594
$748$	−0.973899	−0.0356093
$749$	−12.0042	−0.438624
$750$	−1.13153	−0.0413175
$751$	−29.6640	−1.08246	−0.541228	−	0.840876i	$-0.682040\pi$
$751$	−29.6640	−1.08246	−0.541228	+	0.840876i	$0.682040\pi$
$752$	9.20650	0.335726
$753$	23.5381	0.857776
$754$	1.00200	0.0364907
$755$	−8.51689	−0.309961
$756$	−1.98890	−0.0723355
$757$	−17.0266	−0.618843	−0.309421	−	0.950925i	$-0.600135\pi$
$757$	−17.0266	−0.618843	−0.309421	+	0.950925i	$0.600135\pi$
$758$	0.514519	0.0186882
$759$	−16.5054	−0.599108
$760$	−3.77942	−0.137094
$761$	22.5132	0.816103	0.408051	−	0.912959i	$-0.366208\pi$
$761$	22.5132	0.816103	0.408051	+	0.912959i	$0.366208\pi$
$762$	−0.144641	−0.00523979
$763$	17.8163	0.644992
$764$	−1.98890	−0.0719558
$765$	−0.235358	−0.00850937
$766$	1.36449	0.0493011
$767$	13.5914	0.490758
$768$	15.1191	0.545565
$769$	39.6480	1.42974	0.714872	−	0.699255i	$-0.246485\pi$
$769$	39.6480	1.42974	0.714872	+	0.699255i	$0.246485\pi$
$770$	0.363155	0.0130872
$771$	−26.3492	−0.948942
$772$	−2.28090	−0.0820912
$773$	27.7809	0.999211	0.499606	−	0.866253i	$-0.333478\pi$
$773$	27.7809	0.999211	0.499606	+	0.866253i	$0.333478\pi$
$774$	0.965313	0.0346974
$775$	18.1874	0.653310
$776$	−0.432487	−0.0155254
$777$	7.15698	0.256755
$778$	−3.51975	−0.126189
$779$	17.2885	0.619424
$780$	−5.57761	−0.199711
$781$	−9.05316	−0.323947
$782$	0.118768	0.00424713
$783$	4.36429	0.155967
$784$	3.93351	0.140482
$785$	20.8946	0.745761
$786$	−0.684705	−0.0244226
$787$	−14.5635	−0.519133	−0.259566	−	0.965725i	$-0.583580\pi$
$787$	−14.5635	−0.519133	−0.259566	+	0.965725i	$0.583580\pi$
$788$	18.7622	0.668377
$789$	−19.7855	−0.704381
$790$	1.76001	0.0626182
$791$	7.91607	0.281463
$792$	1.12550	0.0399928
$793$	17.6911	0.628231
$794$	−3.34841	−0.118831
$795$	−16.6526	−0.590606
$796$	−32.5423	−1.15343
$797$	−6.14350	−0.217614	−0.108807	−	0.994063i	$-0.534703\pi$
$797$	−6.14350	−0.217614	−0.108807	+	0.994063i	$0.534703\pi$
$798$	−0.736159	−0.0260597
$799$	0.427999	0.0151415
$800$	4.19637	0.148364
$801$	1.29328	0.0456957
$802$	1.57254	0.0555282
$803$	31.0651	1.09626
$804$	7.10655	0.250629
$805$	7.93328	0.279611
$806$	−1.24890	−0.0439906
$807$	−5.26646	−0.185388
$808$	4.06683	0.143070
$809$	32.9739	1.15930	0.579650	−	0.814866i	$-0.303189\pi$
$809$	32.9739	1.15930	0.579650	+	0.814866i	$0.303189\pi$
$810$	0.135618	0.00476514
$811$	−46.9315	−1.64799	−0.823994	−	0.566598i	$-0.808259\pi$
$811$	−46.9315	−1.64799	−0.823994	+	0.566598i	$0.808259\pi$
$812$	−8.68012	−0.304613
$813$	2.33908	0.0820351
$814$	−2.01940	−0.0707798
$815$	17.1059	0.599193
$816$	0.719296	0.0251804
$817$	−64.0034	−2.23920
$818$	4.18691	0.146392
$819$	−2.17889	−0.0761367
$820$	6.33456	0.221212
$821$	16.9422	0.591287	0.295644	−	0.955298i	$-0.404466\pi$
$821$	16.9422	0.591287	0.295644	+	0.955298i	$0.404466\pi$
$822$	−1.71522	−0.0598252
$823$	−22.2124	−0.774276	−0.387138	−	0.922022i	$-0.626536\pi$
$823$	−22.2124	−0.774276	−0.387138	+	0.922022i	$0.626536\pi$
$824$	5.78938	0.201682
$825$	−8.95304	−0.311705
$826$	0.657275	0.0228695
$827$	−2.98368	−0.103753	−0.0518763	−	0.998654i	$-0.516520\pi$
$827$	−2.98368	−0.103753	−0.0518763	+	0.998654i	$0.516520\pi$
$828$	12.2593	0.426039
$829$	−40.8630	−1.41923	−0.709615	−	0.704590i	$-0.751131\pi$
$829$	−40.8630	−1.41923	−0.709615	+	0.704590i	$0.751131\pi$
$830$	0.0832485	0.00288960
$831$	14.6041	0.506611
$832$	16.8532	0.584280
$833$	0.182864	0.00633586
$834$	−1.21381	−0.0420307
$835$	−23.1302	−0.800453
$836$	−37.2083	−1.28687
$837$	−5.43968	−0.188023
$838$	3.06276	0.105801
$839$	−18.5608	−0.640790	−0.320395	−	0.947284i	$-0.603816\pi$
$839$	−18.5608	−0.640790	−0.320395	+	0.947284i	$0.603816\pi$
$840$	−0.540968	−0.0186652
$841$	−9.95298	−0.343206
$842$	2.86609	0.0987720
$843$	11.8611	0.408519
$844$	−15.5638	−0.535729
$845$	10.6214	0.365387
$846$	−0.246622	−0.00847906
$847$	−3.82954	−0.131584
$848$	50.8934	1.74769
$849$	−16.9826	−0.582841
$850$	0.0644233	0.00220970
$851$	−44.1146	−1.51223
$852$	6.72417	0.230366
$853$	18.5522	0.635216	0.317608	−	0.948222i	$-0.397120\pi$
$853$	18.5522	0.635216	0.317608	+	0.948222i	$0.397120\pi$
$854$	0.855536	0.0292758
$855$	−8.99195	−0.307518
$856$	−5.04550	−0.172452
$857$	54.4861	1.86121	0.930605	−	0.366026i	$-0.119282\pi$
$857$	54.4861	1.86121	0.930605	+	0.366026i	$0.119282\pi$
$858$	0.614791	0.0209886
$859$	−42.8466	−1.46191	−0.730954	−	0.682427i	$-0.760925\pi$
$859$	−42.8466	−1.46191	−0.730954	+	0.682427i	$0.760925\pi$
$860$	−23.4511	−0.799674
$861$	2.47459	0.0843339
$862$	−4.06215	−0.138357
$863$	−11.2182	−0.381872	−0.190936	−	0.981603i	$-0.561152\pi$
$863$	−11.2182	−0.381872	−0.190936	+	0.981603i	$0.561152\pi$
$864$	−1.25510	−0.0426993
$865$	−18.5428	−0.630475
$866$	−0.777465	−0.0264193
$867$	−16.9666	−0.576215
$868$	10.8190	0.367219
$869$	34.7512	1.17885
$870$	0.591878	0.0200665
$871$	7.78543	0.263799
$872$	7.48837	0.253588
$873$	−1.02897	−0.0348253
$874$	4.53758	0.153486
$875$	10.7386	0.363030
$876$	−23.0734	−0.779577
$877$	−13.5462	−0.457422	−0.228711	−	0.973494i	$-0.573451\pi$
$877$	−13.5462	−0.457422	−0.228711	+	0.973494i	$0.573451\pi$
$878$	1.56628	0.0528594
$879$	8.15198	0.274959
$880$	−13.5567	−0.456996
$881$	−26.0063	−0.876176	−0.438088	−	0.898932i	$-0.644344\pi$
$881$	−26.0063	−0.876176	−0.438088	+	0.898932i	$0.644344\pi$
$882$	−0.105370	−0.00354800
$883$	18.5124	0.622993	0.311496	−	0.950247i	$-0.399170\pi$
$883$	18.5124	0.622993	0.311496	+	0.950247i	$0.399170\pi$
$884$	0.792458	0.0266532
$885$	8.02841	0.269872
$886$	3.31537	0.111382
$887$	5.34181	0.179360	0.0896802	−	0.995971i	$-0.471416\pi$
$887$	5.34181	0.179360	0.0896802	+	0.995971i	$0.471416\pi$
$888$	3.00816	0.100947
$889$	1.37269	0.0460386
$890$	0.175392	0.00587915
$891$	2.67777	0.0897087
$892$	−27.9227	−0.934923
$893$	16.3519	0.547195
$894$	1.69255	0.0566073
$895$	−23.0982	−0.772089
$896$	3.32521	0.111087
$897$	13.4304	0.448427
$898$	2.00858	0.0670271
$899$	−23.7403	−0.791784
$900$	6.64981	0.221660
$901$	2.36597	0.0788219
$902$	−0.698225	−0.0232483
$903$	−9.16115	−0.304864
$904$	3.32721	0.110661
$905$	−0.626978	−0.0208415
$906$	−0.697267	−0.0231651
$907$	0.0969074	0.00321776	0.00160888	−	0.999999i	$-0.499488\pi$
$907$	0.0969074	0.00321776	0.00160888	+	0.999999i	$0.499488\pi$
$908$	−14.4648	−0.480033
$909$	9.67575	0.320924
$910$	−0.295498	−0.00979566
$911$	−37.8099	−1.25270	−0.626349	−	0.779543i	$-0.715451\pi$
$911$	−37.8099	−1.25270	−0.626349	+	0.779543i	$0.715451\pi$
$912$	27.4810	0.909988
$913$	1.64373	0.0543997
$914$	4.20772	0.139179
$915$	10.4501	0.345469
$916$	−28.3173	−0.935630
$917$	6.49809	0.214586
$918$	−0.0192684	−0.000635952 0
$919$	−43.9396	−1.44943	−0.724717	−	0.689047i	$-0.758029\pi$
$919$	−43.9396	−1.44943	−0.724717	+	0.689047i	$0.758029\pi$
$920$	3.33445	0.109933
$921$	−6.01745	−0.198282
$922$	3.34016	0.110002
$923$	7.36652	0.242472
$924$	−5.32581	−0.175206
$925$	−23.9291	−0.786784
$926$	1.12303	0.0369052
$927$	13.7740	0.452398
$928$	−5.47761	−0.179811
$929$	−24.2601	−0.795948	−0.397974	−	0.917397i	$-0.630287\pi$
$929$	−24.2601	−0.795948	−0.397974	+	0.917397i	$0.630287\pi$
$930$	−0.737720	−0.0241908
$931$	6.98640	0.228970
$932$	−49.8628	−1.63331
$933$	19.7311	0.645967
$934$	−1.27744	−0.0417991
$935$	−0.630234	−0.0206109
$936$	−0.915813	−0.0299343
$937$	0.167529	0.00547294	0.00273647	−	0.999996i	$-0.499129\pi$
$937$	0.167529	0.00547294	0.00273647	+	0.999996i	$0.499129\pi$
$938$	0.376500	0.0122932
$939$	−8.76906	−0.286168
$940$	5.99138	0.195417
$941$	39.0007	1.27139	0.635694	−	0.771941i	$-0.280714\pi$
$941$	39.0007	1.27139	0.635694	+	0.771941i	$0.280714\pi$
$942$	1.71062	0.0557349
$943$	−15.2530	−0.496707
$944$	−24.5363	−0.798588
$945$	−1.28706	−0.0418682
$946$	2.58489	0.0840419
$947$	−53.2302	−1.72975	−0.864874	−	0.501989i	$-0.832602\pi$
$947$	−53.2302	−1.72975	−0.864874	+	0.501989i	$0.832602\pi$
$948$	−25.8112	−0.838308
$949$	−25.2775	−0.820543
$950$	2.46132	0.0798558
$951$	−9.36099	−0.303551
$952$	0.0768597	0.00249104
$953$	−9.18238	−0.297446	−0.148723	−	0.988879i	$-0.547516\pi$
$953$	−9.18238	−0.297446	−0.148723	+	0.988879i	$0.547516\pi$
$954$	−1.36333	−0.0441393
$955$	−1.28706	−0.0416484
$956$	−51.3698	−1.66142
$957$	11.6866	0.377773
$958$	−3.30726	−0.106853
$959$	16.2780	0.525645
$960$	9.95514	0.321301
$961$	−1.40991	−0.0454811
$962$	1.64317	0.0529781
$963$	−12.0042	−0.386830
$964$	6.64981	0.214176
$965$	−1.47602	−0.0475149
$966$	0.649487	0.0208969
$967$	22.8477	0.734733	0.367367	−	0.930076i	$-0.380259\pi$
$967$	22.8477	0.734733	0.367367	+	0.930076i	$0.380259\pi$
$968$	−1.60960	−0.0517344
$969$	1.27756	0.0410411
$970$	−0.139547	−0.00448059
$971$	27.9176	0.895919	0.447959	−	0.894054i	$-0.352151\pi$
$971$	27.9176	0.895919	0.447959	+	0.894054i	$0.352151\pi$
$972$	−1.98890	−0.0637939
$973$	11.5195	0.369297
$974$	1.98690	0.0636643
$975$	7.28505	0.233308
$976$	−31.9374	−1.02229
$977$	−38.9720	−1.24682	−0.623412	−	0.781894i	$-0.714254\pi$
$977$	−38.9720	−1.24682	−0.623412	+	0.781894i	$0.714254\pi$
$978$	1.40044	0.0447810
$979$	3.46310	0.110681
$980$	2.55984	0.0817710
$981$	17.8163	0.568829
$982$	3.87422	0.123631
$983$	4.31436	0.137607	0.0688033	−	0.997630i	$-0.478082\pi$
$983$	4.31436	0.137607	0.0688033	+	0.997630i	$0.478082\pi$
$984$	1.04010	0.0331571
$985$	12.1415	0.386860
$986$	−0.0840929	−0.00267806
$987$	2.34053	0.0744999
$988$	30.2762	0.963215
$989$	56.4680	1.79558
$990$	0.363155	0.0115418
$991$	24.2216	0.769424	0.384712	−	0.923037i	$-0.374301\pi$
$991$	24.2216	0.769424	0.384712	+	0.923037i	$0.374301\pi$
$992$	6.82732	0.216768
$993$	−3.42752	−0.108769
$994$	0.356242	0.0112993
$995$	−21.0589	−0.667613
$996$	−1.22087	−0.0386848
$997$	−24.9009	−0.788620	−0.394310	−	0.918978i	$-0.629016\pi$
$997$	−24.9009	−0.788620	−0.394310	+	0.918978i	$0.629016\pi$
$998$	−0.881950	−0.0279176
$999$	7.15698	0.226437

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.k.1.11	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.k.1.11	✓	27	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q-0.105370 q^{2} +1.00000 q^{3} -1.98890 q^{4} -1.28706 q^{5} -0.105370 q^{6} +1.00000 q^{7} +0.420311 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.105370 q^{2} +1.00000 q^{3} -1.98890 q^{4} -1.28706 q^{5} -0.105370 q^{6} +1.00000 q^{7} +0.420311 q^{8} +1.00000 q^{9} +0.135618 q^{10} +2.67777 q^{11} -1.98890 q^{12} -2.17889 q^{13} -0.105370 q^{14} -1.28706 q^{15} +3.93351 q^{16} +0.182864 q^{17} -0.105370 q^{18} +6.98640 q^{19} +2.55984 q^{20} +1.00000 q^{21} -0.282158 q^{22} -6.16386 q^{23} +0.420311 q^{24} -3.34347 q^{25} +0.229591 q^{26} +1.00000 q^{27} -1.98890 q^{28} +4.36429 q^{29} +0.135618 q^{30} -5.43968 q^{31} -1.25510 q^{32} +2.67777 q^{33} -0.0192684 q^{34} -1.28706 q^{35} -1.98890 q^{36} +7.15698 q^{37} -0.736159 q^{38} -2.17889 q^{39} -0.540968 q^{40} +2.47459 q^{41} -0.105370 q^{42} -9.16115 q^{43} -5.32581 q^{44} -1.28706 q^{45} +0.649487 q^{46} +2.34053 q^{47} +3.93351 q^{48} +1.00000 q^{49} +0.352302 q^{50} +0.182864 q^{51} +4.33359 q^{52} +12.9384 q^{53} -0.105370 q^{54} -3.44647 q^{55} +0.420311 q^{56} +6.98640 q^{57} -0.459866 q^{58} -6.23777 q^{59} +2.55984 q^{60} -8.11932 q^{61} +0.573180 q^{62} +1.00000 q^{63} -7.73476 q^{64} +2.80438 q^{65} -0.282158 q^{66} -3.57311 q^{67} -0.363697 q^{68} -6.16386 q^{69} +0.135618 q^{70} -3.38085 q^{71} +0.420311 q^{72} +11.6011 q^{73} -0.754133 q^{74} -3.34347 q^{75} -13.8952 q^{76} +2.67777 q^{77} +0.229591 q^{78} +12.9776 q^{79} -5.06268 q^{80} +1.00000 q^{81} -0.260748 q^{82} +0.613844 q^{83} -1.98890 q^{84} -0.235358 q^{85} +0.965313 q^{86} +4.36429 q^{87} +1.12550 q^{88} +1.29328 q^{89} +0.135618 q^{90} -2.17889 q^{91} +12.2593 q^{92} -5.43968 q^{93} -0.246622 q^{94} -8.99195 q^{95} -1.25510 q^{96} -1.02897 q^{97} -0.105370 q^{98} +2.67777 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9}+O(q^{10}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9	\( 27 q + 9 q^{2} + 27 q^{3} + 31 q^{4} + 23 q^{5} + 9 q^{6} + 27 q^{7} + 18 q^{8} + 27 q^{9} + 10 q^{10} + 22 q^{11} + 31 q^{12} + 15 q^{13} + 9 q^{14} + 23 q^{15} + 39 q^{16} + 22 q^{17} + 9 q^{18} + 24 q^{19} + 46 q^{20} + 27 q^{21} - 19 q^{22} + 36 q^{23} + 18 q^{24} + 38 q^{25} + 19 q^{26} + 27 q^{27} + 31 q^{28} + 32 q^{29} + 10 q^{30} + 11 q^{31} + 15 q^{32} + 22 q^{33} - 4 q^{34} + 23 q^{35} + 31 q^{36} + 6 q^{37} + 8 q^{38} + 15 q^{39} + 16 q^{41} + 9 q^{42} - 11 q^{43} + 22 q^{44} + 23 q^{45} - 56 q^{46} + 39 q^{47} + 39 q^{48} + 27 q^{49} - 7 q^{50} + 22 q^{51} + 10 q^{52} + 24 q^{53} + 9 q^{54} + 16 q^{55} + 18 q^{56} + 24 q^{57} - 31 q^{58} + 31 q^{59} + 46 q^{60} + 28 q^{61} - 4 q^{62} + 27 q^{63} + 40 q^{64} + 33 q^{65} - 19 q^{66} - 7 q^{67} + 25 q^{68} + 36 q^{69} + 10 q^{70} + 49 q^{71} + 18 q^{72} - 13 q^{73} + 7 q^{74} + 38 q^{75} + 15 q^{76} + 22 q^{77} + 19 q^{78} - 18 q^{79} + 78 q^{80} + 27 q^{81} + 31 q^{82} + 59 q^{83} + 31 q^{84} - 20 q^{85} + 35 q^{86} + 32 q^{87} - 49 q^{88} + 49 q^{89} + 10 q^{90} + 15 q^{91} + 52 q^{92} + 11 q^{93} + 17 q^{94} + 38 q^{95} + 15 q^{96} - 7 q^{97} + 9 q^{98} + 22 q^{99}+O(q^{100}) \) 27 * q + 9 * q^2 + 27 * q^3 + 31 * q^4 + 23 * q^5 + 9 * q^6 + 27 * q^7 + 18 * q^8 + 27 * q^9 + 10 * q^10 + 22 * q^11 + 31 * q^12 + 15 * q^13 + 9 * q^14 + 23 * q^15 + 39 * q^16 + 22 * q^17 + 9 * q^18 + 24 * q^19 + 46 * q^20 + 27 * q^21 - 19 * q^22 + 36 * q^23 + 18 * q^24 + 38 * q^25 + 19 * q^26 + 27 * q^27 + 31 * q^28 + 32 * q^29 + 10 * q^30 + 11 * q^31 + 15 * q^32 + 22 * q^33 - 4 * q^34 + 23 * q^35 + 31 * q^36 + 6 * q^37 + 8 * q^38 + 15 * q^39 + 16 * q^41 + 9 * q^42 - 11 * q^43 + 22 * q^44 + 23 * q^45 - 56 * q^46 + 39 * q^47 + 39 * q^48 + 27 * q^49 - 7 * q^50 + 22 * q^51 + 10 * q^52 + 24 * q^53 + 9 * q^54 + 16 * q^55 + 18 * q^56 + 24 * q^57 - 31 * q^58 + 31 * q^59 + 46 * q^60 + 28 * q^61 - 4 * q^62 + 27 * q^63 + 40 * q^64 + 33 * q^65 - 19 * q^66 - 7 * q^67 + 25 * q^68 + 36 * q^69 + 10 * q^70 + 49 * q^71 + 18 * q^72 - 13 * q^73 + 7 * q^74 + 38 * q^75 + 15 * q^76 + 22 * q^77 + 19 * q^78 - 18 * q^79 + 78 * q^80 + 27 * q^81 + 31 * q^82 + 59 * q^83 + 31 * q^84 - 20 * q^85 + 35 * q^86 + 32 * q^87 - 49 * q^88 + 49 * q^89 + 10 * q^90 + 15 * q^91 + 52 * q^92 + 11 * q^93 + 17 * q^94 + 38 * q^95 + 15 * q^96 - 7 * q^97 + 9 * q^98 + 22 * q^99

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